# Extensions 1→N→G→Q→1 with N=C3×SL2(𝔽3) and Q=S3

Direct product G=N×Q with N=C3×SL2(𝔽3) and Q=S3
dρLabelID
C3×S3×SL2(𝔽3)484C3xS3xSL(2,3)432,623

Semidirect products G=N:Q with N=C3×SL2(𝔽3) and Q=S3
extensionφ:Q→Out NdρLabelID
(C3×SL2(𝔽3))⋊1S3 = C6.(S3×A4)φ: S3/C1S3 ⊆ Out C3×SL2(𝔽3)7212+(C3xSL(2,3)):1S3432,269
(C3×SL2(𝔽3))⋊2S3 = Q8⋊He3⋊C2φ: S3/C1S3 ⊆ Out C3×SL2(𝔽3)7212-(C3xSL(2,3)):2S3432,270
(C3×SL2(𝔽3))⋊3S3 = C323GL2(𝔽3)φ: S3/C1S3 ⊆ Out C3×SL2(𝔽3)726(C3xSL(2,3)):3S3432,258
(C3×SL2(𝔽3))⋊4S3 = C325GL2(𝔽3)φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)72(C3xSL(2,3)):4S3432,620
(C3×SL2(𝔽3))⋊5S3 = C3⋊Dic3.2A4φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)144(C3xSL(2,3)):5S3432,625
(C3×SL2(𝔽3))⋊6S3 = C3⋊S3×SL2(𝔽3)φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)72(C3xSL(2,3)):6S3432,626
(C3×SL2(𝔽3))⋊7S3 = C3×C6.6S4φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)484(C3xSL(2,3)):7S3432,617
(C3×SL2(𝔽3))⋊8S3 = C3×Dic3.A4φ: trivial image484(C3xSL(2,3)):8S3432,622

Non-split extensions G=N.Q with N=C3×SL2(𝔽3) and Q=S3
extensionφ:Q→Out NdρLabelID
(C3×SL2(𝔽3)).1S3 = Dic9.A4φ: S3/C1S3 ⊆ Out C3×SL2(𝔽3)14412+(C3xSL(2,3)).1S3432,261
(C3×SL2(𝔽3)).2S3 = D18.A4φ: S3/C1S3 ⊆ Out C3×SL2(𝔽3)7212-(C3xSL(2,3)).2S3432,263
(C3×SL2(𝔽3)).3S3 = C322CSU2(𝔽3)φ: S3/C1S3 ⊆ Out C3×SL2(𝔽3)1446(C3xSL(2,3)).3S3432,257
(C3×SL2(𝔽3)).4S3 = C18.5S4φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)1444-(C3xSL(2,3)).4S3432,252
(C3×SL2(𝔽3)).5S3 = C18.6S4φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)724+(C3xSL(2,3)).5S3432,253
(C3×SL2(𝔽3)).6S3 = Dic9.2A4φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)1444+(C3xSL(2,3)).6S3432,262
(C3×SL2(𝔽3)).7S3 = D9×SL2(𝔽3)φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)724-(C3xSL(2,3)).7S3432,264
(C3×SL2(𝔽3)).8S3 = C324CSU2(𝔽3)φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)144(C3xSL(2,3)).8S3432,619
(C3×SL2(𝔽3)).9S3 = C3×C6.5S4φ: S3/C3C2 ⊆ Out C3×SL2(𝔽3)484(C3xSL(2,3)).9S3432,616

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