Extensions 1→N→G→Q→1 with N=C₆ and Q=C₃.S₄

Direct product G=N×Q with N=C₆ and Q=C₃.S₄

		d	ρ	Label	ID
C₆×C₃.S₄		36	6	C6xC3.S4	432,534

Semidirect products G=N:Q with N=C₆ and Q=C₃.S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆⋊(C₃.S₄) = C₂×C₃².₃S₄	φ: C₃.S₄/C₃.A₄ → C₂ ⊆ Aut C₆	54		C6:(C3.S4)	432,537

Non-split extensions G=N.Q with N=C₆ and Q=C₃.S₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₃.S₄) = Q₈.D₂₇	φ: C₃.S₄/C₃.A₄ → C₂ ⊆ Aut C₆	432	4-	C6.1(C3.S4)	432,37
C₆.₂(C₃.S₄) = Q₈⋊D₂₇	φ: C₃.S₄/C₃.A₄ → C₂ ⊆ Aut C₆	216	4+	C6.2(C3.S4)	432,38
C₆.₃(C₃.S₄) = C₁₈.S₄	φ: C₃.S₄/C₃.A₄ → C₂ ⊆ Aut C₆	108	6-	C6.3(C3.S4)	432,39
C₆.₄(C₃.S₄) = C₂×C₉.S₄	φ: C₃.S₄/C₃.A₄ → C₂ ⊆ Aut C₆	54	6+	C6.4(C3.S4)	432,224
C₆.₅(C₃.S₄) = C₃².₃CSU₂(𝔽₃)	φ: C₃.S₄/C₃.A₄ → C₂ ⊆ Aut C₆	432		C6.5(C3.S4)	432,255
C₆.₆(C₃.S₄) = C₃².₃GL₂(𝔽₃)	φ: C₃.S₄/C₃.A₄ → C₂ ⊆ Aut C₆	216		C6.6(C3.S4)	432,256
C₆.₇(C₃.S₄) = C₆².₁₀Dic₃	φ: C₃.S₄/C₃.A₄ → C₂ ⊆ Aut C₆	108		C6.7(C3.S4)	432,259
C₆.₈(C₃.S₄) = C₃×Q₈.D₉	central extension (φ=1)	144	4	C6.8(C3.S4)	432,244
C₆.₉(C₃.S₄) = C₃×Q₈⋊D₉	central extension (φ=1)	144	4	C6.9(C3.S4)	432,246
C₆.₁₀(C₃.S₄) = C₃×C₆.S₄	central extension (φ=1)	36	6	C6.10(C3.S4)	432,250

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