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Extensions 1→N→G→Q→1 with N=C4 and Q=C13⋊D4

Direct product G=N×Q with N=C4 and Q=C13⋊D4
dρLabelID
C4×C13⋊D4208C4xC13:D4416,149

Semidirect products G=N:Q with N=C4 and Q=C13⋊D4
extensionφ:Q→Aut NdρLabelID
C4⋊1(C13⋊D4) = C52⋊D4φ: C13⋊D4/Dic13 → C2 ⊆ Aut C4208C4:1(C13:D4)416,161
C4⋊2(C13⋊D4) = C52⋊2D4φ: C13⋊D4/D26 → C2 ⊆ Aut C4208C4:2(C13:D4)416,159
C4⋊3(C13⋊D4) = C52⋊7D4φ: C13⋊D4/C2×C26 → C2 ⊆ Aut C4208C4:3(C13:D4)416,151

Non-split extensions G=N.Q with N=C4 and Q=C13⋊D4
extensionφ:Q→Aut NdρLabelID
C4.1(C13⋊D4) = C13⋊D16φ: C13⋊D4/Dic13 → C2 ⊆ Aut C42084+C4.1(C13:D4)416,33
C4.2(C13⋊D4) = D8.D13φ: C13⋊D4/Dic13 → C2 ⊆ Aut C42084-C4.2(C13:D4)416,34
C4.3(C13⋊D4) = C8.6D26φ: C13⋊D4/Dic13 → C2 ⊆ Aut C42084+C4.3(C13:D4)416,35
C4.4(C13⋊D4) = C13⋊Q32φ: C13⋊D4/Dic13 → C2 ⊆ Aut C44164-C4.4(C13:D4)416,36
C4.5(C13⋊D4) = C2×D4⋊D13φ: C13⋊D4/Dic13 → C2 ⊆ Aut C4208C4.5(C13:D4)416,152
C4.6(C13⋊D4) = C2×D4.D13φ: C13⋊D4/Dic13 → C2 ⊆ Aut C4208C4.6(C13:D4)416,154
C4.7(C13⋊D4) = C52.17D4φ: C13⋊D4/Dic13 → C2 ⊆ Aut C4208C4.7(C13:D4)416,157
C4.8(C13⋊D4) = C2×Q8⋊D13φ: C13⋊D4/Dic13 → C2 ⊆ Aut C4208C4.8(C13:D4)416,162
C4.9(C13⋊D4) = C2×C13⋊Q16φ: C13⋊D4/Dic13 → C2 ⊆ Aut C4416C4.9(C13:D4)416,164
C4.10(C13⋊D4) = Dic13⋊Q8φ: C13⋊D4/Dic13 → C2 ⊆ Aut C4416C4.10(C13:D4)416,165
C4.11(C13⋊D4) = C52.23D4φ: C13⋊D4/Dic13 → C2 ⊆ Aut C4208C4.11(C13:D4)416,168
C4.12(C13⋊D4) = D4⋊Dic13φ: C13⋊D4/D26 → C2 ⊆ Aut C4208C4.12(C13:D4)416,39
C4.13(C13⋊D4) = C52.D4φ: C13⋊D4/D26 → C2 ⊆ Aut C41044C4.13(C13:D4)416,40
C4.14(C13⋊D4) = Q8⋊Dic13φ: C13⋊D4/D26 → C2 ⊆ Aut C4416C4.14(C13:D4)416,42
C4.15(C13⋊D4) = C52.10D4φ: C13⋊D4/D26 → C2 ⊆ Aut C42084C4.15(C13:D4)416,43
C4.16(C13⋊D4) = D52⋊6C22φ: C13⋊D4/D26 → C2 ⊆ Aut C41044C4.16(C13:D4)416,153
C4.17(C13⋊D4) = Q8.D26φ: C13⋊D4/D26 → C2 ⊆ Aut C42084C4.17(C13:D4)416,163
C4.18(C13⋊D4) = D26⋊3Q8φ: C13⋊D4/D26 → C2 ⊆ Aut C4208C4.18(C13:D4)416,167
C4.19(C13⋊D4) = C52.44D4φ: C13⋊D4/C2×C26 → C2 ⊆ Aut C4416C4.19(C13:D4)416,23
C4.20(C13⋊D4) = D52⋊5C4φ: C13⋊D4/C2×C26 → C2 ⊆ Aut C4208C4.20(C13:D4)416,28
C4.21(C13⋊D4) = C52.46D4φ: C13⋊D4/C2×C26 → C2 ⊆ Aut C41044+C4.21(C13:D4)416,30
C4.22(C13⋊D4) = C4.12D52φ: C13⋊D4/C2×C26 → C2 ⊆ Aut C42084-C4.22(C13:D4)416,31
C4.23(C13⋊D4) = C52.48D4φ: C13⋊D4/C2×C26 → C2 ⊆ Aut C4208C4.23(C13:D4)416,145
C4.24(C13⋊D4) = D4⋊D26φ: C13⋊D4/C2×C26 → C2 ⊆ Aut C41044+C4.24(C13:D4)416,170
C4.25(C13⋊D4) = D4.9D26φ: C13⋊D4/C2×C26 → C2 ⊆ Aut C42084-C4.25(C13:D4)416,172
C4.26(C13⋊D4) = C52.8Q8central extension (φ=1)416C4.26(C13:D4)416,21
C4.27(C13⋊D4) = D26⋊1C8central extension (φ=1)208C4.27(C13:D4)416,27
C4.28(C13⋊D4) = C52.53D4central extension (φ=1)2084C4.28(C13:D4)416,29
C4.29(C13⋊D4) = D52⋊7C4central extension (φ=1)1044C4.29(C13:D4)416,32
C4.30(C13⋊D4) = C52.55D4central extension (φ=1)208C4.30(C13:D4)416,37
C4.31(C13⋊D4) = C52.56D4central extension (φ=1)1044C4.31(C13:D4)416,44
C4.32(C13⋊D4) = C52.C23central extension (φ=1)2084C4.32(C13:D4)416,171

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