# Extensions 1→N→G→Q→1 with N=C3 and Q=C6×C3⋊S3

Direct product G=N×Q with N=C3 and Q=C6×C3⋊S3
dρLabelID
C3⋊S3×C3×C636C3:S3xC3xC6324,173

Semidirect products G=N:Q with N=C3 and Q=C6×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C31(C6×C3⋊S3) = C3×S3×C3⋊S3φ: C6×C3⋊S3/C3×C3⋊S3C2 ⊆ Aut C336C3:1(C6xC3:S3)324,166
C32(C6×C3⋊S3) = C6×C33⋊C2φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C3108C3:2(C6xC3:S3)324,174

Non-split extensions G=N.Q with N=C3 and Q=C6×C3⋊S3
extensionφ:Q→Aut NdρLabelID
C3.1(C6×C3⋊S3) = C6×C9⋊S3φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C3108C3.1(C6xC3:S3)324,142
C3.2(C6×C3⋊S3) = C2×He34S3φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C354C3.2(C6xC3:S3)324,144
C3.3(C6×C3⋊S3) = C2×C33.S3φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C354C3.3(C6xC3:S3)324,146
C3.4(C6×C3⋊S3) = C2×He3.4S3φ: C6×C3⋊S3/C32×C6C2 ⊆ Aut C3546+C3.4(C6xC3:S3)324,147
C3.5(C6×C3⋊S3) = C18×C3⋊S3central extension (φ=1)108C3.5(C6xC3:S3)324,143
C3.6(C6×C3⋊S3) = C6×He3⋊C2central stem extension (φ=1)54C3.6(C6xC3:S3)324,145
C3.7(C6×C3⋊S3) = C2×He3.4C6central stem extension (φ=1)543C3.7(C6xC3:S3)324,148

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