A gap sub assembly for electromagnetic telemetry used in downhole drilling. The gap sub comprises a female part comprising a female mating section and a male part comprising a male mating section. The male mating section is matingly received within the female mating section and electrically isolated therefrom. One or more electrically insulating bodies secure the male part axially and torsionally relative to the female part. The electrically insulating bodies also electrically isolate the male part from the female part. The electrically insulating bodies can be installed through apertures in the female part or at least some of the electrically insulating bodies can be installed before the male mating section is inserted into the female mating section. The electrically insulating bodies can be held in place on the male mating section using a retention apparatus such as a ring, a scarf, pods or an adhesive.