WP List Categories for sub-categories in a table

Can anyone offer a solution to using child, hierarchical, or taxonomy to achieve the following?:

I want a category page to list all subcategories in 3 even columns. I have it manually mocked up in a table and using various code I can get subcategories to display, but only in a single list (putting in a div only displays the list 1,2,or 3 times depending on repitition).

You can see what I would like on this category page:

https://shutterdown.com/category/photos/nightlife-pictures/nashville-pics/

Where the table displays all of the sub-cats.

This needs to be dynamic, as I have built this so sub categories of cities are created as people upload work.

I am also VERY open to the idea of php creating a dropdown menu of only the subcategories in place of the table. Any ideas on how to do this? I wouldn’t even know where to start…

Thanks!

-JC