The direct products and semidirect products of quasi-crystallographic point groups, were derived from group theory. According to crystallography theory, the stereographic projection of pentagonal system, octagonal system, decagonal system and dodecagonal system, were derived and drawn. Basing upon them, all maximal subgroups of each quasi-crystallographic point group were derived and drawn. As a result, subgroups and supergroups of the three-dimensional crystallographic and quasi-crystallographic point groups (the ‘family tree' of sixty point groups) were derived and depicted in drawing. In the ‘family tree', the minimal supergroups and maximal subgroups of sixty point groups were illustrated in detail in the form of maximal subgroup chains.