# Extensions 1→N→G→Q→1 with N=C3×He3 and Q=C3

Direct product G=N×Q with N=C3×He3 and Q=C3
dρLabelID
C32×He381C3^2xHe3243,62

Semidirect products G=N:Q with N=C3×He3 and Q=C3
extensionφ:Q→Out NdρLabelID
(C3×He3)⋊1C3 = C32.24He3φ: C3/C1C3 ⊆ Out C3×He381(C3xHe3):1C3243,3
(C3×He3)⋊2C3 = C32⋊He3φ: C3/C1C3 ⊆ Out C3×He327(C3xHe3):2C3243,37
(C3×He3)⋊3C3 = C3×C3≀C3φ: C3/C1C3 ⊆ Out C3×He327(C3xHe3):3C3243,51
(C3×He3)⋊4C3 = C3×He3⋊C3φ: C3/C1C3 ⊆ Out C3×He381(C3xHe3):4C3243,53
(C3×He3)⋊5C3 = C33⋊C32φ: C3/C1C3 ⊆ Out C3×He3279(C3xHe3):5C3243,56
(C3×He3)⋊6C3 = He3⋊C32φ: C3/C1C3 ⊆ Out C3×He3279(C3xHe3):6C3243,58
(C3×He3)⋊7C3 = 3+ 1+4φ: C3/C1C3 ⊆ Out C3×He3279(C3xHe3):7C3243,65

Non-split extensions G=N.Q with N=C3×He3 and Q=C3
extensionφ:Q→Out NdρLabelID
(C3×He3).1C3 = C33.C32φ: C3/C1C3 ⊆ Out C3×He381(C3xHe3).1C3243,4
(C3×He3).2C3 = C32.27He3φ: C3/C1C3 ⊆ Out C3×He381(C3xHe3).2C3243,6
(C3×He3).3C3 = He3⋊C9φ: C3/C1C3 ⊆ Out C3×He381(C3xHe3).3C3243,17
(C3×He3).4C3 = C9⋊He3φ: C3/C1C3 ⊆ Out C3×He381(C3xHe3).4C3243,39
(C3×He3).5C3 = C32.23C33φ: C3/C1C3 ⊆ Out C3×He381(C3xHe3).5C3243,40
(C3×He3).6C3 = C3×He3.C3φ: C3/C1C3 ⊆ Out C3×He381(C3xHe3).6C3243,52
(C3×He3).7C3 = He3.C32φ: C3/C1C3 ⊆ Out C3×He3279(C3xHe3).7C3243,57
(C3×He3).8C3 = 3- 1+4φ: C3/C1C3 ⊆ Out C3×He3279(C3xHe3).8C3243,66
(C3×He3).9C3 = C9×He3φ: trivial image81(C3xHe3).9C3243,35
(C3×He3).10C3 = C3×C9○He3φ: trivial image81(C3xHe3).10C3243,64

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