This is a huge reason why this invasion content fell short right from the start. Dont mean to use you as an example but what u say here is stuff that ccp shouldve considered.
There are a few groups that participate in this content on both sides, but the primary public groups ive seen are :
- The Triglavian Initiative
- Edencom Defense Initiative
You can find them both in the ingame channels named exactly as above.
Hope this helps!