Extensions 1→N→G→Q→1 with N=C₄²⋊₄C₄ and Q=C₂

Direct product G=N×Q with N=C₄²⋊₄C₄ and Q=C₂

		d	ρ	Label	ID
C₂×C₄²⋊₄C₄		128		C2xC4^2:4C4	128,999

Semidirect products G=N:Q with N=C₄²⋊₄C₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
C₄²⋊₄C₄⋊₁C₂ = C₂³.₁₆₅C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:1C2	128,1015
C₄²⋊₄C₄⋊₂C₂ = C₄³⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:2C2	128,1030
C₄²⋊₄C₄⋊₃C₂ = C₂³.₃₀₁C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:3C2	128,1133
C₄²⋊₄C₄⋊₄C₂ = C₄².₃₇₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	32	C4^2:4C4:4C2	128,232
C₄²⋊₄C₄⋊₅C₂ = C₄².₅₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	32	C4^2:4C4:5C2	128,237
C₄²⋊₄C₄⋊₆C₂ = D₄.C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	32	C4^2:4C4:6C2	128,491
C₄²⋊₄C₄⋊₇C₂ = C₄²⋊₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	32	C4^2:4C4:7C2	128,695
C₄²⋊₄C₄⋊₈C₂ = D₄⋊₄C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:8C2	128,1007
C₄²⋊₄C₄⋊₉C₂ = C₄²⋊₄₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:9C2	128,1022
C₄²⋊₄C₄⋊₁₀C₂ = C₂³.₂₀₁C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:10C2	128,1051
C₄²⋊₄C₄⋊₁₁C₂ = C₄².₁₆₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:11C2	128,1058
C₄²⋊₄C₄⋊₁₂C₂ = C₄²⋊₁₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:12C2	128,1060
C₄²⋊₄C₄⋊₁₃C₂ = C₂³.₂₂₅C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:13C2	128,1075
C₄²⋊₄C₄⋊₁₄C₂ = C₂⁴.₂₀₈C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:14C2	128,1078
C₄²⋊₄C₄⋊₁₅C₂ = C₂³.₂₃₅C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:15C2	128,1085
C₄²⋊₄C₄⋊₁₆C₂ = C₂⁴.₂₂₁C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:16C2	128,1104
C₄²⋊₄C₄⋊₁₇C₂ = C₂³.₂₅₅C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:17C2	128,1105
C₄²⋊₄C₄⋊₁₈C₂ = C₄²⋊₁₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:18C2	128,1129
C₄²⋊₄C₄⋊₁₉C₂ = C₄².₁₆₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:19C2	128,1130
C₄²⋊₄C₄⋊₂₀C₂ = C₂³.₄₂₆C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:20C2	128,1258
C₄²⋊₄C₄⋊₂₁C₂ = C₂⁴.₃₁₅C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:21C2	128,1259
C₄²⋊₄C₄⋊₂₂C₂ = C₂³.₄₂₉C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:22C2	128,1261
C₄²⋊₄C₄⋊₂₃C₂ = C₂³.₄₃₀C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:23C2	128,1262
C₄²⋊₄C₄⋊₂₄C₂ = C₂³.₄₃₁C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:24C2	128,1263
C₄²⋊₄C₄⋊₂₅C₂ = C₂³.₄₃₂C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:25C2	128,1264
C₄²⋊₄C₄⋊₂₆C₂ = C₄²⋊₂₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:26C2	128,1335
C₄²⋊₄C₄⋊₂₇C₂ = C₄².₁₈₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:27C2	128,1336
C₄²⋊₄C₄⋊₂₈C₂ = C₄²⋊₂₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:28C2	128,1342
C₄²⋊₄C₄⋊₂₉C₂ = C₄².₁₈₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:29C2	128,1343
C₄²⋊₄C₄⋊₃₀C₂ = C₄².₁₉₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:30C2	128,1372
C₄²⋊₄C₄⋊₃₁C₂ = C₄².₁₉₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:31C2	128,1373
C₄²⋊₄C₄⋊₃₂C₂ = C₂³.₅₄₄C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:32C2	128,1376
C₄²⋊₄C₄⋊₃₃C₂ = C₄²⋊₃₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:33C2	128,1389
C₄²⋊₄C₄⋊₃₄C₂ = C₄².₁₉₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	64	C4^2:4C4:34C2	128,1390
C₄²⋊₄C₄⋊₃₅C₂ = C₄×C₄²⋊C₂	φ: trivial image	64	C4^2:4C4:35C2	128,1002

Non-split extensions G=N.Q with N=C₄²⋊₄C₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
C₄²⋊₄C₄.₁C₂ = (C₄×C₈)⋊₁₂C₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.1C2	128,478
C₄²⋊₄C₄.₂C₂ = C₄²⋊₄C₄.C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.2C2	128,572
C₄²⋊₄C₄.₃C₂ = C₄²⋊₁C₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	32	C4^2:4C4.3C2	128,6
C₄²⋊₄C₄.₄C₂ = C₄².₉Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	32	C4^2:4C4.4C2	128,32
C₄²⋊₄C₄.₅C₂ = C₄².₅₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	32	C4^2:4C4.5C2	128,238
C₄²⋊₄C₄.₆C₂ = C₄².₄₅Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.6C2	128,500
C₄²⋊₄C₄.₇C₂ = C₄².₂₃Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.7C2	128,564
C₄²⋊₄C₄.₈C₂ = C₄².₂₅Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.8C2	128,575
C₄²⋊₄C₄.₉C₂ = C₄²⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	32	C4^2:4C4.9C2	128,727
C₄²⋊₄C₄.₁₀C₂ = Q₈⋊₄C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.10C2	128,1008
C₄²⋊₄C₄.₁₁C₂ = C₄²⋊₁₄Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.11C2	128,1027
C₄²⋊₄C₄.₁₂C₂ = C₂³.₂₀₂C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.12C2	128,1052
C₄²⋊₄C₄.₁₃C₂ = C₄².₁₆₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.13C2	128,1059
C₄²⋊₄C₄.₁₄C₂ = C₄².₃₃Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.14C2	128,1062
C₄²⋊₄C₄.₁₅C₂ = C₄²⋊₄Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.15C2	128,1063
C₄²⋊₄C₄.₁₆C₂ = C₂³.₂₃₈C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.16C2	128,1088
C₄²⋊₄C₄.₁₇C₂ = C₂³.₂₅₃C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.17C2	128,1103
C₄²⋊₄C₄.₁₈C₂ = C₄²⋊₅Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.18C2	128,1131
C₄²⋊₄C₄.₁₉C₂ = C₄².₃₄Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.19C2	128,1134
C₄²⋊₄C₄.₂₀C₂ = C₂³.₄₂₈C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.20C2	128,1260
C₄²⋊₄C₄.₂₁C₂ = C₂³.₄₃₃C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.21C2	128,1265
C₄²⋊₄C₄.₂₂C₂ = C₄²⋊₈Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.22C2	128,1337
C₄²⋊₄C₄.₂₃C₂ = C₄².₃₈Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.23C2	128,1338
C₄²⋊₄C₄.₂₄C₂ = C₄²⋊₉Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.24C2	128,1344
C₄²⋊₄C₄.₂₅C₂ = C₄².₁₉₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.25C2	128,1374
C₄²⋊₄C₄.₂₆C₂ = C₂³.₅₄₅C₂⁴	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.26C2	128,1377
C₄²⋊₄C₄.₂₇C₂ = C₄².₃₉Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.27C2	128,1379
C₄²⋊₄C₄.₂₈C₂ = C₄²⋊₁₀Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄²⋊₄C₄	128	C4^2:4C4.28C2	128,1392
C₄²⋊₄C₄.₂₉C₂ = C₂.C₄³	φ: trivial image	128	C4^2:4C4.29C2	128,458

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Extensions 1→N→G→Q→1 with N=C42⋊4C4 and Q=C2

Extensions 1→N→G→Q→1 with N=C₄²⋊₄C₄ and Q=C₂