Facebook plugin for a CLOSED group

We have a facebook group that we use for our club when that we use to post specific ‘members only’ events in, but we also have a ‘public’ group that holds all of our public info & dates for public events.

we can get our WP website to publish & display info from the public page no problem, but what we are wanting / wondering is, is there a way we can pull the info from our private group as well?

we currently have our website setup to require a login to view specific pages for the members but its a slight pain having to post updates on both wordpress and facebook for private events.