Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂³xC₆

Direct product G=NxQ with N=C₆ and Q=C₂³xC₆

		d	ρ	Label	ID
C₂³xC₆²		288		C2^3xC6^2	288,1045

Semidirect products G=N:Q with N=C₆ and Q=C₂³xC₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆:(C₂³xC₆) = S₃xC₂³xC₆	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	96		C6:(C2^3xC6)	288,1043

Non-split extensions G=N.Q with N=C₆ and Q=C₂³xC₆

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆.₁(C₂³xC₆) = C₂xC₆xDic₆	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	96		C6.1(C2^3xC6)	288,988
C₆.₂(C₂³xC₆) = S₃xC₂²xC₁₂	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	96		C6.2(C2^3xC6)	288,989
C₆.₃(C₂³xC₆) = C₂xC₆xD₁₂	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	96		C6.3(C2^3xC6)	288,990
C₆.₄(C₂³xC₆) = C₆xC₄oD₁₂	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	48		C6.4(C2^3xC6)	288,991
C₆.₅(C₂³xC₆) = S₃xC₆xD₄	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	48		C6.5(C2^3xC6)	288,992
C₆.₆(C₂³xC₆) = C₆xD₄:₂S₃	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	48		C6.6(C2^3xC6)	288,993
C₆.₇(C₂³xC₆) = C₃xD₄:₆D₆	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	24	4	C6.7(C2^3xC6)	288,994
C₆.₈(C₂³xC₆) = S₃xC₆xQ₈	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	96		C6.8(C2^3xC6)	288,995
C₆.₉(C₂³xC₆) = C₆xQ₈:₃S₃	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	96		C6.9(C2^3xC6)	288,996
C₆.₁₀(C₂³xC₆) = C₃xQ₈.₁₅D₆	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	48	4	C6.10(C2^3xC6)	288,997
C₆.₁₁(C₂³xC₆) = C₃xS₃xC₄oD₄	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	48	4	C6.11(C2^3xC6)	288,998
C₆.₁₂(C₂³xC₆) = C₃xD₄oD₁₂	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	48	4	C6.12(C2^3xC6)	288,999
C₆.₁₃(C₂³xC₆) = C₃xQ₈oD₁₂	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	48	4	C6.13(C2^3xC6)	288,1000
C₆.₁₄(C₂³xC₆) = Dic₃xC₂²xC₆	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	96		C6.14(C2^3xC6)	288,1001
C₆.₁₅(C₂³xC₆) = C₂xC₆xC₃:D₄	φ: C₂³xC₆/C₂²xC₆ → C₂ ⊆ Aut C₆	48		C6.15(C2^3xC6)	288,1002
C₆.₁₆(C₂³xC₆) = D₄xC₂xC₁₈	central extension (φ=1)	144		C6.16(C2^3xC6)	288,368
C₆.₁₇(C₂³xC₆) = Q₈xC₂xC₁₈	central extension (φ=1)	288		C6.17(C2^3xC6)	288,369
C₆.₁₈(C₂³xC₆) = C₄oD₄xC₁₈	central extension (φ=1)	144		C6.18(C2^3xC6)	288,370
C₆.₁₉(C₂³xC₆) = C₉x2₊¹⁺⁴	central extension (φ=1)	72	4	C6.19(C2^3xC6)	288,371
C₆.₂₀(C₂³xC₆) = C₉x2_-¹⁺⁴	central extension (φ=1)	144	4	C6.20(C2^3xC6)	288,372
C₆.₂₁(C₂³xC₆) = D₄xC₆²	central extension (φ=1)	144		C6.21(C2^3xC6)	288,1019
C₆.₂₂(C₂³xC₆) = Q₈xC₆²	central extension (φ=1)	288		C6.22(C2^3xC6)	288,1020
C₆.₂₃(C₂³xC₆) = C₄oD₄xC₃xC₆	central extension (φ=1)	144		C6.23(C2^3xC6)	288,1021
C₆.₂₄(C₂³xC₆) = C₃²x2₊¹⁺⁴	central extension (φ=1)	72		C6.24(C2^3xC6)	288,1022
C₆.₂₅(C₂³xC₆) = C₃²x2_-¹⁺⁴	central extension (φ=1)	144		C6.25(C2^3xC6)	288,1023

Extensions 1→N→G→Q→1 with N=C6 and Q=C23xC6

Extensions 1→N→G→Q→1 with N=C₆ and Q=C₂³xC₆