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

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

		d	ρ	Label	ID
C₂²xC₅₆		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 = D₇xD₈	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 = D₇xSD₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4	C56:5C2^2	224,108
C₅₆:₆C₂² = D₇xM₄(2)	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4	C56:6C2^2	224,101
C₅₆:₇C₂² = C₇xC₈:C₂²	φ: C₂²/C₁ → C₂² ⊆ Aut C₅₆	56	4	C56:7C2^2	224,171
C₅₆:₈C₂² = C₂xD₅₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:8C2^2	224,98
C₅₆:₉C₂² = C₂xC₅₆:C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:9C2^2	224,97
C₅₆:₁₀C₂² = D₇xC₂xC₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:10C2^2	224,94
C₅₆:₁₁C₂² = C₂xC₈:D₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:11C2^2	224,95
C₅₆:₁₂C₂² = C₁₄xD₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:12C2^2	224,167
C₅₆:₁₃C₂² = C₁₄xSD₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112		C56:13C2^2	224,168
C₅₆:₁₄C₂² = C₁₄xM₄(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 = D₇xQ₁₆	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 = C₇xC₈.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 = C₂xDic₂₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	224		C56.18C2^2	224,100
C₅₆.₁₉C₂² = D₇xC₁₆	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 = C₂xC₇: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 = C₇xD₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.24C2^2	224,60
C₅₆.₂₅C₂² = C₇xSD₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.25C2^2	224,61
C₅₆.₂₆C₂² = C₇xQ₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	224	2	C56.26C2^2	224,62
C₅₆.₂₇C₂² = C₁₄xQ₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	224		C56.27C2^2	224,169
C₅₆.₂₈C₂² = C₇xC₄oD₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₅₆	112	2	C56.28C2^2	224,170
C₅₆.₂₉C₂² = C₇xM₅(2)	central extension (φ=1)	112	2	C56.29C2^2	224,59
C₅₆.₃₀C₂² = C₇xC₈oD₄	central extension (φ=1)	112	2	C56.30C2^2	224,166

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

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