Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×C₂₄⋊C₂

Direct product G=N×Q with N=C₃ and Q=C₃×C₂₄⋊C₂

		d	ρ	Label	ID
C₃²×C₂₄⋊C₂		144		C3^2xC24:C2	432,466

Semidirect products G=N:Q with N=C₃ and Q=C₃×C₂₄⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×C₂₄⋊C₂) = C₃×C₂₄⋊₂S₃	φ: C₃×C₂₄⋊C₂/C₃×C₂₄ → C₂ ⊆ Aut C₃	144		C3:1(C3xC24:C2)	432,482
C₃⋊₂(C₃×C₂₄⋊C₂) = C₃×C₃²⋊₅SD₁₆	φ: C₃×C₂₄⋊C₂/C₃×Dic₆ → C₂ ⊆ Aut C₃	48	4	C3:2(C3xC24:C2)	432,422
C₃⋊₃(C₃×C₂₄⋊C₂) = C₃×D₁₂.S₃	φ: C₃×C₂₄⋊C₂/C₃×D₁₂ → C₂ ⊆ Aut C₃	48	4	C3:3(C3xC24:C2)	432,421

Non-split extensions G=N.Q with N=C₃ and Q=C₃×C₂₄⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×C₂₄⋊C₂) = C₃×C₇₂⋊C₂	φ: C₃×C₂₄⋊C₂/C₃×C₂₄ → C₂ ⊆ Aut C₃	144	2	C3.1(C3xC24:C2)	432,107
C₃.₂(C₃×C₂₄⋊C₂) = He₃⋊₆SD₁₆	φ: C₃×C₂₄⋊C₂/C₃×C₂₄ → C₂ ⊆ Aut C₃	72	6	C3.2(C3xC24:C2)	432,117
C₃.₃(C₃×C₂₄⋊C₂) = C₇₂⋊₂C₆	φ: C₃×C₂₄⋊C₂/C₃×C₂₄ → C₂ ⊆ Aut C₃	72	6	C3.3(C3xC24:C2)	432,122
C₃.₄(C₃×C₂₄⋊C₂) = C₉×C₂₄⋊C₂	central extension (φ=1)	144	2	C3.4(C3xC24:C2)	432,111

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