It is not possible in vanilla WordPress as the tags, and categories are separate entities.

Categories would offer you a hierarchical parent/child relationship, and could accomplish this.

- CategoryParent1
    - CategoryChild1
        - CategoryGrandchild1, CategoryGrandchild2, CategoryGrandchild3

- CategoryParent1
    - CategoryChild2
        - CategoryGrandchild1, CategoryGrandchild2, CategoryGrandchild3

- CategoryParent2
    - CategoryChild1
        - CategoryGrandchild1, CategoryGrandchild2, CategoryGrandchild3

- CategoryParent2
    - CategoryChild2
        - CategoryGrandchild1, CategoryGrandchild2, CategoryGrandchild3


Alternately, if you wish to retain the tags as you have them, you could use WordPress SEO to rewrite the tag URLs, and essentially 'spoof' the URL.

https://wordpress.org/plugins/wordpress-seo/

I hope that helps!