Extensions 1→N→G→Q→1 with N=C₃×C₂₄ and Q=C₆

Direct product G=N×Q with N=C₃×C₂₄ and Q=C₆

		d	ρ	Label	ID
C₃×C₆×C₂₄		432		C3xC6xC24	432,515

Semidirect products G=N:Q with N=C₃×C₂₄ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₂₄)⋊₁C₆ = He₃⋊₄D₈	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6+	(C3xC24):1C6	432,118
(C₃×C₂₄)⋊₂C₆ = He₃⋊₆SD₁₆	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24):2C6	432,117
(C₃×C₂₄)⋊₃C₆ = D₈×He₃	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24):3C6	432,216
(C₃×C₂₄)⋊₄C₆ = C₈×C₃²⋊C₆	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24):4C6	432,115
(C₃×C₂₄)⋊₅C₆ = He₃⋊₅M₄(2)	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24):5C6	432,116
(C₃×C₂₄)⋊₆C₆ = SD₁₆×He₃	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24):6C6	432,219
(C₃×C₂₄)⋊₇C₆ = M₄(2)×He₃	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24):7C6	432,213
(C₃×C₂₄)⋊₈C₆ = C₂×C₈×He₃	φ: C₆/C₂ → C₃ ⊆ Aut C₃×C₂₄	144		(C3xC24):8C6	432,210
(C₃×C₂₄)⋊₉C₆ = C₃×C₃²⋊₅D₈	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24):9C6	432,483
(C₃×C₂₄)⋊₁₀C₆ = C₃²×D₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24):10C6	432,467
(C₃×C₂₄)⋊₁₁C₆ = C₃×C₂₄⋊₂S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24):11C6	432,482
(C₃×C₂₄)⋊₁₂C₆ = C₃²×C₂₄⋊C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24):12C6	432,466
(C₃×C₂₄)⋊₁₃C₆ = D₈×C₃³	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	216		(C3xC24):13C6	432,517
(C₃×C₂₄)⋊₁₄C₆ = S₃×C₃×C₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24):14C6	432,464
(C₃×C₂₄)⋊₁₅C₆ = C₃⋊S₃×C₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24):15C6	432,480
(C₃×C₂₄)⋊₁₆C₆ = C₃×C₂₄⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24):16C6	432,481
(C₃×C₂₄)⋊₁₇C₆ = C₃²×C₈⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24):17C6	432,465
(C₃×C₂₄)⋊₁₈C₆ = SD₁₆×C₃³	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	216		(C3xC24):18C6	432,518
(C₃×C₂₄)⋊₁₉C₆ = M₄(2)×C₃³	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	216		(C3xC24):19C6	432,516

Non-split extensions G=N.Q with N=C₃×C₂₄ and Q=C₆

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃×C₂₄).₁C₆ = He₃⋊₄Q₁₆	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	144	6-	(C3xC24).1C6	432,114
(C₃×C₂₄).₂C₆ = D₈×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24).2C6	432,217
(C₃×C₂₄).₃C₆ = Q₁₆×He₃	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	144	6	(C3xC24).3C6	432,222
(C₃×C₂₄).₄C₆ = Q₁₆×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	144	6	(C3xC24).4C6	432,223
(C₃×C₂₄).₅C₆ = He₃⋊₃C₁₆	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	144	6	(C3xC24).5C6	432,30
(C₃×C₂₄).₆C₆ = SD₁₆×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24).6C6	432,220
(C₃×C₂₄).₇C₆ = M₄(2)×3_-¹⁺²	φ: C₆/C₁ → C₆ ⊆ Aut C₃×C₂₄	72	6	(C3xC24).7C6	432,214
(C₃×C₂₄).₈C₆ = C₁₆×He₃	φ: C₆/C₂ → C₃ ⊆ Aut C₃×C₂₄	144	3	(C3xC24).8C6	432,35
(C₃×C₂₄).₉C₆ = C₁₆×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₃×C₂₄	144	3	(C3xC24).9C6	432,36
(C₃×C₂₄).₁₀C₆ = C₂×C₈×3_-¹⁺²	φ: C₆/C₂ → C₃ ⊆ Aut C₃×C₂₄	144		(C3xC24).10C6	432,211
(C₃×C₂₄).₁₁C₆ = C₃×C₃²⋊₅Q₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24).11C6	432,484
(C₃×C₂₄).₁₂C₆ = C₉×D₂₄	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144	2	(C3xC24).12C6	432,112
(C₃×C₂₄).₁₃C₆ = C₉×Dic₁₂	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144	2	(C3xC24).13C6	432,113
(C₃×C₂₄).₁₄C₆ = C₃²×Dic₁₂	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24).14C6	432,468
(C₃×C₂₄).₁₅C₆ = C₉×C₂₄⋊C₂	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144	2	(C3xC24).15C6	432,111
(C₃×C₂₄).₁₆C₆ = D₈×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	216		(C3xC24).16C6	432,215
(C₃×C₂₄).₁₇C₆ = Q₁₆×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	432		(C3xC24).17C6	432,221
(C₃×C₂₄).₁₈C₆ = Q₁₆×C₃³	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	432		(C3xC24).18C6	432,519
(C₃×C₂₄).₁₉C₆ = C₉×C₃⋊C₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144	2	(C3xC24).19C6	432,29
(C₃×C₂₄).₂₀C₆ = S₃×C₇₂	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144	2	(C3xC24).20C6	432,109
(C₃×C₂₄).₂₁C₆ = C₃²×C₃⋊C₁₆	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24).21C6	432,229
(C₃×C₂₄).₂₂C₆ = C₃×C₂₄.S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144		(C3xC24).22C6	432,230
(C₃×C₂₄).₂₃C₆ = C₉×C₈⋊S₃	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	144	2	(C3xC24).23C6	432,110
(C₃×C₂₄).₂₄C₆ = SD₁₆×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	216		(C3xC24).24C6	432,218
(C₃×C₂₄).₂₅C₆ = M₄(2)×C₃×C₉	φ: C₆/C₃ → C₂ ⊆ Aut C₃×C₂₄	216		(C3xC24).25C6	432,212

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Extensions 1→N→G→Q→1 with N=C3×C24 and Q=C6

Extensions 1→N→G→Q→1 with N=C₃×C₂₄ and Q=C₆