Extensions 1→N→G→Q→1 with N=C₈₄ and Q=C₂

Direct product G=N×Q with N=C₈₄ and Q=C₂

		d	ρ	Label	ID
C₂×C₈₄		168		C2xC84	168,39

Semidirect products G=N:Q with N=C₈₄ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₄⋊₁C₂ = D₈₄	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	84	2+	C84:1C2	168,36
C₈₄⋊₂C₂ = C₄×D₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	84	2	C84:2C2	168,35
C₈₄⋊₃C₂ = C₃×D₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	84	2	C84:3C2	168,26
C₈₄⋊₄C₂ = C₁₂×D₇	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	84	2	C84:4C2	168,25
C₈₄⋊₅C₂ = C₇×D₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	84	2	C84:5C2	168,31
C₈₄⋊₆C₂ = S₃×C₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	84	2	C84:6C2	168,30
C₈₄⋊₇C₂ = D₄×C₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	84	2	C84:7C2	168,40

Non-split extensions G=N.Q with N=C₈₄ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₄.₁C₂ = Dic₄₂	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	168	2-	C84.1C2	168,34
C₈₄.₂C₂ = C₂₁⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	168	2	C84.2C2	168,5
C₈₄.₃C₂ = C₃×Dic₁₄	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	168	2	C84.3C2	168,24
C₈₄.₄C₂ = C₃×C₇⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	168	2	C84.4C2	168,4
C₈₄.₅C₂ = C₇×Dic₆	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	168	2	C84.5C2	168,29
C₈₄.₆C₂ = C₇×C₃⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	168	2	C84.6C2	168,3
C₈₄.₇C₂ = Q₈×C₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₈₄	168	2	C84.7C2	168,41

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁