CBS shut down the CBS Radio Network in 1994 as part of its deal with Westwood One. So CBS does not own a radio network. Just stations. Disney/ABC still owns a number of radio stations, either through Radio Disney or ESPN. NBC got out of the radio business in 1988. It still operates the NBC Sports Radio Network in collaboration with Westwood One. There is also a CNBC Radio Network. NBC also revived its NBC News Radio service for a few years, but it's since been shut down.
The network radio business for the most part ended in the 1950s. The one remaining part of the radio network business was national news. But entertainment programming became more diversified in the 1970s and 80s with the emergence of radio syndication companies. They handled the distribution without the overhead of a network. The old networks attempted to adapt to the new model in the 1980s. CBS started RadioRadio, NBC launched The Source. ABC outsourced some of its entertainment programming to Radio Express. So while the TV networks retained their companion radio operations for a while, the business itself had changed. The need for a "network" using the old AT&T long lines ended in the 1980s with satellite distribution. It changed again with the internet. Now virtually anyone can be in the radio network business and the centralized distribution system no longer exists.