Extensions 1→N→G→Q→1 with N=C₇₂ and Q=C₄

Direct product G=N×Q with N=C₇₂ and Q=C₄

		d	ρ	Label	ID
C₄×C₇₂		288		C4xC72	288,46

Semidirect products G=N:Q with N=C₇₂ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₂⋊₁C₄ = C₇₂⋊₁C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288		C72:1C4	288,26
C₇₂⋊₂C₄ = C₈⋊Dic₉	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288		C72:2C4	288,25
C₇₂⋊₃C₄ = C₈×Dic₉	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288		C72:3C4	288,21
C₇₂⋊₄C₄ = C₇₂⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288		C72:4C4	288,23
C₇₂⋊₅C₄ = C₉×C₂.D₈	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288		C72:5C4	288,57
C₇₂⋊₆C₄ = C₉×C₄.Q₈	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288		C72:6C4	288,56
C₇₂⋊₇C₄ = C₉×C₈⋊C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288		C72:7C4	288,47

Non-split extensions G=N.Q with N=C₇₂ and Q=C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₇₂.₁C₄ = C₇₂.C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	144	2	C72.1C4	288,20
C₇₂.₂C₄ = C₉⋊C₃₂	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288	2	C72.2C4	288,1
C₇₂.₃C₄ = C₂×C₉⋊C₁₆	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	288		C72.3C4	288,18
C₇₂.₄C₄ = C₃₆.C₈	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	144	2	C72.4C4	288,19
C₇₂.₅C₄ = C₉×C₈.C₄	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	144	2	C72.5C4	288,58
C₇₂.₆C₄ = C₉×M₅(2)	φ: C₄/C₂ → C₂ ⊆ Aut C₇₂	144	2	C72.6C4	288,60

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