# Extensions 1→N→G→Q→1 with N=C6 and Q=C2×C62

Direct product G=N×Q with N=C6 and Q=C2×C62
dρLabelID
C2×C63432C2xC6^3432,775

Semidirect products G=N:Q with N=C6 and Q=C2×C62
extensionφ:Q→Aut NdρLabelID
C6⋊(C2×C62) = S3×C2×C62φ: C2×C62/C62C2 ⊆ Aut C6144C6:(C2xC6^2)432,772

Non-split extensions G=N.Q with N=C6 and Q=C2×C62
extensionφ:Q→Aut NdρLabelID
C6.1(C2×C62) = C3×C6×Dic6φ: C2×C62/C62C2 ⊆ Aut C6144C6.1(C2xC6^2)432,700
C6.2(C2×C62) = S3×C6×C12φ: C2×C62/C62C2 ⊆ Aut C6144C6.2(C2xC6^2)432,701
C6.3(C2×C62) = C3×C6×D12φ: C2×C62/C62C2 ⊆ Aut C6144C6.3(C2xC6^2)432,702
C6.4(C2×C62) = C32×C4○D12φ: C2×C62/C62C2 ⊆ Aut C672C6.4(C2xC6^2)432,703
C6.5(C2×C62) = S3×D4×C32φ: C2×C62/C62C2 ⊆ Aut C672C6.5(C2xC6^2)432,704
C6.6(C2×C62) = C32×D42S3φ: C2×C62/C62C2 ⊆ Aut C672C6.6(C2xC6^2)432,705
C6.7(C2×C62) = S3×Q8×C32φ: C2×C62/C62C2 ⊆ Aut C6144C6.7(C2xC6^2)432,706
C6.8(C2×C62) = C32×Q83S3φ: C2×C62/C62C2 ⊆ Aut C6144C6.8(C2xC6^2)432,707
C6.9(C2×C62) = Dic3×C62φ: C2×C62/C62C2 ⊆ Aut C6144C6.9(C2xC6^2)432,708
C6.10(C2×C62) = C3×C6×C3⋊D4φ: C2×C62/C62C2 ⊆ Aut C672C6.10(C2xC6^2)432,709
C6.11(C2×C62) = C22×C4×He3central extension (φ=1)144C6.11(C2xC6^2)432,401
C6.12(C2×C62) = C22×C4×3- 1+2central extension (φ=1)144C6.12(C2xC6^2)432,402
C6.13(C2×C62) = D4×C3×C18central extension (φ=1)216C6.13(C2xC6^2)432,403
C6.14(C2×C62) = Q8×C3×C18central extension (φ=1)432C6.14(C2xC6^2)432,406
C6.15(C2×C62) = C4○D4×C3×C9central extension (φ=1)216C6.15(C2xC6^2)432,409
C6.16(C2×C62) = C24×He3central extension (φ=1)144C6.16(C2xC6^2)432,563
C6.17(C2×C62) = C24×3- 1+2central extension (φ=1)144C6.17(C2xC6^2)432,564
C6.18(C2×C62) = D4×C32×C6central extension (φ=1)216C6.18(C2xC6^2)432,731
C6.19(C2×C62) = Q8×C32×C6central extension (φ=1)432C6.19(C2xC6^2)432,732
C6.20(C2×C62) = C4○D4×C33central extension (φ=1)216C6.20(C2xC6^2)432,733
C6.21(C2×C62) = C2×D4×He3central stem extension (φ=1)72C6.21(C2xC6^2)432,404
C6.22(C2×C62) = C2×D4×3- 1+2central stem extension (φ=1)72C6.22(C2xC6^2)432,405
C6.23(C2×C62) = C2×Q8×He3central stem extension (φ=1)144C6.23(C2xC6^2)432,407
C6.24(C2×C62) = C2×Q8×3- 1+2central stem extension (φ=1)144C6.24(C2xC6^2)432,408
C6.25(C2×C62) = C4○D4×He3central stem extension (φ=1)726C6.25(C2xC6^2)432,410
C6.26(C2×C62) = C4○D4×3- 1+2central stem extension (φ=1)726C6.26(C2xC6^2)432,411

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