Originally concieved after the Russo-Japanese war the Hachi-Hachi (eight-eight) fleet policy provided the need for two battle groups composed of eight ships each, eight battleships and eight battlecruisers: the plan came into light in 1910 when the four Kongo-class battlecruisers where ordered, followed in the next years by the Fuso and Ise class battleships. The first fulfillment of the hachi-hachi plan was initially cut back by the naval ministry to a four-four plan, only later four more battleships (two Nagato and two Tosa class) where approved to reach an eight-four fleet.
Just after the end of WWI in response to the ambitious capital ship program started by the US navy the Hachi-Hachi fleet plan was proposed once again: Nagato and Tosa class where retained in the program, but other twelve ships where added, four Amagi-class battlecruisers, four of the Kii class and four of the enormous n°13 class battleships. In order to achieve the whole plan by 1927 all ships where already allocated and ordered by october 1921.
Still, the Washington Naval conference called in november, and the subsequent Washington Naval Treaty put an end to the enormous IJN naval armament plan, which saw all the warships planned to be canceled, halted and scrapped (with the exception of the already completed Nagato-class). Only Akagi (a battlecrusier of the Amagi class) and Kaga (a battleship of the Tosa class) managed to live on after being converted into aircraft carriers, the latter just because Amagi, initially planned to be converted in her place, was destroyed during the Great Kanto Earthquake in 1923.
The Nagato Class Battleship:
the only battleship class that was ultimately completed, can be found here
The Tosa Class Battleship:
canceled when both ships where less than 5 months before completion, Tosa was used as a target ship, Kaga became an aircraft carrier; carriercan be found here
The Amagi class Battlecruiser:
the first two ships of the Amagi class Battlecruisers, Amagi herself and Akagi, where laid down on december 6th and 16th 1920; by the time the other two, Atago and Takao, where started on november 22nd and december 19th 1921 smoke problems around the bridge where emerging from the trials of the Nagato class Battleships, so the project for the two late ships was revised with the introduction of trunked funnels in order to move the uptakes away from the bridge.
The Kii Class Battleship (initially designed as Battleship A):
the Kii class design was basically a repeat of the Amagi class battlecruisers, the main differences where a thicker armour belt and a slightly inferior top speed.
Battleship B armed with 12x16.1-inch guns in four triple turrets
Battleship C armed with 12x16.1-inch guns in three twin and two triple guns
Battleship D, armed with twelve 16.1-inch guns in six twin turrets, it could be nicknamed "Fuso on steroids" given her resemblance to the early IJN battleship in her main gun layout:
Battleship E, armed with twelve 16.1-inch guns in three quad turrets:
Battleship F, armed with twelve 16.1-inch guns in two twin and two quadruple turrets:
Battleship G, armed with 14x16.1-inch guns in three twin and two quad turrets:
Battleship H, armed with fourteen 16.1-inch guns in one twin and three quad mounts:
Battleship I, armed with sixteen 16-1.inch guns if four quad turrets:
Battleship J, the "Battlecruiser" version of Battleship I featuring the same armament, but with a 12-inch belt compared to ther 13-inch of her sibling:
N°13 class (initially designed as Battleship K), armed with eight 18-inch guns in 4 twin mounts:
Designed by Yuzuru Hiraga, the four planned sister would have been be the first japanese Battleships sporting the massive 18-inch guns in four twin turrets. With a planned top speed of 30 knots they would have been among the fastest and most powerful battleship ever built, their massive dimensions matched only by the Yamato class some 10 years later. Planned to be completed by the late 20's all were canceled because of the Washington Naval Treaty.
Battleship L, armed with ten 18-inch guns in 5 twin mounts:
Battleship M, armed with twelve 18-inch guns in four triple turrets:
Battleship N, armed with thirteen 18-inch guns in two twins and three triple turrets:
Battleship O, armed with six 18-inch guns in three triple turrets, sacrificing armament and armor for a very high top speed of 37 knots: