What is open group & closed group?

When you create a group in facebook you can chose privacy as your wish. There are three types of access levels in privacy settings

• Open group : For Open groups, everyone on Facebook can view the group and join. The group will appear in search results. All content & posts (e.g., photos, videos and discussions) are visible to anyone viewing the group.
  
• Closed group : For Closed groups, everyone on Facebook can see the name and members of a group, but only group members can view content in the group.
  
• Secret: These groups cannot be found in searches, and non-members can’t see anything about the group, including its name and membership list. The name of the group will not display on the profiles of members.

Admins of groups with fewer than 250 people can change the privacy setting of their groups by clicking the "Edit Group" button at the upper-right corner of the group page. All members of the group will receive a notification that the settings have changed.

How to add new members to a group?

To add members to your group, go to the group and click "Add Friends to Group" in the right column. From there, you will be able to type your friends' names to add them to the group.

For all types of groups (open, closed and secret), group members can add their friends. Other people can request to join an open or closed group and be confirmed by a group admin.