# Extensions 1→N→G→Q→1 with N=C32 and Q=C3×C4○D4

Direct product G=N×Q with N=C32 and Q=C3×C4○D4
dρLabelID
C4○D4×C33216C4oD4xC3^3432,733

Semidirect products G=N:Q with N=C32 and Q=C3×C4○D4
extensionφ:Q→Aut NdρLabelID
C321(C3×C4○D4) = C62.36D6φ: C3×C4○D4/C2×C4C6 ⊆ Aut C32726C3^2:1(C3xC4oD4)432,351
C322(C3×C4○D4) = C62.13D6φ: C3×C4○D4/D4C6 ⊆ Aut C327212-C3^2:2(C3xC4oD4)432,361
C323(C3×C4○D4) = (Q8×He3)⋊C2φ: C3×C4○D4/Q8C6 ⊆ Aut C327212+C3^2:3(C3xC4oD4)432,369
C324(C3×C4○D4) = C3×D125S3φ: C3×C4○D4/C12C22 ⊆ Aut C32484C3^2:4(C3xC4oD4)432,643
C325(C3×C4○D4) = C3×D12⋊S3φ: C3×C4○D4/C12C22 ⊆ Aut C32484C3^2:5(C3xC4oD4)432,644
C326(C3×C4○D4) = C3×D6.D6φ: C3×C4○D4/C12C22 ⊆ Aut C32484C3^2:6(C3xC4oD4)432,646
C327(C3×C4○D4) = C3×D6.6D6φ: C3×C4○D4/C12C22 ⊆ Aut C32484C3^2:7(C3xC4oD4)432,647
C328(C3×C4○D4) = C3×D6.3D6φ: C3×C4○D4/C2×C6C22 ⊆ Aut C32244C3^2:8(C3xC4oD4)432,652
C329(C3×C4○D4) = C3×D6.4D6φ: C3×C4○D4/C2×C6C22 ⊆ Aut C32244C3^2:9(C3xC4oD4)432,653
C3210(C3×C4○D4) = C4○D4×He3φ: C3×C4○D4/C4○D4C3 ⊆ Aut C32726C3^2:10(C3xC4oD4)432,410
C3211(C3×C4○D4) = C32×C4○D12φ: C3×C4○D4/C2×C12C2 ⊆ Aut C3272C3^2:11(C3xC4oD4)432,703
C3212(C3×C4○D4) = C3×C12.59D6φ: C3×C4○D4/C2×C12C2 ⊆ Aut C3272C3^2:12(C3xC4oD4)432,713
C3213(C3×C4○D4) = C32×D42S3φ: C3×C4○D4/C3×D4C2 ⊆ Aut C3272C3^2:13(C3xC4oD4)432,705
C3214(C3×C4○D4) = C3×C12.D6φ: C3×C4○D4/C3×D4C2 ⊆ Aut C3272C3^2:14(C3xC4oD4)432,715
C3215(C3×C4○D4) = C32×Q83S3φ: C3×C4○D4/C3×Q8C2 ⊆ Aut C32144C3^2:15(C3xC4oD4)432,707
C3216(C3×C4○D4) = C3×C12.26D6φ: C3×C4○D4/C3×Q8C2 ⊆ Aut C32144C3^2:16(C3xC4oD4)432,717

Non-split extensions G=N.Q with N=C32 and Q=C3×C4○D4
extensionφ:Q→Aut NdρLabelID
C32.(C3×C4○D4) = C4○D4×3- 1+2φ: C3×C4○D4/C4○D4C3 ⊆ Aut C32726C3^2.(C3xC4oD4)432,411
C32.2(C3×C4○D4) = C9×C4○D12φ: C3×C4○D4/C2×C12C2 ⊆ Aut C32722C3^2.2(C3xC4oD4)432,347
C32.3(C3×C4○D4) = C9×D42S3φ: C3×C4○D4/C3×D4C2 ⊆ Aut C32724C3^2.3(C3xC4oD4)432,359
C32.4(C3×C4○D4) = C9×Q83S3φ: C3×C4○D4/C3×Q8C2 ⊆ Aut C321444C3^2.4(C3xC4oD4)432,367
C32.5(C3×C4○D4) = C4○D4×C3×C9central extension (φ=1)216C3^2.5(C3xC4oD4)432,409

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