Extensions 1→N→G→Q→1 with N=C₅₆ and Q=C₆

Direct product G=N×Q with N=C₅₆ and Q=C₆

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

Semidirect products G=N:Q with N=C₅₆ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆⋊₁C₆ = D₅₆⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6+	C56:1C6	336,10
C₅₆⋊₂C₆ = C₅₆⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:2C6	336,9
C₅₆⋊₃C₆ = C₈×F₇	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:3C6	336,7
C₅₆⋊₄C₆ = C₈⋊F₇	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:4C6	336,8
C₅₆⋊₅C₆ = D₈×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:5C6	336,53
C₅₆⋊₆C₆ = SD₁₆×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:6C6	336,54
C₅₆⋊₇C₆ = M₄(2)×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:7C6	336,52
C₅₆⋊₈C₆ = C₂×C₈×C₇⋊C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₅₆	112		C56:8C6	336,51
C₅₆⋊₉C₆ = C₃×D₅₆	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:9C6	336,61
C₅₆⋊₁₀C₆ = C₃×C₅₆⋊C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:10C6	336,60
C₅₆⋊₁₁C₆ = D₇×C₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:11C6	336,58
C₅₆⋊₁₂C₆ = C₃×C₈⋊D₇	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:12C6	336,59
C₅₆⋊₁₃C₆ = D₈×C₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:13C6	336,111
C₅₆⋊₁₄C₆ = SD₁₆×C₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:14C6	336,112
C₅₆⋊₁₅C₆ = M₄(2)×C₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:15C6	336,110

Non-split extensions G=N.Q with N=C₅₆ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₅₆.₁C₆ = C₈.F₇	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	112	6-	C56.1C6	336,11
C₅₆.₂C₆ = C₇⋊C₄₈	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	112	6	C56.2C6	336,1
C₅₆.₃C₆ = Q₁₆×C₇⋊C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	112	6	C56.3C6	336,55
C₅₆.₄C₆ = C₁₆×C₇⋊C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₅₆	112	3	C56.4C6	336,2
C₅₆.₅C₆ = C₃×Dic₂₈	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.5C6	336,62
C₅₆.₆C₆ = C₃×C₇⋊C₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.6C6	336,4
C₅₆.₇C₆ = Q₁₆×C₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.7C6	336,113

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