The Goetia mentions figures who stand above its seventy-two without ever placing them in a structure. Paimon's entry is the clearest case: he is said to be most obedient to Lucifer, a name that appears nowhere in the catalogue as an entry of its own.
Other superiors surface in the same glancing way. Amaymon is named in the surrounding apparatus as a power associated with a quarter of the world, and one or two entries note that a given spirit is under his authority or must be invoked in a particular relation to him. Weyer's brazen-vessel passage names Bileth, Beliall and Asmoday as chief among the seventy-two kings. The Lemegeton's Book Two, the Theurgia Goetia, has an entirely separate hierarchy of aerial princes with their own subordinates.
None of these fit together. Lucifer is not one of the seventy-two. Amaymon is not one of the seventy-two. The three chiefs named by Weyer are, but they are not the first three in either list, and nothing in the Goetia's own text sets them above their fellows. The Book Two hierarchy shares no names with Book One at all.
The reasonable reading is that the Lemegeton is a compilation of materials that were never reconciled, which is what the manuscript evidence independently suggests. Peterson describes the whole work as drawn from earlier printed sources and manuscripts and integrated rather than composed, and the loose ends in the demonology are exactly what that process would produce.
Modern accounts often supply the missing structure, a chain of command from Lucifer down through the four directional kings to the seventy-two. That structure is a later reconstruction. It is coherent, it is popular, and it is not in the text.