Illuminated Conclave

Illuminated Conclave is a conglomerate of several dozen lesser organizations united by their common political agenda and philosophical outlook on life and society. They are actually the Illuminatii, although unlike the organization by the same name from the conspiracy theories, it's far from being united (although it most certainly has a lot of influence. In fact, the organization is considered to be at a high risk of open split, especially in modern times.

Structure

The Illuminated Conclave is split internally between a varied number of lodges, some of them more stable and long-term while others coming and going. They are basically speaking a combination between secret societies and political parties. Older lodges tend to amass at least some specific traditions and the likes. It's also not uncommon for new lodges to spring off from the old ones over political disagreements to inherit some of those from the group they were a part of.
The exact details of the organizations of each lodge varies greatly. Some of them have a single individual as its head, some decide on everything by voting. Lots of them are to a larger or smaller degree connected to various influential elements of the mundane world. If board members of some corporation or notable members of some NGO are initiated, there is a significant chance that they were at least offered a membership in one of the lodges.

Public Agenda

The Illuminated Conclave's official agenda is furthering goals of human enlightmented and rationalism, attempting to expand their understanding on the parts of the world that are still somewhat avoiding it (this is both in terms of conventional science and the magical studies. This is, however, the official policy. In practice the situation comes out a bit differently (and far from a force of pure good).
The problems with the Conclave are twofold.
1. 'Progress' is a bit of a wide term. This, together with the Conclave's internal division led to many lodges supporting questionably moral groups for as long as they were challenging the status quo (that they see as evil). Parts of the Conclave supported both bolsheviks and the Nazis, while having a worrying tendency to downplay attrocities as 'necessary evil' or a part of the process leading to a greater good.
2. The Illuminated Conclave is actively attempting to influence the world of the non-initiated through their numerous supporters among the influential people. They are rather heavily invested in at least some of modern societal issues, which causes both an internal stife between lodges over the exact sociopolitical lines they support and irritates a lot of other organizations that are sticking to a more non-intervention policy.

History

The Illuminated Conclave was officially born in the late 19th Century (although exact date is unknown). It was, however, in fact merely a codification of pre-existing supernatural branches of the freemasonry into a single organization, together with its merger with the few remaining holdouts of the Order of the Illuminatii, a mostly Bavarian-centered magical organization that was crushed in late 18th Century following a failed attempt to overthrow the Arcane Ordo Europae.
The organization in question originally didn't mean a lot and only managed to properly expand its power in the following few decades, in big part thanks to connection to influential individuals from the mundane world via the freemason lodges. This has managed to elevate it into its current position, only to facilitate a significant pushback from opposing superpowers of the magical world.
The Illuminated Conclave has participated in the First Occult War, however its support was heavily limited due to lack of sides of the mundane conflict that aligned with their political agenda. They have instead supported organizations in various countries, hoping to gain influence in every country.
After its end it was known to pitch their support to the bolsheviks, only to terminate it soon after their victory due to the mages among the bolsheviks merely using them to gain support without planning to return the favour. Worst of all, it was seen as a betrayal by many of the initiated elements of old Russian aristocracy, leading to minority of them that supported the Conclave to switch their allegiances, primarily to the Arcane Ordo Europae.
Their growth in power after the war has been rather significant. It is often said that if the Second World War (and its concurrent Second Occult War) didn't erupt when it did, the Second Occult War would be waged between the Illuminated Conclave and its numerous enemies. The Conclave has been, once again, partially split between the more liberal and more progressive wings, leading to them supporting all the sides to a various degree.
In the end, however, this proved to be an undoing for large part of the Conclave's influence. The Axis' fell, the Soviets once again didn't want to cooperate with the Illuminatii leading to the formation of 11th Directorate that was largely hostile to the Illuminatii. The US Government Department of Eschatology has been slightly more positive towards the Conclave, seeing it as effective counterbalance for the power of Arcane Ordo Europae and a potential ally against the Reds. But it was far from enthusiastic support.
The Illuminated Conclave has refocused its activity afterwards, focusing on regaining its influence while at least slightly violating the UN Supernatural Security Committee's unofficial policy of limited interventionism in the matters of the non-initiated by leveraging their political influence over them to further their own power.