Extensions 1→N→G→Q→1 with N=C₁₂² and Q=C₂

Direct product G=N×Q with N=C₁₂² and Q=C₂

		d	ρ	Label	ID
C₂×C₁₂²		288		C2xC12^2	288,811

Semidirect products G=N:Q with N=C₁₂² and Q=C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₁₂²⋊₁C₂ = C₃×C₄²⋊₃S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96		C12^2:1C2	288,647
C₁₂²⋊₂C₂ = C₁₂²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:2C2	288,733
C₁₂²⋊₃C₂ = C₃²×C₄²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:3C2	288,814
C₁₂²⋊₄C₂ = C₃²×C₄²⋊₂C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:4C2	288,823
C₁₂²⋊₅C₂ = C₁₂⋊₄D₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:5C2	288,731
C₁₂²⋊₆C₂ = C₁₂²⋊₆C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:6C2	288,732
C₁₂²⋊₇C₂ = C₁₂²⋊C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	72		C12^2:7C2	288,280
C₁₂²⋊₈C₂ = C₄×C₁₂⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:8C2	288,730
C₁₂²⋊₉C₂ = C₃×C₄²⋊₄S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	24	2	C12^2:9C2	288,239
C₁₂²⋊₁₀C₂ = C₁₂×D₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96		C12^2:10C2	288,644
C₁₂²⋊₁₁C₂ = C₃×C₄⋊D₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96		C12^2:11C2	288,645
C₁₂²⋊₁₂C₂ = C₃×C₄²⋊₇S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96		C12^2:12C2	288,646
C₁₂²⋊₁₃C₂ = S₃×C₄×C₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96		C12^2:13C2	288,642
C₁₂²⋊₁₄C₂ = C₃×C₄²⋊₂S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96		C12^2:14C2	288,643
C₁₂²⋊₁₅C₂ = C₄²×C₃⋊S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:15C2	288,728
C₁₂²⋊₁₆C₂ = C₁₂²⋊₁₆C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:16C2	288,729
C₁₂²⋊₁₇C₂ = C₃²×C₄≀C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	72		C12^2:17C2	288,322
C₁₂²⋊₁₈C₂ = D₄×C₃×C₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:18C2	288,815
C₁₂²⋊₁₉C₂ = C₃²×C₄.₄D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:19C2	288,821
C₁₂²⋊₂₀C₂ = C₃²×C₄⋊₁D₄	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	144		C12^2:20C2	288,824

Non-split extensions G=N.Q with N=C₁₂² and Q=C₂

extension	φ:Q→Aut N	d	Label	ID
C₁₂².₁C₂ = C₃²×C₈⋊C₄	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.1C2	288,315
C₁₂².₂C₂ = C₁₂⋊₆Dic₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.2C2	288,726
C₁₂².₃C₂ = C₁₂.₂₅Dic₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.3C2	288,727
C₁₂².₄C₂ = C₁₂.₅₇D₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.4C2	288,279
C₁₂².₅C₂ = C₄×C₃²⋊₄Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.5C2	288,725
C₁₂².₆C₂ = C₃×C₁₂⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96	C12^2.6C2	288,238
C₁₂².₇C₂ = C₁₂×Dic₆	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96	C12^2.7C2	288,639
C₁₂².₈C₂ = C₃×C₁₂⋊₂Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96	C12^2.8C2	288,640
C₁₂².₉C₂ = C₃×C₁₂.₆Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96	C12^2.9C2	288,641
C₁₂².₁₀C₂ = C₁₂×C₃⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96	C12^2.10C2	288,236
C₁₂².₁₁C₂ = C₃×C₄².S₃	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	96	C12^2.11C2	288,237
C₁₂².₁₂C₂ = C₄×C₃²⋊₄C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.12C2	288,277
C₁₂².₁₃C₂ = C₁₂².C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.13C2	288,278
C₁₂².₁₄C₂ = C₃²×C₄⋊C₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.14C2	288,323
C₁₂².₁₅C₂ = Q₈×C₃×C₁₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.15C2	288,816
C₁₂².₁₆C₂ = C₃²×C₄².C₂	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.16C2	288,822
C₁₂².₁₇C₂ = C₃²×C₄⋊Q₈	φ: C₂/C₁ → C₂ ⊆ Aut C₁₂²	288	C12^2.17C2	288,825

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Extensions 1→N→G→Q→1 with N=C122 and Q=C2

Extensions 1→N→G→Q→1 with N=C₁₂² and Q=C₂