Kategorien mit jeweiligen Posts darstellen

<h1 id="quicknav_head">Quicknavigation nach Themen</h1>
  <div id="quicknav" class="clearfix">
   <div id="quicknav_cats">
    <!--<h3 class="cat1">Kategorie1</h3>
    <h3 class="cat2">Kategorie2</h3>
    <h3 class="cat3">Kategorie3</h3>
    <h3 class="cat4">Kategorie4</h3>
    <h3 class="cat5">Kategorie5</h3>
    <h3 class="cat6">Kategorie6</h3>-->
    <?php 
    /* Query to get all the categories and style them for h3 */   
    $categories = $wpdb->get_results("SELECT term_id, name FROM $wpdb->terms");
    $i=1;
    foreach ($categories as $category) {    
     echo "<h3 class=\"cat$i\">$category->name</h3>";
     $i++;
    }   
    ?>
   </div>
   
   <div id="quicknav_posts">
    <p id="quicknav_posts_head">Artikelübersicht</p>
    <?php
    $count=1;
    while ($count <= $i) {
     echo "<ul class=\"cat".$count."\">";
     $posts = get_posts("category=$count");
     foreach($posts as $post) :
      setup_postdata($post);
      ?> <li><a href="<?php the_permalink() ?>" rel="bookmark" title=" <?php the_title(); ?>"><?php the_title(); ?></a>&nbsp;&raquo;&raquo;</li>
     <?php endforeach; 
     $count++;
     echo "</ul>";
    }
    ?>  
    <!--<ul class="cat1">
     <li><a href="#">Kategorie1 Post 1</a></li>
     <li><a href="#">Kategorie1 Post 2</a></li>
     <li><a href="#">Kategorie1 Post 3</a></li>
     <li><a href="#">Kategorie1 Post 4</a></li>
    </ul>
    <ul class="posts cat2">
     <li><a href="#">Kategorie2 Post 1</a></li>
     <li><a href="#">Kategorie2 Post 2</a></li>
     <li><a href="#">Kategorie2 Post 3</a></li>
     <li><a href="#">Kategorie2 Post 4</a></li>
    </ul>
    <ul class="posts cat3">
     <li><a href="#">Kategorie3 Post 1</a></li>
     <li><a href="#">Kategorie3 Post 2</a></li>
     <li><a href="#">Kategorie3 Post 3</a></li>
     <li><a href="#">Kategorie3 Post 4</a></li>
    </ul>-->
   </div>  
  </div>