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

Direct product G=N×Q with N=C₅₆⋊C₂ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₅₆⋊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 = D₇×C₈⋊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 = D₇×C₈.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 = C₂×C₈⋊D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆⋊C₂	112		C56:C2:8C2^2	448,1199
C₅₆⋊C₂⋊₉C₂² = C₂×C₈.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 = C₂×D₈⋊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 = C₂×Q₁₆⋊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 = C₂×D₇×SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₅₆⋊C₂	112		C56:C2:17C2^2	448,1211
C₅₆⋊C₂⋊₁₈C₂² = C₂×SD₁₆⋊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 = D₇×C₄○D₈	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 = C₂×D₅₆⋊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

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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