Extensions 1→N→G→Q→1 with N=C₅₆:C₂ and Q=C₂²

Direct product G=NxQ with N=C₅₆:C₂ and Q=C₂²

		d	ρ	Label	ID
C₂²xC₅₆:C₂		224		C2^2xC56:C2	448,1192

Semidirect products G=N:Q with N=C₅₆:C₂ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₅₆:C₂:₁C₂² = D₇xC₈:C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₅₆:C₂	56	8+	C56:C2:1C2^2	448,1225
C₅₆:C₂:₂C₂² = SD₁₆:D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅₆:C₂	112	8-	C56:C2:2C2^2	448,1226
C₅₆:C₂:₃C₂² = D₈:₅D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅₆:C₂	112	8+	C56:C2:3C2^2	448,1227
C₅₆:C₂:₄C₂² = D₈:₆D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅₆:C₂	112	8-	C56:C2:4C2^2	448,1228
C₅₆:C₂:₅C₂² = D₇xC₈.C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₅₆:C₂	112	8-	C56:C2:5C2^2	448,1229
C₅₆:C₂:₆C₂² = D₅₆:C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₅₆:C₂	112	8+	C56:C2:6C2^2	448,1230
C₅₆:C₂:₇C₂² = C₅₆.C₂³	φ: C₂²/C₁ → C₂² ⊆ Out C₅₆:C₂	112	8+	C56:C2:7C2^2	448,1231
C₅₆:C₂:₈C₂² = C₂xC₈:D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112		C56:C2:8C2^2	448,1199
C₅₆:C₂:₉C₂² = C₂xC₈.D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	224		C56:C2:9C2^2	448,1200
C₅₆:C₂:₁₀C₂² = C₅₆.₉C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112	4	C56:C2:10C2^2	448,1201
C₅₆:C₂:₁₁C₂² = D₄.₁₁D₂₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112	4	C56:C2:11C2^2	448,1204
C₅₆:C₂:₁₂C₂² = D₄.₁₂D₂₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112	4+	C56:C2:12C2^2	448,1205
C₅₆:C₂:₁₃C₂² = C₂xD₈:D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112		C56:C2:13C2^2	448,1208
C₅₆:C₂:₁₄C₂² = D₈:₁₃D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112	4	C56:C2:14C2^2	448,1210
C₅₆:C₂:₁₅C₂² = C₂xQ₁₆:D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	224		C56:C2:15C2^2	448,1217
C₅₆:C₂:₁₆C₂² = D₈:₁₀D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112	4	C56:C2:16C2^2	448,1221
C₅₆:C₂:₁₇C₂² = C₂xD₇xSD₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112		C56:C2:17C2^2	448,1211
C₅₆:C₂:₁₈C₂² = C₂xSD₁₆:₃D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	224		C56:C2:18C2^2	448,1214
C₅₆:C₂:₁₉C₂² = D₂₈.₂₉D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112	4	C56:C2:19C2^2	448,1215
C₅₆:C₂:₂₀C₂² = D₇xC₄oD₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112	4	C56:C2:20C2^2	448,1220
C₅₆:C₂:₂₁C₂² = D₈:₁₁D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	112	4	C56:C2:21C2^2	448,1223
C₅₆:C₂:₂₂C₂² = C₂xD₅₆:₇C₂	φ: trivial image	224		C56:C2:22C2^2	448,1194

Non-split extensions G=N.Q with N=C₅₆:C₂ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₅₆:C₂.C₂² = D₂₈.₄₄D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₅₆:C₂	224	8-	C56:C2.C2^2	448,1232
C₅₆:C₂.₂C₂² = D₄.₁₃D₂₈	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	224	4-	C56:C2.2C2^2	448,1206
C₅₆:C₂.₃C₂² = D₂₈.₃₀D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆:C₂	224	4	C56:C2.3C2^2	448,1219

Extensions 1→N→G→Q→1 with N=C56:C2 and Q=C22

Extensions 1→N→G→Q→1 with N=C₅₆:C₂ and Q=C₂²