The Communist Parivar

A 2004 conference lays out organizational affiliation of the communist parivar (however divided they might be).

Political activist of parties like
CPI
CPI(ML)-Red Flag
CPI(ML)-New Democracy

Unions like
Ladaku Garment Union
Britania Employees Union
HLL Employees Union
General Insurance Employees Union
Sarva Shramik Sangh
TUCI

Democratic (if you will) organizations like
Lok Raj Sangathan
Maharashtra Jan Andolan
All India Youth Federation
Vidrohi
Ajinkya Pathak

Wikipedia has another good set of organizational layout of Communist Party of India... um.. Marxist. The CPI's uncountable splits and spills leaves one guessing on how ingenous the communists are - different name but same motto. Similar to Ram Bhakta's "Ram Tere Kitne Naam".

Splits and offshoots
A large number of parties have been formed from splits of the CPI(M), such as
Communist Party of India (Marxist-Leninist),
Marxist Communist Party of India,
Marxist Coordination Committee in Jharkhand,
Janathipathiya Samrakshana Samithy and
Communist Marxist Party in Kerala,
Party of Democratic Socialism in West Bengal,
Janganotantrik Morcha in Tripura,
the Ram Pasla group in Punjab,
Orissa Communist Party in Orissa, etc. etc. etc.

But hold your breath: There are hundreds more.