Extensions 1→N→G→Q→1 with N=C₁₁₂ and Q=C₂²

Direct product G=N×Q with N=C₁₁₂ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₁₁₂		448		C2^2xC112	448,910

Semidirect products G=N:Q with N=C₁₁₂ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₁₂⋊₁C₂² = C₁₆⋊D₁₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	112	4+	C112:1C2^2	448,442
C₁₁₂⋊₂C₂² = D₇×D₁₆	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	112	4+	C112:2C2^2	448,444
C₁₁₂⋊₃C₂² = D₁₁₂⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	112	4+	C112:3C2^2	448,448
C₁₁₂⋊₄C₂² = D₈⋊D₁₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	112	4	C112:4C2^2	448,445
C₁₁₂⋊₅C₂² = D₇×SD₃₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	112	4	C112:5C2^2	448,447
C₁₁₂⋊₆C₂² = C₇×C₁₆⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	112	4	C112:6C2^2	448,917
C₁₁₂⋊₇C₂² = D₇×M₅(2)	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	112	4	C112:7C2^2	448,440
C₁₁₂⋊₈C₂² = C₂×D₁₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224		C112:8C2^2	448,436
C₁₁₂⋊₉C₂² = C₂×C₁₁₂⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224		C112:9C2^2	448,437
C₁₁₂⋊₁₀C₂² = C₁₄×D₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224		C112:10C2^2	448,913
C₁₁₂⋊₁₁C₂² = D₇×C₂×C₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224		C112:11C2^2	448,433
C₁₁₂⋊₁₂C₂² = C₂×C₁₆⋊D₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224		C112:12C2^2	448,434
C₁₁₂⋊₁₃C₂² = C₁₄×SD₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224		C112:13C2^2	448,914
C₁₁₂⋊₁₄C₂² = C₁₄×M₅(2)	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224		C112:14C2^2	448,911

Non-split extensions G=N.Q with N=C₁₁₂ and Q=C₂²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₁₂.₁C₂² = C₁₆.D₁₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4-	C112.1C2^2	448,443
C₁₁₂.₂C₂² = C₇⋊D₃₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4+	C112.2C2^2	448,76
C₁₁₂.₃C₂² = D₁₆.D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4-	C112.3C2^2	448,77
C₁₁₂.₄C₂² = C₇⋊SD₆₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4+	C112.4C2^2	448,78
C₁₁₂.₅C₂² = C₇⋊Q₆₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	448	4-	C112.5C2^2	448,79
C₁₁₂.₆C₂² = D₁₆⋊₃D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4-	C112.6C2^2	448,446
C₁₁₂.₇C₂² = D₇×Q₃₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4-	C112.7C2^2	448,451
C₁₁₂.₈C₂² = Q₃₂⋊₃D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4+	C112.8C2^2	448,453
C₁₁₂.₉C₂² = SD₃₂⋊D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4-	C112.9C2^2	448,449
C₁₁₂.₁₀C₂² = Q₃₂⋊D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4	C112.10C2^2	448,452
C₁₁₂.₁₁C₂² = SD₃₂⋊₃D₇	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4	C112.11C2^2	448,450
C₁₁₂.₁₂C₂² = C₇×Q₃₂⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4	C112.12C2^2	448,918
C₁₁₂.₁₃C₂² = C₁₆.₁₂D₁₄	φ: C₂²/C₁ → C₂² ⊆ Aut C₁₁₂	224	4	C112.13C2^2	448,441
C₁₁₂.₁₄C₂² = D₂₂₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2+	C112.14C2^2	448,5
C₁₁₂.₁₅C₂² = C₂₂₄⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.15C2^2	448,6
C₁₁₂.₁₆C₂² = Dic₁₁₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	448	2-	C112.16C2^2	448,7
C₁₁₂.₁₇C₂² = C₂×Dic₅₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112.17C2^2	448,439
C₁₁₂.₁₈C₂² = D₁₁₂⋊₇C₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.18C2^2	448,438
C₁₁₂.₁₉C₂² = C₇×D₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.19C2^2	448,175
C₁₁₂.₂₀C₂² = C₇×SD₆₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.20C2^2	448,176
C₁₁₂.₂₁C₂² = C₇×Q₆₄	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	448	2	C112.21C2^2	448,177
C₁₁₂.₂₂C₂² = C₁₄×Q₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112.22C2^2	448,915
C₁₁₂.₂₃C₂² = C₇×C₄○D₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.23C2^2	448,916
C₁₁₂.₂₄C₂² = D₇×C₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.24C2^2	448,3
C₁₁₂.₂₅C₂² = C₃₂⋊D₇	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.25C2^2	448,4
C₁₁₂.₂₆C₂² = C₂×C₇⋊C₃₂	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	448		C112.26C2^2	448,55
C₁₁₂.₂₇C₂² = C₇⋊M₆(2)	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.27C2^2	448,56
C₁₁₂.₂₈C₂² = D₂₈.₄C₈	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.28C2^2	448,435
C₁₁₂.₂₉C₂² = C₇×D₄○C₁₆	φ: C₂²/C₂ → C₂ ⊆ Aut C₁₁₂	224	2	C112.29C2^2	448,912
C₁₁₂.₃₀C₂² = C₇×M₆(2)	central extension (φ=1)	224	2	C112.30C2^2	448,174

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Extensions 1→N→G→Q→1 with N=C112 and Q=C22

Extensions 1→N→G→Q→1 with N=C₁₁₂ and Q=C₂²