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

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

		d	ρ	Label	ID
C₂²×C₈₄		336		C2^2xC84	336,204

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄⋊(C₂×C₄₂) = D₄×C₄₂	φ: C₂×C₄₂/C₄₂ → C₂ ⊆ Aut C₄	168		C4:(C2xC42)	336,205

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₄.₁(C₂×C₄₂) = D₈×C₂₁	φ: C₂×C₄₂/C₄₂ → C₂ ⊆ Aut C₄	168	2	C4.1(C2xC42)	336,111
C₄.₂(C₂×C₄₂) = SD₁₆×C₂₁	φ: C₂×C₄₂/C₄₂ → C₂ ⊆ Aut C₄	168	2	C4.2(C2xC42)	336,112
C₄.₃(C₂×C₄₂) = Q₁₆×C₂₁	φ: C₂×C₄₂/C₄₂ → C₂ ⊆ Aut C₄	336	2	C4.3(C2xC42)	336,113
C₄.₄(C₂×C₄₂) = Q₈×C₄₂	φ: C₂×C₄₂/C₄₂ → C₂ ⊆ Aut C₄	336		C4.4(C2xC42)	336,206
C₄.₅(C₂×C₄₂) = C₄○D₄×C₂₁	φ: C₂×C₄₂/C₄₂ → C₂ ⊆ Aut C₄	168	2	C4.5(C2xC42)	336,207
C₄.₆(C₂×C₄₂) = M₄(2)×C₂₁	central extension (φ=1)	168	2	C4.6(C2xC42)	336,110

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁