So in a Sigil that's 80 years after Faction War, the Lady's decree of no factions still more or less stands. At least no group is calling themselves factions any more at least officially.
At lot of things are more or less the same around Sigil, the only exception is the technology has advanced considerably (up to the 19th century, or PL 4 in D20M terms), but for the most part it doesn't change a thing about organizations.
Anyways some of the power groups that I can think of would be the old factions, exiled factions trying to come back, planar sects trying to get in and various guilds that could be around as "Affiliations" to join in Sigil.
One of the things I see happening in this setting is competing corporations even though the PTC is perhaps the one at the top.
I see competing 'law enforcement' or security groups, each one influencing only a certain parts of Sigil. Along with criminal organizations in direct conflict, and 'tribes' that sort of pop up in Undersigil and the city above.
Here's an incomplete list of affiliations I can think of, both and small organizations.
Athar (Still not quite welcomed)
Bleak Cabal (Going strong despite not being a faction)
Chainmen (Slavers guild from Spelljammer)
Clockmaker's/Mechanic's Guild (The closest thing to a 'technology' guild)
Daughters of the Light (The "anti-faction" watchdogs)
Doomguard (slowly "recovering" still)
Dustmen (still going strong)
Expansionists (making their return)
Fated (slowly making their way back in)
Fraternity of Order (Still mostly Mechanus based)
Free League (still going strong, though often in conflict with the PTC and Merkhants)
Gate-Seekers Guild (Lissandra's guild)
Guardians (Elysian sect)
Harmonium (Not really welcome, but back in a few places competing against the Sodkillers and Sons of Mercy)
Illuminated (from Plague Mort causing trouble in Sigil)
Ishtaritu (prostitute guild/cult, because they're my idea)
Merkhants (the competitors of the PTC)
Mind's Eye (growing in strength)
Order of Eternal Vigilance (Another watchdog/enforcer group)
Planarists (anti-prime group that's seeing it's number grow)
Planar Cartographers Society
Planar Trade Consortium (the strongest commercial interest in the multiverse now)
Planes Militant (Trying to come into Sigil and prevent the Hardheads from coming back)
Planewalkers Guild (has a strong base in Sigil)
Pragmatic Order of Thought (loosely aligned with the Anarchists, from SJ)
Regulators (defenders of the status quo from ELH, just ignore the epic level stuff)
Revolutionary League (never went away)
Ring-Givers (coming back)
Seekers (from the Spelljammer setting)
Sigil Advisory Council (the "governing" council)
Society of Sensation (still around)
Sodkillers/ Minder's Guild (One of the primary enforcers)
Sons of Mercy (The other primary enforcer)
Touts Guild (growing strong)
Transcendent Order (still strong)
Xaositects (currently called the SoXanites as of the last few months)
Xenos (human supremacists)
So, the Ishtaritu, who I presume pay some kind of tribute to Ishtar: what kind of role do they play in the city's social structure? Are they like a union for prostitutes or do they engage more actively in protecting collegues, in the lines of the Old Town prostitutes from Sin City (not that a union wouldn't protect members, but they usually do it in a less throat-cutting manner)?