Extensions 1→N→G→Q→1 with N=C₈₄ and Q=C₄

Direct product G=N×Q with N=C₈₄ and Q=C₄

		d	ρ	Label	ID
C₄×C₈₄		336		C4xC84	336,106

Semidirect products G=N:Q with N=C₈₄ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₄⋊₁C₄ = C₈₄⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84:1C4	336,99
C₈₄⋊₂C₄ = C₄×Dic₂₁	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84:2C4	336,97
C₈₄⋊₃C₄ = C₃×C₄⋊Dic₇	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84:3C4	336,67
C₈₄⋊₄C₄ = C₁₂×Dic₇	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84:4C4	336,65
C₈₄⋊₅C₄ = C₇×C₄⋊Dic₃	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84:5C4	336,83
C₈₄⋊₆C₄ = Dic₃×C₂₈	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84:6C4	336,81
C₈₄⋊₇C₄ = C₄⋊C₄×C₂₁	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84:7C4	336,108

Non-split extensions G=N.Q with N=C₈₄ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₈₄.₁C₄ = C₈₄.C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	168	2	C84.1C4	336,96
C₈₄.₂C₄ = C₂₁⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336	2	C84.2C4	336,5
C₈₄.₃C₄ = C₂×C₂₁⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84.3C4	336,95
C₈₄.₄C₄ = C₃×C₄.Dic₇	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	168	2	C84.4C4	336,64
C₈₄.₅C₄ = C₃×C₇⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336	2	C84.5C4	336,4
C₈₄.₆C₄ = C₆×C₇⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84.6C4	336,63
C₈₄.₇C₄ = C₇×C₄.Dic₃	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	168	2	C84.7C4	336,80
C₈₄.₈C₄ = C₇×C₃⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336	2	C84.8C4	336,3
C₈₄.₉C₄ = C₁₄×C₃⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	336		C84.9C4	336,79
C₈₄.₁₀C₄ = M₄(2)×C₂₁	φ: C₄/C₂ → C₂ ⊆ Aut C₈₄	168	2	C84.10C4	336,110

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