# Extensions 1→N→G→Q→1 with N=C32 and Q=C2×SL2(𝔽3)

Direct product G=N×Q with N=C32 and Q=C2×SL2(𝔽3)
dρLabelID
C3×C6×SL2(𝔽3)144C3xC6xSL(2,3)432,698

Semidirect products G=N:Q with N=C32 and Q=C2×SL2(𝔽3)
extensionφ:Q→Aut NdρLabelID
C32⋊(C2×SL2(𝔽3)) = C2×ASL2(𝔽3)φ: C2×SL2(𝔽3)/C2SL2(𝔽3) ⊆ Aut C32188+C3^2:(C2xSL(2,3))432,735
C322(C2×SL2(𝔽3)) = Q8⋊He3⋊C2φ: C2×SL2(𝔽3)/Q8C6 ⊆ Aut C327212-C3^2:2(C2xSL(2,3))432,270
C323(C2×SL2(𝔽3)) = C2×Q8⋊He3φ: C2×SL2(𝔽3)/C2×Q8C3 ⊆ Aut C32144C3^2:3(C2xSL(2,3))432,336
C324(C2×SL2(𝔽3)) = C3×S3×SL2(𝔽3)φ: C2×SL2(𝔽3)/SL2(𝔽3)C2 ⊆ Aut C32484C3^2:4(C2xSL(2,3))432,623
C325(C2×SL2(𝔽3)) = C3⋊S3×SL2(𝔽3)φ: C2×SL2(𝔽3)/SL2(𝔽3)C2 ⊆ Aut C3272C3^2:5(C2xSL(2,3))432,626

Non-split extensions G=N.Q with N=C32 and Q=C2×SL2(𝔽3)
extensionφ:Q→Aut NdρLabelID
C32.(C2×SL2(𝔽3)) = C2×Q8⋊3- 1+2φ: C2×SL2(𝔽3)/C2×Q8C3 ⊆ Aut C32144C3^2.(C2xSL(2,3))432,335
C32.2(C2×SL2(𝔽3)) = S3×Q8⋊C9φ: C2×SL2(𝔽3)/SL2(𝔽3)C2 ⊆ Aut C321444C3^2.2(C2xSL(2,3))432,268
C32.3(C2×SL2(𝔽3)) = C6×Q8⋊C9central extension (φ=1)432C3^2.3(C2xSL(2,3))432,334

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