The government in my world covers the entire Earth, but is run by 3 separate, cooperating continental governments (Europe, North and Central Africa, and Australasia). The rest of the world is a nuclear wasteland. There is a highly feared Inquisition, famous for highly effective interrogations, frequent executions and terrible tortures.
They control a commando force called the Interrogen to 'combat, capture and control.' The heads of the Inquisition in their respective continents are considered to be nearly as powerful as the President of the Continent. There is no military per se, but a force called the 'Civil Defense Force' which is controlled by the President and counters terrorism, provides security and acts as a regular police in normal situations. It is also not nearly as powerful as a modern military, but still outnumbers the Interrogen by a 1:50 ratio. Due to a fuel crisis in the future, vehicles are pretty rare. Basically, all the investigation and counter terrorism/counter rebellion, along with fighting major organisational crime, is done by the Interrogen. In cases of emergency, high-ranked Inquisitors can control a portion of the CDF.
My question is, this Inquisition being a highly powerful secret police, how would it go about tackling major threats to the government, especially in a discreet manner and with enough power to be able to have a lot of free will(acting autonomously without being controlled by the government)?