There has been talk on social media about active fighting between Russian elites, which inevitably leads to talks about a potential coup in Moscow, but that might not end the Ukraine war or result in an outcome everyone wants.
The tensions have been mounting over the last 24 hours as videos have poured onto social media from Wagner-associated pages and account criticizing the Ministry of Defence and other military leaders. At first, this seemed like a war of words, but more evidence has come out of Russia suggesting this has become a hot fight with a Wagner elite being held at gunpoint by Russian police.
The sides of this fight are not clear to everyone, so let us sum it up:
The Old Guard

Sergei Shoigu
Shoigu has been the Minister of Defence for 10 years and is generally considered to be a more moderate voice in the Kremlin. A lot of the vitriol from the frontline and from Wagner-backed groups has been focused on him. He is blamed for the lack of logistics and air support in the Ukraine war. He has also been blamed for not telling Putin the truth about what is going on, on the frontlines of the war.
Shoigu has been an enduring presence in Russian federal politics but he is now in danger. Ironically, he is being blamed for Russian failures more than Putin himself is.

Valery Gerasimov
Just like Shoigu, Gerasimov has been around for 10 years but in the position of Chief of Staff of the Armed Forces of the Russian Federation. Like his boss, he is a more moderate voice in the Kremlin but has been more key to the actions on the frontline in Ukraine. Gerasimov oversaw the advancement and upgrade of the Russian military, a process which seems to have failed.
Whether or not Gerasimov is one of the primary voices or not, won’t be relevant in the power struggle going on in Moscow. As the second-in-command of the Russian army, he will be seen as being in line with Shoigu and their fates are likely tied.
The Rebels

Ramzan Kadryov
A long-time Putin loyalist and de factor leader of the semi-autonomous Chechen region in Russia. He has been an extreme voice and is considered to be part of the hawkish Kremlin elite that not only supports the war but pushes for further escalation. Most recently Kadyrov called for low-yield nuclear weapons to be used on Ukraine.
Along with his extreme compatriots, he has been publicly critical of the Ministry of Defence but has stopped short of openly criticizing people by name. It is likely he would back serious escalations.

Yevgeny Prigozhin
Often referred to as Putin’s chef, has is a close confidant of the Russian president and controls a network of companies including Wagner group, a mercenary group with strong ties to the Kremlin itself which has been fighting in Ukraine. He also leads several companies which have been accused of influencing the 2016 and 2020 general elections in the United States.
His character is marked by the far-right beliefs he holds publicly. Wagner group has also been accused of not only killing Russian officers in Ukraine but actively producing propaganda videos which criticize the Ministry of Defence and also exaggerate the depth of the issues being faced on the frontline. In March Wagner group publicly stated that 300,000 soldiers were needed to win the war. A demand that now appears Putin has met.

Nikolai Patrushev
One of Putin’s closest confidants Patrushev is also extremely hawkish and has promoted anti-western conspiracy theories. He is currently the head of the National Security Council and was formerly head of the Federal Security Service which was the successor to the Soviet KGB of which Putin was also a member of.
Patrushev is among the Kremlin elite who are set to supplant Shoigu and Gerasimov and also advocate for more extreme escalations against Ukraine. Further, is he considered a possible successor to Putin.

Dmitry Medvedev
One of the closest allies of Putin, he stood in for him as President when Putin’s constitutional term limit was up in 2008. Reports indicate he’s among the most hawkish of the Kremlin elites. However, he has not publicly made comments to tip the scales in favour of any side in this brewing conflict. Medvedev has always been a calculating and stoic leader who doesn’t ever tip his hand.
While not as extreme as others in the group, it is safe to assume he will side with his fellow hawks to support the war in Ukraine. After all, it is reported that during his time as President he did not get along with Shoigu during his own tenure as Governor of Moscow Oblast briefly in 2012 after he was removed from the Ministry of Emergency Situations.
Summary
Many people believe that overthrowing Putin and the military will lead to an end of the war in Ukraine and a cooling off of the currently fierce and hot rhetoric around the war. However, the current slate of people set to have the power, motive and opportunity to take power in the Russian Federation will have no interest in ending the war. It is instead likely that the movement of the Russian army will be disrupted by power struggles in Moscow, but will come back with renewed organization and leadership. Wagner has consistently been one of the only competent fighting forces in the conflict against the invaders, with them leading the effort the damage to Ukraine will dramatically increase.
A coup in Russia will not lead to a liberalized and peaceful nation. It will be a far-right coup beholden to deeply religious values, values often used to advocate for mankind to bring about the biblical end of days. The chance of nuclear warfare dramatically increases with the change in leadership as do escalations of other kinds. Provoking NATO strikes against mainland Russia would prove valuable to new leadership which specializes in controlling the narrative in a way that convinces Russians. While the Ministry of Defence lies to Russians about losses of young men on the frontline and territorial losses, Russians have become wise to these lies. On the other hand, they are actively slurping up the lies being portrayed by Wagner-affiliated channels on Telegram and stories spread by Kadyrov and Patrushev.
Even without western support for a coup, it is now likely that the days for Shoigu and Gerasimov are numbered. Russians are quickly beginning to blame them for the war, but unfortunately, Putin has thus far been safe from the blame among the general public. The Ministry of Defence and FSB have been blamed for not telling Putin the truth. If Shoigu and Gerasimov are successful in defeating the power play by the rebel group, it is actually more likely they will force Putin to stand down from Ukraine and negotiate with the west as the rebels lead the hawkish clique in the Kremlin.