Extensions 1→N→G→Q→1 with N=C₄ and Q=C₂²×C₂₂

Direct product G=N×Q with N=C₄ and Q=C₂²×C₂₂

		d	ρ	Label	ID
C₂³×C₄₄		352		C2^3xC44	352,188

Semidirect products G=N:Q with N=C₄ and Q=C₂²×C₂₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₂²×C₂₂) = D₄×C₂×C₂₂	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	176		C4:(C2^2xC22)	352,189

Non-split extensions G=N.Q with N=C₄ and Q=C₂²×C₂₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂²×C₂₂) = D₈×C₂₂	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	176		C4.1(C2^2xC22)	352,167
C₄.₂(C₂²×C₂₂) = SD₁₆×C₂₂	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	176		C4.2(C2^2xC22)	352,168
C₄.₃(C₂²×C₂₂) = Q₁₆×C₂₂	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	352		C4.3(C2^2xC22)	352,169
C₄.₄(C₂²×C₂₂) = C₁₁×C₄○D₈	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	176	2	C4.4(C2^2xC22)	352,170
C₄.₅(C₂²×C₂₂) = C₁₁×C₈⋊C₂²	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	88	4	C4.5(C2^2xC22)	352,171
C₄.₆(C₂²×C₂₂) = C₁₁×C₈.C₂²	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	176	4	C4.6(C2^2xC22)	352,172
C₄.₇(C₂²×C₂₂) = Q₈×C₂×C₂₂	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	352		C4.7(C2^2xC22)	352,190
C₄.₈(C₂²×C₂₂) = C₄○D₄×C₂₂	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	176		C4.8(C2^2xC22)	352,191
C₄.₉(C₂²×C₂₂) = C₁₁×2₊¹⁺⁴	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	88	4	C4.9(C2^2xC22)	352,192
C₄.₁₀(C₂²×C₂₂) = C₁₁×2_-¹⁺⁴	φ: C₂²×C₂₂/C₂×C₂₂ → C₂ ⊆ Aut C₄	176	4	C4.10(C2^2xC22)	352,193
C₄.₁₁(C₂²×C₂₂) = M₄(2)×C₂₂	central extension (φ=1)	176		C4.11(C2^2xC22)	352,165
C₄.₁₂(C₂²×C₂₂) = C₁₁×C₈○D₄	central extension (φ=1)	176	2	C4.12(C2^2xC22)	352,166

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁