The Greek warship with three rows of oars was called a trireme. Its name comes from the Greek word for “three,” referring to the three banks or levels of oars arranged along each side of the vessel.
A typical Athenian trireme carried about 170 rowers, with one man assigned to each oar. The rowers occupied three groups: the thranites on the upper level, the zygites in the middle, and the thalamites below. Including marines, officers, and deck crew, the full complement was roughly 200 people.
Triremes were narrow, light, fast warships designed especially for ramming enemy vessels. They became dominant in Mediterranean naval warfare from roughly the 7th through the 4th centuries BC and played a major role in the Persian Wars and the Athenian Empire.
The main mix-up is with a bireme, which had two banks of oars, or a penteconter, which traditionally had a single row. A quinquereme was a later, larger warship; its name referred to the number of rowers associated with each vertical section, not five literal rows of oars.