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The Collaborative International Dictionary
Trierarchy

Trierarchy \Tri"er*arch`y\, n.; pl. Trierarchises. [ Gr. ?.] The office duty of a trierarch.

Wiktionary
trierarchy

n. 1 A system in http://en.wikipedia.org/wiki/Ancient%20Greece whereby triremes were commanded and maintained by citizens known as trierarchs. 2 The collective noun for trierarchs. 3 A period of time during which one was a trierarch.

Wikipedia
Trierarchy

A Trierarchy was a type of obligation called a liturgy, a debt similar to a tax on the very wealthy in ancient Athens. The person (or persons) up on whom the duty fell is called a Trierarch. The Trierarch was responsible for the outfitting, maintenance, operation and leadership of a warship known as a trireme, the hull and mast of the ship being provided by the State. The responsibility might fall on one person or be shared, in which case it was known as a syntrierarchy. The cost of a whole Trierarchy was not less than forty minas nor more than a talent with the average being 50 minas. The burden of the Trierarchy was so great that during some years no other liturgy could be assessed in the same or the following year.