# Extensions 1→N→G→Q→1 with N=C3 and Q=S3×C3×C9

Direct product G=N×Q with N=C3 and Q=S3×C3×C9
dρLabelID
S3×C32×C9162S3xC3^2xC9486,221

Semidirect products G=N:Q with N=C3 and Q=S3×C3×C9
extensionφ:Q→Aut NdρLabelID
C3⋊(S3×C3×C9) = C3⋊S3×C3×C9φ: S3×C3×C9/C32×C9C2 ⊆ Aut C354C3:(S3xC3xC9)486,228

Non-split extensions G=N.Q with N=C3 and Q=S3×C3×C9
extensionφ:Q→Aut NdρLabelID
C3.1(S3×C3×C9) = D9×C3×C9φ: S3×C3×C9/C32×C9C2 ⊆ Aut C354C3.1(S3xC3xC9)486,91
C3.2(S3×C3×C9) = C3×C32⋊C18φ: S3×C3×C9/C32×C9C2 ⊆ Aut C354C3.2(S3xC3xC9)486,93
C3.3(S3×C3×C9) = C3×C9⋊C18φ: S3×C3×C9/C32×C9C2 ⊆ Aut C354C3.3(S3xC3xC9)486,96
C3.4(S3×C3×C9) = C9×C32⋊C6φ: S3×C3×C9/C32×C9C2 ⊆ Aut C3546C3.4(S3xC3xC9)486,98
C3.5(S3×C3×C9) = C9×C9⋊C6φ: S3×C3×C9/C32×C9C2 ⊆ Aut C3546C3.5(S3xC3xC9)486,100
C3.6(S3×C3×C9) = S3×C92central extension (φ=1)162C3.6(S3xC3xC9)486,92
C3.7(S3×C3×C9) = S3×C3×C27central extension (φ=1)162C3.7(S3xC3xC9)486,112
C3.8(S3×C3×C9) = S3×C32⋊C9central stem extension (φ=1)54C3.8(S3xC3xC9)486,95
C3.9(S3×C3×C9) = S3×C9⋊C9central stem extension (φ=1)162C3.9(S3xC3xC9)486,97
C3.10(S3×C3×C9) = S3×C27⋊C3central stem extension (φ=1)546C3.10(S3xC3xC9)486,114

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