Like the mythical hydra, the Illuminati have many heads and even more hands. The minions of the Illuminati might work to their hidden master's ends without ever knowing the design of their work, or for whom they indeed work for.
"Yn these landes, theye do ryde upone greate flowtinge beastes alike as those thate ye fyshermen do calle nawtilus; Ande these beastes, callede 'pyky-pyky' because of ye noises thate the beastes make, are troubelsome ande beastlye mountes, withe fowle temperes." -Telliamed ap Ynris, "Ye Westerne Landes".
(A levitating giant nautilus that makes a noise like "piki-piki" and is thus called a Great Piki-piki.)