Extensions 1→N→G→Q→1 with N=C₂×C₃⋊S₃ and Q=C₄

Direct product G=N×Q with N=C₂×C₃⋊S₃ and Q=C₄

		d	ρ	Label	ID
C₂×C₄×C₃⋊S₃		72		C2xC4xC3:S3	144,169

Semidirect products G=N:Q with N=C₂×C₃⋊S₃ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×C₃⋊S₃)⋊₁C₄ = C₆.D₁₂	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	24		(C2xC3:S3):1C4	144,65
(C₂×C₃⋊S₃)⋊₂C₄ = C₆.₁₁D₁₂	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	72		(C2xC3:S3):2C4	144,95
(C₂×C₃⋊S₃)⋊₃C₄ = C₆²⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	12	4+	(C2xC3:S3):3C4	144,136
(C₂×C₃⋊S₃)⋊₄C₄ = C₂×C₆.D₆	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	24		(C2xC3:S3):4C4	144,149
(C₂×C₃⋊S₃)⋊₅C₄ = C₂²×C₃²⋊C₄	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	24		(C2xC3:S3):5C4	144,191

Non-split extensions G=N.Q with N=C₂×C₃⋊S₃ and Q=C₄

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂×C₃⋊S₃).C₄ = C₂×F₉	φ: C₄/C₁ → C₄ ⊆ Out C₂×C₃⋊S₃	18	8+	(C2xC3:S3).C4	144,185
(C₂×C₃⋊S₃).₂C₄ = C₁₂.₂₉D₆	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	24	4	(C2xC3:S3).2C4	144,53
(C₂×C₃⋊S₃).₃C₄ = C₁₂.₃₁D₆	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	24	4	(C2xC3:S3).3C4	144,55
(C₂×C₃⋊S₃).₄C₄ = C₂₄⋊S₃	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	72		(C2xC3:S3).4C4	144,86
(C₂×C₃⋊S₃).₅C₄ = C₃⋊S₃⋊₃C₈	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	24	4	(C2xC3:S3).5C4	144,130
(C₂×C₃⋊S₃).₆C₄ = C₃²⋊M₄(2)	φ: C₄/C₂ → C₂ ⊆ Out C₂×C₃⋊S₃	24	4	(C2xC3:S3).6C4	144,131
(C₂×C₃⋊S₃).₇C₄ = C₈×C₃⋊S₃	φ: trivial image	72		(C2xC3:S3).7C4	144,85

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁