I don’t get the question. What do you mean with “address group”?
A group in NC contacts is way to group single contacts inside a address book.
For sure you can have different address books inside NC and share them individually.
Please keep in mind, that not every client software (Apple MacOS) can handle multiple addressbooks from one resource.
OK, when I looked again at the contacts app. You have groups listed on the left hand side of the screen. These, as it seems, are a way to organize the contacts with in an address book.
When I looked ounder settings, I discovered a way to add a new address book. I created one and I did nto see it show up anywhere. I found the address book option when looking under a contact, where it allows you to choose an address book.
Is there a way to make visible only one addressbook at a time? Otherwise, all the contacts could be mixed up between groups and addressbooks(visually on the screen anyway).
Is there a way to move a contact between two address books more than one at a time? I am happy I can change it. But, if I could save a little time, even better:)
Unfortunately that function doesn’t exist yet in the Nextcloud Contacts app, but you can use any other application which supports Carddav to connect to your Nextcloud server, so that you can e.g. use an app on your smartphone to do the job.