Japan - Electing a new PM

Note that in this post I will be using the preferred name order, which, by in large, the english world has yet to catch up on. 

With the resignation of Abe Shinzo as Prime Minister, a leadership election is being held within the governing Liberal Democratic Party to replace him.

As far as I can tell, there are two main candidates in the running. Ishiba Shigeru has run in the last two major contested leadership elections in 2012 and 2018. 

He is associated with both Heisei Kenkyukai (a party faction) and Nippon Kaigi (a far-right non-party organization). Trying to pin down his positions is this difficult, but my best guess is it comes down as "Imperialist" in nature. 

Kishida Fumio is his main opponent. His faction of choice is more moderate in some ways, and while he is not of the same faction as Abe Shinzo, this faction is closer in many ways to that of Abe's faction. 

Abe, supposedly, supports Kishida to succeed him, and this may give him a huge boost towards winning the leadership.

There are, however, other possible candidates. Koizumi Shinjiro is seen as more moderate than either of the two and would lead the LDP back closer to where it was under his father, Koizumi Junichiro. Suga Yoshihide is also often mentioned, he probably has views closer to Abe than anyone else mentioned yet. 

Other possibilities include Nota Seiko, Kono Taro, and Motegi Toshimitsu. The latter especially strikes me as not having the intangible 'stuff' a leader needs to win, and would require significant backing. Noda could get a boost by being the only woman on the list; and Kono a boost due to his father being a former PM. All three of them, along with almost everyone else mentioned (with the possible exception of Koizumi) hold views close enough to that of Abe that we are unlikely to see any drastic shift after the election of the new leader on September 15th. 

One important thing to keep in mind, however, is what impact the new leader will have on the factions with the LDP. The party is famously factional, and it is not unheard of for unhappy politicians to leave the party and take friends with them. This can result in the creation of new parties, which, have had a historic tendency to merge with one another. Any such moves could re-balance the political game board in Japan.