Extensions 1→N→G→Q→1 with N=D₅₆ and Q=C₂²

Direct product G=N×Q with N=D₅₆ and Q=C₂²

		d	ρ	Label	ID
C₂²×D₅₆		224		C2^2xD56	448,1193

Semidirect products G=N:Q with N=D₅₆ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₆⋊₁C₂² = D₇×C₈⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	56	8+	D56:1C2^2	448,1225
D₅₆⋊₂C₂² = D₈⋊₅D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	112	8+	D56:2C2^2	448,1227
D₅₆⋊₃C₂² = D₅₆⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	112	8+	D56:3C2^2	448,1230
D₅₆⋊₄C₂² = C₅₆.C₂³	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	112	8+	D56:4C2^2	448,1231
D₅₆⋊₅C₂² = D₇×D₁₆	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	112	4+	D56:5C2^2	448,444
D₅₆⋊₆C₂² = D₁₁₂⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	112	4+	D56:6C2^2	448,448
D₅₆⋊₇C₂² = C₂×D₁₁₂	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224		D56:7C2^2	448,436
D₅₆⋊₈C₂² = C₁₆⋊D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4+	D56:8C2^2	448,442
D₅₆⋊₉C₂² = C₂×C₈⋊D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112		D56:9C2^2	448,1199
D₅₆⋊₁₀C₂² = C₅₆.₉C₂³	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4	D56:10C2^2	448,1201
D₅₆⋊₁₁C₂² = D₄.₁₁D₂₈	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4	D56:11C2^2	448,1204
D₅₆⋊₁₂C₂² = D₄.₁₂D₂₈	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4+	D56:12C2^2	448,1205
D₅₆⋊₁₃C₂² = C₂×C₇⋊D₁₆	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224		D56:13C2^2	448,680
D₅₆⋊₁₄C₂² = D₈.D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4	D56:14C2^2	448,681
D₅₆⋊₁₅C₂² = C₂×D₇×D₈	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112		D56:15C2^2	448,1207
D₅₆⋊₁₆C₂² = D₈⋊₁₃D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4	D56:16C2^2	448,1210
D₅₆⋊₁₇C₂² = C₂×Q₈.D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224		D56:17C2^2	448,1218
D₅₆⋊₁₈C₂² = D₇×C₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4	D56:18C2^2	448,1220
D₅₆⋊₁₉C₂² = D₈⋊₁₅D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4+	D56:19C2^2	448,1222
D₅₆⋊₂₀C₂² = C₂×D₅₆⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112		D56:20C2^2	448,1212
D₅₆⋊₂₁C₂² = D₂₈.₂₉D₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4	D56:21C2^2	448,1215
D₅₆⋊₂₂C₂² = D₈⋊₁₀D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4	D56:22C2^2	448,1221
D₅₆⋊₂₃C₂² = C₂×D₅₆⋊₇C₂	φ: trivial image	224		D56:23C2^2	448,1194

Non-split extensions G=N.Q with N=D₅₆ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
D₅₆.₁C₂² = D₈⋊D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	112	4	D56.1C2^2	448,445
D₅₆.₂C₂² = D₇×SD₃₂	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	112	4	D56.2C2^2	448,447
D₅₆.₃C₂² = SD₃₂⋊₃D₇	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	224	4	D56.3C2^2	448,450
D₅₆.₄C₂² = Q₃₂⋊D₇	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	224	4	D56.4C2^2	448,452
D₅₆.₅C₂² = Q₃₂⋊₃D₇	φ: C₂²/C₁ → C₂² ⊆ Out D₅₆	224	4+	D56.5C2^2	448,453
D₅₆.₆C₂² = C₂×C₁₁₂⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224		D56.6C2^2	448,437
D₅₆.₇C₂² = D₁₁₂⋊₇C₂	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224	2	D56.7C2^2	448,438
D₅₆.₈C₂² = C₁₆.D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224	4-	D56.8C2^2	448,443
D₅₆.₉C₂² = C₂×C₇⋊SD₃₂	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224		D56.9C2^2	448,712
D₅₆.₁₀C₂² = Q₁₆.D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224	4	D56.10C2^2	448,713
D₅₆.₁₁C₂² = Q₁₆⋊D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	112	4+	D56.11C2^2	448,727
D₅₆.₁₂C₂² = C₅₆.₃₀C₂³	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224	4	D56.12C2^2	448,728
D₅₆.₁₃C₂² = D₂₈.₃₀D₄	φ: C₂²/C₂ → C₂ ⊆ Out D₅₆	224	4	D56.13C2^2	448,1219
D₅₆.₁₄C₂² = D₄.₁₃D₂₈	φ: trivial image	224	4-	D56.14C2^2	448,1206

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Extensions 1→N→G→Q→1 with N=D56 and Q=C22

Extensions 1→N→G→Q→1 with N=D₅₆ and Q=C₂²