Or can I determine Domain User Group(s), members of which are allowed to use the database and the rights they will have there?
Yes you can. It is called "external authentication". The role is expressed in the FM privilege set. You create as many as there are roles in your solution. Then you can specify which domain group gets what privilege set.
With FileMaker Server you can use External Authentication. Either Active or Open Directory.
It's a deeper subject, but basically the idea is that in filemaker security panel you create accounts named as the groups which are defined in you directory that are allowed to connect. You also need to assign an appropriate privilege set for those accounts in filemaker.
The account you create should have the option Account is authenticated via: set to External Server.
The machine where the server runs needs to be configured to access the Directory Domain.
Look up the documentation, as there's more to find out: like the order of authentication etc.
Thanks to all!
The ansvers were a relief