Can an open group be converted to a closed group?

Yes, but only by group owners and for groups with less than 10,000 members.

1. Go to your group.
2. Open the "Admin" tab and choose "Settings".
3. In the "Danger Zone!" section, click "Switch Privacy to Closed".
4. Enter the group name to confirm and click "Switch Privacy to Closed".

Important: Once the group is closed it can never become open again, that would be a major privacy violation!