So I'm a bit confused as to whose side the major characters are on and the alignments of each ninja organisation.
The Kuros, the store clerks, Susuki who still has one leg, are all NIN which i think works for the united nations and operates in Japan as official ninja forces, but they are not part of the Japanese goverment, we don't really know who is really behind NIN, it could be the CIA instead of the united nations, but either way they are not aligned with the jap gov
Sasama the lactating woman that uses a hobo disguise, is allegedly a renegade ninja, however she is taking care of one of the 7 elders of NIN who got his brain transplanted into a baby, so chances are she is still working for NIN, and she is forming her own squad i think, that squad is recruiting all kind of ninjas from NIN and even foreign terrorists
The cat used to be a NIN ninja but went rouge, was captured by NIN, transplanted into a cat, and as revenge he went to the school to film the videos to get NIN into trouble
Yamada the woman that sometimes has dem legs and no nose, is an Under Ninja, and so was the other renegade ninja that attacked the school (this guy used to be NIN), that group that has been using the cube bomb shurikens are all Under Ninjas, and they seems to be a paramilitary group with ties to the Japanese Goverment, they are not an official group, pretty much a guerrilla but founded by the Japanese government, their goal seems to be to ruin the reputation of NIN so that they will lose all public support
And finally we had all those gyarus at the school, the ones whose leader had the kabuki theater makeup, those girls work for the Ministry of Health Welfare and Labor, they are also ninjas, and they legally work for the Japanese Goverment
So Jap gov has 2 ninja forces, the legal one that is publicly known which are the ninjas from the ministry of health, and the Under Ninjas the paramilitary group that they use to carry out domestic terrorist attacks in order to ruin the reputation of NIN
NIN operates within Japan and other parts of the world, but it doesn't has to answer to the Jap Gov, and even opposes it, and they are backed by some foreign body, probably the United Nations, NIN are the biggest ninja group within Japan, and the face of ninjas when people think of ninjas
Also all of this info may be wrong