According to the material available, the Shunga government was like the Mauryan one though it was not that tightly knit. The founder of the dynasty, Pushyamitra, held two royal sacrifices (horse-sacrifies) to assert his authority but still called himself senapat.
His successors called themselves rajan Pushyamitra’s son ruled in Vidisa as a viceroy on behalf of his father, and this indicates the continuation of the Mauryan practice of prince-viceroys. However, unlike the Mauryas, they added royal titles to their names subsequently.
The king and the viceroy (at his provincial capital) had a council of ministers like the Mauryas had. Agnimitra, a powerful ruler, probably did not consult his council much but instructed them to carry out his decrees.
The Shungas had a number of feudatories (some of them being blood relatives) who struck coins in their own names and sometimes took on royal tides too. These feudatories merely owed the Shungas political allegiance.