# Extensions 1→N→G→Q→1 with N=C2×3- 1+2 and Q=S3

Direct product G=N×Q with N=C2×3- 1+2 and Q=S3
dρLabelID
C2×S3×3- 1+2366C2xS3xES-(3,1)324,141

Semidirect products G=N:Q with N=C2×3- 1+2 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×3- 1+2)⋊1S3 = C2×C33⋊S3φ: S3/C1S3 ⊆ Out C2×3- 1+2186+(C2xES-(3,1)):1S3324,77
(C2×3- 1+2)⋊2S3 = C2×He3.3S3φ: S3/C1S3 ⊆ Out C2×3- 1+2546+(C2xES-(3,1)):2S3324,78
(C2×3- 1+2)⋊3S3 = C2×C33.S3φ: S3/C3C2 ⊆ Out C2×3- 1+254(C2xES-(3,1)):3S3324,146
(C2×3- 1+2)⋊4S3 = C2×He3.4S3φ: S3/C3C2 ⊆ Out C2×3- 1+2546+(C2xES-(3,1)):4S3324,147

Non-split extensions G=N.Q with N=C2×3- 1+2 and Q=S3
extensionφ:Q→Out NdρLabelID
(C2×3- 1+2).1S3 = C33⋊Dic3φ: S3/C1S3 ⊆ Out C2×3- 1+2366-(C2xES-(3,1)).1S3324,22
(C2×3- 1+2).2S3 = He3.3Dic3φ: S3/C1S3 ⊆ Out C2×3- 1+21086-(C2xES-(3,1)).2S3324,23
(C2×3- 1+2).3S3 = 3- 1+2.Dic3φ: S3/C1S3 ⊆ Out C2×3- 1+21086-(C2xES-(3,1)).3S3324,25
(C2×3- 1+2).4S3 = C2×3- 1+2.S3φ: S3/C1S3 ⊆ Out C2×3- 1+2546+(C2xES-(3,1)).4S3324,80
(C2×3- 1+2).5S3 = C33.Dic3φ: S3/C3C2 ⊆ Out C2×3- 1+2108(C2xES-(3,1)).5S3324,100
(C2×3- 1+2).6S3 = He3.4Dic3φ: S3/C3C2 ⊆ Out C2×3- 1+21086-(C2xES-(3,1)).6S3324,101
(C2×3- 1+2).7S3 = Dic3×3- 1+2φ: trivial image366(C2xES-(3,1)).7S3324,95

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