Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂³

Direct product G=N×Q with N=C₂³ and Q=C₂³

		d	ρ	Label	ID
C₂⁶		64		C2^6	64,267

Semidirect products G=N:Q with N=C₂³ and Q=C₂³

extension	φ:Q→Aut N	d	Label	ID
C₂³⋊₁C₂³ = C₂×C₂²≀C₂	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16	C2^3:1C2^3	64,202
C₂³⋊₂C₂³ = C₂×2₊¹⁺⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16	C2^3:2C2^3	64,264
C₂³⋊₃C₂³ = D₄×C₂³	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32	C2^3:3C2^3	64,261

Non-split extensions G=N.Q with N=C₂³ and Q=C₂³

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁C₂³ = C₂×C₂³⋊C₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16		C2^3.1C2^3	64,90
C₂³.₂C₂³ = C₂³.C₂³	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16	4	C2^3.2C2^3	64,91
C₂³.₃C₂³ = C₂≀C₂²	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	8	4+	C2^3.3C2^3	64,138
C₂³.₄C₂³ = C₂³.₇D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16	4	C2^3.4C2^3	64,139
C₂³.₅C₂³ = C₂×C₄⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.5C2^3	64,203
C₂³.₆C₂³ = C₂².₁₉C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16		C2^3.6C2^3	64,206
C₂³.₇C₂³ = C₂×C₄.₄D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.7C2^3	64,207
C₂³.₈C₂³ = C₂×C₄⋊₁D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.8C2^3	64,211
C₂³.₉C₂³ = C₂².₂₆C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.9C2^3	64,213
C₂³.₁₀C₂³ = C₂³⋊₃D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16		C2^3.10C2^3	64,215
C₂³.₁₁C₂³ = C₂².₂₉C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16		C2^3.11C2^3	64,216
C₂³.₁₂C₂³ = C₂².₃₁C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.12C2^3	64,218
C₂³.₁₃C₂³ = C₂².₃₂C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16		C2^3.13C2^3	64,219
C₂³.₁₄C₂³ = C₂².₃₄C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.14C2^3	64,221
C₂³.₁₅C₂³ = C₂².₃₅C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.15C2^3	64,222
C₂³.₁₆C₂³ = C₂².₃₆C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.16C2^3	64,223
C₂³.₁₇C₂³ = Q₈⋊₆D₄	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.17C2^3	64,231
C₂³.₁₈C₂³ = C₂².₄₅C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16		C2^3.18C2^3	64,232
C₂³.₁₉C₂³ = C₂².₄₇C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.19C2^3	64,234
C₂³.₂₀C₂³ = C₂².₄₉C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.20C2^3	64,236
C₂³.₂₁C₂³ = C₂².₅₀C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.21C2^3	64,237
C₂³.₂₂C₂³ = C₂².₅₃C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.22C2^3	64,240
C₂³.₂₃C₂³ = C₂².₅₄C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16		C2^3.23C2^3	64,241
C₂³.₂₄C₂³ = C₂⁴⋊C₂²	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16		C2^3.24C2^3	64,242
C₂³.₂₅C₂³ = C₂².₅₆C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.25C2^3	64,243
C₂³.₂₆C₂³ = C₂².₅₇C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	32		C2^3.26C2^3	64,244
C₂³.₂₇C₂³ = C₂.C₂⁵	φ: C₂³/C₂ → C₂² ⊆ Aut C₂³	16	4	C2^3.27C2^3	64,266
C₂³.₂₈C₂³ = C₂×C₄²⋊C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.28C2^3	64,195
C₂³.₂₉C₂³ = C₂×C₄×D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.29C2^3	64,196
C₂³.₃₀C₂³ = C₄×C₄○D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.30C2^3	64,198
C₂³.₃₁C₂³ = C₂².₁₁C₂⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	16		C2^3.31C2^3	64,199
C₂³.₃₂C₂³ = C₂³.₃₂C₂³	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.32C2^3	64,200
C₂³.₃₃C₂³ = C₂³.₃₃C₂³	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.33C2^3	64,201
C₂³.₃₄C₂³ = C₂×C₂²⋊Q₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.34C2^3	64,204
C₂³.₃₅C₂³ = C₂×C₂².D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.35C2^3	64,205
C₂³.₃₆C₂³ = C₂³.₃₆C₂³	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.36C2^3	64,210
C₂³.₃₇C₂³ = C₂³.₃₇C₂³	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.37C2^3	64,214
C₂³.₃₈C₂³ = C₂³.₃₈C₂³	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.38C2^3	64,217
C₂³.₃₉C₂³ = C₂².₃₃C₂⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.39C2^3	64,220
C₂³.₄₀C₂³ = C₂³⋊₂Q₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	16		C2^3.40C2^3	64,224
C₂³.₄₁C₂³ = C₂³.₄₁C₂³	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.41C2^3	64,225
C₂³.₄₂C₂³ = D₄²	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	16		C2^3.42C2^3	64,226
C₂³.₄₃C₂³ = D₄⋊₅D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	16		C2^3.43C2^3	64,227
C₂³.₄₄C₂³ = D₄⋊₆D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.44C2^3	64,228
C₂³.₄₅C₂³ = Q₈⋊₅D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.45C2^3	64,229
C₂³.₄₆C₂³ = D₄×Q₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.46C2^3	64,230
C₂³.₄₇C₂³ = C₂².₄₆C₂⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.47C2^3	64,233
C₂³.₄₈C₂³ = D₄⋊₃Q₈	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.48C2^3	64,235
C₂³.₄₉C₂³ = C₂²×C₄○D₄	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.49C2^3	64,263
C₂³.₅₀C₂³ = C₂×2_-¹⁺⁴	φ: C₂³/C₂² → C₂ ⊆ Aut C₂³	32		C2^3.50C2^3	64,265
C₂³.₅₁C₂³ = C₂×C₂.C₄²	central extension (φ=1)	64		C2^3.51C2^3	64,56
C₂³.₅₂C₂³ = C₄²⋊₄C₄	central extension (φ=1)	64		C2^3.52C2^3	64,57
C₂³.₅₃C₂³ = C₄×C₂²⋊C₄	central extension (φ=1)	32		C2^3.53C2^3	64,58
C₂³.₅₄C₂³ = C₄×C₄⋊C₄	central extension (φ=1)	64		C2^3.54C2^3	64,59
C₂³.₅₅C₂³ = C₂⁴⋊₃C₄	central extension (φ=1)	16		C2^3.55C2^3	64,60
C₂³.₅₆C₂³ = C₂³.₇Q₈	central extension (φ=1)	32		C2^3.56C2^3	64,61
C₂³.₅₇C₂³ = C₂³.₃₄D₄	central extension (φ=1)	32		C2^3.57C2^3	64,62
C₂³.₅₈C₂³ = C₄²⋊₈C₄	central extension (φ=1)	64		C2^3.58C2^3	64,63
C₂³.₅₉C₂³ = C₄²⋊₅C₄	central extension (φ=1)	64		C2^3.59C2^3	64,64
C₂³.₆₀C₂³ = C₄²⋊₉C₄	central extension (φ=1)	64		C2^3.60C2^3	64,65
C₂³.₆₁C₂³ = C₂³.₈Q₈	central extension (φ=1)	32		C2^3.61C2^3	64,66
C₂³.₆₂C₂³ = C₂³.₂₃D₄	central extension (φ=1)	32		C2^3.62C2^3	64,67
C₂³.₆₃C₂³ = C₂³.₆₃C₂³	central extension (φ=1)	64		C2^3.63C2^3	64,68
C₂³.₆₄C₂³ = C₂⁴.C₂²	central extension (φ=1)	32		C2^3.64C2^3	64,69
C₂³.₆₅C₂³ = C₂³.₆₅C₂³	central extension (φ=1)	64		C2^3.65C2^3	64,70
C₂³.₆₆C₂³ = C₂⁴.₃C₂²	central extension (φ=1)	32		C2^3.66C2^3	64,71
C₂³.₆₇C₂³ = C₂³.₆₇C₂³	central extension (φ=1)	64		C2^3.67C2^3	64,72
C₂³.₆₈C₂³ = C₂²×C₂²⋊C₄	central extension (φ=1)	32		C2^3.68C2^3	64,193
C₂³.₆₉C₂³ = C₂²×C₄⋊C₄	central extension (φ=1)	64		C2^3.69C2^3	64,194
C₂³.₇₀C₂³ = C₂×C₄×Q₈	central extension (φ=1)	64		C2^3.70C2^3	64,197
C₂³.₇₁C₂³ = C₂×C₄².C₂	central extension (φ=1)	64		C2^3.71C2^3	64,208
C₂³.₇₂C₂³ = C₂×C₄²⋊₂C₂	central extension (φ=1)	32		C2^3.72C2^3	64,209
C₂³.₇₃C₂³ = C₂×C₄⋊Q₈	central extension (φ=1)	64		C2^3.73C2^3	64,212
C₂³.₇₄C₂³ = Q₈×C₂³	central extension (φ=1)	64		C2^3.74C2^3	64,262
C₂³.₇₅C₂³ = C₂³⋊₂D₄	central stem extension (φ=1)	32		C2^3.75C2^3	64,73
C₂³.₇₆C₂³ = C₂³⋊Q₈	central stem extension (φ=1)	32		C2^3.76C2^3	64,74
C₂³.₇₇C₂³ = C₂³.₁₀D₄	central stem extension (φ=1)	32		C2^3.77C2^3	64,75
C₂³.₇₈C₂³ = C₂³.₇₈C₂³	central stem extension (φ=1)	64		C2^3.78C2^3	64,76
C₂³.₇₉C₂³ = C₂³.Q₈	central stem extension (φ=1)	32		C2^3.79C2^3	64,77
C₂³.₈₀C₂³ = C₂³.₁₁D₄	central stem extension (φ=1)	32		C2^3.80C2^3	64,78
C₂³.₈₁C₂³ = C₂³.₈₁C₂³	central stem extension (φ=1)	64		C2^3.81C2^3	64,79
C₂³.₈₂C₂³ = C₂³.₄Q₈	central stem extension (φ=1)	32		C2^3.82C2^3	64,80
C₂³.₈₃C₂³ = C₂³.₈₃C₂³	central stem extension (φ=1)	64		C2^3.83C2^3	64,81
C₂³.₈₄C₂³ = C₂³.₈₄C₂³	central stem extension (φ=1)	64		C2^3.84C2^3	64,82

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Extensions 1→N→G→Q→1 with N=C23 and Q=C23

Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂³