What is the main conflict in A Clockwork Orange by Anthony Burgess?

Burgess, a self-avowed anarchist, visited Leningrad (in what was then the Soviet Union) in 1961 and was appalled at the degree to which the communist state controlled people's lives. He based the character of Alex and his band of thugs ("droogs" in Nadsat) on Russian and British gangs of the 1950s and 1960s.