Extensions 1→N→G→Q→1 with N=C₃ and Q=C₆×C₃⋊C₈

Direct product G=N×Q with N=C₃ and Q=C₆×C₃⋊C₈

		d	ρ	Label	ID
C₃×C₆×C₃⋊C₈		144		C3xC6xC3:C8	432,469

Semidirect products G=N:Q with N=C₃ and Q=C₆×C₃⋊C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₆×C₃⋊C₈) = C₃×S₃×C₃⋊C₈	φ: C₆×C₃⋊C₈/C₃×C₃⋊C₈ → C₂ ⊆ Aut C₃	48	4	C3:1(C6xC3:C8)	432,414
C₃⋊₂(C₆×C₃⋊C₈) = C₆×C₃²⋊₄C₈	φ: C₆×C₃⋊C₈/C₆×C₁₂ → C₂ ⊆ Aut C₃	144		C3:2(C6xC3:C8)	432,485

Non-split extensions G=N.Q with N=C₃ and Q=C₆×C₃⋊C₈

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₆×C₃⋊C₈) = C₆×C₉⋊C₈	φ: C₆×C₃⋊C₈/C₆×C₁₂ → C₂ ⊆ Aut C₃	144		C3.1(C6xC3:C8)	432,124
C₃.₂(C₆×C₃⋊C₈) = C₂×He₃⋊₃C₈	φ: C₆×C₃⋊C₈/C₆×C₁₂ → C₂ ⊆ Aut C₃	144		C3.2(C6xC3:C8)	432,136
C₃.₃(C₆×C₃⋊C₈) = C₂×C₉⋊C₂₄	φ: C₆×C₃⋊C₈/C₆×C₁₂ → C₂ ⊆ Aut C₃	144		C3.3(C6xC3:C8)	432,142
C₃.₄(C₆×C₃⋊C₈) = C₁₈×C₃⋊C₈	central extension (φ=1)	144		C3.4(C6xC3:C8)	432,126

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