How to use three different themes on one site.

On my site i want to use three different themes.

One of the themes is for authenticated users only.
One is for school department A.(for anonymous users)
One is for school department B.(for anonymous users)

Untill now i have explored the 'domain module' that seems capable of doing such thing however,
looks a bit complicated as well.

Another module that i have explored was role theme switcher.
However this module is not usable with themeswitching between anonymous users.

What would be the most appropriate module to use to create such a setup?

Thanks