Extensions 1→N→G→Q→1 with N=C₃ and Q=C₂₄⋊₂S₃

Direct product G=N×Q with N=C₃ and Q=C₂₄⋊₂S₃

		d	ρ	Label	ID
C₃×C₂₄⋊₂S₃		144		C3xC24:2S3	432,482

Semidirect products G=N:Q with N=C₃ and Q=C₂₄⋊₂S₃

extension	φ:Q→Aut N	d	Label	ID
C₃⋊₁(C₂₄⋊₂S₃) = C₃³⋊₂₁SD₁₆	φ: C₂₄⋊₂S₃/C₃×C₂₄ → C₂ ⊆ Aut C₃	216	C3:1(C24:2S3)	432,498
C₃⋊₂(C₂₄⋊₂S₃) = C₃³⋊₁₇SD₁₆	φ: C₂₄⋊₂S₃/C₃²⋊₄Q₈ → C₂ ⊆ Aut C₃	72	C3:2(C24:2S3)	432,444
C₃⋊₃(C₂₄⋊₂S₃) = C₃³⋊₁₆SD₁₆	φ: C₂₄⋊₂S₃/C₁₂⋊S₃ → C₂ ⊆ Aut C₃	144	C3:3(C24:2S3)	432,443

Non-split extensions G=N.Q with N=C₃ and Q=C₂₄⋊₂S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.(C₂₄⋊₂S₃) = C₂₄⋊D₉	φ: C₂₄⋊₂S₃/C₃×C₂₄ → C₂ ⊆ Aut C₃	216		C3.(C24:2S3)	432,171
C₃.₂(C₂₄⋊₂S₃) = He₃⋊₇SD₁₆	central stem extension (φ=1)	72	6	C3.2(C24:2S3)	432,175

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Extensions 1→N→G→Q→1 with N=C3 and Q=C24⋊2S3