# Extensions 1→N→G→Q→1 with N=SL2(𝔽3) and Q=C23

Direct product G=N×Q with N=SL2(𝔽3) and Q=C23
dρLabelID
C23×SL2(𝔽3)64C2^3xSL(2,3)192,1498

Semidirect products G=N:Q with N=SL2(𝔽3) and Q=C23
extensionφ:Q→Out NdρLabelID
SL2(𝔽3)⋊1C23 = C22×GL2(𝔽3)φ: C23/C22C2 ⊆ Out SL2(𝔽3)32SL(2,3):1C2^3192,1475
SL2(𝔽3)⋊2C23 = C2×C4.3S4φ: C23/C22C2 ⊆ Out SL2(𝔽3)32SL(2,3):2C2^3192,1481
SL2(𝔽3)⋊3C23 = C22×C4.A4φ: trivial image64SL(2,3):3C2^3192,1500
SL2(𝔽3)⋊4C23 = C2×Q8.A4φ: trivial image48SL(2,3):4C2^3192,1502

Non-split extensions G=N.Q with N=SL2(𝔽3) and Q=C23
extensionφ:Q→Out NdρLabelID
SL2(𝔽3).1C23 = C22×CSU2(𝔽3)φ: C23/C22C2 ⊆ Out SL2(𝔽3)64SL(2,3).1C2^3192,1474
SL2(𝔽3).2C23 = C2×Q8.D6φ: C23/C22C2 ⊆ Out SL2(𝔽3)32SL(2,3).2C2^3192,1476
SL2(𝔽3).3C23 = C2×C4.S4φ: C23/C22C2 ⊆ Out SL2(𝔽3)64SL(2,3).3C2^3192,1479
SL2(𝔽3).4C23 = C2×C4.6S4φ: C23/C22C2 ⊆ Out SL2(𝔽3)32SL(2,3).4C2^3192,1480
SL2(𝔽3).5C23 = GL2(𝔽3)⋊C22φ: C23/C22C2 ⊆ Out SL2(𝔽3)324SL(2,3).5C2^3192,1482
SL2(𝔽3).6C23 = Q8.6S4φ: C23/C22C2 ⊆ Out SL2(𝔽3)324SL(2,3).6C2^3192,1483
SL2(𝔽3).7C23 = Q8.7S4φ: C23/C22C2 ⊆ Out SL2(𝔽3)324+SL(2,3).7C2^3192,1484
SL2(𝔽3).8C23 = D4.4S4φ: C23/C22C2 ⊆ Out SL2(𝔽3)164SL(2,3).8C2^3192,1485
SL2(𝔽3).9C23 = D4.5S4φ: C23/C22C2 ⊆ Out SL2(𝔽3)324-SL(2,3).9C2^3192,1486
SL2(𝔽3).10C23 = C2×D4.A4φ: trivial image32SL(2,3).10C2^3192,1503
SL2(𝔽3).11C23 = 2- 1+43C6φ: trivial image324SL(2,3).11C2^3192,1504

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