A model of a periodic defect (supercell model) is often used for studying the electronic and vibrational structure of point defects in crystals. The symmetry of this model is determined by the site symmetry of the point defect embedded in a crystal and the symmetry of the host crystal. The procedure of the determination of all the possible space groups describing the symmetry of the model of a periodic defect is elaborated in the present paper. This procedure is applied to point defects in MgO crystal. There are generated the space groups of the supercell model of an interstitial oxygen atom in volume-, face- and edge-centered positions and of molecular oxygen ion O₂^2- in anion site oriented along the [111], [110] and [001] directions. For the case of [110] orientation the results of nonempirical Hartree-Fock LCAO calculations are given for different supercell choices.