Is the site really private? I see groups in the find a group section?

Yes, your group is private, however to get all the members in your group you need a public page where people can request to join the group. We have tried different techniques to get people in the same group and there were tons of problems.

The public page only shows the name of the group and if the site administrator wants to show a picture they can. It does not show any of the other content created in the group. 

The public profile page can also be turned off when all the members are in the group. These settings are found in your 'Group Settings' page.