Under the regime of Islamist-military ruler Omar al-Bashir, Islamists dominated the government, building powerful networks of financial, commercial and political influence.
al-Burhan has attempted to distance himself from the Islamists, including by releasing statements against Bashir's old party.
According to one military analyst from the region, who spoke to AFP on condition of anonymity for safety reasons, "the Islamists have worked since 1989 to gain their hold over the army."
"al-Burhan tried to get rid of some of them," he said, but was only able to dismiss a few.
The Islamists maintained powerful positions in Sudan's security apparatus and on October 25, 2021, Burhan "bowed to pressure and launched his coup," Sudanese author Amir Babiker told AFP.
The takeover - for which he collaborated with now-enemy Rapid Support Force leader Mohamed Dagalo - ousted civilian officials from a power-sharing arrangement that was to lead to full civilian rule.
Quickly, al-Burhan cracked down on a commission responsible for dismantling the financial networks and economic empires that Bashir's allies had built.
Pro-democracy activists warned their revolution was being reversed, as several high-ranking officials from the Bashir era found roles in al-Burhan's administration.
In the early weeks of the war, more top officials from Bashir's regime escaped from prison, and the NCP itself reappeared to voice its support for the army.
"They're taking advantage of the exceptional situation the country is in to secure their place" in the future political landscape, according to Mirghani.
According to experts, al-Burhan seems to be facing more and more pressure from his own camp.
On Friday, he sent a letter to United Nations' Secretary=General Antonio Guterres requesting the dismissal of special envoy Volker Perthes, who has long been the target of accusations of "foreign intervention."
Thousands of military and Islamist supporters held protests in the months leading up to the war, demanding the U.N. mission chief's dismissal.
Days before fighting began, the U.N. urged Sudanese authorities to investigate after a man publicly called for Perthes' murder at a conference of Islamist parties and others linked to the Bashir regime.
In his letter, Burhan accused Perthes of bias and of stoking the war by presenting a misleading picture of the situation in Sudan.
"Without these signs of encouragement, the rebel leader Daglo would not have launched his military operations," the letter read.
It has never been possible to verify who fired the first shots of the war, which al-Burhan must fight on multiple fronts in order to survive, according to Mirghani.
His own supporters readily remind the public that Burhan himself named Dagalo as his second-in-command - an ambitious militia leader originally armed by Bashir to crush rebels in Darfur.
Islamist and pro-Bashir television channels in exile now accuse al-Burhan of giving too much leeway to Dagalo, which some suggest lays the groundwork for his eventual sidelining.
"At the end of the day, he's a soldier whose job is done when the mission is over," Mirghani told AFP.
"This could happen with this war."