# Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=D4

Direct product G=N×Q with N=SL2(𝔽3) and Q=D4
dρLabelID
D4×SL2(𝔽3)32D4xSL(2,3)192,1004

Semidirect products G=N:Q with N=SL2(𝔽3) and Q=D4
extensionφ:Q→Out NdρLabelID
SL2(𝔽3)⋊1D4 = Q8⋊D12φ: D4/C4C2 ⊆ Out SL2(𝔽3)32SL(2,3):1D4192,952
SL2(𝔽3)⋊2D4 = C23.16S4φ: D4/C22C2 ⊆ Out SL2(𝔽3)32SL(2,3):2D4192,980
SL2(𝔽3)⋊3D4 = SL2(𝔽3)⋊D4φ: D4/C22C2 ⊆ Out SL2(𝔽3)32SL(2,3):3D4192,986
SL2(𝔽3)⋊4D4 = Q8.5S4φ: D4/C22C2 ⊆ Out SL2(𝔽3)244+SL(2,3):4D4192,988
SL2(𝔽3)⋊5D4 = SL2(𝔽3)⋊5D4φ: trivial image32SL(2,3):5D4192,1003
SL2(𝔽3)⋊6D4 = SL2(𝔽3)⋊6D4φ: trivial image64SL(2,3):6D4192,1005

Non-split extensions G=N.Q with N=SL2(𝔽3) and Q=D4
extensionφ:Q→Out NdρLabelID
SL2(𝔽3).1D4 = Q8.D12φ: D4/C4C2 ⊆ Out SL2(𝔽3)64SL(2,3).1D4192,949
SL2(𝔽3).2D4 = Q8.2D12φ: D4/C4C2 ⊆ Out SL2(𝔽3)32SL(2,3).2D4192,954
SL2(𝔽3).3D4 = C8.S4φ: D4/C4C2 ⊆ Out SL2(𝔽3)644-SL(2,3).3D4192,962
SL2(𝔽3).4D4 = C8.4S4φ: D4/C4C2 ⊆ Out SL2(𝔽3)324SL(2,3).4D4192,965
SL2(𝔽3).5D4 = C8.3S4φ: D4/C4C2 ⊆ Out SL2(𝔽3)324+SL(2,3).5D4192,966
SL2(𝔽3).6D4 = C23.14S4φ: D4/C22C2 ⊆ Out SL2(𝔽3)32SL(2,3).6D4192,978
SL2(𝔽3).7D4 = SL2(𝔽3).D4φ: D4/C22C2 ⊆ Out SL2(𝔽3)64SL(2,3).7D4192,984
SL2(𝔽3).8D4 = Q8.4S4φ: D4/C22C2 ⊆ Out SL2(𝔽3)484SL(2,3).8D4192,987
SL2(𝔽3).9D4 = D4.S4φ: D4/C22C2 ⊆ Out SL2(𝔽3)324-SL(2,3).9D4192,989
SL2(𝔽3).10D4 = D4.3S4φ: D4/C22C2 ⊆ Out SL2(𝔽3)324SL(2,3).10D4192,990
SL2(𝔽3).11D4 = Q16.A4φ: trivial image484+SL(2,3).11D4192,1017
SL2(𝔽3).12D4 = SD16.A4φ: trivial image324SL(2,3).12D4192,1018
SL2(𝔽3).13D4 = D8.A4φ: trivial image324-SL(2,3).13D4192,1019

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