In this paper, we classify fuzzy subgroups of the symmetric group  taking membership values in the unit interval, according to preferential equality and fuzzy isomorphism. In the process, we obtain a complete set of preferential fuzzy subgroups and isomorphic fuzzy subgroups of the alternating group  and the full symmetric group We develop here a convenient diagram depicting the lattice of subgroups of Gwith suggestive labeling of nodes for this purpose.

preferential fuzzy subgroup, symmetric group, alternating group, lattice of subgroups.