Extensions 1→N→G→Q→1 with N=C₃ and Q=He₃⋊₄S₃

Direct product G=N×Q with N=C₃ and Q=He₃⋊₄S₃

		d	ρ	Label	ID
C₃×He₃⋊₄S₃		54		C3xHe3:4S3	486,229

Semidirect products G=N:Q with N=C₃ and Q=He₃⋊₄S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(He₃⋊₄S₃) = C₃⁴⋊₁₀C₆	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3:(He3:4S3)	486,242

Non-split extensions G=N.Q with N=C₃ and Q=He₃⋊₄S₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(He₃⋊₄S₃) = C₃³⋊D₉	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.1(He3:4S3)	486,137
C₃.₂(He₃⋊₄S₃) = He₃⋊₃D₉	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.2(He3:4S3)	486,142
C₃.₃(He₃⋊₄S₃) = C₃⁴⋊₄C₆	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	27		C3.3(He3:4S3)	486,146
C₃.₄(He₃⋊₄S₃) = C₉⋊He₃⋊₂C₂	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.4(He3:4S3)	486,148
C₃.₅(He₃⋊₄S₃) = (C₃²×C₉)⋊C₆	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.5(He3:4S3)	486,151
C₃.₆(He₃⋊₄S₃) = C₃⁴⋊₅C₆	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	27		C3.6(He3:4S3)	486,167
C₃.₇(He₃⋊₄S₃) = C₃²⋊₄D₉⋊C₃	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.7(He3:4S3)	486,170
C₃.₈(He₃⋊₄S₃) = He₃⋊C₃⋊₃S₃	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	81		C3.8(He3:4S3)	486,173
C₃.₉(He₃⋊₄S₃) = C₃≀C₃.S₃	φ: He₃⋊₄S₃/C₃×He₃ → C₂ ⊆ Aut C₃	27	6+	C3.9(He3:4S3)	486,175
C₃.₁₀(He₃⋊₄S₃) = C₃³⋊C₁₈	central extension (φ=1)	54		C3.10(He3:4S3)	486,136
C₃.₁₁(He₃⋊₄S₃) = C₃⁴⋊₃S₃	central stem extension (φ=1)	18	6	C3.11(He3:4S3)	486,145
C₃.₁₂(He₃⋊₄S₃) = (C₃²×C₉)⋊₈S₃	central stem extension (φ=1)	54	6	C3.12(He3:4S3)	486,150
C₃.₁₃(He₃⋊₄S₃) = C₃⁴⋊₅S₃	central stem extension (φ=1)	18	6	C3.13(He3:4S3)	486,166
C₃.₁₄(He₃⋊₄S₃) = He₃.C₃⋊S₃	central stem extension (φ=1)	54	6	C3.14(He3:4S3)	486,169
C₃.₁₅(He₃⋊₄S₃) = He₃⋊C₃⋊₂S₃	central stem extension (φ=1)	54	6	C3.15(He3:4S3)	486,172

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