If you're the group owner, you can stop members from posting or viewing topics.
Stop members from posting to a group
You can stop members from creating new posts. Anyone with permission can still browse and search for past posts unless you also change the "View topics" setting (Step 6).
-
Sign in to Google Groups.
-
Click My Groups.
-
Choose a group.
-
Near the top right, click Manage.
-
Click Permissions
Basic permissions.
-
In the "Post" section, click Select groups of users. Uncheck the group types that should no longer be able to post.
-
Optional: Stop members from seeing past posts by unchecking their group type in the "View topics" section.
-
-
At the top of the screen, click Save.
<source: https://support.google.com/groups/answer/2646833?hl=en&ref_topic=2458761>