Extensions 1→N→G→Q→1 with N=C₂³ and Q=C₃³⋊C₂

Direct product G=N×Q with N=C₂³ and Q=C₃³⋊C₂

		d	ρ	Label	ID
C₂³×C₃³⋊C₂		216		C2^3xC3^3:C2	432,774

Semidirect products G=N:Q with N=C₂³ and Q=C₃³⋊C₂

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂³⋊(C₃³⋊C₂) = C₂×C₃²⋊₄S₄	φ: C₃³⋊C₂/C₃² → S₃ ⊆ Aut C₂³	54		C2^3:(C3^3:C2)	432,762
C₂³⋊₂(C₃³⋊C₂) = C₂×C₃³⋊₁₅D₄	φ: C₃³⋊C₂/C₃³ → C₂ ⊆ Aut C₂³	216		C2^3:2(C3^3:C2)	432,729

Non-split extensions G=N.Q with N=C₂³ and Q=C₃³⋊C₂

extension	φ:Q→Aut N	d	Label	ID
C₂³.(C₃³⋊C₂) = C₆²⋊₁₀Dic₃	φ: C₃³⋊C₂/C₃² → S₃ ⊆ Aut C₂³	108	C2^3.(C3^3:C2)	432,621
C₂³.₂(C₃³⋊C₂) = C₆³.C₂	φ: C₃³⋊C₂/C₃³ → C₂ ⊆ Aut C₂³	216	C2^3.2(C3^3:C2)	432,511
C₂³.₃(C₃³⋊C₂) = C₂²×C₃³⋊₅C₄	central extension (φ=1)	432	C2^3.3(C3^3:C2)	432,728

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Extensions 1→N→G→Q→1 with N=C23 and Q=C33⋊C2