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

Direct product G=N×Q with N=C4 and Q=D4×C32
dρLabelID
D4×C3×C12144D4xC3xC12288,815

Semidirect products G=N:Q with N=C4 and Q=D4×C32
extensionφ:Q→Aut NdρLabelID
C41(D4×C32) = C32×C41D4φ: D4×C32/C3×C12C2 ⊆ Aut C4144C4:1(D4xC3^2)288,824
C42(D4×C32) = C32×C4⋊D4φ: D4×C32/C62C2 ⊆ Aut C4144C4:2(D4xC3^2)288,818

Non-split extensions G=N.Q with N=C4 and Q=D4×C32
extensionφ:Q→Aut NdρLabelID
C4.1(D4×C32) = C32×D16φ: D4×C32/C3×C12C2 ⊆ Aut C4144C4.1(D4xC3^2)288,329
C4.2(D4×C32) = C32×SD32φ: D4×C32/C3×C12C2 ⊆ Aut C4144C4.2(D4xC3^2)288,330
C4.3(D4×C32) = C32×Q32φ: D4×C32/C3×C12C2 ⊆ Aut C4288C4.3(D4xC3^2)288,331
C4.4(D4×C32) = C32×C4.4D4φ: D4×C32/C3×C12C2 ⊆ Aut C4144C4.4(D4xC3^2)288,821
C4.5(D4×C32) = C32×C4⋊Q8φ: D4×C32/C3×C12C2 ⊆ Aut C4288C4.5(D4xC3^2)288,825
C4.6(D4×C32) = D8×C3×C6φ: D4×C32/C3×C12C2 ⊆ Aut C4144C4.6(D4xC3^2)288,829
C4.7(D4×C32) = SD16×C3×C6φ: D4×C32/C3×C12C2 ⊆ Aut C4144C4.7(D4xC3^2)288,830
C4.8(D4×C32) = Q16×C3×C6φ: D4×C32/C3×C12C2 ⊆ Aut C4288C4.8(D4xC3^2)288,831
C4.9(D4×C32) = C32×C4.D4φ: D4×C32/C62C2 ⊆ Aut C472C4.9(D4xC3^2)288,318
C4.10(D4×C32) = C32×C4.10D4φ: D4×C32/C62C2 ⊆ Aut C4144C4.10(D4xC3^2)288,319
C4.11(D4×C32) = C32×D4⋊C4φ: D4×C32/C62C2 ⊆ Aut C4144C4.11(D4xC3^2)288,320
C4.12(D4×C32) = C32×Q8⋊C4φ: D4×C32/C62C2 ⊆ Aut C4288C4.12(D4xC3^2)288,321
C4.13(D4×C32) = C32×C22⋊Q8φ: D4×C32/C62C2 ⊆ Aut C4144C4.13(D4xC3^2)288,819
C4.14(D4×C32) = C32×C8⋊C22φ: D4×C32/C62C2 ⊆ Aut C472C4.14(D4xC3^2)288,833
C4.15(D4×C32) = C32×C8.C22φ: D4×C32/C62C2 ⊆ Aut C4144C4.15(D4xC3^2)288,834
C4.16(D4×C32) = C32×C22⋊C8central extension (φ=1)144C4.16(D4xC3^2)288,316
C4.17(D4×C32) = C32×C4≀C2central extension (φ=1)72C4.17(D4xC3^2)288,322
C4.18(D4×C32) = C32×C4⋊C8central extension (φ=1)288C4.18(D4xC3^2)288,323
C4.19(D4×C32) = C32×C8.C4central extension (φ=1)144C4.19(D4xC3^2)288,326
C4.20(D4×C32) = C32×C4○D8central extension (φ=1)144C4.20(D4xC3^2)288,832

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