Extensions 1→N→G→Q→1 with N=C₆² and Q=Dic₃

Direct product G=N×Q with N=C₆² and Q=Dic₃

		d	ρ	Label	ID
Dic₃×C₆²		144		Dic3xC6^2	432,708

Semidirect products G=N:Q with N=C₆² and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆²⋊Dic₃ = C₆²⋊Dic₃	φ: Dic₃/C₁ → Dic₃ ⊆ Aut C₆²	24	12+	C6^2:Dic3	432,743
C₆²⋊₂Dic₃ = C₃²×A₄⋊C₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	108		C6^2:2Dic3	432,615
C₆²⋊₃Dic₃ = C₆²⋊₃C₁₂	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	72		C6^2:3Dic3	432,166
C₆²⋊₄Dic₃ = C₆²⋊₄Dic₃	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	72		C6^2:4Dic3	432,199
C₆²⋊₅Dic₃ = C₆²⋊₅Dic₃	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	36	6-	C6^2:5Dic3	432,251
C₆²⋊₆Dic₃ = C₆²⋊₆Dic₃	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	36	3	C6^2:6Dic3	432,260
C₆²⋊₇Dic₃ = C₂²×C₃²⋊C₁₂	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	144		C6^2:7Dic3	432,376
C₆²⋊₈Dic₃ = C₂²×He₃⋊₃C₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	144		C6^2:8Dic3	432,398
C₆²⋊₉Dic₃ = C₃×C₆.₇S₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	36	6	C6^2:9Dic3	432,618
C₆²⋊₁₀Dic₃ = C₆²⋊₁₀Dic₃	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	108		C6^2:10Dic3	432,621
C₆²⋊₁₁Dic₃ = C₆²⋊₁₁Dic₃	φ: Dic₃/C₃ → C₄ ⊆ Aut C₆²	24	4	C6^2:11Dic3	432,641
C₆²⋊₁₂Dic₃ = C₂²×C₃³⋊C₄	φ: Dic₃/C₃ → C₄ ⊆ Aut C₆²	48		C6^2:12Dic3	432,766
C₆²⋊₁₃Dic₃ = C₃²×C₆.D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	72		C6^2:13Dic3	432,479
C₆²⋊₁₄Dic₃ = C₃×C₆²⋊₅C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	72		C6^2:14Dic3	432,495
C₆²⋊₁₅Dic₃ = C₆³.C₂	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	216		C6^2:15Dic3	432,511
C₆²⋊₁₆Dic₃ = C₂×C₆×C₃⋊Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	144		C6^2:16Dic3	432,718
C₆²⋊₁₇Dic₃ = C₂²×C₃³⋊₅C₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	432		C6^2:17Dic3	432,728

Non-split extensions G=N.Q with N=C₆² and Q=Dic₃

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆².₁Dic₃ = C₂×He₃⋊₃C₈	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	144		C6^2.1Dic3	432,136
C₆².₂Dic₃ = He₃⋊₇M₄(2)	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	72	6	C6^2.2Dic3	432,137
C₆².₃Dic₃ = C₂×C₉⋊C₂₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	144		C6^2.3Dic3	432,142
C₆².₄Dic₃ = C₃₆.C₁₂	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	72	6	C6^2.4Dic3	432,143
C₆².₅Dic₃ = C₆².₂₇D₆	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	72		C6^2.5Dic3	432,167
C₆².₆Dic₃ = C₂×He₃⋊₄C₈	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	144		C6^2.6Dic3	432,184
C₆².₇Dic₃ = He₃⋊₈M₄(2)	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	72	6	C6^2.7Dic3	432,185
C₆².₈Dic₃ = C₆².Dic₃	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	36	6-	C6^2.8Dic3	432,249
C₆².₉Dic₃ = C₃×C₆.S₄	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	36	6	C6^2.9Dic3	432,250
C₆².₁₀Dic₃ = C₆².₁₀Dic₃	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	108		C6^2.10Dic3	432,259
C₆².₁₁Dic₃ = C₂²×C₉⋊C₁₂	φ: Dic₃/C₂ → S₃ ⊆ Aut C₆²	144		C6^2.11Dic3	432,378
C₆².₁₂Dic₃ = C₂×C₃³⋊₄C₈	φ: Dic₃/C₃ → C₄ ⊆ Aut C₆²	48		C6^2.12Dic3	432,639
C₆².₁₃Dic₃ = C₃³⋊₁₂M₄(2)	φ: Dic₃/C₃ → C₄ ⊆ Aut C₆²	24	4	C6^2.13Dic3	432,640
C₆².₁₄Dic₃ = C₃²×C₄.Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	72		C6^2.14Dic3	432,470
C₆².₁₅Dic₃ = C₆×C₉⋊C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	144		C6^2.15Dic3	432,124
C₆².₁₆Dic₃ = C₃×C₄.Dic₉	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	72	2	C6^2.16Dic3	432,125
C₆².₁₇Dic₃ = C₃×C₁₈.D₄	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	72		C6^2.17Dic3	432,164
C₆².₁₈Dic₃ = C₂×C₃₆.S₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	432		C6^2.18Dic3	432,178
C₆².₁₉Dic₃ = C₃₆.₆₉D₆	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	216		C6^2.19Dic3	432,179
C₆².₂₀Dic₃ = C₆².₁₂₇D₆	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	216		C6^2.20Dic3	432,198
C₆².₂₁Dic₃ = C₂×C₆×Dic₉	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	144		C6^2.21Dic3	432,372
C₆².₂₂Dic₃ = C₂²×C₉⋊Dic₃	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	432		C6^2.22Dic3	432,396
C₆².₂₃Dic₃ = C₆×C₃²⋊₄C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	144		C6^2.23Dic3	432,485
C₆².₂₄Dic₃ = C₃×C₁₂.₅₈D₆	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	72		C6^2.24Dic3	432,486
C₆².₂₅Dic₃ = C₂×C₃³⋊₇C₈	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	432		C6^2.25Dic3	432,501
C₆².₂₆Dic₃ = C₃³⋊₁₈M₄(2)	φ: Dic₃/C₆ → C₂ ⊆ Aut C₆²	216		C6^2.26Dic3	432,502
C₆².₂₇Dic₃ = C₃×C₆×C₃⋊C₈	central extension (φ=1)	144		C6^2.27Dic3	432,469

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C62 and Q=Dic3

Extensions 1→N→G→Q→1 with N=C₆² and Q=Dic₃