Extensions 1→N→G→Q→1 with N=C₆² and Q=C₄

Direct product G=N×Q with N=C₆² and Q=C₄

		d	ρ	Label	ID
C₂×C₆×C₁₂		144		C2xC6xC12	144,178

Semidirect products G=N:Q with N=C₆² and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆²⋊₁C₄ = C₆²⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₆²	12	4+	C6^2:1C4	144,136
C₆²⋊₂C₄ = C₂²×C₃²⋊C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₆²	24		C6^2:2C4	144,191
C₆²⋊₃C₄ = C₃²×C₂²⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	72		C6^2:3C4	144,102
C₆²⋊₄C₄ = C₃×C₆.D₄	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	24		C6^2:4C4	144,84
C₆²⋊₅C₄ = C₆²⋊₅C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	72		C6^2:5C4	144,100
C₆²⋊₆C₄ = Dic₃×C₂×C₆	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	48		C6^2:6C4	144,166
C₆²⋊₇C₄ = C₂²×C₃⋊Dic₃	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	144		C6^2:7C4	144,176

Non-split extensions G=N.Q with N=C₆² and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₆².₁C₄ = C₂×C₃²⋊₂C₈	φ: C₄/C₁ → C₄ ⊆ Aut C₆²	48		C6^2.1C4	144,134
C₆².₂C₄ = C₆².C₄	φ: C₄/C₁ → C₄ ⊆ Aut C₆²	24	4-	C6^2.2C4	144,135
C₆².₃C₄ = C₃²×M₄(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	72		C6^2.3C4	144,105
C₆².₄C₄ = C₆×C₃⋊C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	48		C6^2.4C4	144,74
C₆².₅C₄ = C₃×C₄.Dic₃	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	24	2	C6^2.5C4	144,75
C₆².₆C₄ = C₂×C₃²⋊₄C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	144		C6^2.6C4	144,90
C₆².₇C₄ = C₁₂.₅₈D₆	φ: C₄/C₂ → C₂ ⊆ Aut C₆²	72		C6^2.7C4	144,91

׿

×

⋊

ℤ

𝔽

○

≀

ℚ

◁