Extensions 1→N→G→Q→1 with N=C₅₆ and Q=Q₈

Direct product G=N×Q with N=C₅₆ and Q=Q₈

		d	ρ	Label	ID
Q₈×C₅₆		448		Q8xC56	448,853

Semidirect products G=N:Q with N=C₅₆ and Q=Q₈

extension	φ:Q→Aut N	d	Label	ID
C₅₆⋊₁Q₈ = C₈⋊Dic₁₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448	C56:1Q8	448,236
C₅₆⋊₂Q₈ = C₅₆⋊₂Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448	C56:2Q8	448,408
C₅₆⋊₃Q₈ = C₅₆⋊₃Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448	C56:3Q8	448,390
C₅₆⋊₄Q₈ = C₅₆⋊₄Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448	C56:4Q8	448,410
C₅₆⋊₅Q₈ = C₅₆⋊₅Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448	C56:5Q8	448,389
C₅₆⋊₆Q₈ = C₅₆⋊Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448	C56:6Q8	448,235
C₅₆⋊₇Q₈ = C₇×C₈⋊Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448	C56:7Q8	448,909
C₅₆⋊₈Q₈ = C₅₆⋊₈Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448	C56:8Q8	448,216
C₅₆⋊₉Q₈ = C₅₆⋊₉Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448	C56:9Q8	448,214
C₅₆⋊₁₀Q₈ = C₈×Dic₁₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448	C56:10Q8	448,212
C₅₆⋊₁₁Q₈ = C₅₆⋊₁₁Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448	C56:11Q8	448,213
C₅₆⋊₁₂Q₈ = C₇×C₈⋊₂Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448	C56:12Q8	448,908
C₅₆⋊₁₃Q₈ = C₇×C₈⋊₃Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448	C56:13Q8	448,906
C₅₆⋊₁₄Q₈ = C₇×C₈⋊₄Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448	C56:14Q8	448,854

Non-split extensions G=N.Q with N=C₅₆ and Q=Q₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆.₁Q₈ = C₁₆⋊Dic₇	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.1Q8	448,70
C₅₆.₂Q₈ = C₈.₄Dic₁₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448		C56.2Q8	448,46
C₅₆.₃Q₈ = C₈.₅Dic₁₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448		C56.3Q8	448,47
C₅₆.₄Q₈ = C₅₆.₄Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448		C56.4Q8	448,412
C₅₆.₅Q₈ = C₅₆.Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.5Q8	448,44
C₅₆.₆Q₈ = C₈.Dic₁₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.6Q8	448,51
C₅₆.₇Q₈ = C₈.₇Dic₁₄	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	224	4	C56.7Q8	448,50
C₅₆.₈Q₈ = C₅₆.₈Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	448		C56.8Q8	448,392
C₅₆.₉Q₈ = C₅₆.₉Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.9Q8	448,68
C₅₆.₁₀Q₈ = C₇×C₈.Q₈	φ: Q₈/C₂ → C₂² ⊆ Aut C₅₆	112	4	C56.10Q8	448,169
C₅₆.₁₁Q₈ = C₁₁₂⋊₅C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.11Q8	448,61
C₅₆.₁₂Q₈ = C₁₁₂⋊₆C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.12Q8	448,62
C₅₆.₁₃Q₈ = C₅₆.₁₃Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.13Q8	448,217
C₅₆.₁₄Q₈ = C₁₁₂.C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.14Q8	448,63
C₅₆.₁₅Q₈ = C₂₈⋊C₁₆	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.15Q8	448,19
C₅₆.₁₆Q₈ = C₅₆.₁₆Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	112	2	C56.16Q8	448,20
C₅₆.₁₇Q₈ = Dic₇⋊C₁₆	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.17Q8	448,58
C₅₆.₁₈Q₈ = C₇×C₁₆⋊₃C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.18Q8	448,170
C₅₆.₁₉Q₈ = C₇×C₁₆⋊₄C₄	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.19Q8	448,171
C₅₆.₂₀Q₈ = C₇×C₈.₄Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	224	2	C56.20Q8	448,172
C₅₆.₂₁Q₈ = C₇×C₈.₅Q₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	448		C56.21Q8	448,907
C₅₆.₂₂Q₈ = C₇×C₈.C₈	φ: Q₈/C₄ → C₂ ⊆ Aut C₅₆	112	2	C56.22Q8	448,168
C₅₆.₂₃Q₈ = C₇×C₄⋊C₁₆	central extension (φ=1)	448		C56.23Q8	448,167

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Extensions 1→N→G→Q→1 with N=C56 and Q=Q8

Extensions 1→N→G→Q→1 with N=C₅₆ and Q=Q₈