Divine Wisdom

Divine Wisdom is one of the most terrific 'mundane' organizations that the Grand Empire has to deal with. In fact, it's so dangerous that's countering their operations is typically left to the Chosen Ones and their entourage, the entire batallions of the Warforged, magisters of the Imperial Magic Guild, and in each case with substantial adventurer support.
It has started as a splinter group of the Imperial Magic Guild, which separated from the main body four hundred fifty years ago. The Divine Wisdom's creators were exiled from the Magic Guild (and 'exiled' should be read as 'they tried to wiped them out but some fled into the Lost Lands so the Grand Empire announced they aren't allowed to return and hoped that the Lost Lands will eat them all, unfortunately they didn't) due to their unhealthy fascination with the Imperial Cult's theurgies and through it, the nature of godhood.
Divine Wisdom persisted in the Lost Lands, and has overtime - through their usage of numerous forbidden practices, including the dreaded soul magic - has evolved into a menace that makes majority of the Fallen deeply uncomfortable with their insanity. It has somehow managed to descend to the level previously occupied only by the legions of the Pentagram, in that all other factions of the Fallen (even the Rampant Bloom) are willing to consider a temporary alliance when Divine Wisdom forces are spotted in the area. In the past there were even cases of Umbral Bond forces redirecting their entire operations due to apparently seeing the Wisdom as much greater threat.
Divine Wisdom is considered by the Grand Empire to be a domestic threat of utmost danger, due to its reckless human experimentations, recurrent indulgement in truly heretical acts and the willingness to kill any number of people to gain what they want. And that's without mentioning their preternatural foresight (allowing them to - somehow - foresee majority of imperial counters and actions before they even planned) and the growing risk of it causing end of all life through their attempts to achieve mass ascendency event.

Structure

Noone knows what exactly is the inner structure of the Divine Wisdom, primarily because it seems to change and fluctuate overtime. Each operation of the Wisdom is entirely independent (until they achieve their goals - or decide that it's no longer achievable - they appear to have no contact with the Wisdom as a whole), and each of them appears to have widely different internal structure. The Grand Empire guesses that it's intentional, in order to further complicate all resistance attempts.
What exists above the level of such an independent operations is anyone's guess. The field operatives of the Divine Wisdom undergo procedure that erases all memories concerning the higher leadership (which is then reversed when they return to the fold). Even the head of the operation knows nothing, save for when should they proceed to when they succeed in their mission (or fail entirely) in order to be picked up by the Wisdom.
Each time the Empire managed to annihilate an entire operational detachment and tried to follow on their return-home instructions, the result was no one being found in the designated zone.

Public Agenda

The Divine Wisdom's eventual goal is understanding the nature of the gods - and causing a mass ascendancy event during which significant part (if not all) of the inhabitants of the Grand Empire will ascend into a form of lesser godhood. For the Wisdom, this is the mortals' birthright - especially if accompanied by the collapse of the Imperial Cult grip on Reality, which would result with such 'lesser gods' being able to create worlds on their own.
With past attempts of mass ascendancy events typically leading to annihilation of entire civilizations through some mistakes in their process, the Grand Empire is reasonably worried.

Military

The 'regular' armed forces of the Divine Wisdom are all horrifically powerful mages, who through some soul manipulations managed to empower their own magic to level that shouldn't be humanly (or elvenly or etc.) possible. They essentially bridge the gap between mages and sorcerers, since they are not only capable of buffing and debuffing but also have enough mana (and it quickly regenerates) to cast sorcerer-style large scale offensive magic. And with similar frequency, too.
They are supported by wide array of elementals and golems (sometimes just as horrificially powerful as their summoners are), and various much stranger things. There are also martial artists, who are reinforced to similar level to the mages.
Godlikes are the most dangerous members of the Divine Wisdom, who typically also serve as the leadership of its operations (and, presumably, its high command - unless the Wisdom has something even more powerful). Their souls have been warped with magic to the point where they can no longer be classified as mortals. They are immortals whose souls seems to be in at least few percents divines, giving them limited precognition and ability to warp reality around themselves.
All of that without mentioning the fact that they are also a merger between three classic forms of imperial magic users (so mages, sorcerers and martial artists - at once), while also being monstrously tall, extremely intelligent, completely amoral and capable of shattering a steel anvil with a punch, even WITHOUT resorting to their dedicated martial arts. Two or three godlikes are actually capable of fighting a fully developed Chosen One on an equal terms.