Extensions 1→N→G→Q→1 with N=C₃xC₂₄ and Q=S₃

Direct product G=NxQ with N=C₃xC₂₄ and Q=S₃

		d	ρ	Label	ID
S₃xC₃xC₂₄		144		S3xC3xC24	432,464

Semidirect products G=N:Q with N=C₃xC₂₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃xC₂₄):₁S₃ = He₃:₄D₈	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6+	(C3xC24):1S3	432,118
(C₃xC₂₄):₂S₃ = He₃:₅D₈	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24):2S3	432,176
(C₃xC₂₄):₃S₃ = He₃:₆SD₁₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24):3S3	432,117
(C₃xC₂₄):₄S₃ = He₃:₇SD₁₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24):4S3	432,175
(C₃xC₂₄):₅S₃ = C₈xC₃²:C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24):5S3	432,115
(C₃xC₂₄):₆S₃ = C₈xHe₃:C₂	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	3	(C3xC24):6S3	432,173
(C₃xC₂₄):₇S₃ = He₃:₅M₄(2)	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24):7S3	432,116
(C₃xC₂₄):₈S₃ = He₃:₆M₄(2)	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24):8S3	432,174
(C₃xC₂₄):₉S₃ = C₃³:₁₂D₈	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	216		(C3xC24):9S3	432,499
(C₃xC₂₄):₁₀S₃ = C₃xC₃²:₅D₈	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24):10S3	432,483
(C₃xC₂₄):₁₁S₃ = C₃³:₂₁SD₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	216		(C3xC24):11S3	432,498
(C₃xC₂₄):₁₂S₃ = C₃xC₂₄:₂S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24):12S3	432,482
(C₃xC₂₄):₁₃S₃ = C₃²xD₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24):13S3	432,467
(C₃xC₂₄):₁₄S₃ = C₃:S₃xC₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24):14S3	432,480
(C₃xC₂₄):₁₅S₃ = C₈xC₃³:C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	216		(C3xC24):15S3	432,496
(C₃xC₂₄):₁₆S₃ = C₃³:₁₅M₄(2)	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	216		(C3xC24):16S3	432,497
(C₃xC₂₄):₁₇S₃ = C₃xC₂₄:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24):17S3	432,481
(C₃xC₂₄):₁₈S₃ = C₃²xC₂₄:C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24):18S3	432,466
(C₃xC₂₄):₁₉S₃ = C₃²xC₈:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24):19S3	432,465

Non-split extensions G=N.Q with N=C₃xC₂₄ and Q=S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
(C₃xC₂₄).₁S₃ = He₃:₄Q₁₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	144	6-	(C3xC24).1S3	432,114
(C₃xC₂₄).₂S₃ = C₇₂.C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	144	6-	(C3xC24).2S3	432,119
(C₃xC₂₄).₃S₃ = D₇₂:C₃	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6+	(C3xC24).3S3	432,123
(C₃xC₂₄).₄S₃ = He₃:₅Q₁₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	144	6	(C3xC24).4S3	432,177
(C₃xC₂₄).₅S₃ = C₇₂:₂C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24).5S3	432,122
(C₃xC₂₄).₆S₃ = He₃:₃C₁₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	144	6	(C3xC24).6S3	432,30
(C₃xC₂₄).₇S₃ = C₉:C₄₈	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	144	6	(C3xC24).7S3	432,31
(C₃xC₂₄).₈S₃ = He₃:₄C₁₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	144	3	(C3xC24).8S3	432,33
(C₃xC₂₄).₉S₃ = C₈xC₉:C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24).9S3	432,120
(C₃xC₂₄).₁₀S₃ = C₇₂:C₆	φ: S₃/C₁ → S₃ ⊆ Aut C₃xC₂₄	72	6	(C3xC24).10S3	432,121
(C₃xC₂₄).₁₁S₃ = C₂₄.D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	432		(C3xC24).11S3	432,168
(C₃xC₂₄).₁₂S₃ = C₇₂:₁S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	216		(C3xC24).12S3	432,172
(C₃xC₂₄).₁₃S₃ = C₃³:₁₂Q₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	432		(C3xC24).13S3	432,500
(C₃xC₂₄).₁₄S₃ = C₃xDic₃₆	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144	2	(C3xC24).14S3	432,104
(C₃xC₂₄).₁₅S₃ = C₃xD₇₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144	2	(C3xC24).15S3	432,108
(C₃xC₂₄).₁₆S₃ = C₃xC₃²:₅Q₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24).16S3	432,484
(C₃xC₂₄).₁₇S₃ = C₂₄:D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	216		(C3xC24).17S3	432,171
(C₃xC₂₄).₁₈S₃ = C₃xC₇₂:C₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144	2	(C3xC24).18S3	432,107
(C₃xC₂₄).₁₉S₃ = C₃²xDic₁₂	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24).19S3	432,468
(C₃xC₂₄).₂₀S₃ = C₃xC₉:C₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144	2	(C3xC24).20S3	432,28
(C₃xC₂₄).₂₁S₃ = C₇₂.S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	432		(C3xC24).21S3	432,32
(C₃xC₂₄).₂₂S₃ = D₉xC₂₄	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144	2	(C3xC24).22S3	432,105
(C₃xC₂₄).₂₃S₃ = C₈xC₉:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	216		(C3xC24).23S3	432,169
(C₃xC₂₄).₂₄S₃ = C₇₂:S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	216		(C3xC24).24S3	432,170
(C₃xC₂₄).₂₅S₃ = C₃xC₂₄.S₃	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144		(C3xC24).25S3	432,230
(C₃xC₂₄).₂₆S₃ = C₃³:₇C₁₆	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	432		(C3xC24).26S3	432,231
(C₃xC₂₄).₂₇S₃ = C₃xC₈:D₉	φ: S₃/C₃ → C₂ ⊆ Aut C₃xC₂₄	144	2	(C3xC24).27S3	432,106
(C₃xC₂₄).₂₈S₃ = C₃²xC₃:C₁₆	central extension (φ=1)	144		(C3xC24).28S3	432,229

Extensions 1→N→G→Q→1 with N=C3xC24 and Q=S3

Extensions 1→N→G→Q→1 with N=C₃xC₂₄ and Q=S₃