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Extensions 1→N→G→Q→1 with N=C14 and Q=C3⋊D4

Direct product G=N×Q with N=C14 and Q=C3⋊D4
dρLabelID
C14×C3⋊D4168C14xC3:D4336,193

Semidirect products G=N:Q with N=C14 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
C14⋊1(C3⋊D4) = C2×C3⋊D28φ: C3⋊D4/Dic3 → C2 ⊆ Aut C14168C14:1(C3:D4)336,158
C14⋊2(C3⋊D4) = C2×C21⋊D4φ: C3⋊D4/D6 → C2 ⊆ Aut C14168C14:2(C3:D4)336,157
C14⋊3(C3⋊D4) = C2×C21⋊7D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C14168C14:3(C3:D4)336,203

Non-split extensions G=N.Q with N=C14 and Q=C3⋊D4
extensionφ:Q→Aut NdρLabelID
C14.1(C3⋊D4) = C3⋊D56φ: C3⋊D4/Dic3 → C2 ⊆ Aut C141684+C14.1(C3:D4)336,30
C14.2(C3⋊D4) = C6.D28φ: C3⋊D4/Dic3 → C2 ⊆ Aut C141684-C14.2(C3:D4)336,34
C14.3(C3⋊D4) = C21⋊SD16φ: C3⋊D4/Dic3 → C2 ⊆ Aut C141684+C14.3(C3:D4)336,35
C14.4(C3⋊D4) = C3⋊Dic28φ: C3⋊D4/Dic3 → C2 ⊆ Aut C143364-C14.4(C3:D4)336,39
C14.5(C3⋊D4) = D42⋊C4φ: C3⋊D4/Dic3 → C2 ⊆ Aut C14168C14.5(C3:D4)336,44
C14.6(C3⋊D4) = C14.Dic6φ: C3⋊D4/Dic3 → C2 ⊆ Aut C14336C14.6(C3:D4)336,47
C14.7(C3⋊D4) = C21⋊D8φ: C3⋊D4/D6 → C2 ⊆ Aut C141684C14.7(C3:D4)336,29
C14.8(C3⋊D4) = C28.D6φ: C3⋊D4/D6 → C2 ⊆ Aut C141684C14.8(C3:D4)336,32
C14.9(C3⋊D4) = C42.D4φ: C3⋊D4/D6 → C2 ⊆ Aut C141684C14.9(C3:D4)336,33
C14.10(C3⋊D4) = C21⋊Q16φ: C3⋊D4/D6 → C2 ⊆ Aut C143364C14.10(C3:D4)336,38
C14.11(C3⋊D4) = D14⋊Dic3φ: C3⋊D4/D6 → C2 ⊆ Aut C14168C14.11(C3:D4)336,42
C14.12(C3⋊D4) = D6⋊Dic7φ: C3⋊D4/D6 → C2 ⊆ Aut C14168C14.12(C3:D4)336,43
C14.13(C3⋊D4) = Dic21⋊C4φ: C3⋊D4/D6 → C2 ⊆ Aut C14336C14.13(C3:D4)336,46
C14.14(C3⋊D4) = C42.4Q8φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C14336C14.14(C3:D4)336,98
C14.15(C3⋊D4) = C2.D84φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C14168C14.15(C3:D4)336,100
C14.16(C3⋊D4) = D4⋊D21φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C141684+C14.16(C3:D4)336,101
C14.17(C3⋊D4) = D4.D21φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C141684-C14.17(C3:D4)336,102
C14.18(C3⋊D4) = Q8⋊2D21φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C141684+C14.18(C3:D4)336,103
C14.19(C3⋊D4) = C21⋊7Q16φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C143364-C14.19(C3:D4)336,104
C14.20(C3⋊D4) = C42.38D4φ: C3⋊D4/C2×C6 → C2 ⊆ Aut C14168C14.20(C3:D4)336,105
C14.21(C3⋊D4) = C7×Dic3⋊C4central extension (φ=1)336C14.21(C3:D4)336,82
C14.22(C3⋊D4) = C7×D6⋊C4central extension (φ=1)168C14.22(C3:D4)336,84
C14.23(C3⋊D4) = C7×D4⋊S3central extension (φ=1)1684C14.23(C3:D4)336,85
C14.24(C3⋊D4) = C7×D4.S3central extension (φ=1)1684C14.24(C3:D4)336,86
C14.25(C3⋊D4) = C7×Q8⋊2S3central extension (φ=1)1684C14.25(C3:D4)336,87
C14.26(C3⋊D4) = C7×C3⋊Q16central extension (φ=1)3364C14.26(C3:D4)336,88
C14.27(C3⋊D4) = C7×C6.D4central extension (φ=1)168C14.27(C3:D4)336,89

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