Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₆²

Direct product G=N×Q with N=C₂³ and Q=C₆²

		d	ρ	Label	ID
C₂³×C₆²		288		C2^3xC6^2	288,1045

Semidirect products G=N:Q with N=C₂³ and Q=C₆²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊₁C₆² = C₃²×C₂²≀C₂	φ: C₆²/C₃² → C₂² ⊆ Aut C₂³	72		C2^3:1C6^2	288,817
C₂³⋊₂C₆² = C₃²×2₊¹⁺⁴	φ: C₆²/C₃² → C₂² ⊆ Aut C₂³	72		C2^3:2C6^2	288,1022
C₂³⋊₃C₆² = A₄×C₂²×C₆	φ: C₆²/C₂×C₆ → C₃ ⊆ Aut C₂³	72		C2^3:3C6^2	288,1041
C₂³⋊₄C₆² = D₄×C₆²	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₂³	144		C2^3:4C6^2	288,1019

Non-split extensions G=N.Q with N=C₂³ and Q=C₆²

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³.₁C₆² = C₃²×C₂³⋊C₄	φ: C₆²/C₃² → C₂² ⊆ Aut C₂³	72		C2^3.1C6^2	288,317
C₂³.₂C₆² = C₃²×C₄⋊D₄	φ: C₆²/C₃² → C₂² ⊆ Aut C₂³	144		C2^3.2C6^2	288,818
C₂³.₃C₆² = C₃²×C₄.₄D₄	φ: C₆²/C₃² → C₂² ⊆ Aut C₂³	144		C2^3.3C6^2	288,821
C₂³.₄C₆² = C₃²×C₄²⋊₂C₂	φ: C₆²/C₃² → C₂² ⊆ Aut C₂³	144		C2^3.4C6^2	288,823
C₂³.₅C₆² = C₃²×C₄⋊₁D₄	φ: C₆²/C₃² → C₂² ⊆ Aut C₂³	144		C2^3.5C6^2	288,824
C₂³.₆C₆² = A₄×C₂×C₁₂	φ: C₆²/C₂×C₆ → C₃ ⊆ Aut C₂³	72		C2^3.6C6^2	288,979
C₂³.₇C₆² = C₃×D₄×A₄	φ: C₆²/C₂×C₆ → C₃ ⊆ Aut C₂³	36	6	C2^3.7C6^2	288,980
C₂³.₈C₆² = C₃×Q₈×A₄	φ: C₆²/C₂×C₆ → C₃ ⊆ Aut C₂³	72	6	C2^3.8C6^2	288,982
C₂³.₉C₆² = C₂²⋊C₄×C₃×C₆	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₂³	144		C2^3.9C6^2	288,812
C₂³.₁₀C₆² = C₃²×C₄²⋊C₂	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₂³	144		C2^3.10C6^2	288,814
C₂³.₁₁C₆² = D₄×C₃×C₁₂	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₂³	144		C2^3.11C6^2	288,815
C₂³.₁₂C₆² = C₃²×C₂²⋊Q₈	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₂³	144		C2^3.12C6^2	288,819
C₂³.₁₃C₆² = C₃²×C₂².D₄	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₂³	144		C2^3.13C6^2	288,820
C₂³.₁₄C₆² = C₄○D₄×C₃×C₆	φ: C₆²/C₃×C₆ → C₂ ⊆ Aut C₂³	144		C2^3.14C6^2	288,1021
C₂³.₁₅C₆² = C₃²×C₂.C₄²	central extension (φ=1)	288		C2^3.15C6^2	288,313
C₂³.₁₆C₆² = C₄⋊C₄×C₃×C₆	central extension (φ=1)	288		C2^3.16C6^2	288,813
C₂³.₁₇C₆² = Q₈×C₆²	central extension (φ=1)	288		C2^3.17C6^2	288,1020

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