List all subcategories from category
$args = array('child_of' => 17);
$categories = get_categories( $args );
foreach($categories as $category) {
echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
echo '<p> Description:'. $category->description . '</p>';
echo '<p> Post Count: '. $category->count . '</p>';
}