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Extensions 1→N→G→Q→1 with N=Q8 and Q=C7⋊D4

Direct product G=N×Q with N=Q8 and Q=C7⋊D4
dρLabelID
Q8×C7⋊D4224Q8xC7:D4448,1268

Semidirect products G=N:Q with N=Q8 and Q=C7⋊D4
extensionφ:Q→Out NdρLabelID
Q8⋊1(C7⋊D4) = Dic7⋊5SD16φ: C7⋊D4/Dic7 → C2 ⊆ Out Q8224Q8:1(C7:D4)448,697
Q8⋊2(C7⋊D4) = Dic14⋊7D4φ: C7⋊D4/D14 → C2 ⊆ Out Q8224Q8:2(C7:D4)448,704
Q8⋊3(C7⋊D4) = D28⋊7D4φ: C7⋊D4/D14 → C2 ⊆ Out Q8224Q8:3(C7:D4)448,706
Q8⋊4(C7⋊D4) = D28⋊18D4φ: C7⋊D4/D14 → C2 ⊆ Out Q8568+Q8:4(C7:D4)448,732
Q8⋊5(C7⋊D4) = (C7×Q8)⋊13D4φ: C7⋊D4/C2×C14 → C2 ⊆ Out Q8224Q8:5(C7:D4)448,761
Q8⋊6(C7⋊D4) = (C7×D4)⋊14D4φ: C7⋊D4/C2×C14 → C2 ⊆ Out Q8224Q8:6(C7:D4)448,772
Q8⋊7(C7⋊D4) = 2+ 1+4⋊D7φ: C7⋊D4/C2×C14 → C2 ⊆ Out Q8568+Q8:7(C7:D4)448,775
Q8⋊8(C7⋊D4) = C14.452- 1+4φ: trivial image224Q8:8(C7:D4)448,1270
Q8⋊9(C7⋊D4) = C14.1072- 1+4φ: trivial image224Q8:9(C7:D4)448,1284
Q8⋊10(C7⋊D4) = C14.1482+ 1+4φ: trivial image224Q8:10(C7:D4)448,1287

Non-split extensions G=N.Q with N=Q8 and Q=C7⋊D4
extensionφ:Q→Out NdρLabelID
Q8.1(C7⋊D4) = (C7×Q8).D4φ: C7⋊D4/Dic7 → C2 ⊆ Out Q8224Q8.1(C7:D4)448,700
Q8.2(C7⋊D4) = Dic7⋊3Q16φ: C7⋊D4/Dic7 → C2 ⊆ Out Q8448Q8.2(C7:D4)448,716
Q8.3(C7⋊D4) = (C2×Q16)⋊D7φ: C7⋊D4/Dic7 → C2 ⊆ Out Q8224Q8.3(C7:D4)448,719
Q8.4(C7⋊D4) = M4(2).D14φ: C7⋊D4/Dic7 → C2 ⊆ Out Q81128+Q8.4(C7:D4)448,733
Q8.5(C7⋊D4) = M4(2).13D14φ: C7⋊D4/Dic7 → C2 ⊆ Out Q81128-Q8.5(C7:D4)448,734
Q8.6(C7⋊D4) = M4(2).15D14φ: C7⋊D4/Dic7 → C2 ⊆ Out Q81128+Q8.6(C7:D4)448,737
Q8.7(C7⋊D4) = M4(2).16D14φ: C7⋊D4/Dic7 → C2 ⊆ Out Q82248-Q8.7(C7:D4)448,738
Q8.8(C7⋊D4) = D14⋊5Q16φ: C7⋊D4/D14 → C2 ⊆ Out Q8224Q8.8(C7:D4)448,720
Q8.9(C7⋊D4) = D28.17D4φ: C7⋊D4/D14 → C2 ⊆ Out Q8224Q8.9(C7:D4)448,721
Q8.10(C7⋊D4) = D28.38D4φ: C7⋊D4/D14 → C2 ⊆ Out Q81128-Q8.10(C7:D4)448,735
Q8.11(C7⋊D4) = D28.39D4φ: C7⋊D4/D14 → C2 ⊆ Out Q81128+Q8.11(C7:D4)448,736
Q8.12(C7⋊D4) = D28.40D4φ: C7⋊D4/D14 → C2 ⊆ Out Q81128-Q8.12(C7:D4)448,739
Q8.13(C7⋊D4) = (C2×C14)⋊8Q16φ: C7⋊D4/C2×C14 → C2 ⊆ Out Q8224Q8.13(C7:D4)448,762
Q8.14(C7⋊D4) = (C7×D4).32D4φ: C7⋊D4/C2×C14 → C2 ⊆ Out Q8224Q8.14(C7:D4)448,773
Q8.15(C7⋊D4) = 2+ 1+4.D7φ: C7⋊D4/C2×C14 → C2 ⊆ Out Q81128-Q8.15(C7:D4)448,776
Q8.16(C7⋊D4) = 2- 1+4⋊D7φ: C7⋊D4/C2×C14 → C2 ⊆ Out Q81128+Q8.16(C7:D4)448,779
Q8.17(C7⋊D4) = 2- 1+4.D7φ: C7⋊D4/C2×C14 → C2 ⊆ Out Q81128-Q8.17(C7:D4)448,780
Q8.18(C7⋊D4) = D28.32C23φ: trivial image1128+Q8.18(C7:D4)448,1288
Q8.19(C7⋊D4) = D28.33C23φ: trivial image1128-Q8.19(C7:D4)448,1289
Q8.20(C7⋊D4) = D28.34C23φ: trivial image1128+Q8.20(C7:D4)448,1290
Q8.21(C7⋊D4) = D28.35C23φ: trivial image2248-Q8.21(C7:D4)448,1291

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