The set of all 51 possible12C/13C isotopomers of a C8 cluster of D2d symmetry has been studied by means of the harmonic vibration analysis based on the force field resulting from the second order Møller-Plesset (MP2) perturbation treatment with the 6-31G* basis set. The isotopomers can undergo 200 isomerizations which can be classified into 5 distinct groups using the properties of sums of the squares of harmonic vibrational frequencies.