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Extensions 1→N→G→Q→1 with N=C22 and Q=C7⋊D4

Direct product G=N×Q with N=C22 and Q=C7⋊D4
dρLabelID
C22×C7⋊D4112C2^2xC7:D4224,188

Semidirect products G=N:Q with N=C22 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C22⋊1(C7⋊D4) = Dic7⋊D4φ: C7⋊D4/Dic7 → C2 ⊆ Aut C22112C2^2:1(C7:D4)224,134
C22⋊2(C7⋊D4) = C23⋊D14φ: C7⋊D4/D14 → C2 ⊆ Aut C2256C2^2:2(C7:D4)224,132
C22⋊3(C7⋊D4) = C24⋊D7φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C2256C2^2:3(C7:D4)224,148

Non-split extensions G=N.Q with N=C22 and Q=C7⋊D4
extensionφ:Q→Aut NdρLabelID
C22.1(C7⋊D4) = D4.8D14φ: C7⋊D4/Dic7 → C2 ⊆ Aut C221124C2^2.1(C7:D4)224,145
C22.2(C7⋊D4) = C23⋊Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C22564C2^2.2(C7:D4)224,40
C22.3(C7⋊D4) = D4⋊2Dic7φ: C7⋊D4/D14 → C2 ⊆ Aut C22564C2^2.3(C7:D4)224,43
C22.4(C7⋊D4) = C23.18D14φ: C7⋊D4/D14 → C2 ⊆ Aut C22112C2^2.4(C7:D4)224,130
C22.5(C7⋊D4) = D4⋊D14φ: C7⋊D4/D14 → C2 ⊆ Aut C22564+C2^2.5(C7:D4)224,144
C22.6(C7⋊D4) = D4.9D14φ: C7⋊D4/D14 → C2 ⊆ Aut C221124-C2^2.6(C7:D4)224,146
C22.7(C7⋊D4) = Dic14⋊C4φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C22562C2^2.7(C7:D4)224,11
C22.8(C7⋊D4) = C23.1D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C22564C2^2.8(C7:D4)224,12
C22.9(C7⋊D4) = C23.23D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C22112C2^2.9(C7:D4)224,124
C22.10(C7⋊D4) = D4.D14φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C22564C2^2.10(C7:D4)224,127
C22.11(C7⋊D4) = C28.C23φ: C7⋊D4/C2×C14 → C2 ⊆ Aut C221124C2^2.11(C7:D4)224,137
C22.12(C7⋊D4) = C28.Q8central extension (φ=1)224C2^2.12(C7:D4)224,13
C22.13(C7⋊D4) = C4.Dic14central extension (φ=1)224C2^2.13(C7:D4)224,14
C22.14(C7⋊D4) = C14.D8central extension (φ=1)112C2^2.14(C7:D4)224,15
C22.15(C7⋊D4) = C14.Q16central extension (φ=1)224C2^2.15(C7:D4)224,16
C22.16(C7⋊D4) = C14.C42central extension (φ=1)224C2^2.16(C7:D4)224,37
C22.17(C7⋊D4) = D4⋊Dic7central extension (φ=1)112C2^2.17(C7:D4)224,38
C22.18(C7⋊D4) = Q8⋊Dic7central extension (φ=1)224C2^2.18(C7:D4)224,41
C22.19(C7⋊D4) = C2×Dic7⋊C4central extension (φ=1)224C2^2.19(C7:D4)224,118
C22.20(C7⋊D4) = C2×D14⋊C4central extension (φ=1)112C2^2.20(C7:D4)224,122
C22.21(C7⋊D4) = C2×D4⋊D7central extension (φ=1)112C2^2.21(C7:D4)224,126
C22.22(C7⋊D4) = C2×D4.D7central extension (φ=1)112C2^2.22(C7:D4)224,128
C22.23(C7⋊D4) = C2×Q8⋊D7central extension (φ=1)112C2^2.23(C7:D4)224,136
C22.24(C7⋊D4) = C2×C7⋊Q16central extension (φ=1)224C2^2.24(C7:D4)224,138
C22.25(C7⋊D4) = C2×C23.D7central extension (φ=1)112C2^2.25(C7:D4)224,147

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