I noticed that, regardless of the group-type, it will show up in the group directory. I was just wondering if there was a way to either make groups private (not show up in the list) or if I could simply lock all of the discussions/posts from being viewable by non-members?
It is only with the heart that one can see rightly;
what is essential is invisible to the eye.
TUMBLR.
I'm afraid that option isn't available with our system right now. All groups are going to be visible, but at least you can retain a bit of privacy by making them either Moderated or Invite Only. Any user can post within a Public or Moderated group, but Invite Only allows you to restrict access.
It's a little unfortunate, but it's best to use PMs for anything that you want to discuss privately. It's easy enough to PM multiple people at one time. It's a little more tedious than using the forums, but PMs at least get the job done.