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+// Compiler avec par exemple:
+// dot -Tpng sous-groupes-de-s6.dot -o sous-groupes-de-s6.png
+// (le programme dot vient du package graphviz).
+
+// La numérotation des sous-groupes est celle de Sage(=GAP-1);
+// quelques commandes:
+// s6 = SymmetricGroup(6)
+// lsttrans = [h for h in s6.conjugacy_classes_subgroups() if h.is_transitive()]
+// desctrans = [(h.order(),gap.StructureDescription(h),h.is_subgroup(a6)) for h in lsttrans]
+// def subgroup_up_to_conjugacy(g,h):
+// for x in gap.ConjugateSubgroups(s6,g):
+// if gap.IsSubgroup(x,h):
+// return True
+// return False
+// subidx = [[j for j in range(16) if gcd(lsttrans[j].order(),lsttrans[i].order()) == lsttrans[j].order() and subgroup_up_to_conjugacy(lsttrans[i],lsttrans[j])] for i in range(16)]
+// maxsubidx = [[j for j in range(16) if is_maximal_subidx(i,j)] for i in range(16)]
+
+digraph sous_groupes_de_s6 {
+ g3 -> g0;
+ g3 -> g1;
+ g4 -> g0;
+ g4 -> g1;
+ g5 -> g1;
+ g5 -> g2;
+ g6 -> g2;
+ g7 -> g0;
+ g7 -> g2;
+ g8 -> g3;
+ g8 -> g4;
+ g10 -> g3;
+ g10 -> g5;
+ g10 -> g6;
+ g10 -> g7;
+ g11 -> g2;
+ g12 -> g8;
+ g12 -> g9;
+ g13 -> g3;
+ g13 -> g7;
+ g13 -> g11;
+ g14 -> g6;
+ g14 -> g9;
+ g14 -> g11;
+ g15 -> g10;
+ g15 -> g12;
+ g15 -> g13;
+ g15 -> g14;
+ g0 [label="S3"];
+ g1 [label="C6"];
+ g2 [label="A4"];
+ g3 [label="D6"];
+ g4 [label="S3 × C3"];
+ g5 [label="C2 × A4"];
+ g6 [label="S4+"];
+ g7 [label="S4−"];
+ g8 [label="S3 × S3"];
+ g9 [label="(C3 × C3) : C4"];
+ g10 [label="S4 × C2"];
+ g11 [label="A5"];
+ g12 [label="(S3 × S3) : C2"];
+ g13 [label="S5"];
+ g14 [label="A6"];
+ g15 [label="S6"];
+ g2 [color=blue,fontcolor=blue];
+ g6 [color=blue,fontcolor=blue];
+ g9 [color=blue,fontcolor=blue];
+ g11 [color=blue,fontcolor=blue];
+ g14 [color=blue,fontcolor=blue];
+}