As of October, 2008, these seem to be the main hives. In fact, in late October, these are the only places I detect mantis activity.

Six of these pics have appeared in my blog, but the numbers I affixed to the image names at the time often bear no relation to the numbers the mantises use.
I am not sure whether the numbers are heirarchical, other than that the lead hive is #1. These are the numbers the mantises themselves use:

      1

      2

      3

      4

      5: weather mod base of operations for Earth

      6

      7

      8

      9

Update Jan, 9, '09: For some time, hive #1 has seemed nearly defunct. It was hit very hard by a bunch of very powerful allies.
Since then, hive #9 has been the strongest, and quite nasty indeed. But lately it has been under siege by the same forces, and has gotten much weaker. The other hives have not picked up the slack so far, suggesting #9 was the true big one. It still needs a fair bit of work, though.

Update Jan. 15, '09: It now appears the mantises may be smashed. I have not been hit by them in a good while, and many of the good guys have moved on to the grey hive. There are still crews cleaning up what's left of the mantis hives.

Update March 21, '11: Subsequent to this, this mantis species received therapy, and they have been working on our side since.

Then a different species, physical mantid humanoids, became noticeable. These have triangular faces that one sometimes spots RVing oneself. But they don't have astral bodies or really astral travel.

Recently a different type of non-physical mantis demon has become very active. They are jailable, but I can't get the entire species at once nor have it deleted. These guys seem to reside primarily in the Orion Nebula.

Update March 26, '11: That species has now been deleted by The Recyclers. I was finally able to break whatever spell was preventing me from having The Recyclers delete them.
So the only evil mantid species left that I am aware of is the physical one.