Yep, most likely in an underground bunker.
I am thinking that unlike the US Germany set up several government bunkers, a bit like NORAD.
A coup takes place in one, most likely the largest, followed by a second coup and purge. What follows next is militarization, and the establishment of a police state. Ghouls are singled out as a subversive element. Pogroms and forced labor.
The current dictator is Franz Krupp - possibly related to the manufacturing family of the same name. Certainly his family controls manufacturing in the Bunker - the armor pictured above is of Krupp manufacture, as is the gun.
There are two such bunkers in the surrounds of Berlin, with the second calling itself Free Berlin. (Stealing loosely from post WWII Berlin & East Berlin.)
An uneasy peace between the two, check points, armed guards, and the reestablishment of The Wall.
Underground The Wall is permeable - sewers, power conduits, water mains - all crisscrossing under the streets.
Crime controls the Underground, making for three power blocs.
A near copy of Super Mutants are called Trolls. Intended as shock troops by the militarists a large number of the Trolls broke free and into the city and its surrounds. Some joined Free Berlin, some joined the crime families of The Underground, some became simple marauders. A fourth group that shares elements with all of the others schemes to seize control of the Vats needed to create more of their kind.
Trolls are resistant to radiation, and have taken over mining and heavy construction.
Meanwhile, I have this amusing image of Switzerland moving its entire population into Vaults, surviving largely unscathed. A pacifistic military state with a fully armed populace. The Super Mutants there are volunteers, and only those that have either already had children or those that are sterile are allowed to take part in the program. The Swiss are very worried about limiting their available gene pool.
All Swiss Super Mutants are trained in martial arts, and all are part of the military. Each Swiss diplomat is escorted by two Super Mutants. Foreigners believe that the Swiss Super Mutants are slow of thought - simple, stupid brutes. In fact every one of them learns multiple languages and all are trained observers....
Don't mess with the Swiss....
The Auld Grump