Novus Ordo Seclorum
The very definition of the shadow-lodge, the Novus Ordo Seclorum is a legend even among those who know of the magical world. No one admits to being a member, assuming it does exist, and for good reason: the Novus Ordo Seclorum (the "New Order of the Ages") is the magical ur-conspiracy behind the politics and economics of the mundane world.
In many ways, the NOS serve as a boogey-man for sorcerers and others: "Do not use your magic to meddle too deeply in the affairs of the mundane world, or the Novus Ordo Seclorum will come for you."
If they do exist, they do more than simply secure their own power bases, however. According to legend, they are also the self-appointed guardians of the mundane population. They actively work to keep knowledge of the magical world secret, blinding mortal institutions that might come too close to the truth, but also punishing sorcerers and other entities whose actions threaten the carefully cultivated ignorance of mankind as a whole.