Extensions 1→N→G→Q→1 with N=C₃ and Q=C₃×C₃⋊D₄

Direct product G=N×Q with N=C₃ and Q=C₃×C₃⋊D₄

		d	ρ	Label	ID
C₃²×C₃⋊D₄		36		C3^2xC3:D4	216,139

Semidirect products G=N:Q with N=C₃ and Q=C₃×C₃⋊D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃⋊₁(C₃×C₃⋊D₄) = C₃×C₃⋊D₁₂	φ: C₃×C₃⋊D₄/C₃×Dic₃ → C₂ ⊆ Aut C₃	24	4	C3:1(C3xC3:D4)	216,122
C₃⋊₂(C₃×C₃⋊D₄) = C₃×D₆⋊S₃	φ: C₃×C₃⋊D₄/S₃×C₆ → C₂ ⊆ Aut C₃	24	4	C3:2(C3xC3:D4)	216,121
C₃⋊₃(C₃×C₃⋊D₄) = C₃×C₃²⋊₇D₄	φ: C₃×C₃⋊D₄/C₆² → C₂ ⊆ Aut C₃	36		C3:3(C3xC3:D4)	216,144

Non-split extensions G=N.Q with N=C₃ and Q=C₃×C₃⋊D₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₃.₁(C₃×C₃⋊D₄) = C₃×C₉⋊D₄	φ: C₃×C₃⋊D₄/C₆² → C₂ ⊆ Aut C₃	36	2	C3.1(C3xC3:D4)	216,57
C₃.₂(C₃×C₃⋊D₄) = He₃⋊₆D₄	φ: C₃×C₃⋊D₄/C₆² → C₂ ⊆ Aut C₃	36	6	C3.2(C3xC3:D4)	216,60
C₃.₃(C₃×C₃⋊D₄) = Dic₉⋊C₆	φ: C₃×C₃⋊D₄/C₆² → C₂ ⊆ Aut C₃	36	6	C3.3(C3xC3:D4)	216,62
C₃.₄(C₃×C₃⋊D₄) = C₉×C₃⋊D₄	central extension (φ=1)	36	2	C3.4(C3xC3:D4)	216,58

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁