Extensions 1→N→G→Q→1 with N=C₈ and Q=C₇×D₄

Direct product G=N×Q with N=C₈ and Q=C₇×D₄

		d	ρ	Label	ID
D₄×C₅₆		224		D4xC56	448,842

Semidirect products G=N:Q with N=C₈ and Q=C₇×D₄

extension	φ:Q→Aut N	d	Label	ID
C₈⋊₁(C₇×D₄) = C₇×C₈⋊D₄	φ: C₇×D₄/C₁₄ → C₂² ⊆ Aut C₈	224	C8:1(C7xD4)	448,876
C₈⋊₂(C₇×D₄) = C₇×C₈⋊₂D₄	φ: C₇×D₄/C₁₄ → C₂² ⊆ Aut C₈	224	C8:2(C7xD4)	448,877
C₈⋊₃(C₇×D₄) = C₇×C₈⋊₃D₄	φ: C₇×D₄/C₁₄ → C₂² ⊆ Aut C₈	224	C8:3(C7xD4)	448,904
C₈⋊₄(C₇×D₄) = C₇×C₈⋊₄D₄	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224	C8:4(C7xD4)	448,901
C₈⋊₅(C₇×D₄) = C₇×C₈⋊₅D₄	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224	C8:5(C7xD4)	448,900
C₈⋊₆(C₇×D₄) = C₇×C₈⋊₆D₄	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224	C8:6(C7xD4)	448,844
C₈⋊₇(C₇×D₄) = C₇×C₈⋊₇D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	224	C8:7(C7xD4)	448,874
C₈⋊₈(C₇×D₄) = C₇×C₈⋊₈D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	224	C8:8(C7xD4)	448,873
C₈⋊₉(C₇×D₄) = C₇×C₈⋊₉D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	224	C8:9(C7xD4)	448,843

Non-split extensions G=N.Q with N=C₈ and Q=C₇×D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈.₁(C₇×D₄) = C₇×C₈.D₄	φ: C₇×D₄/C₁₄ → C₂² ⊆ Aut C₈	224		C8.1(C7xD4)	448,878
C₈.₂(C₇×D₄) = C₇×C₈.₂D₄	φ: C₇×D₄/C₁₄ → C₂² ⊆ Aut C₈	224		C8.2(C7xD4)	448,905
C₈.₃(C₇×D₄) = C₇×C₁₆⋊C₂²	φ: C₇×D₄/C₁₄ → C₂² ⊆ Aut C₈	112	4	C8.3(C7xD4)	448,917
C₈.₄(C₇×D₄) = C₇×Q₃₂⋊C₂	φ: C₇×D₄/C₁₄ → C₂² ⊆ Aut C₈	224	4	C8.4(C7xD4)	448,918
C₈.₅(C₇×D₄) = C₇×D₃₂	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224	2	C8.5(C7xD4)	448,175
C₈.₆(C₇×D₄) = C₇×SD₆₄	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224	2	C8.6(C7xD4)	448,176
C₈.₇(C₇×D₄) = C₇×Q₆₄	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	448	2	C8.7(C7xD4)	448,177
C₈.₈(C₇×D₄) = C₇×C₄⋊Q₁₆	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	448		C8.8(C7xD4)	448,902
C₈.₉(C₇×D₄) = C₁₄×D₁₆	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224		C8.9(C7xD4)	448,913
C₈.₁₀(C₇×D₄) = C₁₄×SD₃₂	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224		C8.10(C7xD4)	448,914
C₈.₁₁(C₇×D₄) = C₁₄×Q₃₂	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	448		C8.11(C7xD4)	448,915
C₈.₁₂(C₇×D₄) = C₇×C₈.₁₂D₄	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224		C8.12(C7xD4)	448,903
C₈.₁₃(C₇×D₄) = C₇×C₄○D₁₆	φ: C₇×D₄/C₂₈ → C₂ ⊆ Aut C₈	224	2	C8.13(C7xD4)	448,916
C₈.₁₄(C₇×D₄) = C₇×C₂.D₁₆	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	224		C8.14(C7xD4)	448,161
C₈.₁₅(C₇×D₄) = C₇×C₂.Q₃₂	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	448		C8.15(C7xD4)	448,162
C₈.₁₆(C₇×D₄) = C₇×M₅(2)⋊C₂	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	112	4	C8.16(C7xD4)	448,165
C₈.₁₇(C₇×D₄) = C₇×C₈.₁₇D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	224	4	C8.17(C7xD4)	448,166
C₈.₁₈(C₇×D₄) = C₇×C₈.₁₈D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	224		C8.18(C7xD4)	448,875
C₈.₁₉(C₇×D₄) = C₇×D₄.₄D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	112	4	C8.19(C7xD4)	448,880
C₈.₂₀(C₇×D₄) = C₇×D₄.₅D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	224	4	C8.20(C7xD4)	448,881
C₈.₂₁(C₇×D₄) = C₇×D₈.C₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	224	2	C8.21(C7xD4)	448,163
C₈.₂₂(C₇×D₄) = C₇×D₈⋊₂C₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	112	4	C8.22(C7xD4)	448,164
C₈.₂₃(C₇×D₄) = C₇×D₄.₃D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	112	4	C8.23(C7xD4)	448,879
C₈.₂₄(C₇×D₄) = C₇×C₂³.C₈	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	112	4	C8.24(C7xD4)	448,153
C₈.₂₅(C₇×D₄) = C₇×C₈.₂₆D₄	φ: C₇×D₄/C₂×C₁₄ → C₂ ⊆ Aut C₈	112	4	C8.25(C7xD4)	448,852
C₈.₂₆(C₇×D₄) = C₇×C₂²⋊C₁₆	central extension (φ=1)	224		C8.26(C7xD4)	448,152
C₈.₂₇(C₇×D₄) = C₇×D₄.C₈	central extension (φ=1)	224	2	C8.27(C7xD4)	448,154
C₈.₂₈(C₇×D₄) = C₇×C₄⋊C₁₆	central extension (φ=1)	448		C8.28(C7xD4)	448,167
C₈.₂₉(C₇×D₄) = C₇×C₈.C₈	central extension (φ=1)	112	2	C8.29(C7xD4)	448,168
C₈.₃₀(C₇×D₄) = C₇×C₈○D₈	central extension (φ=1)	112	2	C8.30(C7xD4)	448,851

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Extensions 1→N→G→Q→1 with N=C8 and Q=C7×D4

Extensions 1→N→G→Q→1 with N=C₈ and Q=C₇×D₄