Extensions 1→N→G→Q→1 with N=C₄².₁₂C₄ and Q=C₂

Direct product G=N×Q with N=C₄².₁₂C₄ and Q=C₂

		d	ρ	Label	ID
C₂×C₄².₁₂C₄		64		C2xC4^2.12C4	128,1649

Semidirect products G=N:Q with N=C₄².₁₂C₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
C₄².₁₂C₄⋊₁C₂ = C₄².₃₇₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:1C2	128,190
C₄².₁₂C₄⋊₂C₂ = C₄².₃₉₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:2C2	128,192
C₄².₁₂C₄⋊₃C₂ = C₄².₃₉₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:3C2	128,201
C₄².₁₂C₄⋊₄C₂ = C₄².₃₇₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:4C2	128,205
C₄².₁₂C₄⋊₅C₂ = C₄².₄₅₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:5C2	128,208
C₄².₁₂C₄⋊₆C₂ = C₄².₃₉₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:6C2	128,209
C₄².₁₂C₄⋊₇C₂ = C₄².₃₉₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:7C2	128,210
C₄².₁₂C₄⋊₈C₂ = C₄².₄₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:8C2	128,212
C₄².₁₂C₄⋊₉C₂ = C₄².₃₇₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:9C2	128,214
C₄².₁₂C₄⋊₁₀C₂ = C₄².₄₀₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:10C2	128,216
C₄².₁₂C₄⋊₁₁C₂ = D₄⋊M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:11C2	128,218
C₄².₁₂C₄⋊₁₂C₂ = C₄².₃₇₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:12C2	128,220
C₄².₁₂C₄⋊₁₃C₂ = C₄².₅₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:13C2	128,227
C₄².₁₂C₄⋊₁₄C₂ = C₄².₅₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:14C2	128,228
C₄².₁₂C₄⋊₁₅C₂ = C₄².₃₇₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:15C2	128,232
C₄².₁₂C₄⋊₁₆C₂ = C₄².₄₀₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:16C2	128,234
C₄².₁₂C₄⋊₁₇C₂ = C₄².₆₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:17C2	128,249
C₄².₁₂C₄⋊₁₈C₂ = C₄².₆₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:18C2	128,253
C₄².₁₂C₄⋊₁₉C₂ = C₄².₄₀₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:19C2	128,272
C₄².₁₂C₄⋊₂₀C₂ = C₄².₄₁₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:20C2	128,275
C₄².₁₂C₄⋊₂₁C₂ = C₄².₄₁₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:21C2	128,277
C₄².₁₂C₄⋊₂₂C₂ = C₄².₄₁₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:22C2	128,285
C₄².₁₂C₄⋊₂₃C₂ = C₄².₆₉₁C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:23C2	128,1704
C₄².₁₂C₄⋊₂₄C₂ = C₄².₆₉₇C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:24C2	128,1720
C₄².₁₂C₄⋊₂₅C₂ = C₄².₂₂₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:25C2	128,1832
C₄².₁₂C₄⋊₂₆C₂ = C₄².₂₆₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:26C2	128,1937
C₄².₁₂C₄⋊₂₇C₂ = C₄².₂₇₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:27C2	128,1958
C₄².₁₂C₄⋊₂₈C₂ = C₄².₃₈₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:28C2	128,1834
C₄².₁₂C₄⋊₂₉C₂ = C₄².₂₂₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:29C2	128,1837
C₄².₁₂C₄⋊₃₀C₂ = C₄².₄₅₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:30C2	128,1838
C₄².₁₂C₄⋊₃₁C₂ = C₄².₄₅₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:31C2	128,1839
C₄².₁₂C₄⋊₃₂C₂ = C₄².₂₂₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:32C2	128,1840
C₄².₁₂C₄⋊₃₃C₂ = C₄².₂₆₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:33C2	128,1939
C₄².₁₂C₄⋊₃₄C₂ = C₄².₂₆₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:34C2	128,1942
C₄².₁₂C₄⋊₃₅C₂ = C₄².₂₆₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:35C2	128,1943
C₄².₁₂C₄⋊₃₆C₂ = C₄².₂₇₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:36C2	128,1944
C₄².₁₂C₄⋊₃₇C₂ = C₄².₂₈₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:37C2	128,1960
C₄².₁₂C₄⋊₃₈C₂ = C₄².₂₈₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:38C2	128,1964
C₄².₁₂C₄⋊₃₉C₂ = C₄².₂₈₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:39C2	128,1965
C₄².₁₂C₄⋊₄₀C₂ = C₄².₂₂₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:40C2	128,1833
C₄².₁₂C₄⋊₄₁C₂ = C₄².₂₂₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:41C2	128,1835
C₄².₁₂C₄⋊₄₂C₂ = C₄².₂₆₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:42C2	128,1938
C₄².₁₂C₄⋊₄₃C₂ = C₄².₂₆₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:43C2	128,1940
C₄².₁₂C₄⋊₄₄C₂ = C₄².₂₇₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:44C2	128,1959
C₄².₁₂C₄⋊₄₅C₂ = C₄².₆₇₇C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:45C2	128,1652
C₄².₁₂C₄⋊₄₆C₂ = C₄².₂₆₀C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:46C2	128,1654
C₄².₁₂C₄⋊₄₇C₂ = C₄².₂₆₂C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:47C2	128,1656
C₄².₁₂C₄⋊₄₈C₂ = C₄².₆₇₈C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:48C2	128,1657
C₄².₁₂C₄⋊₄₉C₂ = C₄².₂₉₀C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:49C2	128,1697
C₄².₁₂C₄⋊₅₀C₂ = C₄².₂₉₃C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:50C2	128,1700
C₄².₁₂C₄⋊₅₁C₂ = C₄².₂₉₄C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:51C2	128,1701
C₄².₁₂C₄⋊₅₂C₂ = D₄⋊₇M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:52C2	128,1706
C₄².₁₂C₄⋊₅₃C₂ = C₄².₆₉₃C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4:53C2	128,1707
C₄².₁₂C₄⋊₅₄C₂ = C₄².₆₉₄C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:54C2	128,1711
C₄².₁₂C₄⋊₅₅C₂ = C₄².₃₀₁C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:55C2	128,1713
C₄².₁₂C₄⋊₅₆C₂ = C₄².₆₉₈C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:56C2	128,1721
C₄².₁₂C₄⋊₅₇C₂ = D₄⋊₈M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:57C2	128,1722
C₄².₁₂C₄⋊₅₈C₂ = Q₈⋊₇M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:58C2	128,1723
C₄².₁₂C₄⋊₅₉C₂ = C₄².₃₀₈C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:59C2	128,1725
C₄².₁₂C₄⋊₆₀C₂ = C₄².₃₀₉C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4:60C2	128,1726
C₄².₁₂C₄⋊₆₁C₂ = C₈×C₄○D₄	φ: trivial image	64	C4^2.12C4:61C2	128,1696

Non-split extensions G=N.Q with N=C₄².₁₂C₄ and Q=C₂

extension	φ:Q→Out N	d	Label	ID
C₄².₁₂C₄.₁C₂ = C₄²⋊₁C₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4.1C2	128,6
C₄².₁₂C₄.₂C₂ = C₄².₂₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.2C2	128,7
C₄².₁₂C₄.₃C₂ = C₄²⋊₆C₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4.3C2	128,8
C₄².₁₂C₄.₄C₂ = M₄(2)⋊C₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.4C2	128,10
C₄².₁₂C₄.₅C₂ = C₄².₂Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.5C2	128,13
C₄².₁₂C₄.₆C₂ = C₄².₃Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.6C2	128,15
C₄².₁₂C₄.₇C₂ = C₄².₅Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4.7C2	128,18
C₄².₁₂C₄.₈C₂ = C₄².₂₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.8C2	128,19
C₄².₁₂C₄.₉C₂ = C₄².₃₈₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.9C2	128,31
C₄².₁₂C₄.₁₀C₂ = C₄².₃₈₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.10C2	128,33
C₄².₁₂C₄.₁₁C₂ = C₄².₃₇₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.11C2	128,34
C₄².₁₂C₄.₁₂C₂ = C₄².₁₀Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4.12C2	128,35
C₄².₁₂C₄.₁₃C₂ = C₄².₃₉₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.13C2	128,193
C₄².₁₂C₄.₁₄C₂ = C₄².₃₉₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.14C2	128,202
C₄².₁₂C₄.₁₅C₂ = C₄².₃₉₉D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.15C2	128,211
C₄².₁₂C₄.₁₆C₂ = C₄².₄₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.16C2	128,213
C₄².₁₂C₄.₁₇C₂ = C₄².₄₀₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.17C2	128,217
C₄².₁₂C₄.₁₈C₂ = Q₈⋊M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.18C2	128,219
C₄².₁₂C₄.₁₉C₂ = C₄².₅₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.19C2	128,229
C₄².₁₂C₄.₂₀C₂ = C₄².₄₀₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4.20C2	128,235
C₄².₁₂C₄.₂₁C₂ = C₄².₆₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	32	C4^2.12C4.21C2	128,250
C₄².₁₂C₄.₂₂C₂ = C₄².₄₁₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.22C2	128,274
C₄².₁₂C₄.₂₃C₂ = C₄².₄₁₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.23C2	128,276
C₄².₁₂C₄.₂₄C₂ = C₄².₄₁₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.24C2	128,278
C₄².₁₂C₄.₂₅C₂ = C₄².₄₁₅D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.25C2	128,280
C₄².₁₂C₄.₂₆C₂ = C₄².₄₁₆D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.26C2	128,281
C₄².₁₂C₄.₂₇C₂ = C₄².₄₁₈D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.27C2	128,286
C₄².₁₂C₄.₂₈C₂ = C₄².₄₂Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.28C2	128,296
C₄².₁₂C₄.₂₉C₂ = M₄(2)⋊₁C₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.29C2	128,297
C₄².₁₂C₄.₃₀C₂ = C₄².Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.30C2	128,304
C₄².₁₂C₄.₃₁C₂ = C₄².₂₁Q₈	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.31C2	128,306
C₄².₁₂C₄.₃₂C₂ = C₄².₆₉₅C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.32C2	128,1714
C₄².₁₂C₄.₃₃C₂ = C₄².₉₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.33C2	128,303
C₄².₁₂C₄.₃₄C₂ = C₄².₂₂₄D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.34C2	128,1836
C₄².₁₂C₄.₃₅C₂ = C₄².₂₆₇D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.35C2	128,1941
C₄².₁₂C₄.₃₆C₂ = C₄².₂₈₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.36C2	128,1962
C₄².₁₂C₄.₃₇C₂ = C₄².₉₂D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.37C2	128,305
C₄².₁₂C₄.₃₈C₂ = C₄².₂₈₃D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.38C2	128,1963
C₄².₁₂C₄.₃₉C₂ = C₄².₉₀D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.39C2	128,302
C₄².₁₂C₄.₄₀C₂ = C₄².₂₈₁D₄	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.40C2	128,1961
C₄².₁₂C₄.₄₁C₂ = C₈⋊₉M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.41C2	128,183
C₄².₁₂C₄.₄₂C₂ = C₂³.₂₇C₄²	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.42C2	128,184
C₄².₁₂C₄.₄₃C₂ = C₈²⋊₁₅C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.43C2	128,185
C₄².₁₂C₄.₄₄C₂ = C₈²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.44C2	128,186
C₄².₁₂C₄.₄₅C₂ = C₄².₃₀₂C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.45C2	128,1715
C₄².₁₂C₄.₄₆C₂ = Q₈.₄M₄(2)	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.46C2	128,1716
C₄².₁₂C₄.₄₇C₂ = C₄².₆₉₆C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.47C2	128,1717
C₄².₁₂C₄.₄₈C₂ = C₄².₃₀₄C₂³	φ: C₂/C₁ → C₂ ⊆ Out C₄².₁₂C₄	64	C4^2.12C4.48C2	128,1718
C₄².₁₂C₄.₄₉C₂ = C₈×M₄(2)	φ: trivial image	64	C4^2.12C4.49C2	128,181
C₄².₁₂C₄.₅₀C₂ = C₈²⋊C₂	φ: trivial image	64	C4^2.12C4.50C2	128,182

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Extensions 1→N→G→Q→1 with N=C42.12C4 and Q=C2

Extensions 1→N→G→Q→1 with N=C₄².₁₂C₄ and Q=C₂