From “The Greek Origin of Freemasonry” 1956, 2nd edition, p. 126 (hyperlinks have been added by me):

“…the number Three was representative of the universe and of the Trinity. It was divided into three parts by the ancient Greeks: into the Olympus, habitat of the gods, the Globe, and the Heavens. Zeus, Poseidon and Pluto formed the Greek Triad. Zeus was represented by a three-forked lightning; Poseidon by the Trident; and Pluto by the three-headed Cerberus. The Orphic Triad consisted of Chronos, Uranos, and Phanes. Agathon, Psyche and Nous was the Triad of Plato. The Triad of the Eleusinian Mysteries consisted of Demeter, Persephone and Dionysos. And Aristotle tells us that the number Three was considered sacred and mystic because it represented the beginning, the middle and the end. Upon the Tripod of Truth, at the Temple of Apollo in Delos, sat the priestess to deliver her oracle, according to Athenaeus.”

On p. 127:

“The Greeks divided their gods in three groups, the celestial, the terrestrial and the infernal. The Grecian Dionysos was considered thrice born or Trigenis…”