Confusion on Yoshitomo support in Heiji Rebellion

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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?