The laser induced fluorescence spectrum of jet-cooled CoC near 750 nm has been measured at high resolution following the reaction of laser-ablated cobalt atoms with methane. The X(2) Sigma(+) ground state of CoC is an unusually good example of Hund’s case (b(beta S)) coupling. Since Co has a nuclear spin I=7/2, each rotational level is split by the Fermi contact interaction into G=3 and G=4 components, where G=I+S; the splitting for N=0 is more than 0.5 cm(-1). The X(2) Sigma(+) state begins to uncouple toward case (b(beta J)) with increasing rotation. Transitions to various (II)-I-2 excited states occur in the region 13 000-14 500 cm(-1); the most prominent of these (for which high resolution spectra have been recorded) lie at 13 079 cm(-1) ((II3/2)-I-2) and 13 343 cm(-1) ((II1/2)-I-2). The (b(beta S)) coupling in the ground state produces some unexpected hyperfine intensity patterns, which have been studied in detail. A very low-lying (2) Delta(i) state, whose Omega=5/2 and Omega=3/2 components lie at 221 and 1173 cm(-1), has been identified. Laser excitation of the (II3/2)-I-2-(2) Delta(5/2) transition has been observed by monitoring the strong (II3/2)-I-2-X(2) Sigma(+) emission, which has allowed the (2) Delta(5/2) state to be characterized at high resolution. A total of 879 rotational-hyperfine transitions between the various (II1/2)-I-2, (II3/2)-I-2, (2) Delta(5/2), and (2) Sigma(+) states have been assigned and fitted. Matrix elements for a (2) Sigma(+) state in case (bps) coupling are listed.