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

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

		d	ρ	Label	ID
C₆³		216		C6^3	216,177

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

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃³⋊C₂³ = S₃³	φ: C₂³/C₁ → C₂³ ⊆ Aut C₃³	12	8+	C3^3:C2^3	216,162
C₃³⋊₂C₂³ = S₃²×C₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₃³	24	4	C3^3:2C2^3	216,170
C₃³⋊₃C₂³ = C₂×S₃×C₃⋊S₃	φ: C₂³/C₂ → C₂² ⊆ Aut C₃³	36		C3^3:3C2^3	216,171
C₃³⋊₄C₂³ = C₂×C₃²⋊₄D₆	φ: C₂³/C₂ → C₂² ⊆ Aut C₃³	24	4	C3^3:4C2^3	216,172
C₃³⋊₅C₂³ = S₃×C₆²	φ: C₂³/C₂² → C₂ ⊆ Aut C₃³	72		C3^3:5C2^3	216,174
C₃³⋊₆C₂³ = C₂×C₆×C₃⋊S₃	φ: C₂³/C₂² → C₂ ⊆ Aut C₃³	72		C3^3:6C2^3	216,175
C₃³⋊₇C₂³ = C₂²×C₃³⋊C₂	φ: C₂³/C₂² → C₂ ⊆ Aut C₃³	108		C3^3:7C2^3	216,176

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁