Post formating on Home page

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...