i'm developing a theme featuring its two pages, blog and portfolio. well, i have groups which associated with the portfolio posts (ie. website design, graphics) and groups relevant towards the blogs (ie. lessons, todos)

i've two pages (/blog and /portfolio), in every, i must show their email list of groups related onto the particular types

(i might not be obvious) making this a good example:

all groups: cat1, cat2, cat3, cat4, cat5,cat6

for portfolio: 
<ul>
<li><a>cat1</a></li>
<li><a>cat2</a></li>
<li><a>cat3</a></li>
</ul>

for blog:
<ul>
<li><a>cat4</a></li>
<li><a>cat5</a></li>
<li><a>cat6</a></li>
</ul> 

so it is possible to method to split them like this

thanks

This is actually the method I personally use to manage which group of posts shows which pages of the WordPress blog. I place this type of code in to the page.php file, right before the loop is known as:

<?php
$catID = 0;
if (is_page('videos')) {
 $catID=3;
} elseif (is_page('music')) {
 $catID=4;
}
 elseif (is_page('poetry')) {
 $catID=5;
}

if ($catID) {
 $paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
 query_posts("cat=$catID&amp;paged=$paged");
} ?>

Note: What they are called in parentheses after "is_page=" would be the page slugs, not the page game titles.

By using this type of code, you are able to tell which page to show which group of posts.

Read more information relating to this inside my blog if you want it: WordPress: How to control which category of posts displays on particular pages

You should use wordpress_list_groups() method inside your template, this process takes an "exclude" or "exclude_tree" parameter, which enables you to definitely exclude blog groups within the first list, and portfolio within the second.

http://codex.wordpress.org/Template_Tags/wp_list_categories