Extensions 1→N→G→Q→1 with N=C32 and Q=GL2(𝔽3)

Direct product G=N×Q with N=C32 and Q=GL2(𝔽3)

Semidirect products G=N:Q with N=C32 and Q=GL2(𝔽3)
extensionφ:Q→Aut NdρLabelID
C32⋊GL2(𝔽3) = AGL2(𝔽3)φ: GL2(𝔽3)/C1GL2(𝔽3) ⊆ Aut C3298+C3^2:GL(2,3)432,734
C322GL2(𝔽3) = C322GL2(𝔽3)φ: GL2(𝔽3)/Q8S3 ⊆ Aut C327212+C3^2:2GL(2,3)432,248
C323GL2(𝔽3) = C323GL2(𝔽3)φ: GL2(𝔽3)/Q8S3 ⊆ Aut C32726C3^2:3GL(2,3)432,258
C324GL2(𝔽3) = C3×C6.6S4φ: GL2(𝔽3)/SL2(𝔽3)C2 ⊆ Aut C32484C3^2:4GL(2,3)432,617
C325GL2(𝔽3) = C325GL2(𝔽3)φ: GL2(𝔽3)/SL2(𝔽3)C2 ⊆ Aut C3272C3^2:5GL(2,3)432,620

Non-split extensions G=N.Q with N=C32 and Q=GL2(𝔽3)
extensionφ:Q→Aut NdρLabelID
C32.GL2(𝔽3) = C32.GL2(𝔽3)φ: GL2(𝔽3)/Q8S3 ⊆ Aut C327212+C3^2.GL(2,3)432,245
C32.2GL2(𝔽3) = C3×Q8⋊D9φ: GL2(𝔽3)/SL2(𝔽3)C2 ⊆ Aut C321444C3^2.2GL(2,3)432,246
C32.3GL2(𝔽3) = C32.3GL2(𝔽3)φ: GL2(𝔽3)/SL2(𝔽3)C2 ⊆ Aut C32216C3^2.3GL(2,3)432,256