I've got a problem. I've this groups and subcategories

Main CAT #1
---- Child CAT#1
---- Child CAT#2
---- Child CAT#3

Main CAT #2
---- Child CAT#4
---- Child CAT#5
---- Child CAT#6

What I am attempting to do would be to retrieve just the child from the Primary CAT #2 and Primary CAT #1 mashed up and purchased by count.

<?php wp_list_categories('orderby=count&order=DESC&title_li' . $category->cat_ID); ?>

What's missing? Any idea?

I do not think there is a dynamic query that you can do, but training regimen the next two parameters to flatten their email list, and exclude parents groups:

depth=-1 //all groups displayed in flat (no indent) form

exclude=1,5,7 //exclude certain groups, which means you could list your parent groups here by id..