Confusion on Yoshitomo support in Heiji Rebellion edit

In this article, it doesn't explicitly state Yoshitomo's and Nobuyori's support for anyone, but it seems to imply that Kiyomori allied himself to both Go-Shirakawa and Nijo.

However, in the second paragraph of the main article on Fujiwara no Nobuyori, it states that the Minamoto supported Go-Shirakawa against Emperor Nijo. Then in the third paragraph, it states that the Minamoto abducted Go-Shirakawa and killed his chief councilor Michinori. Okay, so which is it?

For comparison, the main article on Minamoto no Yoshitomo never states that Yoshitomo and Nobuyori supported Go-Shirakawa, but just says they abucted him and killed Minchinori (implying they didn't support Go-Shirakawa). However, the article does state explicitly that Taira no Kiyomori fought in SUPPORT OF Go-Shirakawa (contrary to what it says in the second paragraph of the main article on Nobuyori).

In the main article on Minamoto no Yoritomo, it states that Yoshitomo supported Go-Shirakawa and Michinori. (In addition, it seems to incorrectly state that Nobuyori supported Nijo and Kiyomori).

So what's the real story? Was it just that Nobuyori and Yoshitomo attempted a coup d'etat over the Taira and the imperial court of Nijo and Go-Shirakawa? Or was there really a two-sided rivarlry between Nijo and Go-Shirakawa, and did Yoshitomo and Nobuyori really support Go-Shirakawa? And if so, what are the unstated details of what happened--why did Yoshitomo and Nobuyori turn on Go-Shirakawa and Michinori?

If someone knows these answers, can they go through and clean up the confusion on those articles mentioned here?