# Extensions 1→N→G→Q→1 with N=C22×C6 and Q=S3

Direct product G=N×Q with N=C22×C6 and Q=S3
dρLabelID
S3×C22×C648S3xC2^2xC6144,195

Semidirect products G=N:Q with N=C22×C6 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C22×C6)⋊1S3 = C6×S4φ: S3/C1S3 ⊆ Aut C22×C6183(C2^2xC6):1S3144,188
(C22×C6)⋊2S3 = C2×C3⋊S4φ: S3/C1S3 ⊆ Aut C22×C6186+(C2^2xC6):2S3144,189
(C22×C6)⋊3S3 = C6×C3⋊D4φ: S3/C3C2 ⊆ Aut C22×C624(C2^2xC6):3S3144,167
(C22×C6)⋊4S3 = C2×C327D4φ: S3/C3C2 ⊆ Aut C22×C672(C2^2xC6):4S3144,177
(C22×C6)⋊5S3 = C23×C3⋊S3φ: S3/C3C2 ⊆ Aut C22×C672(C2^2xC6):5S3144,196

Non-split extensions G=N.Q with N=C22×C6 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C22×C6).1S3 = C3×A4⋊C4φ: S3/C1S3 ⊆ Aut C22×C6363(C2^2xC6).1S3144,123
(C22×C6).2S3 = C6.S4φ: S3/C1S3 ⊆ Aut C22×C6366-(C2^2xC6).2S3144,33
(C22×C6).3S3 = C2×C3.S4φ: S3/C1S3 ⊆ Aut C22×C6186+(C2^2xC6).3S3144,109
(C22×C6).4S3 = C6.7S4φ: S3/C1S3 ⊆ Aut C22×C6366-(C2^2xC6).4S3144,126
(C22×C6).5S3 = C3×C6.D4φ: S3/C3C2 ⊆ Aut C22×C624(C2^2xC6).5S3144,84
(C22×C6).6S3 = C18.D4φ: S3/C3C2 ⊆ Aut C22×C672(C2^2xC6).6S3144,19
(C22×C6).7S3 = C22×Dic9φ: S3/C3C2 ⊆ Aut C22×C6144(C2^2xC6).7S3144,45
(C22×C6).8S3 = C2×C9⋊D4φ: S3/C3C2 ⊆ Aut C22×C672(C2^2xC6).8S3144,46
(C22×C6).9S3 = C625C4φ: S3/C3C2 ⊆ Aut C22×C672(C2^2xC6).9S3144,100
(C22×C6).10S3 = C23×D9φ: S3/C3C2 ⊆ Aut C22×C672(C2^2xC6).10S3144,112
(C22×C6).11S3 = C22×C3⋊Dic3φ: S3/C3C2 ⊆ Aut C22×C6144(C2^2xC6).11S3144,176
(C22×C6).12S3 = Dic3×C2×C6central extension (φ=1)48(C2^2xC6).12S3144,166

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