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Extensions 1→N→G→Q→1 with N=C2×C4 and Q=S4

Direct product G=N×Q with N=C2×C4 and Q=S4
dρLabelID
C2×C4×S424C2xC4xS4192,1469

Semidirect products G=N:Q with N=C2×C4 and Q=S4
extensionφ:Q→Aut NdρLabelID
(C2×C4)⋊1S4 = C24.5D6φ: S4/A4 → C2 ⊆ Aut C2×C424(C2xC4):1S4192,972
(C2×C4)⋊2S4 = C2×C4⋊S4φ: S4/A4 → C2 ⊆ Aut C2×C424(C2xC4):2S4192,1470
(C2×C4)⋊3S4 = C24.10D6φ: S4/A4 → C2 ⊆ Aut C2×C4246(C2xC4):3S4192,1471

Non-split extensions G=N.Q with N=C2×C4 and Q=S4
extensionφ:Q→Aut NdρLabelID
(C2×C4).1S4 = CSU2(𝔽3)⋊C4φ: S4/A4 → C2 ⊆ Aut C2×C464(C2xC4).1S4192,947
(C2×C4).2S4 = Q8.Dic6φ: S4/A4 → C2 ⊆ Aut C2×C464(C2xC4).2S4192,948
(C2×C4).3S4 = GL2(𝔽3)⋊C4φ: S4/A4 → C2 ⊆ Aut C2×C432(C2xC4).3S4192,953
(C2×C4).4S4 = Q8.2D12φ: S4/A4 → C2 ⊆ Aut C2×C432(C2xC4).4S4192,954
(C2×C4).5S4 = C24.3D6φ: S4/A4 → C2 ⊆ Aut C2×C448(C2xC4).5S4192,970
(C2×C4).6S4 = SL2(𝔽3).D4φ: S4/A4 → C2 ⊆ Aut C2×C464(C2xC4).6S4192,984
(C2×C4).7S4 = SL2(𝔽3)⋊D4φ: S4/A4 → C2 ⊆ Aut C2×C432(C2xC4).7S4192,986
(C2×C4).8S4 = Q8⋊Dic6φ: S4/A4 → C2 ⊆ Aut C2×C464(C2xC4).8S4192,945
(C2×C4).9S4 = Q8.D12φ: S4/A4 → C2 ⊆ Aut C2×C464(C2xC4).9S4192,949
(C2×C4).10S4 = SL2(𝔽3)⋊Q8φ: S4/A4 → C2 ⊆ Aut C2×C464(C2xC4).10S4192,950
(C2×C4).11S4 = Q8⋊D12φ: S4/A4 → C2 ⊆ Aut C2×C432(C2xC4).11S4192,952
(C2×C4).12S4 = A4⋊M4(2)φ: S4/A4 → C2 ⊆ Aut C2×C4246(C2xC4).12S4192,968
(C2×C4).13S4 = C24.4D6φ: S4/A4 → C2 ⊆ Aut C2×C448(C2xC4).13S4192,971
(C2×C4).14S4 = U2(𝔽3)⋊C2φ: S4/A4 → C2 ⊆ Aut C2×C4324(C2xC4).14S4192,982
(C2×C4).15S4 = (C2×C4).S4φ: S4/A4 → C2 ⊆ Aut C2×C464(C2xC4).15S4192,985
(C2×C4).16S4 = C2×A4⋊Q8φ: S4/A4 → C2 ⊆ Aut C2×C448(C2xC4).16S4192,1468
(C2×C4).17S4 = C2×C4.S4φ: S4/A4 → C2 ⊆ Aut C2×C464(C2xC4).17S4192,1479
(C2×C4).18S4 = C2×C4.3S4φ: S4/A4 → C2 ⊆ Aut C2×C432(C2xC4).18S4192,1481
(C2×C4).19S4 = GL2(𝔽3)⋊C22φ: S4/A4 → C2 ⊆ Aut C2×C4324(C2xC4).19S4192,1482
(C2×C4).20S4 = C2.U2(𝔽3)central extension (φ=1)64(C2xC4).20S4192,183
(C2×C4).21S4 = C4×CSU2(𝔽3)central extension (φ=1)64(C2xC4).21S4192,946
(C2×C4).22S4 = C4×GL2(𝔽3)central extension (φ=1)32(C2xC4).22S4192,951
(C2×C4).23S4 = C2×A4⋊C8central extension (φ=1)48(C2xC4).23S4192,967
(C2×C4).24S4 = C4×A4⋊C4central extension (φ=1)48(C2xC4).24S4192,969
(C2×C4).25S4 = C2×U2(𝔽3)central extension (φ=1)48(C2xC4).25S4192,981
(C2×C4).26S4 = C4.A4⋊C4central extension (φ=1)64(C2xC4).26S4192,983
(C2×C4).27S4 = C2×C4.6S4central extension (φ=1)32(C2xC4).27S4192,1480

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