# Extensions 1→N→G→Q→1 with N=C23 and Q=C3×A4

Direct product G=N×Q with N=C23 and Q=C3×A4
dρLabelID
A4×C22×C672A4xC2^2xC6288,1041

Semidirect products G=N:Q with N=C23 and Q=C3×A4
extensionφ:Q→Aut NdρLabelID
C231(C3×A4) = C3×C24⋊C6φ: C3×A4/C3A4 ⊆ Aut C23246C2^3:1(C3xA4)288,634
C232(C3×A4) = C3×C23⋊A4φ: C3×A4/C3A4 ⊆ Aut C23244C2^3:2(C3xA4)288,987
C233(C3×A4) = C2×A42φ: C3×A4/A4C3 ⊆ Aut C23189+C2^3:3(C3xA4)288,1029
C234(C3×A4) = C6×C22⋊A4φ: C3×A4/C2×C6C3 ⊆ Aut C2336C2^3:4(C3xA4)288,1042

Non-split extensions G=N.Q with N=C23 and Q=C3×A4
extensionφ:Q→Aut NdρLabelID
C23.1(C3×A4) = C3×C42⋊C6φ: C3×A4/C3A4 ⊆ Aut C23486C2^3.1(C3xA4)288,635
C23.2(C3×A4) = C3×C23.A4φ: C3×A4/C3A4 ⊆ Aut C23366C2^3.2(C3xA4)288,636
C23.3(C3×A4) = A4×SL2(𝔽3)φ: C3×A4/A4C3 ⊆ Aut C23246-C2^3.3(C3xA4)288,859
C23.4(C3×A4) = C3×C23.3A4φ: C3×A4/C2×C6C3 ⊆ Aut C23366C2^3.4(C3xA4)288,230
C23.5(C3×A4) = C6×C42⋊C3φ: C3×A4/C2×C6C3 ⊆ Aut C23363C2^3.5(C3xA4)288,632
C23.6(C3×A4) = C3×Q8⋊A4φ: C3×A4/C2×C6C3 ⊆ Aut C23726C2^3.6(C3xA4)288,986
C23.7(C3×A4) = C2×C6×SL2(𝔽3)central extension (φ=1)96C2^3.7(C3xA4)288,981

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