Group Posting in Private Groups

When I enter a group as a user, post a blog item within the group - of course I can't see the blog as it has now been submitted for approval. However, will that blog posting be visible to anyone seeing my home page, or only to group members?

I would assume only to group members. However, once I posted the test blog, I was returned not to the group, but to my home page under EasyBlog - making it look as if perhaps the blog entry I just posted from within the group is now visible to all.

For a private group, we would need all posting within the group to also be private to that group. Is it possible to accomplish this?