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

Direct product G=N×Q with N=C3×C6 and Q=S3
dρLabelID
S3×C3×C636S3xC3xC6108,42

Semidirect products G=N:Q with N=C3×C6 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1S3 = C2×C32⋊C6φ: S3/C1S3 ⊆ Aut C3×C6186+(C3xC6):1S3108,25
(C3×C6)⋊2S3 = C2×He3⋊C2φ: S3/C1S3 ⊆ Aut C3×C6183(C3xC6):2S3108,28
(C3×C6)⋊3S3 = C6×C3⋊S3φ: S3/C3C2 ⊆ Aut C3×C636(C3xC6):3S3108,43
(C3×C6)⋊4S3 = C2×C33⋊C2φ: S3/C3C2 ⊆ Aut C3×C654(C3xC6):4S3108,44

Non-split extensions G=N.Q with N=C3×C6 and Q=S3
extensionφ:Q→Aut NdρLabelID
(C3×C6).1S3 = C32⋊C12φ: S3/C1S3 ⊆ Aut C3×C6366-(C3xC6).1S3108,8
(C3×C6).2S3 = C9⋊C12φ: S3/C1S3 ⊆ Aut C3×C6366-(C3xC6).2S3108,9
(C3×C6).3S3 = He33C4φ: S3/C1S3 ⊆ Aut C3×C6363(C3xC6).3S3108,11
(C3×C6).4S3 = C2×C9⋊C6φ: S3/C1S3 ⊆ Aut C3×C6186+(C3xC6).4S3108,26
(C3×C6).5S3 = C3×Dic9φ: S3/C3C2 ⊆ Aut C3×C6362(C3xC6).5S3108,6
(C3×C6).6S3 = C9⋊Dic3φ: S3/C3C2 ⊆ Aut C3×C6108(C3xC6).6S3108,10
(C3×C6).7S3 = C6×D9φ: S3/C3C2 ⊆ Aut C3×C6362(C3xC6).7S3108,23
(C3×C6).8S3 = C2×C9⋊S3φ: S3/C3C2 ⊆ Aut C3×C654(C3xC6).8S3108,27
(C3×C6).9S3 = C3×C3⋊Dic3φ: S3/C3C2 ⊆ Aut C3×C636(C3xC6).9S3108,33
(C3×C6).10S3 = C335C4φ: S3/C3C2 ⊆ Aut C3×C6108(C3xC6).10S3108,34
(C3×C6).11S3 = C32×Dic3central extension (φ=1)36(C3xC6).11S3108,32

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