Maybe the better suggestion is that the Your Groups drop-list adopt aOops.
I forgot to take into account that the Your Groups drop-list shows the primary and subgroups indented under the domain (common to the primary and subgroups). In the examples in my list the primary is always first in the indented list, hopefully that can be relied upon.
So I think I would propose:
name / title (for groups without subgroups), and
name / title (for the primary group)
name / title (for each subgroup)
I considered whether the "domain" above should show only the subdomain (omit ".groups.io") for the normal case of groups without a custom domain, but consistently showing the entire thing is probably better, and I think will be much more understandable from the point of view of any user who is a member of both types of groups (custom domain and not).
I see that in the prior message I have been somewhat inconsistent in the nomenclature for groups with subgroups. In some places I've treated the subdomain (original name of the primary) as part of "name" or the entirety of it, and in others as part of "domain". In this message "name" includes only the part to the left of the @ in the Group Email Address of groups with subgroups, the "subdomain" is the first part in the field to the right of the @.