The Nine Families Navy

Structure

The Nine Families Navy isn't a single organisation like the rest of the kingdom it is split between the families, and each contributes towards the total as required. While the other kingdoms of Godai have more standard ocean going ships, the Nine tend to coop the larger ocean going creatures, like Dragon Turtles, Krakens and Whales, and build structures which fit onto the creatures to be used as other kingdoms would use ships, as a means of travelling and if need be fighting a sea battle. Obviously the Families have a massive advantage if fighting on or in the water, as ocean living creatures able to breath water and to attack from the depths, and their large friendly sea creatures are weapons in themselves, so are not related on mechanical weaponary which can fail in the midest of combat.
If a full naval conflict is likely the families will denote one member of their families to be overall commander-in-chief of the forces involved, they don't denote a different between army or navy as all their forces are ocean going. So all fall under the one command structure.

Ships

Not exactly ships but large sea creatures, like Dragon Turtles, Krakens and Whales, with structures built to fit around them to hold the Umijins fighters, during the travelling and to protect them while advancing on their enemies.