Extensions 1→N→G→Q→1 with N=C₂² and Q=He₃⋊₃C₄

Direct product G=N×Q with N=C₂² and Q=He₃⋊₃C₄

		d	ρ	Label	ID
C₂²×He₃⋊₃C₄		144		C2^2xHe3:3C4	432,398

Semidirect products G=N:Q with N=C₂² and Q=He₃⋊₃C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂²⋊(He₃⋊₃C₄) = C₆²⋊₆Dic₃	φ: He₃⋊₃C₄/C₃×C₆ → S₃ ⊆ Aut C₂²	36	3	C2^2:(He3:3C4)	432,260
C₂²⋊₂(He₃⋊₃C₄) = C₆²⋊₄Dic₃	φ: He₃⋊₃C₄/C₂×He₃ → C₂ ⊆ Aut C₂²	72		C2^2:2(He3:3C4)	432,199

Non-split extensions G=N.Q with N=C₂² and Q=He₃⋊₃C₄

extension	φ:Q→Aut N	d	ρ	Label	ID
C₂².(He₃⋊₃C₄) = He₃⋊₈M₄(2)	φ: He₃⋊₃C₄/C₂×He₃ → C₂ ⊆ Aut C₂²	72	6	C2^2.(He3:3C4)	432,185
C₂².₂(He₃⋊₃C₄) = C₂×He₃⋊₄C₈	central extension (φ=1)	144		C2^2.2(He3:3C4)	432,184

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C22 and Q=He3⋊3C4