# Extensions 1→N→G→Q→1 with N=C2×C6 and Q=S4

Direct product G=N×Q with N=C2×C6 and Q=S4
dρLabelID
C2×C6×S436C2xC6xS4288,1033

Semidirect products G=N:Q with N=C2×C6 and Q=S4
extensionφ:Q→Aut NdρLabelID
(C2×C6)⋊1S4 = C3×C22⋊S4φ: S4/C22S3 ⊆ Aut C2×C6246(C2xC6):1S4288,1035
(C2×C6)⋊2S4 = (C2×C6)⋊S4φ: S4/C22S3 ⊆ Aut C2×C6246(C2xC6):2S4288,1036
(C2×C6)⋊3S4 = C3×A4⋊D4φ: S4/A4C2 ⊆ Aut C2×C6366(C2xC6):3S4288,906
(C2×C6)⋊4S4 = (C2×C6)⋊4S4φ: S4/A4C2 ⊆ Aut C2×C6366(C2xC6):4S4288,917
(C2×C6)⋊5S4 = C22×C3⋊S4φ: S4/A4C2 ⊆ Aut C2×C636(C2xC6):5S4288,1034

Non-split extensions G=N.Q with N=C2×C6 and Q=S4
extensionφ:Q→Aut NdρLabelID
(C2×C6).1S4 = C3×C42⋊S3φ: S4/C22S3 ⊆ Aut C2×C6363(C2xC6).1S4288,397
(C2×C6).2S4 = C42⋊D9φ: S4/C22S3 ⊆ Aut C2×C6366+(C2xC6).2S4288,67
(C2×C6).3S4 = (C4×C12)⋊S3φ: S4/C22S3 ⊆ Aut C2×C6366+(C2xC6).3S4288,401
(C2×C6).4S4 = C24⋊D9φ: S4/C22S3 ⊆ Aut C2×C6366(C2xC6).4S4288,836
(C2×C6).5S4 = C3×Q8.D6φ: S4/A4C2 ⊆ Aut C2×C6484(C2xC6).5S4288,901
(C2×C6).6S4 = Q8⋊Dic9φ: S4/A4C2 ⊆ Aut C2×C6288(C2xC6).6S4288,69
(C2×C6).7S4 = C2×Q8.D9φ: S4/A4C2 ⊆ Aut C2×C6288(C2xC6).7S4288,335
(C2×C6).8S4 = C2×Q8⋊D9φ: S4/A4C2 ⊆ Aut C2×C6144(C2xC6).8S4288,336
(C2×C6).9S4 = Q8.D18φ: S4/A4C2 ⊆ Aut C2×C61444(C2xC6).9S4288,337
(C2×C6).10S4 = C2×C6.S4φ: S4/A4C2 ⊆ Aut C2×C672(C2xC6).10S4288,341
(C2×C6).11S4 = C23.D18φ: S4/A4C2 ⊆ Aut C2×C6366(C2xC6).11S4288,342
(C2×C6).12S4 = C6.GL2(𝔽3)φ: S4/A4C2 ⊆ Aut C2×C696(C2xC6).12S4288,403
(C2×C6).13S4 = C22×C3.S4φ: S4/A4C2 ⊆ Aut C2×C636(C2xC6).13S4288,835
(C2×C6).14S4 = C2×C6.5S4φ: S4/A4C2 ⊆ Aut C2×C696(C2xC6).14S4288,910
(C2×C6).15S4 = C2×C6.6S4φ: S4/A4C2 ⊆ Aut C2×C648(C2xC6).15S4288,911
(C2×C6).16S4 = SL2(𝔽3).D6φ: S4/A4C2 ⊆ Aut C2×C6484(C2xC6).16S4288,912
(C2×C6).17S4 = C2×C6.7S4φ: S4/A4C2 ⊆ Aut C2×C672(C2xC6).17S4288,916
(C2×C6).18S4 = C3×Q8⋊Dic3central extension (φ=1)96(C2xC6).18S4288,399
(C2×C6).19S4 = C6×CSU2(𝔽3)central extension (φ=1)96(C2xC6).19S4288,899
(C2×C6).20S4 = C6×GL2(𝔽3)central extension (φ=1)48(C2xC6).20S4288,900
(C2×C6).21S4 = C6×A4⋊C4central extension (φ=1)72(C2xC6).21S4288,905

׿
×
𝔽