# Extensions 1→N→G→Q→1 with N=C4 and Q=C7⋊D4

Direct product G=N×Q with N=C4 and Q=C7⋊D4
dρLabelID
C4×C7⋊D4112C4xC7:D4224,123

Semidirect products G=N:Q with N=C4 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C41(C7⋊D4) = C28⋊D4φ: C7⋊D4/Dic7C2 ⊆ Aut C4112C4:1(C7:D4)224,135
C42(C7⋊D4) = C282D4φ: C7⋊D4/D14C2 ⊆ Aut C4112C4:2(C7:D4)224,133
C43(C7⋊D4) = C287D4φ: C7⋊D4/C2×C14C2 ⊆ Aut C4112C4:3(C7:D4)224,125

Non-split extensions G=N.Q with N=C4 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C4.1(C7⋊D4) = C7⋊D16φ: C7⋊D4/Dic7C2 ⊆ Aut C41124+C4.1(C7:D4)224,32
C4.2(C7⋊D4) = D8.D7φ: C7⋊D4/Dic7C2 ⊆ Aut C41124-C4.2(C7:D4)224,33
C4.3(C7⋊D4) = C7⋊SD32φ: C7⋊D4/Dic7C2 ⊆ Aut C41124+C4.3(C7:D4)224,34
C4.4(C7⋊D4) = C7⋊Q32φ: C7⋊D4/Dic7C2 ⊆ Aut C42244-C4.4(C7:D4)224,35
C4.5(C7⋊D4) = C2×D4⋊D7φ: C7⋊D4/Dic7C2 ⊆ Aut C4112C4.5(C7:D4)224,126
C4.6(C7⋊D4) = C2×D4.D7φ: C7⋊D4/Dic7C2 ⊆ Aut C4112C4.6(C7:D4)224,128
C4.7(C7⋊D4) = C28.17D4φ: C7⋊D4/Dic7C2 ⊆ Aut C4112C4.7(C7:D4)224,131
C4.8(C7⋊D4) = C2×Q8⋊D7φ: C7⋊D4/Dic7C2 ⊆ Aut C4112C4.8(C7:D4)224,136
C4.9(C7⋊D4) = C2×C7⋊Q16φ: C7⋊D4/Dic7C2 ⊆ Aut C4224C4.9(C7:D4)224,138
C4.10(C7⋊D4) = Dic7⋊Q8φ: C7⋊D4/Dic7C2 ⊆ Aut C4224C4.10(C7:D4)224,139
C4.11(C7⋊D4) = C28.23D4φ: C7⋊D4/Dic7C2 ⊆ Aut C4112C4.11(C7:D4)224,142
C4.12(C7⋊D4) = D4⋊Dic7φ: C7⋊D4/D14C2 ⊆ Aut C4112C4.12(C7:D4)224,38
C4.13(C7⋊D4) = C28.D4φ: C7⋊D4/D14C2 ⊆ Aut C4564C4.13(C7:D4)224,39
C4.14(C7⋊D4) = Q8⋊Dic7φ: C7⋊D4/D14C2 ⊆ Aut C4224C4.14(C7:D4)224,41
C4.15(C7⋊D4) = C28.10D4φ: C7⋊D4/D14C2 ⊆ Aut C41124C4.15(C7:D4)224,42
C4.16(C7⋊D4) = D4.D14φ: C7⋊D4/D14C2 ⊆ Aut C4564C4.16(C7:D4)224,127
C4.17(C7⋊D4) = C28.C23φ: C7⋊D4/D14C2 ⊆ Aut C41124C4.17(C7:D4)224,137
C4.18(C7⋊D4) = D143Q8φ: C7⋊D4/D14C2 ⊆ Aut C4112C4.18(C7:D4)224,141
C4.19(C7⋊D4) = C28.44D4φ: C7⋊D4/C2×C14C2 ⊆ Aut C4224C4.19(C7:D4)224,22
C4.20(C7⋊D4) = C2.D56φ: C7⋊D4/C2×C14C2 ⊆ Aut C4112C4.20(C7:D4)224,27
C4.21(C7⋊D4) = C28.46D4φ: C7⋊D4/C2×C14C2 ⊆ Aut C4564+C4.21(C7:D4)224,29
C4.22(C7⋊D4) = C4.12D28φ: C7⋊D4/C2×C14C2 ⊆ Aut C41124-C4.22(C7:D4)224,30
C4.23(C7⋊D4) = C28.48D4φ: C7⋊D4/C2×C14C2 ⊆ Aut C4112C4.23(C7:D4)224,119
C4.24(C7⋊D4) = D4⋊D14φ: C7⋊D4/C2×C14C2 ⊆ Aut C4564+C4.24(C7:D4)224,144
C4.25(C7⋊D4) = D4.9D14φ: C7⋊D4/C2×C14C2 ⊆ Aut C41124-C4.25(C7:D4)224,146
C4.26(C7⋊D4) = Dic7⋊C8central extension (φ=1)224C4.26(C7:D4)224,20
C4.27(C7⋊D4) = D14⋊C8central extension (φ=1)112C4.27(C7:D4)224,26
C4.28(C7⋊D4) = C28.53D4central extension (φ=1)1124C4.28(C7:D4)224,28
C4.29(C7⋊D4) = D284C4central extension (φ=1)564C4.29(C7:D4)224,31
C4.30(C7⋊D4) = C28.55D4central extension (φ=1)112C4.30(C7:D4)224,36
C4.31(C7⋊D4) = D42Dic7central extension (φ=1)564C4.31(C7:D4)224,43
C4.32(C7⋊D4) = D4.8D14central extension (φ=1)1124C4.32(C7:D4)224,145

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