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Extensions 1→N→G→Q→1 with N=C6 and Q=C3×C4○D4

Direct product G=N×Q with N=C6 and Q=C3×C4○D4
dρLabelID
C4○D4×C3×C6144C4oD4xC3xC6288,1021

Semidirect products G=N:Q with N=C6 and Q=C3×C4○D4
extensionφ:Q→Aut NdρLabelID
C6⋊1(C3×C4○D4) = C6×C4○D12φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6:1(C3xC4oD4)288,991
C6⋊2(C3×C4○D4) = C6×D4⋊2S3φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6:2(C3xC4oD4)288,993
C6⋊3(C3×C4○D4) = C6×Q8⋊3S3φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C696C6:3(C3xC4oD4)288,996

Non-split extensions G=N.Q with N=C6 and Q=C3×C4○D4
extensionφ:Q→Aut NdρLabelID
C6.1(C3×C4○D4) = C12×Dic6φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.1(C3xC4oD4)288,639
C6.2(C3×C4○D4) = C3×C12.6Q8φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.2(C3xC4oD4)288,641
C6.3(C3×C4○D4) = C3×C42⋊2S3φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.3(C3xC4oD4)288,643
C6.4(C3×C4○D4) = C12×D12φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.4(C3xC4oD4)288,644
C6.5(C3×C4○D4) = C3×C42⋊7S3φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.5(C3xC4oD4)288,646
C6.6(C3×C4○D4) = C3×C42⋊3S3φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.6(C3xC4oD4)288,647
C6.7(C3×C4○D4) = C3×C23.8D6φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6.7(C3xC4oD4)288,650
C6.8(C3×C4○D4) = C3×Dic3⋊D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6.8(C3xC4oD4)288,655
C6.9(C3×C4○D4) = C3×C23.11D6φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6.9(C3xC4oD4)288,656
C6.10(C3×C4○D4) = C3×Dic3.Q8φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.10(C3xC4oD4)288,660
C6.11(C3×C4○D4) = C3×D6.D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.11(C3xC4oD4)288,665
C6.12(C3×C4○D4) = C3×D6⋊Q8φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.12(C3xC4oD4)288,667
C6.13(C3×C4○D4) = C3×C4⋊C4⋊S3φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C696C6.13(C3xC4oD4)288,669
C6.14(C3×C4○D4) = C3×C12.48D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6.14(C3xC4oD4)288,695
C6.15(C3×C4○D4) = C3×C23.26D6φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6.15(C3xC4oD4)288,697
C6.16(C3×C4○D4) = C12×C3⋊D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6.16(C3xC4oD4)288,699
C6.17(C3×C4○D4) = C3×C23.28D6φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6.17(C3xC4oD4)288,700
C6.18(C3×C4○D4) = C3×C12⋊7D4φ: C3×C4○D4/C2×C12 → C2 ⊆ Aut C648C6.18(C3xC4oD4)288,701
C6.19(C3×C4○D4) = C3×C23.16D6φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.19(C3xC4oD4)288,648
C6.20(C3×C4○D4) = C3×Dic3.D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.20(C3xC4oD4)288,649
C6.21(C3×C4○D4) = C3×Dic3⋊4D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.21(C3xC4oD4)288,652
C6.22(C3×C4○D4) = C3×C23.9D6φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.22(C3xC4oD4)288,654
C6.23(C3×C4○D4) = C3×C23.21D6φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.23(C3xC4oD4)288,657
C6.24(C3×C4○D4) = C3×Dic6⋊C4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C696C6.24(C3xC4oD4)288,658
C6.25(C3×C4○D4) = C3×C4.Dic6φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C696C6.25(C3xC4oD4)288,661
C6.26(C3×C4○D4) = C3×C4⋊C4⋊7S3φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C696C6.26(C3xC4oD4)288,663
C6.27(C3×C4○D4) = C3×C4.D12φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C696C6.27(C3xC4oD4)288,668
C6.28(C3×C4○D4) = C3×D4×Dic3φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.28(C3xC4oD4)288,705
C6.29(C3×C4○D4) = C3×C23.23D6φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.29(C3xC4oD4)288,706
C6.30(C3×C4○D4) = C3×C23.12D6φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.30(C3xC4oD4)288,707
C6.31(C3×C4○D4) = C3×D6⋊3D4φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.31(C3xC4oD4)288,709
C6.32(C3×C4○D4) = C3×C23.14D6φ: C3×C4○D4/C3×D4 → C2 ⊆ Aut C648C6.32(C3xC4oD4)288,710
C6.33(C3×C4○D4) = C3×Dic3⋊5D4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C696C6.33(C3xC4oD4)288,664
C6.34(C3×C4○D4) = C3×C12⋊D4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C696C6.34(C3xC4oD4)288,666
C6.35(C3×C4○D4) = C3×Q8×Dic3φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C696C6.35(C3xC4oD4)288,716
C6.36(C3×C4○D4) = C3×D6⋊3Q8φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C696C6.36(C3xC4oD4)288,717
C6.37(C3×C4○D4) = C3×C12.23D4φ: C3×C4○D4/C3×Q8 → C2 ⊆ Aut C696C6.37(C3xC4oD4)288,718
C6.38(C3×C4○D4) = C9×C42⋊C2central extension (φ=1)144C6.38(C3xC4oD4)288,167
C6.39(C3×C4○D4) = D4×C36central extension (φ=1)144C6.39(C3xC4oD4)288,168
C6.40(C3×C4○D4) = Q8×C36central extension (φ=1)288C6.40(C3xC4oD4)288,169
C6.41(C3×C4○D4) = C9×C4⋊D4central extension (φ=1)144C6.41(C3xC4oD4)288,171
C6.42(C3×C4○D4) = C9×C22⋊Q8central extension (φ=1)144C6.42(C3xC4oD4)288,172
C6.43(C3×C4○D4) = C9×C22.D4central extension (φ=1)144C6.43(C3xC4oD4)288,173
C6.44(C3×C4○D4) = C9×C4.4D4central extension (φ=1)144C6.44(C3xC4oD4)288,174
C6.45(C3×C4○D4) = C9×C42.C2central extension (φ=1)288C6.45(C3xC4oD4)288,175
C6.46(C3×C4○D4) = C9×C42⋊2C2central extension (φ=1)144C6.46(C3xC4oD4)288,176
C6.47(C3×C4○D4) = C4○D4×C18central extension (φ=1)144C6.47(C3xC4oD4)288,370
C6.48(C3×C4○D4) = C32×C42⋊C2central extension (φ=1)144C6.48(C3xC4oD4)288,814
C6.49(C3×C4○D4) = D4×C3×C12central extension (φ=1)144C6.49(C3xC4oD4)288,815
C6.50(C3×C4○D4) = Q8×C3×C12central extension (φ=1)288C6.50(C3xC4oD4)288,816
C6.51(C3×C4○D4) = C32×C4⋊D4central extension (φ=1)144C6.51(C3xC4oD4)288,818
C6.52(C3×C4○D4) = C32×C22⋊Q8central extension (φ=1)144C6.52(C3xC4oD4)288,819
C6.53(C3×C4○D4) = C32×C22.D4central extension (φ=1)144C6.53(C3xC4oD4)288,820
C6.54(C3×C4○D4) = C32×C4.4D4central extension (φ=1)144C6.54(C3xC4oD4)288,821
C6.55(C3×C4○D4) = C32×C42.C2central extension (φ=1)288C6.55(C3xC4oD4)288,822
C6.56(C3×C4○D4) = C32×C42⋊2C2central extension (φ=1)144C6.56(C3xC4oD4)288,823

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