Extensions 1→N→G→Q→1 with N=C3 and Q=He3:C2

Direct product G=NxQ with N=C3 and Q=He3:C2
dρLabelID
C3xHe3:C227C3xHe3:C2162,41

Semidirect products G=N:Q with N=C3 and Q=He3:C2
extensionφ:Q→Aut NdρLabelID
C3:(He3:C2) = He3:5S3φ: He3:C2/He3C2 ⊆ Aut C3186C3:(He3:C2)162,46

Non-split extensions G=N.Q with N=C3 and Q=He3:C2
extensionφ:Q→Aut NdρLabelID
C3.1(He3:C2) = C32:2D9φ: He3:C2/He3C2 ⊆ Aut C3186C3.1(He3:C2)162,17
C3.2(He3:C2) = C33:S3φ: He3:C2/He3C2 ⊆ Aut C396+C3.2(He3:C2)162,19
C3.3(He3:C2) = He3.3S3φ: He3:C2/He3C2 ⊆ Aut C3276+C3.3(He3:C2)162,20
C3.4(He3:C2) = He3:S3φ: He3:C2/He3C2 ⊆ Aut C3276+C3.4(He3:C2)162,21
C3.5(He3:C2) = 3- 1+2.S3φ: He3:C2/He3C2 ⊆ Aut C3276+C3.5(He3:C2)162,22

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