Adding links to sub-categories within a category

I have Category.php showing all posts that relate to each category, but what I would like to include is a link to any Sub-Categories that are also related to that category.

The code attached shows all Parent Categories, can this be simply edited to show Sub-Categories?

   <div class="category-advert-wrapper">
     <?php
       // display all child categories
       $args = array(
         'orderby' => 'name',
         'hierarchical' => 1,
         'taxonomy' => 'category',
         'hide_empty' => 1,
         'parent' => 0,
         // 'child_of' => 0,
       );
       $categories = get_categories($args);
     ?>
       <?php
         foreach($categories as $category) :
       ?>
     <div class="category-advert">
        <a href="<?php echo get_category_link($category->cat_ID) ?>"
           title="<?php echo esc_attr($category->name) ?>">
           <?php echo z_taxonomy_image($category->cat_ID) ?>
           <div class="category-advert-title">
           <?php echo $category->name; ?>
           </div>
        </a>
     </div>
       <?php
         endforeach;
       ?>
   </div>

It would really apricated if I can get the code amended for what I require.

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