Extensions 1→N→G→Q→1 with N=C₁₆₈ and Q=C₂

Direct product G=N×Q with N=C₁₆₈ and Q=C₂

		d	ρ	Label	ID
C₂×C₁₆₈		336		C2xC168	336,109

Semidirect products G=N:Q with N=C₁₆₈ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₆₈⋊₁C₂ = D₁₆₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2+	C168:1C2	336,93
C₁₆₈⋊₂C₂ = C₈⋊D₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:2C2	336,92
C₁₆₈⋊₃C₂ = C₃×D₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:3C2	336,61
C₁₆₈⋊₄C₂ = C₈×D₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:4C2	336,90
C₁₆₈⋊₅C₂ = C₅₆⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:5C2	336,91
C₁₆₈⋊₆C₂ = C₃×C₅₆⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:6C2	336,60
C₁₆₈⋊₇C₂ = C₇×D₂₄	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:7C2	336,77
C₁₆₈⋊₈C₂ = D₇×C₂₄	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:8C2	336,58
C₁₆₈⋊₉C₂ = C₃×C₈⋊D₇	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:9C2	336,59
C₁₆₈⋊₁₀C₂ = C₇×C₂₄⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:10C2	336,76
C₁₆₈⋊₁₁C₂ = D₈×C₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:11C2	336,111
C₁₆₈⋊₁₂C₂ = S₃×C₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:12C2	336,74
C₁₆₈⋊₁₃C₂ = C₇×C₈⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:13C2	336,75
C₁₆₈⋊₁₄C₂ = SD₁₆×C₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:14C2	336,112
C₁₆₈⋊₁₅C₂ = M₄(2)×C₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	168	2	C168:15C2	336,110

Non-split extensions G=N.Q with N=C₁₆₈ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₆₈.₁C₂ = Dic₈₄	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	336	2-	C168.1C2	336,94
C₁₆₈.₂C₂ = C₃×Dic₂₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	336	2	C168.2C2	336,62
C₁₆₈.₃C₂ = C₂₁⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	336	2	C168.3C2	336,5
C₁₆₈.₄C₂ = C₇×Dic₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	336	2	C168.4C2	336,78
C₁₆₈.₅C₂ = C₃×C₇⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	336	2	C168.5C2	336,4
C₁₆₈.₆C₂ = Q₁₆×C₂₁	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	336	2	C168.6C2	336,113
C₁₆₈.₇C₂ = C₇×C₃⋊C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₆₈	336	2	C168.7C2	336,3

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