Extensions 1→N→G→Q→1 with N=C₁₁₂ and Q=C₂

Direct product G=N×Q with N=C₁₁₂ and Q=C₂

		d	ρ	Label	ID
C₂×C₁₁₂		224		C2xC112	224,58

Semidirect products G=N:Q with N=C₁₁₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₁₂⋊₁C₂ = D₁₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	112	2+	C112:1C2	224,5
C₁₁₂⋊₂C₂ = C₁₁₂⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	112	2	C112:2C2	224,6
C₁₁₂⋊₃C₂ = C₇×D₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	112	2	C112:3C2	224,60
C₁₁₂⋊₄C₂ = D₇×C₁₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	112	2	C112:4C2	224,3
C₁₁₂⋊₅C₂ = C₁₆⋊D₇	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	112	2	C112:5C2	224,4
C₁₁₂⋊₆C₂ = C₇×SD₃₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	112	2	C112:6C2	224,61
C₁₁₂⋊₇C₂ = C₇×M₅(2)	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	112	2	C112:7C2	224,59

Non-split extensions G=N.Q with N=C₁₁₂ and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₁₂.₁C₂ = Dic₅₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	224	2-	C112.1C2	224,7
C₁₁₂.₂C₂ = C₇×Q₃₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	224	2	C112.2C2	224,62
C₁₁₂.₃C₂ = C₇⋊C₃₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₁₂	224	2	C112.3C2	224,1

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