How to display data in categories from database?
===

So my website allows users to create a contacts list and now I have added user-named categories. I am currently displaying the list of contacts using a while loop of the associative array generated from my SQL query. 

So it looks like this:

    Contacts:
    Contact 1 
    Contact 2
    Contact 3

Now I have a new column in the database for categories of contacts, and I cannot figure out how to order them by, and display the name of the contact category. I am trying to get it to look like this:

    Contacts:
    Category 1
    Contact 1
    Contact 2
    Contact 3
    Category 2
    Contact 1
    Contact 2
    Contact 3


My actual code if you need it:
    
    <?php
					//START CONTACTS LOOP		
				$contacts_query = "SELECT id, name FROM contacts WHERE ownerid = '$userID' ORDER BY `name` ASC";
				$run_contacts_query = mysql_query($contacts_query);
				
				if($run_contacts_query){
					
					while($c_data = mysql_fetch_assoc($run_contacts_query)){
						$id = $c_data['id'];
						$name = $c_data['name'];
						?>
						<li><a href="contact.php?id=<?=$id?>"><?=$name?></a></li>
						<?php
						}} //END CONTACTS LOOP 
				?>