Extensions 1→N→G→Q→1 with N=GL2(𝔽3) and Q=C22

Direct product G=N×Q with N=GL2(𝔽3) and Q=C22

Semidirect products G=N:Q with N=GL2(𝔽3) and Q=C22
extensionφ:Q→Out NdρLabelID
GL2(𝔽3)⋊1C22 = C2×Q8.D6φ: C22/C2C2 ⊆ Out GL2(𝔽3)32GL(2,3):1C2^2192,1476
GL2(𝔽3)⋊2C22 = C2×C4.3S4φ: C22/C2C2 ⊆ Out GL2(𝔽3)32GL(2,3):2C2^2192,1481
GL2(𝔽3)⋊3C22 = GL2(𝔽3)⋊C22φ: C22/C2C2 ⊆ Out GL2(𝔽3)324GL(2,3):3C2^2192,1482
GL2(𝔽3)⋊4C22 = Q8.7S4φ: C22/C2C2 ⊆ Out GL2(𝔽3)324+GL(2,3):4C2^2192,1484
GL2(𝔽3)⋊5C22 = D4.4S4φ: C22/C2C2 ⊆ Out GL2(𝔽3)164GL(2,3):5C2^2192,1485
GL2(𝔽3)⋊6C22 = C2×C4.6S4φ: trivial image32GL(2,3):6C2^2192,1480
GL2(𝔽3)⋊7C22 = Q8.6S4φ: trivial image324GL(2,3):7C2^2192,1483

Non-split extensions G=N.Q with N=GL2(𝔽3) and Q=C22
extensionφ:Q→Out NdρLabelID
GL2(𝔽3).C22 = D4.5S4φ: C22/C2C2 ⊆ Out GL2(𝔽3)324-GL(2,3).C2^2192,1486