Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=D6

Direct product G=N×Q with N=SL2(𝔽3) and Q=D6
dρLabelID
C2×S3×SL2(𝔽3)48C2xS3xSL(2,3)288,922

Semidirect products G=N:Q with N=SL2(𝔽3) and Q=D6
extensionφ:Q→Out NdρLabelID
SL2(𝔽3)⋊1D6 = GL2(𝔽3)⋊S3φ: D6/S3C2 ⊆ Out SL2(𝔽3)484+SL(2,3):1D6288,847
SL2(𝔽3)⋊2D6 = S3×GL2(𝔽3)φ: D6/S3C2 ⊆ Out SL2(𝔽3)244SL(2,3):2D6288,851
SL2(𝔽3)⋊3D6 = C2×C6.6S4φ: D6/C6C2 ⊆ Out SL2(𝔽3)48SL(2,3):3D6288,911
SL2(𝔽3)⋊4D6 = C12.7S4φ: D6/C6C2 ⊆ Out SL2(𝔽3)484+SL(2,3):4D6288,915
SL2(𝔽3)⋊5D6 = C2×Dic3.A4φ: trivial image96SL(2,3):5D6288,921
SL2(𝔽3)⋊6D6 = Dic6.A4φ: trivial image724+SL(2,3):6D6288,924
SL2(𝔽3)⋊7D6 = S3×C4.A4φ: trivial image484SL(2,3):7D6288,925

Non-split extensions G=N.Q with N=SL2(𝔽3) and Q=D6
extensionφ:Q→Out NdρLabelID
SL2(𝔽3).1D6 = CSU2(𝔽3)⋊S3φ: D6/S3C2 ⊆ Out SL2(𝔽3)964SL(2,3).1D6288,844
SL2(𝔽3).2D6 = Dic3.4S4φ: D6/S3C2 ⊆ Out SL2(𝔽3)484SL(2,3).2D6288,845
SL2(𝔽3).3D6 = Dic3.5S4φ: D6/S3C2 ⊆ Out SL2(𝔽3)484+SL(2,3).3D6288,846
SL2(𝔽3).4D6 = S3×CSU2(𝔽3)φ: D6/S3C2 ⊆ Out SL2(𝔽3)484-SL(2,3).4D6288,848
SL2(𝔽3).5D6 = D6.S4φ: D6/S3C2 ⊆ Out SL2(𝔽3)484-SL(2,3).5D6288,849
SL2(𝔽3).6D6 = D6.2S4φ: D6/S3C2 ⊆ Out SL2(𝔽3)484SL(2,3).6D6288,850
SL2(𝔽3).7D6 = C2×C6.5S4φ: D6/C6C2 ⊆ Out SL2(𝔽3)96SL(2,3).7D6288,910
SL2(𝔽3).8D6 = SL2(𝔽3).D6φ: D6/C6C2 ⊆ Out SL2(𝔽3)484SL(2,3).8D6288,912
SL2(𝔽3).9D6 = C12.6S4φ: D6/C6C2 ⊆ Out SL2(𝔽3)964-SL(2,3).9D6288,913
SL2(𝔽3).10D6 = C12.14S4φ: D6/C6C2 ⊆ Out SL2(𝔽3)484SL(2,3).10D6288,914
SL2(𝔽3).11D6 = SL2(𝔽3).11D6φ: trivial image484SL(2,3).11D6288,923
SL2(𝔽3).12D6 = D12.A4φ: trivial image484-SL(2,3).12D6288,926

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