There should be 2 buttons on the page: Allow and Restrict. While clicking on them, a dialog window should be shown to be able to shuffle groups around. For the reference take a look at Forum Structure->Branch Permissions.
Technically the SIDs should be the Groups and the Object Identities should be the same group.
Acceptance criteria:

• After adding group to Allowed or Restricted and reopening the window, it should show the same state as while saving
• The dialog has Save and Cancel, and also Enter and Esc strokes should simulate those buttons.