In this paper we report the classification of all 394 magnetic rod groups into seven spin splitting prototypes, in analogy to a similar classification previously reported for the 1651 magnetic space groups and 528 magnetic layer groups. According to this classification, electrically induced (Pekar-Rashba) spin splitting is possible in the antiferromagnetic (AFM) structures described by magnetic rod groups of type I (no antiunitary operations) and type III, both in the presence and in the absence of the space inversion operation. A novel symmetry-based procedure is proposed for determining spin projection distribution in nanorods. DFT calculations are performed for cobalt oxide based nanorods with magnetic symmetry P6₃mc (type I) and P₆₃^′mc′ (type III), corresponding to two different AFM spin distributions over cobalt atoms. In agreement with group-theoretical analysis, a colossal spin splitting (on the order of electronvolts) is obtained for the nanorod described by the magnetic symmetry group of type I.