In[]:=
(PermutationList[#,3]&/@GroupElements[PermutationGroup[{#}]])&/@Permutations[Range[3]]
Out[]=
{{{1,2,3}},{{1,2,3},{1,3,2}},{{1,2,3},{2,1,3}},{{1,2,3},{2,3,1},{3,1,2}},{{1,2,3},{2,3,1},{3,1,2}},{{1,2,3},{3,2,1}}}
In[]:=
FiniteGroupData[{"SymmetricGroup",3},"Subgroups"]
Out[]=
{Trivial,{CyclicGroup,2},{CyclicGroup,3},{SymmetricGroup,3}}
In[]:=
Gather[PermutationGroup/@Subsets[Permutations[Range[3]]],Equal]
Out[]=
In[]:=
Length[%]
Out[]=
6
Lattice