Extensions 1→N→G→Q→1 with N=C₁₁₂ and Q=C₄

Direct product G=N×Q with N=C₁₁₂ and Q=C₄

		d	ρ	Label	ID
C₄×C₁₁₂		448		C4xC112	448,149

Semidirect products G=N:Q with N=C₁₁₂ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₁₂⋊₁C₄ = C₁₆⋊Dic₇	φ: C₄/C₁ → C₄ ⊆ Aut C₁₁₂	112	4	C112:1C4	448,70
C₁₁₂⋊₂C₄ = C₁₁₂⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₁₁₂	112	4	C112:2C4	448,69
C₁₁₂⋊₃C₄ = C₇×C₈.Q₈	φ: C₄/C₁ → C₄ ⊆ Aut C₁₁₂	112	4	C112:3C4	448,169
C₁₁₂⋊₄C₄ = C₇×C₁₆⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₁₁₂	112	4	C112:4C4	448,151
C₁₁₂⋊₅C₄ = C₁₁₂⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112:5C4	448,61
C₁₁₂⋊₆C₄ = C₁₁₂⋊₆C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112:6C4	448,62
C₁₁₂⋊₇C₄ = C₇×C₁₆⋊₃C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112:7C4	448,170
C₁₁₂⋊₈C₄ = C₁₆×Dic₇	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112:8C4	448,57
C₁₁₂⋊₉C₄ = C₁₁₂⋊₉C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112:9C4	448,59
C₁₁₂⋊₁₀C₄ = C₇×C₁₆⋊₄C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112:10C4	448,171
C₁₁₂⋊₁₁C₄ = C₇×C₁₆⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112:11C4	448,150

Non-split extensions G=N.Q with N=C₁₁₂ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₁₂.₁C₄ = C₁₁₂.C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.1C4	448,63
C₁₁₂.₂C₄ = C₇⋊C₆₄	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448	2	C112.2C4	448,1
C₁₁₂.₃C₄ = C₂×C₇⋊C₃₂	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112.3C4	448,55
C₁₁₂.₄C₄ = C₇⋊M₆(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.4C4	448,56
C₁₁₂.₅C₄ = C₇×C₈.₄Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.5C4	448,172
C₁₁₂.₆C₄ = C₇×M₆(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.6C4	448,174

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