# Extensions 1→N→G→Q→1 with N=C23×C6 and Q=C6

Direct product G=N×Q with N=C23×C6 and Q=C6
dρLabelID
C23×C62288C2^3xC6^2288,1045

Semidirect products G=N:Q with N=C23×C6 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C23×C6)⋊1C6 = C3×C24⋊C6φ: C6/C1C6 ⊆ Aut C23×C6246(C2^3xC6):1C6288,634
(C23×C6)⋊2C6 = C3×D4×A4φ: C6/C1C6 ⊆ Aut C23×C6366(C2^3xC6):2C6288,980
(C23×C6)⋊3C6 = (C22×S3)⋊A4φ: C6/C1C6 ⊆ Aut C23×C6246(C2^3xC6):3C6288,411
(C23×C6)⋊4C6 = A4×C3⋊D4φ: C6/C1C6 ⊆ Aut C23×C6366(C2^3xC6):4C6288,928
(C23×C6)⋊5C6 = C22×S3×A4φ: C6/C1C6 ⊆ Aut C23×C636(C2^3xC6):5C6288,1037
(C23×C6)⋊6C6 = S3×C22⋊A4φ: C6/C1C6 ⊆ Aut C23×C636(C2^3xC6):6C6288,1038
(C23×C6)⋊7C6 = A4×C22×C6φ: C6/C2C3 ⊆ Aut C23×C672(C2^3xC6):7C6288,1041
(C23×C6)⋊8C6 = C6×C22⋊A4φ: C6/C2C3 ⊆ Aut C23×C636(C2^3xC6):8C6288,1042
(C23×C6)⋊9C6 = C32×C22≀C2φ: C6/C3C2 ⊆ Aut C23×C672(C2^3xC6):9C6288,817
(C23×C6)⋊10C6 = D4×C62φ: C6/C3C2 ⊆ Aut C23×C6144(C2^3xC6):10C6288,1019
(C23×C6)⋊11C6 = C3×C244S3φ: C6/C3C2 ⊆ Aut C23×C624(C2^3xC6):11C6288,724
(C23×C6)⋊12C6 = C2×C6×C3⋊D4φ: C6/C3C2 ⊆ Aut C23×C648(C2^3xC6):12C6288,1002
(C23×C6)⋊13C6 = S3×C23×C6φ: C6/C3C2 ⊆ Aut C23×C696(C2^3xC6):13C6288,1043

Non-split extensions G=N.Q with N=C23×C6 and Q=C6
extensionφ:Q→Aut NdρLabelID
(C23×C6).1C6 = C24⋊C18φ: C6/C1C6 ⊆ Aut C23×C6366(C2^3xC6).1C6288,73
(C23×C6).2C6 = D4×C3.A4φ: C6/C1C6 ⊆ Aut C23×C6366(C2^3xC6).2C6288,344
(C23×C6).3C6 = C2×Dic3×A4φ: C6/C1C6 ⊆ Aut C23×C672(C2^3xC6).3C6288,927
(C23×C6).4C6 = C2×C4×C3.A4φ: C6/C2C3 ⊆ Aut C23×C672(C2^3xC6).4C6288,343
(C23×C6).5C6 = C23×C3.A4φ: C6/C2C3 ⊆ Aut C23×C672(C2^3xC6).5C6288,837
(C23×C6).6C6 = C2×C24⋊C9φ: C6/C2C3 ⊆ Aut C23×C636(C2^3xC6).6C6288,838
(C23×C6).7C6 = A4×C2×C12φ: C6/C2C3 ⊆ Aut C23×C672(C2^3xC6).7C6288,979
(C23×C6).8C6 = C22⋊C4×C18φ: C6/C3C2 ⊆ Aut C23×C6144(C2^3xC6).8C6288,165
(C23×C6).9C6 = C9×C22≀C2φ: C6/C3C2 ⊆ Aut C23×C672(C2^3xC6).9C6288,170
(C23×C6).10C6 = D4×C2×C18φ: C6/C3C2 ⊆ Aut C23×C6144(C2^3xC6).10C6288,368
(C23×C6).11C6 = C22⋊C4×C3×C6φ: C6/C3C2 ⊆ Aut C23×C6144(C2^3xC6).11C6288,812
(C23×C6).12C6 = C6×C6.D4φ: C6/C3C2 ⊆ Aut C23×C648(C2^3xC6).12C6288,723
(C23×C6).13C6 = Dic3×C22×C6φ: C6/C3C2 ⊆ Aut C23×C696(C2^3xC6).13C6288,1001

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