It deals with the images URL and if it's too big/small it won't show up. Well looks like you also took the words out of my mouth, but I was way too tired last night.
Sad that we can't go back to the past and then back to the present/future. ;(
Since i am one of the few users who also own a group and is still active in the community, i would like to answer this question.
You can add an image to your group by clicking on "Edit", you will be presented with various options in which add image is one of them.
Just paste any working image URL and click save.
You can specify some of the things like size and shape while pasting the link.
The group system is pretty much dead now so i recommend not to waste time on asthetics of group.