We have a church group we set up and we always take pictures at activities. We have tons of albums from all the pictures we take but the problem is they don't show up on peoples' timeline even though they are tagged in the picture. Our group is 'open' and we feel like it would be a great way to get the word out for our activities. And share some of the fun activities we are doing with others!
I am sorry to say, but what you are asking for is as such not possible currently in Facebook.
The whole concept of Groups is separate from your profile:
Your posts on a Group are separate from your status updates.
Visibility of posts in a group are separate from each member's setting.
Group members list is separate from your friend list.
In a Facebook group you can freely tag any member in your post, photo but you cannot interact with the same person outside the group if you are not friends.
In the same way, your photos in a Facebook Group are separate from your own photos.
The only thing that you can do is to upload multiple copies of the photos, one in the Group and another in your profile, tag separately in both the photos.