You can use get_categories & wp_list_categories with specific parameters (to use directly in you category.php template):
// List sub cats
$params = array(
'parent' => get_queried_object_id(), //id of current category displayed
'orderby' => 'name',
'order' => 'ASC',
'hide_empty' => false // do not hide sub cats without posts
);
if ( count( get_categories( $params ) ) ) {
wp_list_categories( $params );
}
Full list of arguments can be found here
You can also customize the output by user your own Walker extending WP’s Walker_Category class.