Anyone with a Facebook profile is allowed to make a group to share content with friends or Facebook users who have a similar interest. You can make your Facebook group mostly private by setting the privacy to "Closed." Regardless of your group's privacy setting, someone who is not logged in to a Facebook profile can never see it.
When your group privacy setting is "Closed," anyone with a Facebook account will be able to view the name of the group. The group name appears in search results on the social networking site, on the profile of its members and a news story with the group name appears on the wall of new members when they join. Anyone who clicks on a link directing her to the group page will see its name at the top of the screen.
The member list of a Closed group is visible to all Facebook users, regardless of whether they belong to the group themselves. The member list appears on the right side of the group profile for members and in the middle of the profile for non-members. A small number of random group members appears on the profile and clicking the "See All" link below those members reveals the full list.
When your Facebook group is Closed, only members have access to the content contributed by other members -- non-members are unable to view the content. Group content includes photos, videos, discussions and wall posts. Anything uploaded or submitted to the page by group members is visible to all other group members, however -- you may not post something that is only available to certain group members.
A Facebook user who wants to join a Closed group must request permission to join. A group administrator reviews each request for membership and approves or rejects the request. No member is able to view the full content of the group until her request is officially approved.