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Extensions 1→N→G→Q→1 with N=C2×C3⋊S3 and Q=S3

Direct product G=N×Q with N=C2×C3⋊S3 and Q=S3
dρLabelID
C2×S3×C3⋊S336C2xS3xC3:S3216,171

Semidirect products G=N:Q with N=C2×C3⋊S3 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3)⋊1S3 = He3⋊2D4φ: S3/C1 → S3 ⊆ Out C2×C3⋊S3366+(C2xC3:S3):1S3216,35
(C2×C3⋊S3)⋊2S3 = He3⋊3D4φ: S3/C1 → S3 ⊆ Out C2×C3⋊S3366(C2xC3:S3):2S3216,37
(C2×C3⋊S3)⋊3S3 = C2×C32⋊D6φ: S3/C1 → S3 ⊆ Out C2×C3⋊S3186+(C2xC3:S3):3S3216,102
(C2×C3⋊S3)⋊4S3 = C33⋊6D4φ: S3/C3 → C2 ⊆ Out C2×C3⋊S372(C2xC3:S3):4S3216,127
(C2×C3⋊S3)⋊5S3 = C33⋊8D4φ: S3/C3 → C2 ⊆ Out C2×C3⋊S336(C2xC3:S3):5S3216,129
(C2×C3⋊S3)⋊6S3 = C33⋊9D4φ: S3/C3 → C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3):6S3216,132
(C2×C3⋊S3)⋊7S3 = C2×C32⋊4D6φ: S3/C3 → C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3):7S3216,172

Non-split extensions G=N.Q with N=C2×C3⋊S3 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×C3⋊S3).S3 = C6.S32φ: S3/C1 → S3 ⊆ Out C2×C3⋊S3366(C2xC3:S3).S3216,34
(C2×C3⋊S3).2S3 = C33⋊9(C2×C4)φ: S3/C3 → C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).2S3216,131
(C2×C3⋊S3).3S3 = C2×C33⋊C4φ: S3/C3 → C2 ⊆ Out C2×C3⋊S3244(C2xC3:S3).3S3216,169
(C2×C3⋊S3).4S3 = Dic3×C3⋊S3φ: trivial image72(C2xC3:S3).4S3216,125

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