show subcategories in category page in a certain way

Good afternoon.

I want to create a single category.php template that shows the subcategories of any given category.
So the parent category is a variable.

In each listed subcategory I want to show several things:

1.- the subcategory title
2.- the thumbnails of the posts belonging to that particular subcategory.

So, in resume, the category page will show thumbnails of posts organized by subcategory groups belonging to a specific category.

Is it possible?

Thank you very much