(1) Levels of Notifications:
(2) How to turn off notifications for a particular post/thread:
(3) You can choose to temporarily step-away from the group entirely.
Option A: You can choose to "Unfollow" any group. You will remain a member, but not receive any type of notifications from the group.
Option B: If you select "Leave Group", you will be removed from the group entirely. This is the least favorable option for a closed group as you would need to submit a new application and have it approved for readmittance to the group.