Extensions 1→N→G→Q→1 with N=C₅₆ and Q=C₂²

Direct product G=N×Q with N=C₅₆ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₅₆		224		C2^2xC56	224,164

Semidirect products G=N:Q with N=C₅₆ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆⋊₁C₂² = C₈⋊D₁₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4+	C56:1C2^2	224,103
C₅₆⋊₂C₂² = D₇×D₈	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4+	C56:2C2^2	224,105
C₅₆⋊₃C₂² = D₅₆⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4+	C56:3C2^2	224,109
C₅₆⋊₄C₂² = D₈⋊D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4	C56:4C2^2	224,106
C₅₆⋊₅C₂² = D₇×SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4	C56:5C2^2	224,108
C₅₆⋊₆C₂² = D₇×M₄(2)	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4	C56:6C2^2	224,101
C₅₆⋊₇C₂² = C₇×C₈⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4	C56:7C2^2	224,171
C₅₆⋊₈C₂² = C₂×D₅₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:8C2^2	224,98
C₅₆⋊₉C₂² = C₂×C₅₆⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:9C2^2	224,97
C₅₆⋊₁₀C₂² = D₇×C₂×C₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:10C2^2	224,94
C₅₆⋊₁₁C₂² = C₂×C₈⋊D₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:11C2^2	224,95
C₅₆⋊₁₂C₂² = C₁₄×D₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:12C2^2	224,167
C₅₆⋊₁₃C₂² = C₁₄×SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:13C2^2	224,168
C₅₆⋊₁₄C₂² = C₁₄×M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:14C2^2	224,165

Non-split extensions G=N.Q with N=C₅₆ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆.₁C₂² = C₈.D₁₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4-	C56.1C2^2	224,104
C₅₆.₂C₂² = C₇⋊D₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4+	C56.2C2^2	224,32
C₅₆.₃C₂² = D₈.D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4-	C56.3C2^2	224,33
C₅₆.₄C₂² = C₇⋊SD₃₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4+	C56.4C2^2	224,34
C₅₆.₅C₂² = C₇⋊Q₃₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	224	4-	C56.5C2^2	224,35
C₅₆.₆C₂² = D₈⋊₃D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4-	C56.6C2^2	224,107
C₅₆.₇C₂² = D₇×Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4-	C56.7C2^2	224,112
C₅₆.₈C₂² = Q₈.D₁₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4+	C56.8C2^2	224,114
C₅₆.₉C₂² = SD₁₆⋊D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4-	C56.9C2^2	224,110
C₅₆.₁₀C₂² = Q₁₆⋊D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4	C56.10C2^2	224,113
C₅₆.₁₁C₂² = SD₁₆⋊₃D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4	C56.11C2^2	224,111
C₅₆.₁₂C₂² = D₂₈.C₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4	C56.12C2^2	224,102
C₅₆.₁₃C₂² = C₇×C₈.C₂²	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	112	4	C56.13C2^2	224,172
C₅₆.₁₄C₂² = D₁₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2+	C56.14C2^2	224,5
C₅₆.₁₅C₂² = C₁₁₂⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.15C2^2	224,6
C₅₆.₁₆C₂² = Dic₅₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	224	2-	C56.16C2^2	224,7
C₅₆.₁₇C₂² = D₅₆⋊₇C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.17C2^2	224,99
C₅₆.₁₈C₂² = C₂×Dic₂₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	224		C56.18C2^2	224,100
C₅₆.₁₉C₂² = D₇×C₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.19C2^2	224,3
C₅₆.₂₀C₂² = C₁₆⋊D₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.20C2^2	224,4
C₅₆.₂₁C₂² = C₂×C₇⋊C₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	224		C56.21C2^2	224,17
C₅₆.₂₂C₂² = C₂₈.C₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.22C2^2	224,18
C₅₆.₂₃C₂² = D₂₈.₂C₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.23C2^2	224,96
C₅₆.₂₄C₂² = C₇×D₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.24C2^2	224,60
C₅₆.₂₅C₂² = C₇×SD₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.25C2^2	224,61
C₅₆.₂₆C₂² = C₇×Q₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	224	2	C56.26C2^2	224,62
C₅₆.₂₇C₂² = C₁₄×Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	224		C56.27C2^2	224,169
C₅₆.₂₈C₂² = C₇×C₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.28C2^2	224,170
C₅₆.₂₉C₂² = C₇×M₅(2)	central extension (φ=1)	112	2	C56.29C2^2	224,59
C₅₆.₃₀C₂² = C₇×C₈○D₄	central extension (φ=1)	112	2	C56.30C2^2	224,166

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Extensions 1→N→G→Q→1 with N=C56 and Q=C22

Extensions 1→N→G→Q→1 with N=C₅₆ and Q=C₂²