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

Direct product G=N×Q with N=D4 and Q=C7⋊D4
dρLabelID
D4×C7⋊D4112D4xC7:D4448,1254

Semidirect products G=N:Q with N=D4 and Q=C7⋊D4
extensionφ:Q→Out NdρLabelID
D4⋊1(C7⋊D4) = Dic7⋊D8φ: C7⋊D4/Dic7 → C2 ⊆ Out D4224D4:1(C7:D4)448,684
D4⋊2(C7⋊D4) = D28⋊D4φ: C7⋊D4/D14 → C2 ⊆ Out D4112D4:2(C7:D4)448,690
D4⋊3(C7⋊D4) = Dic14⋊D4φ: C7⋊D4/D14 → C2 ⊆ Out D4224D4:3(C7:D4)448,692
D4⋊4(C7⋊D4) = D28⋊18D4φ: C7⋊D4/D14 → C2 ⊆ Out D4568+D4:4(C7:D4)448,732
D4⋊5(C7⋊D4) = (C2×C14)⋊8D8φ: C7⋊D4/C2×C14 → C2 ⊆ Out D4112D4:5(C7:D4)448,751
D4⋊6(C7⋊D4) = (C7×D4)⋊14D4φ: C7⋊D4/C2×C14 → C2 ⊆ Out D4224D4:6(C7:D4)448,772
D4⋊7(C7⋊D4) = 2+ (1+4)⋊D7φ: C7⋊D4/C2×C14 → C2 ⊆ Out D4568+D4:7(C7:D4)448,775
D4⋊8(C7⋊D4) = C24.42D14φ: trivial image112D4:8(C7:D4)448,1259
D4⋊9(C7⋊D4) = C14.1042- (1+4)φ: trivial image224D4:9(C7:D4)448,1277
D4⋊10(C7⋊D4) = C14.1452+ (1+4)φ: trivial image112D4:10(C7:D4)448,1282

Non-split extensions G=N.Q with N=D4 and Q=C7⋊D4
extensionφ:Q→Out NdρLabelID
D4.1(C7⋊D4) = (C2×D8).D7φ: C7⋊D4/Dic7 → C2 ⊆ Out D4224D4.1(C7:D4)448,687
D4.2(C7⋊D4) = Dic7⋊3SD16φ: C7⋊D4/Dic7 → C2 ⊆ Out D4224D4.2(C7:D4)448,696
D4.3(C7⋊D4) = (C7×D4).D4φ: C7⋊D4/Dic7 → C2 ⊆ Out D4224D4.3(C7:D4)448,699
D4.4(C7⋊D4) = M4(2).D14φ: C7⋊D4/Dic7 → C2 ⊆ Out D41128+D4.4(C7:D4)448,733
D4.5(C7⋊D4) = M4(2).13D14φ: C7⋊D4/Dic7 → C2 ⊆ Out D41128-D4.5(C7:D4)448,734
D4.6(C7⋊D4) = M4(2).15D14φ: C7⋊D4/Dic7 → C2 ⊆ Out D41128+D4.6(C7:D4)448,737
D4.7(C7⋊D4) = M4(2).16D14φ: C7⋊D4/Dic7 → C2 ⊆ Out D42248-D4.7(C7:D4)448,738
D4.8(C7⋊D4) = D14⋊6SD16φ: C7⋊D4/D14 → C2 ⊆ Out D4112D4.8(C7:D4)448,703
D4.9(C7⋊D4) = Dic14.16D4φ: C7⋊D4/D14 → C2 ⊆ Out D4224D4.9(C7:D4)448,707
D4.10(C7⋊D4) = D28.38D4φ: C7⋊D4/D14 → C2 ⊆ Out D41128-D4.10(C7:D4)448,735
D4.11(C7⋊D4) = D28.39D4φ: C7⋊D4/D14 → C2 ⊆ Out D41128+D4.11(C7:D4)448,736
D4.12(C7⋊D4) = D28.40D4φ: C7⋊D4/D14 → C2 ⊆ Out D41128-D4.12(C7:D4)448,739
D4.13(C7⋊D4) = (C7×D4).31D4φ: C7⋊D4/C2×C14 → C2 ⊆ Out D4112D4.13(C7:D4)448,752
D4.14(C7⋊D4) = (C7×D4).32D4φ: C7⋊D4/C2×C14 → C2 ⊆ Out D4224D4.14(C7:D4)448,773
D4.15(C7⋊D4) = 2+ (1+4).D7φ: C7⋊D4/C2×C14 → C2 ⊆ Out D41128-D4.15(C7:D4)448,776
D4.16(C7⋊D4) = 2- (1+4)⋊D7φ: C7⋊D4/C2×C14 → C2 ⊆ Out D41128+D4.16(C7:D4)448,779
D4.17(C7⋊D4) = 2- (1+4).D7φ: C7⋊D4/C2×C14 → C2 ⊆ Out D41128-D4.17(C7:D4)448,780
D4.18(C7⋊D4) = D28.32C23φ: trivial image1128+D4.18(C7:D4)448,1288
D4.19(C7⋊D4) = D28.33C23φ: trivial image1128-D4.19(C7:D4)448,1289
D4.20(C7⋊D4) = D28.34C23φ: trivial image1128+D4.20(C7:D4)448,1290
D4.21(C7⋊D4) = D28.35C23φ: trivial image2248-D4.21(C7:D4)448,1291

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