Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆×He₃

Direct product G=N×Q with N=C₃ and Q=C₆×He₃

		d	ρ	Label	ID
C₃×C₆×He₃		162		C3xC6xHe3	486,251

Semidirect products G=N:Q with N=C₃ and Q=C₆×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊(C₆×He₃) = C₃×S₃×He₃	φ: C₆×He₃/C₃×He₃ → C₂ ⊆ Aut C₃	54		C3:(C6xHe3)	486,223

Non-split extensions G=N.Q with N=C₃ and Q=C₆×He₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₆×He₃) = C₆×C₃²⋊C₉	central extension (φ=1)	162		C3.1(C6xHe3)	486,191
C₃.₂(C₆×He₃) = C₁₈×He₃	central extension (φ=1)	162		C3.2(C6xHe3)	486,194
C₃.₃(C₆×He₃) = C₂×C₃²⋊He₃	central stem extension (φ=1)	54		C3.3(C6xHe3)	486,196
C₃.₄(C₆×He₃) = C₂×C₃⁴.C₃	central stem extension (φ=1)	54		C3.4(C6xHe3)	486,197
C₃.₅(C₆×He₃) = C₂×C₉⋊He₃	central stem extension (φ=1)	162		C3.5(C6xHe3)	486,198
C₃.₆(C₆×He₃) = C₂×C₃².₂₃C₃³	central stem extension (φ=1)	162		C3.6(C6xHe3)	486,199
C₃.₇(C₆×He₃) = C₆×C₃≀C₃	central stem extension (φ=1)	54		C3.7(C6xHe3)	486,210
C₃.₈(C₆×He₃) = C₆×He₃.C₃	central stem extension (φ=1)	162		C3.8(C6xHe3)	486,211
C₃.₉(C₆×He₃) = C₆×He₃⋊C₃	central stem extension (φ=1)	162		C3.9(C6xHe3)	486,212
C₃.₁₀(C₆×He₃) = C₆×C₃.He₃	central stem extension (φ=1)	162		C3.10(C6xHe3)	486,213
C₃.₁₁(C₆×He₃) = C₂×C₉.He₃	central stem extension (φ=1)	54	3	C3.11(C6xHe3)	486,214
C₃.₁₂(C₆×He₃) = C₂×C₃³⋊C₃²	central stem extension (φ=1)	54	9	C3.12(C6xHe3)	486,215
C₃.₁₃(C₆×He₃) = C₂×He₃.C₃²	central stem extension (φ=1)	54	9	C3.13(C6xHe3)	486,216
C₃.₁₄(C₆×He₃) = C₂×He₃⋊C₃²	central stem extension (φ=1)	54	9	C3.14(C6xHe3)	486,217
C₃.₁₅(C₆×He₃) = C₂×C₃².C₃³	central stem extension (φ=1)	54	9	C3.15(C6xHe3)	486,218
C₃.₁₆(C₆×He₃) = C₂×C₉.₂He₃	central stem extension (φ=1)	54	9	C3.16(C6xHe3)	486,219

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