Hide your Public Groups and other information displaying on your timeline. You can access the feature by clicking the “More Button” below your Cover Photo.
Navigate to your Timeline and click on the ‘More” drop down arrow & then go to the bottom and click on the ‘Manage Sections’ link.
You now have the option of hiding your Groups and other sections by un-checking the corresponding box.
Although you are hiding these from your Timeline but the disclaimer at the bottom states, “Individual stories in hidden sections can still appear on your Timeline, in News Feed and elsewhere on Facebook.”
Additionally with regards to Public Groups people in these groups will see that you are a member.