Thank you for your post.
I'm not sure what you mean by "groups". Is this a table separate from your "contact" table? If so, you can have a "key" field that links the two tables together, where you can assign the same contact id to several group records.
Providing an example may help me better understanding of what you are trying to accomplish.
Sounds like you may be struggling with a many to many relationship. A contact can be a member of many different groups and a group can consist of many different contacts.
Let me know if this is the case and we'll talk about how to make it happen with a join table.