calling categories

i already have 60+ categories and that should not change except category (24). my category.php is set up to call categories by naming each category via an array below…

<?php $this_category = get_category($cat);
// echo $this_category->cat_ID; ?>
<?php if ( is_category(array(212, 255, 258, 251, 252, // products
                             2232, 2233, 2234) //designers )) ?>

with this setup, every time i add a category i am adding an ID to the array. i now expect to add a large # of children (designers = 2232, 2233, 2234) to a parent category (designer = 24). is there a syntax like childof= for the designer (24) category ? not sure how to write with current setup.