Since are somewhat deeply nested and most are named group sometimes it's hard to discover what means what. The tree below represents the include structure for all lists of groups.
base.html.twig
group_categories.html.twig
my_groups.html.twig
_sort.html.twig
my_groups-groups.html.twig (my-owner)
_memberships.html.twig
my_groups-groups.html.twig (my-admin)
_memberships.html.twig
my_groups-groups.html.twig (my-member)
_memberships.html.twig
organisation_groups.html.twig
_sort.html.twig
organisation_groups-groups.html.twig (org-owner)
_memberships.html.twig
organisation_groups-groups.html.twig (org-admin)
_memberships.html.twig
organisation_groups-groups.html.twig (org-member)
_memberships.html.twig
all_groups.html.twig
_sort.html.twig
all_groups-groups.html.twig
_groups.html.twig
search.html.twig
_sort.html.twig [organisationGroups.sort]
search-results.html.twig