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You would have place if statements around the post loop that ask if a member is of a certain group. Then you would need to create a custom post field on the new post admin page that held the group name and this field would populate into the if statement on the loop.

In short the loop would only spit out posts if the user was in the group the if statement allows.

If this is not understandable you may need to hire a developer to code this for you.