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

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

		d	ρ	Label	ID
C₂xC₁₆₈		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 = C₈xF₇	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 = D₈xC₇:C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:5C6	336,53
C₅₆:₆C₆ = SD₁₆xC₇:C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:6C6	336,54
C₅₆:₇C₆ = M₄(2)xC₇:C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	56	6	C56:7C6	336,52
C₅₆:₈C₆ = C₂xC₈xC₇:C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₅₆	112		C56:8C6	336,51
C₅₆:₉C₆ = C₃xD₅₆	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:9C6	336,61
C₅₆:₁₀C₆ = C₃xC₅₆:C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:10C6	336,60
C₅₆:₁₁C₆ = D₇xC₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:11C6	336,58
C₅₆:₁₂C₆ = C₃xC₈:D₇	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:12C6	336,59
C₅₆:₁₃C₆ = D₈xC₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:13C6	336,111
C₅₆:₁₄C₆ = SD₁₆xC₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	168	2	C56:14C6	336,112
C₅₆:₁₅C₆ = M₄(2)xC₂₁	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 = Q₁₆xC₇:C₃	φ: C₆/C₁ → C₆ ⊆ Aut C₅₆	112	6	C56.3C6	336,55
C₅₆.₄C₆ = C₁₆xC₇:C₃	φ: C₆/C₂ → C₃ ⊆ Aut C₅₆	112	3	C56.4C6	336,2
C₅₆.₅C₆ = C₃xDic₂₈	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.5C6	336,62
C₅₆.₆C₆ = C₃xC₇:C₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.6C6	336,4
C₅₆.₇C₆ = Q₁₆xC₂₁	φ: C₆/C₃ → C₂ ⊆ Aut C₅₆	336	2	C56.7C6	336,113

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