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Extensions 1→N→G→Q→1 with N=C3×C6 and Q=S4

Direct product G=N×Q with N=C3×C6 and Q=S4
dρLabelID
C3×C6×S454C3xC6xS4432,760

Semidirect products G=N:Q with N=C3×C6 and Q=S4
extensionφ:Q→Aut NdρLabelID
(C3×C6)⋊1S4 = C2×C62⋊S3φ: S4/C22 → S3 ⊆ Aut C3×C6186+(C3xC6):1S4432,535
(C3×C6)⋊2S4 = C2×C32⋊S4φ: S4/C22 → S3 ⊆ Aut C3×C6183(C3xC6):2S4432,538
(C3×C6)⋊3S4 = C6×C3⋊S4φ: S4/A4 → C2 ⊆ Aut C3×C6366(C3xC6):3S4432,761
(C3×C6)⋊4S4 = C2×C32⋊4S4φ: S4/A4 → C2 ⊆ Aut C3×C654(C3xC6):4S4432,762

Non-split extensions G=N.Q with N=C3×C6 and Q=S4
extensionφ:Q→Aut NdρLabelID
(C3×C6).1S4 = C32.CSU2(𝔽3)φ: S4/C22 → S3 ⊆ Aut C3×C614412-(C3xC6).1S4432,243
(C3×C6).2S4 = C32.GL2(𝔽3)φ: S4/C22 → S3 ⊆ Aut C3×C67212+(C3xC6).2S4432,245
(C3×C6).3S4 = C32⋊CSU2(𝔽3)φ: S4/C22 → S3 ⊆ Aut C3×C614412-(C3xC6).3S4432,247
(C3×C6).4S4 = C32⋊2GL2(𝔽3)φ: S4/C22 → S3 ⊆ Aut C3×C67212+(C3xC6).4S4432,248
(C3×C6).5S4 = C62.Dic3φ: S4/C22 → S3 ⊆ Aut C3×C6366-(C3xC6).5S4432,249
(C3×C6).6S4 = C62⋊5Dic3φ: S4/C22 → S3 ⊆ Aut C3×C6366-(C3xC6).6S4432,251
(C3×C6).7S4 = C32⋊2CSU2(𝔽3)φ: S4/C22 → S3 ⊆ Aut C3×C61446(C3xC6).7S4432,257
(C3×C6).8S4 = C32⋊3GL2(𝔽3)φ: S4/C22 → S3 ⊆ Aut C3×C6726(C3xC6).8S4432,258
(C3×C6).9S4 = C62⋊6Dic3φ: S4/C22 → S3 ⊆ Aut C3×C6363(C3xC6).9S4432,260
(C3×C6).10S4 = C2×C32.S4φ: S4/C22 → S3 ⊆ Aut C3×C6186+(C3xC6).10S4432,533
(C3×C6).11S4 = C3×Q8.D9φ: S4/A4 → C2 ⊆ Aut C3×C61444(C3xC6).11S4432,244
(C3×C6).12S4 = C3×Q8⋊D9φ: S4/A4 → C2 ⊆ Aut C3×C61444(C3xC6).12S4432,246
(C3×C6).13S4 = C3×C6.S4φ: S4/A4 → C2 ⊆ Aut C3×C6366(C3xC6).13S4432,250
(C3×C6).14S4 = C32.3CSU2(𝔽3)φ: S4/A4 → C2 ⊆ Aut C3×C6432(C3xC6).14S4432,255
(C3×C6).15S4 = C32.3GL2(𝔽3)φ: S4/A4 → C2 ⊆ Aut C3×C6216(C3xC6).15S4432,256
(C3×C6).16S4 = C62.10Dic3φ: S4/A4 → C2 ⊆ Aut C3×C6108(C3xC6).16S4432,259
(C3×C6).17S4 = C6×C3.S4φ: S4/A4 → C2 ⊆ Aut C3×C6366(C3xC6).17S4432,534
(C3×C6).18S4 = C2×C32.3S4φ: S4/A4 → C2 ⊆ Aut C3×C654(C3xC6).18S4432,537
(C3×C6).19S4 = C3×C6.5S4φ: S4/A4 → C2 ⊆ Aut C3×C6484(C3xC6).19S4432,616
(C3×C6).20S4 = C3×C6.6S4φ: S4/A4 → C2 ⊆ Aut C3×C6484(C3xC6).20S4432,617
(C3×C6).21S4 = C3×C6.7S4φ: S4/A4 → C2 ⊆ Aut C3×C6366(C3xC6).21S4432,618
(C3×C6).22S4 = C32⋊4CSU2(𝔽3)φ: S4/A4 → C2 ⊆ Aut C3×C6144(C3xC6).22S4432,619
(C3×C6).23S4 = C32⋊5GL2(𝔽3)φ: S4/A4 → C2 ⊆ Aut C3×C672(C3xC6).23S4432,620
(C3×C6).24S4 = C62⋊10Dic3φ: S4/A4 → C2 ⊆ Aut C3×C6108(C3xC6).24S4432,621
(C3×C6).25S4 = C32×CSU2(𝔽3)central extension (φ=1)144(C3xC6).25S4432,613
(C3×C6).26S4 = C32×GL2(𝔽3)central extension (φ=1)72(C3xC6).26S4432,614
(C3×C6).27S4 = C32×A4⋊C4central extension (φ=1)108(C3xC6).27S4432,615

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