Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₂×C₂₂

Direct product G=N×Q with N=C₂³ and Q=C₂×C₂₂

		d	ρ	Label	ID
C₂⁴×C₂₂		352		C2^4xC22	352,195

Semidirect products G=N:Q with N=C₂³ and Q=C₂×C₂₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁(C₂×C₂₂) = C₁₁×C₂²≀C₂	φ: C₂×C₂₂/C₁₁ → C₂² ⊆ Aut C₂³	88		C2^3:1(C2xC22)	352,155
C₂³⋊₂(C₂×C₂₂) = C₁₁×2₊¹⁺⁴	φ: C₂×C₂₂/C₁₁ → C₂² ⊆ Aut C₂³	88	4	C2^3:2(C2xC22)	352,192
C₂³⋊₃(C₂×C₂₂) = D₄×C₂×C₂₂	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Aut C₂³	176		C2^3:3(C2xC22)	352,189

Non-split extensions G=N.Q with N=C₂³ and Q=C₂×C₂₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁(C₂×C₂₂) = C₁₁×C₂³⋊C₄	φ: C₂×C₂₂/C₁₁ → C₂² ⊆ Aut C₂³	88	4	C2^3.1(C2xC22)	352,48
C₂³.₂(C₂×C₂₂) = C₁₁×C₄.₄D₄	φ: C₂×C₂₂/C₁₁ → C₂² ⊆ Aut C₂³	176		C2^3.2(C2xC22)	352,159
C₂³.₃(C₂×C₂₂) = C₁₁×C₄²⋊₂C₂	φ: C₂×C₂₂/C₁₁ → C₂² ⊆ Aut C₂³	176		C2^3.3(C2xC22)	352,161
C₂³.₄(C₂×C₂₂) = C₁₁×C₄⋊₁D₄	φ: C₂×C₂₂/C₁₁ → C₂² ⊆ Aut C₂³	176		C2^3.4(C2xC22)	352,162
C₂³.₅(C₂×C₂₂) = C₂²⋊C₄×C₂₂	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Aut C₂³	176		C2^3.5(C2xC22)	352,150
C₂³.₆(C₂×C₂₂) = C₁₁×C₄²⋊C₂	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Aut C₂³	176		C2^3.6(C2xC22)	352,152
C₂³.₇(C₂×C₂₂) = D₄×C₄₄	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Aut C₂³	176		C2^3.7(C2xC22)	352,153
C₂³.₈(C₂×C₂₂) = C₁₁×C₄⋊D₄	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Aut C₂³	176		C2^3.8(C2xC22)	352,156
C₂³.₉(C₂×C₂₂) = C₁₁×C₂²⋊Q₈	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Aut C₂³	176		C2^3.9(C2xC22)	352,157
C₂³.₁₀(C₂×C₂₂) = C₁₁×C₂².D₄	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Aut C₂³	176		C2^3.10(C2xC22)	352,158
C₂³.₁₁(C₂×C₂₂) = C₄○D₄×C₂₂	φ: C₂×C₂₂/C₂₂ → C₂ ⊆ Aut C₂³	176		C2^3.11(C2xC22)	352,191
C₂³.₁₂(C₂×C₂₂) = C₁₁×C₂.C₄²	central extension (φ=1)	352		C2^3.12(C2xC22)	352,44
C₂³.₁₃(C₂×C₂₂) = C₄⋊C₄×C₂₂	central extension (φ=1)	352		C2^3.13(C2xC22)	352,151
C₂³.₁₄(C₂×C₂₂) = Q₈×C₂×C₂₂	central extension (φ=1)	352		C2^3.14(C2xC22)	352,190

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