The Vampires of the Clans of Death are all quite unique creatures, but all of them have come to this event with a handful of goals and desires for the outcome of the events. They have gathered themselves into three distinct groups, called factions, that will shape a great deal of their arguments and approaches at the Reunion.
They are…

The Progressives
Goal: Unify the disparate Clans of Death into something new, shift the balance of power into the hands of younger, more modern Kindred

The Progressive faction is a diverse movement of young movers and shakers from a wide array of the Clans of Death. Though they come from disparate ideologies and bloodlines, the Progressives have spent the past several decades coming together, growing in numbers, power, and influence until at last they were able to assist in facilitating the downfall of the Anziani and the destruction of Augustus Giovanni. Largely led by Ferrucio Giovanni, a single-blooded Premascine, this faction is the reason for the Family Reunion being called, and they are the ones who have taken care of arranging travel, security, etc. for the negotiations herein. 
Despite their recent gains, the Progressives are also keenly aware that they are putting their unlives on the line here and placing targets directly on their backs in claiming responsibility for facilitating the demise of Augustus, the demise of the Anziani, and in identifying themselves as breaking away from the usual party lines. All of them have arrived here with the knowledge that if things don’t go their way, they will not be leaving alive. An unexpected alliance with Frances Milliner has given many of them high hopes that the scales will tip in favor of their survival - a view that has definitely been amplified by the number of Milliner family members in their ranks -  but they also remain aware that his allegiance is likely to carry a high price (or at least a guarantee that Boston is his).

The Traditionalists
Goal: Preserve the status quo and destroy the Progressives - change is anathema to the clan and will lead to it’s downfall 

Largely made up of older, single-blooded, non-Premascine Giovanni, helmed by Tomasso Giovanni and whomever pulls his strings, the Traditionalists are frankly pissed off to high hell that they’re even here - and they’re even more pissed off that members of their own family have so brazenly announced themselves to be traitors. They have absolutely no interest in making an alliance of any kind with the other inferior “clans” of death, and have absolutely no interest in recognizing any of the branch families of the Giovanni as equal to the single-blooded. That isn’t to say all of them are ancient - the faction has a respectable number of young single-blooded Giovanni who simply can’t imagine existing without their privileged roles. Many of those younger single-bloods have blood relatives or broodmates who are members of the Progressive faction, and see their actions as the greatest betrayal ever imaginable. 
A handful of Traditionalists hail from other Clans of Death - notably the Harbingers and the Lamiae - however instead of recognizing the supremacy of the Giovanni, they simply do not desire reconciliation or peace, and instead wish to bring about the end of the Giovanni and all of the branch families therein. Essentially, non-Giovanni Traditionalists want the inter-clan war to continue.
Ultimately, the Traditionalists are here to do their damn best to grind the upstarts of the Progressive faction under their bootheels and to beat them back into submission/back into toeing the line. These kids need to learn some fucking respect and need to get back into line so that you can clean up the mess they’ve made with the death of Augustus and the Anziani.

The Nihilists
Goal: Get the Clans of Death to recognize the very real threat that Augustus’ released Specters present, leverage your power as a swing vote

The Nihilists are an oddity among the clans of death in that, unlike the Progressives and the Traditionalists, they aren’t particularly invested in either this hope-y change-y bullshit, or the continuation of this millennia-old blood feud. As disparate as the Progressives in terms of their originating ideologies, as diverse in age and generation as the Traditionalists, the Nihilist faction does not genuinely believe that there is any hope of reconciliation, and believes that with the release of all these powerful Specters in the wake of Augustus’ demise, all of the clans of death should be focused on doubling down on their necromantic capabilities to solve that particular issue. They’re here to ensure that ideal makes it onto the negotiations table in a position of prominence, as they believe that if care isn’t taken to address that threat, that the only inevitability for all necromantically-aspected Oblivion users is an impending, agonizing demise at the hands of the spirits that they once claimed dominion over. 
The Nihilists are willing to wheel and deal, willing to throw their weight - and their votes - behind whatever outcomes that will enable them to be able to ensure that someone actually deals with what they perceive to be the greatest threat that the Clans of Death have ever faced since the dawn of time. They are, likewise, willing to sabotage anyone that tries to bury their agenda items in favor of some personal pet project, and they eye Francis Milliner as a potential liability to their concerns being heard and given the appropriate weight they deserve in favor of the senior Milliner’s desires to control Boston. The Nihilists are extremely aware of the power they hold as swing votes without the agendas driving the other two factions, and they are willing to use it.