Pure css submenu

Question

I have been fighting with the following code to no avail, I can´t get the submenu appearing as a column on hovering.

I can`t figure out which could be the best approach to get it working as expected.

I don't understand why the following rule doesn't make the submenu items appear in a column (as block elements):

.dropdown:hover ul, .dropdown ul li {display: block;}

Could you tell me what I`m doing wrong?

Thanks !!

/*---------------------------- HEADER  */

.header {
    background-color: #fff;
    box-shadow: 1px 1px 4px 0 rgba(0,0,0,.1);
    display: block;
    width: 100%;
    z-index: 3;
}

.header ul {
    margin: 0 0;
    padding: 0;
    list-style: none;
    overflow: hidden;
    background-color: rgba(255,255,255,0.9);;
}

.header li a {
    display: block;
    padding: 20px 20px;
    border-bottom: 1px solid #f4f4f4;
    text-decoration: none;
}

.header li a:hover,
.header .menu-btn:hover {
  background-color: #f4f4f4;
}


/* menu */
nav{
    position: relative;
    z-index: 1;
}
.header .menu {
  clear: both;
  max-height: 0;
  transition: max-height .2s ease-out;   
}

.menu {
    color: blue;
    font-size: 1.3rem;
}

.menu a{
    color: darkseagreen;
    font-size: 1.3rem;   
}

.menu a:hover{
    color: seagreen;
    font-size: 1.3rem;   
}




/* menu icon */


.header .menu-icon {
    cursor: pointer;
    display: inline-block;
    float: right;
    padding: 25px 17px;
    position: relative;
    user-select: none;
    border: 2px solid #999;
    border-radius: 5px;
    margin: 40px 25px 0 0;
}

.header .menu-icon .navicon {
  background: #999;
  display: block;
  height: 2px;
  position: relative;
  transition: background .2s ease-out;
  width: 18px;
}

.header .menu-icon .navicon:before,
.header .menu-icon .navicon:after {
  background: #999;
  content: '';
  display: block;
  height: 100%;
  position: absolute;
  transition: all .2s ease-out;
  width: 100%;
}

.header .menu-icon .navicon:before {
  top: 5px;
}

.header .menu-icon .navicon:after {
  top: -5px;
}

/* menu btn */

.header .menu-btn {
  display: none;
}

.header .menu-btn:checked ~ .menu {
  max-height: 260px;
}

.header .menu-btn:checked ~ .menu-icon .navicon {
  background: transparent;
}

.header .menu-btn:checked ~ .menu-icon .navicon:before {
  transform: rotate(-45deg);
}

.header .menu-btn:checked ~ .menu-icon .navicon:after {
  transform: rotate(45deg);
}

.header .menu-btn:checked ~ .menu-icon:not(.steps) .navicon:before,
.header .menu-btn:checked ~ .menu-icon:not(.steps) .navicon:after {
  top: 0;
}

.logo{
    position: absolute;
    top: 10px;
    left: 3%;
    width: 70%;
    max-width: 200px;
}

/* SUBMENU TEST */
.menu li > ul{
  display: none;
}

.dropdown:hover ul, .dropdown ul li {
  display: block;
}

/* 48em = 768px */

@media (min-width: 48em) {
    

    .header li {
    float: left;
  }
    .header li a {
        padding: 20px 30px;
        border-bottom: none;
        border-right: 1px solid #f4f4f4;
}

  .header .menu {
    clear: none;
    float: right;
    max-height: none;
  }

  .header .menu-icon {
    display: none;
  }
}

<header class="header">
        <div class="logo">
            <img src="images/logo.png" />
        </div>
        <nav>
          <input class="menu-btn" type="checkbox" id="menu-btn" />
          <label class="menu-icon" for="menu-btn"><span class="navicon"></span></label>
          <ul class="menu">
            <li><a href="index.html">Inicio</a></li>
            <li><a href="nosotros.html">Nosotros</a></li>
            <li><a href="diferencial.html">Diferencial</a></li>
            <li class="dropdown">Divisiones
                <ul>
                  <li><a href="1.html">1</a></li>
                  <li><a href="2.html">2</a></li>
                  <li><a href="3.html">3</a></li>
                </ul></li>
            <li><a href="centros.html">Centros</a></li>
            <li><a href="contacto.html">Contacto</a></li>
          </ul>
        </nav>
    </header>    

Answer 1

You are floating all li in the .head. You just need to float the li in the .menu

Change

.header  li {
  float: left;
}

To

.header .menu > li {
    float: left;
}

Full version:

/*---------------------------- HEADER  */

.header {
  background-color: #fff;
  box-shadow: 1px 1px 4px 0 rgba(0, 0, 0, .1);
  display: block;
  width: 100%;
  z-index: 3;
}

.header ul {
  margin: 0 0;
  padding: 0;
  list-style: none;
  overflow: hidden;
  background-color: rgba(255, 255, 255, 0.9);
  ;
}

.header li a {
  display: block;
  padding: 20px 20px;
  border-bottom: 1px solid #f4f4f4;
  text-decoration: none;
}

.header li a:hover,
.header .menu-btn:hover {
  background-color: #f4f4f4;
}


/* menu */

nav {
  position: relative;
  z-index: 1;
}

.header .menu {
  clear: both;
  max-height: 0;
  transition: max-height .2s ease-out;
}

.menu {
  color: blue;
  font-size: 1.3rem;
}

.menu a {
  color: darkseagreen;
  font-size: 1.3rem;
}

.menu a:hover {
  color: seagreen;
  font-size: 1.3rem;
}


/* menu icon */

.header .menu-icon {
  cursor: pointer;
  display: inline-block;
  float: right;
  padding: 25px 17px;
  position: relative;
  user-select: none;
  border: 2px solid #999;
  border-radius: 5px;
  margin: 40px 25px 0 0;
}

.header .menu-icon .navicon {
  background: #999;
  display: block;
  height: 2px;
  position: relative;
  transition: background .2s ease-out;
  width: 18px;
}

.header .menu-icon .navicon:before,
.header .menu-icon .navicon:after {
  background: #999;
  content: '';
  display: block;
  height: 100%;
  position: absolute;
  transition: all .2s ease-out;
  width: 100%;
}

.header .menu-icon .navicon:before {
  top: 5px;
}

.header .menu-icon .navicon:after {
  top: -5px;
}


/* menu btn */

.header .menu-btn {
  display: none;
}

.header .menu-btn:checked~.menu {
  max-height: 260px;
}

.header .menu-btn:checked~.menu-icon .navicon {
  background: transparent;
}

.header .menu-btn:checked~.menu-icon .navicon:before {
  transform: rotate(-45deg);
}

.header .menu-btn:checked~.menu-icon .navicon:after {
  transform: rotate(45deg);
}

.header .menu-btn:checked~.menu-icon:not(.steps) .navicon:before,
.header .menu-btn:checked~.menu-icon:not(.steps) .navicon:after {
  top: 0;
}

.logo {
  position: absolute;
  top: 10px;
  left: 3%;
  width: 70%;
  max-width: 200px;
}


/* SUBMENU TEST */

.menu li>ul {
  display: none;
}

.dropdown:hover ul,
.dropdown ul li {
  display: block;
}


/* 48em = 768px */

@media (min-width: 48em) {
  .header .menu > li {
    float: left;
  }
  .header li a {
    padding: 20px 30px;
    border-bottom: none;
    border-right: 1px solid #f4f4f4;
  }
  .header .menu {
    clear: none;
    float: right;
    max-height: none;
  }
  .header .menu-icon {
    display: none;
  }
}

<header class="header">
  <div class="logo">
    <img src="images/logo.png" />
  </div>
  <nav>
    <input class="menu-btn" type="checkbox" id="menu-btn" />
    <label class="menu-icon" for="menu-btn"><span class="navicon"></span></label>
    <ul class="menu">
      <li><a href="index.html">Inicio</a></li>
      <li><a href="nosotros.html">Nosotros</a></li>
      <li><a href="diferencial.html">Diferencial</a></li>
      <li class="dropdown">Divisiones
        <ul>
          <li><a href="1.html">1</a></li>
          <li><a href="2.html">2</a></li>
          <li><a href="3.html">3</a></li>
        </ul>
      </li>
      <li><a href="centros.html">Centros</a></li>
      <li><a href="contacto.html">Contacto</a></li>
    </ul>
  </nav>
</header>