i prefer MY. “My Computer”
I believe that was discussed long ago here in beta, it is a matter of style and Mark made a choice.
Pedantically that's a list of your subscriptions, not his. Your makes more sense to me because you are visiting a web site - you're virtually outside your house -- in that context my actually does carry the connotation of referring to someone else's (your host's) possession. This is a different context than the example of My Computer.
How to shorten this? Certainly not by changing the meaning to Subscription.
When looking at a group's page that link is the only one that contains information specific to your personal subscription in this group. I think Subscription is a much more focused and appropriate word here in the context of the side links than "Settings". Possessive pronoun or lack thereof notwithstanding.
A second reason is that the word Settings is already taken in that list, albeit that's only seen by group owners and mods. Given that all of the links are links to something in the group, (even your subscription) changing this one to Group Settings would seem redundant.