Participant/group icon when sending a direct message to a group?

I’ve sent a direct message to a group as well as two other people who don’t belong to the group:

In the message list, only the three users that don’t belong to the group appear. There is no mention of the group in the recipient list:

It could be a good idea to either add a generic group icon as well: image and/or the group flair if it has one.