Add "other" groups to computer when joining domain

I am trying to find a way to add a number of security groups to a computers Local Administrators when they are joined to a domain, much like the Domain Admins group is dropped into each when they are joined. So a couple of questions...

Is there a way to automatically do this when they are joined?
Can it be applied via Group Policy?

I apologize if this has been addressed, and I can't quite get the phrasing correct to get a result on google...

Thanks!

Not really sure what you are wanting to do..... Are you trying to migrate custom security groups from your DC into client computers? If so, maybe check out the Restricted Groups in Group Policy/Policies/Windows Settings/Security Settings. That may have what you're looking for. Not sure, though since I don't really know what you're trying to accomplish.

I want to be able to add other domain security groups to the local computers Administrators group automatically when the computer is joined to the domain, just like the "Domain Admins" group is dropped in when joined.

The domain security groups are global, so they should be inherited by any computer on the domain.