File:S3latticeofsubgroups.png

Lattice of subgroups of symmetric group on three letters -- created with Graphviz. Here is the code used to create the picture:

digraph G{       rankdir = "BT"; Wholegroup[peripheries=3]; Trivialsubgroup[peripheries=3]; Alternatingsubgroup[peripheries=2]; Transpositionone; Transpositiontwo; Transpositionthree; Trivialsubgroup -> Transpositionone; Trivialsubgroup -> Transpositiontwo; Trivialsubgroup -> Transpositionthree; Trivialsubgroup -> Alternatingsubgroup; Transpositionone -> Wholegroup; Transpositiontwo -> Wholegroup; Transpositionthree -> Wholegroup; Alternatingsubgroup -> Wholegroup; Wholegroup[label="Whole group {, (2,3), (1,3), (1,2), (1,2,3), (1,3,2)}"]; Alternatingsubgroup[label="Alternating group {, (1,2,3), (1,3,2)}, characteristic"]; Transpositionone[label="{, (2,3)}"]; Transpositiontwo[label="{,(1,3)}"]; Transpositionthree[label="{,(1,2)}"]; Trivialsubgroup[label="Trivial subgroup {}"]; }