I have long suspected that groups are exemplary eide. Understanding proceeds by contraction and expansion, implication and explication, so let's try reducing to a few theses.
Identity. Groups are the forms in which the maximum of thick, cross-level, identity between terms and relations is realized.
Ideality. This particular kind of identity is criterial for ideality, so that groups are eide.
Plurality. This maximal identity is only realized in each case of a concrete plurality of individual groups, and neither by a synthesis of all groups (which does not exist), nor by the concept of a group in general (which is much weaker). (Groups behave more like Platonic ideas-forms than the post-Kantian Idea/Concept.)
Participation. A concept of participation seems to fall naturally out of this conception of groups, when we add relations to other groups and to nongroups (as when we speak of the group of a space, etc.)