# Extensions 1→N→G→Q→1 with N=C6 and Q=D4×C32

Direct product G=N×Q with N=C6 and Q=D4×C32
dρLabelID
D4×C32×C6216D4xC3^2xC6432,731

Semidirect products G=N:Q with N=C6 and Q=D4×C32
extensionφ:Q→Aut NdρLabelID
C61(D4×C32) = C3×C6×D12φ: D4×C32/C3×C12C2 ⊆ Aut C6144C6:1(D4xC3^2)432,702
C62(D4×C32) = C3×C6×C3⋊D4φ: D4×C32/C62C2 ⊆ Aut C672C6:2(D4xC3^2)432,709

Non-split extensions G=N.Q with N=C6 and Q=D4×C32
extensionφ:Q→Aut NdρLabelID
C6.1(D4×C32) = C32×C24⋊C2φ: D4×C32/C3×C12C2 ⊆ Aut C6144C6.1(D4xC3^2)432,466
C6.2(D4×C32) = C32×D24φ: D4×C32/C3×C12C2 ⊆ Aut C6144C6.2(D4xC3^2)432,467
C6.3(D4×C32) = C32×Dic12φ: D4×C32/C3×C12C2 ⊆ Aut C6144C6.3(D4xC3^2)432,468
C6.4(D4×C32) = C32×C4⋊Dic3φ: D4×C32/C3×C12C2 ⊆ Aut C6144C6.4(D4xC3^2)432,473
C6.5(D4×C32) = C32×Dic3⋊C4φ: D4×C32/C62C2 ⊆ Aut C6144C6.5(D4xC3^2)432,472
C6.6(D4×C32) = C32×D6⋊C4φ: D4×C32/C62C2 ⊆ Aut C6144C6.6(D4xC3^2)432,474
C6.7(D4×C32) = C32×D4⋊S3φ: D4×C32/C62C2 ⊆ Aut C672C6.7(D4xC3^2)432,475
C6.8(D4×C32) = C32×D4.S3φ: D4×C32/C62C2 ⊆ Aut C672C6.8(D4xC3^2)432,476
C6.9(D4×C32) = C32×Q82S3φ: D4×C32/C62C2 ⊆ Aut C6144C6.9(D4xC3^2)432,477
C6.10(D4×C32) = C32×C3⋊Q16φ: D4×C32/C62C2 ⊆ Aut C6144C6.10(D4xC3^2)432,478
C6.11(D4×C32) = C32×C6.D4φ: D4×C32/C62C2 ⊆ Aut C672C6.11(D4xC3^2)432,479
C6.12(D4×C32) = C22⋊C4×C3×C9central extension (φ=1)216C6.12(D4xC3^2)432,203
C6.13(D4×C32) = C22⋊C4×He3central extension (φ=1)72C6.13(D4xC3^2)432,204
C6.14(D4×C32) = C22⋊C4×3- 1+2central extension (φ=1)72C6.14(D4xC3^2)432,205
C6.15(D4×C32) = C4⋊C4×C3×C9central extension (φ=1)432C6.15(D4xC3^2)432,206
C6.16(D4×C32) = C4⋊C4×He3central extension (φ=1)144C6.16(D4xC3^2)432,207
C6.17(D4×C32) = C4⋊C4×3- 1+2central extension (φ=1)144C6.17(D4xC3^2)432,208
C6.18(D4×C32) = D8×C3×C9central extension (φ=1)216C6.18(D4xC3^2)432,215
C6.19(D4×C32) = SD16×C3×C9central extension (φ=1)216C6.19(D4xC3^2)432,218
C6.20(D4×C32) = Q16×C3×C9central extension (φ=1)432C6.20(D4xC3^2)432,221
C6.21(D4×C32) = D4×C3×C18central extension (φ=1)216C6.21(D4xC3^2)432,403
C6.22(D4×C32) = C2×D4×He3central extension (φ=1)72C6.22(D4xC3^2)432,404
C6.23(D4×C32) = C2×D4×3- 1+2central extension (φ=1)72C6.23(D4xC3^2)432,405
C6.24(D4×C32) = C22⋊C4×C33central extension (φ=1)216C6.24(D4xC3^2)432,513
C6.25(D4×C32) = C4⋊C4×C33central extension (φ=1)432C6.25(D4xC3^2)432,514
C6.26(D4×C32) = D8×C33central extension (φ=1)216C6.26(D4xC3^2)432,517
C6.27(D4×C32) = SD16×C33central extension (φ=1)216C6.27(D4xC3^2)432,518
C6.28(D4×C32) = Q16×C33central extension (φ=1)432C6.28(D4xC3^2)432,519
C6.29(D4×C32) = D8×He3central stem extension (φ=1)726C6.29(D4xC3^2)432,216
C6.30(D4×C32) = D8×3- 1+2central stem extension (φ=1)726C6.30(D4xC3^2)432,217
C6.31(D4×C32) = SD16×He3central stem extension (φ=1)726C6.31(D4xC3^2)432,219
C6.32(D4×C32) = SD16×3- 1+2central stem extension (φ=1)726C6.32(D4xC3^2)432,220
C6.33(D4×C32) = Q16×He3central stem extension (φ=1)1446C6.33(D4xC3^2)432,222
C6.34(D4×C32) = Q16×3- 1+2central stem extension (φ=1)1446C6.34(D4xC3^2)432,223

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