Meaning of trierarchy

tri•er•ar•chy

Pronunciation: (trī'u-rär"kē), [key]
— pl. -chies.
  1. the office of a trierarch.
  2. trierarchs collectively.
  3. (in Athens) the duty of fitting out or furnishing triremes for the public service.
Random House Unabridged Dictionary, Copyright © 1997, by Random House, Inc., on Infoplease.