Yes, it is quite simple, you just need to work in PHP.
Consider you have 36 posts in a loop.
$div_html_1 = '';
$div_html_2 = '';
$div_html_3 = '';
$div_html_4 = '';
$div_html_5 = '';
$div_html_6 = '';
if ( have_posts() ) {
while ( have_posts() ) {
if( category of post == division 1 ) {
$div_html_1 .= "Your HTML here";
} elseif( category of post == division 2 ) {
$div_html_2 .= "Your HTML here";
}
and so on....
}
}
And in the layout, your code would be like,
<div id="prefix_div_one">
<?php echo $div_html_1; ?>
</div>
<div id="prefix_div_two">
<?php echo $div_html_2; ?>
</div>
and so on...