# Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=C2×C4

Direct product G=N×Q with N=SL2(𝔽3) and Q=C2×C4
dρLabelID
C2×C4×SL2(𝔽3)64C2xC4xSL(2,3)192,996

Semidirect products G=N:Q with N=SL2(𝔽3) and Q=C2×C4
extensionφ:Q→Out NdρLabelID
SL2(𝔽3)⋊1(C2×C4) = C4×GL2(𝔽3)φ: C2×C4/C4C2 ⊆ Out SL2(𝔽3)32SL(2,3):1(C2xC4)192,951
SL2(𝔽3)⋊2(C2×C4) = GL2(𝔽3)⋊C4φ: C2×C4/C4C2 ⊆ Out SL2(𝔽3)32SL(2,3):2(C2xC4)192,953
SL2(𝔽3)⋊3(C2×C4) = C2×Q8⋊Dic3φ: C2×C4/C22C2 ⊆ Out SL2(𝔽3)64SL(2,3):3(C2xC4)192,977
SL2(𝔽3)⋊4(C2×C4) = C2×U2(𝔽3)φ: C2×C4/C22C2 ⊆ Out SL2(𝔽3)48SL(2,3):4(C2xC4)192,981
SL2(𝔽3)⋊5(C2×C4) = (C2×C4).S4φ: C2×C4/C22C2 ⊆ Out SL2(𝔽3)64SL(2,3):5(C2xC4)192,985
SL2(𝔽3)⋊6(C2×C4) = C4×C4.A4φ: trivial image64SL(2,3):6(C2xC4)192,997
SL2(𝔽3)⋊7(C2×C4) = C4○D4⋊C12φ: trivial image64SL(2,3):7(C2xC4)192,999

Non-split extensions G=N.Q with N=SL2(𝔽3) and Q=C2×C4
extensionφ:Q→Out NdρLabelID
SL2(𝔽3).1(C2×C4) = C4×CSU2(𝔽3)φ: C2×C4/C4C2 ⊆ Out SL2(𝔽3)64SL(2,3).1(C2xC4)192,946
SL2(𝔽3).2(C2×C4) = CSU2(𝔽3)⋊C4φ: C2×C4/C4C2 ⊆ Out SL2(𝔽3)64SL(2,3).2(C2xC4)192,947
SL2(𝔽3).3(C2×C4) = CU2(𝔽3)φ: C2×C4/C4C2 ⊆ Out SL2(𝔽3)322SL(2,3).3(C2xC4)192,963
SL2(𝔽3).4(C2×C4) = C8.5S4φ: C2×C4/C4C2 ⊆ Out SL2(𝔽3)324SL(2,3).4(C2xC4)192,964
SL2(𝔽3).5(C2×C4) = C23.15S4φ: C2×C4/C22C2 ⊆ Out SL2(𝔽3)32SL(2,3).5(C2xC4)192,979
SL2(𝔽3).6(C2×C4) = U2(𝔽3)⋊C2φ: C2×C4/C22C2 ⊆ Out SL2(𝔽3)324SL(2,3).6(C2xC4)192,982
SL2(𝔽3).7(C2×C4) = C4.A4⋊C4φ: C2×C4/C22C2 ⊆ Out SL2(𝔽3)64SL(2,3).7(C2xC4)192,983
SL2(𝔽3).8(C2×C4) = (C2×Q8)⋊C12φ: trivial image32SL(2,3).8(C2xC4)192,998
SL2(𝔽3).9(C2×C4) = C2×C8.A4φ: trivial image64SL(2,3).9(C2xC4)192,1012
SL2(𝔽3).10(C2×C4) = M4(2).A4φ: trivial image324SL(2,3).10(C2xC4)192,1013

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