Extensions 1→N→G→Q→1 with N=C₂²×He₃ and Q=C₂²

Direct product G=N×Q with N=C₂²×He₃ and Q=C₂²

		d	ρ	Label	ID
C₂⁴×He₃		144		C2^4xHe3	432,563

Semidirect products G=N:Q with N=C₂²×He₃ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃)⋊₁C₂² = C₆²⋊D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	36	12+	(C2^2xHe3):1C2^2	432,323
(C₂²×He₃)⋊₂C₂² = C₆²⋊₂D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	36	6	(C2^2xHe3):2C2^2	432,324
(C₂²×He₃)⋊₃C₂² = D₄×C₃²⋊C₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	36	12+	(C2^2xHe3):3C2^2	432,360
(C₂²×He₃)⋊₄C₂² = D₄×He₃⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	36	6	(C2^2xHe3):4C2^2	432,390
(C₂²×He₃)⋊₅C₂² = C₂²×C₃²⋊D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	36		(C2^2xHe3):5C2^2	432,545
(C₂²×He₃)⋊₆C₂² = C₂×D₄×He₃	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3):6C2^2	432,404
(C₂²×He₃)⋊₇C₂² = C₂×He₃⋊₆D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3):7C2^2	432,377
(C₂²×He₃)⋊₈C₂² = C₂×He₃⋊₇D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3):8C2^2	432,399
(C₂²×He₃)⋊₉C₂² = C₂³×C₃²⋊C₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3):9C2^2	432,558
(C₂²×He₃)⋊₁₀C₂² = C₂³×He₃⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3):10C2^2	432,561

Non-split extensions G=N.Q with N=C₂²×He₃ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₂²×He₃).₁C₂² = He₃⋊C₄²	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	144		(C2^2xHe3).1C2^2	432,94
(C₂²×He₃).₂C₂² = C₆².D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	144		(C2^2xHe3).2C2^2	432,95
(C₂²×He₃).₃C₂² = C₆².₃D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	144		(C2^2xHe3).3C2^2	432,96
(C₂²×He₃).₄C₂² = C₆².₄D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72		(C2^2xHe3).4C2^2	432,97
(C₂²×He₃).₅C₂² = C₆².₅D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72		(C2^2xHe3).5C2^2	432,98
(C₂²×He₃).₆C₂² = C₂×He₃⋊₂Q₈	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	144		(C2^2xHe3).6C2^2	432,316
(C₂²×He₃).₇C₂² = C₂×C₆.S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72		(C2^2xHe3).7C2^2	432,317
(C₂²×He₃).₈C₂² = C₆².₈D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72	12-	(C2^2xHe3).8C2^2	432,318
(C₂²×He₃).₉C₂² = C₆².₉D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).9C2^2	432,319
(C₂²×He₃).₁₀C₂² = C₂×He₃⋊₂D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72		(C2^2xHe3).10C2^2	432,320
(C₂²×He₃).₁₁C₂² = C₂×He₃⋊(C₂×C₄)	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72		(C2^2xHe3).11C2^2	432,321
(C₂²×He₃).₁₂C₂² = C₂×He₃⋊₃D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72		(C2^2xHe3).12C2^2	432,322
(C₂²×He₃).₁₃C₂² = C₆².₁₃D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72	12-	(C2^2xHe3).13C2^2	432,361
(C₂²×He₃).₁₄C₂² = C₆².₁₆D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).14C2^2	432,391
(C₂²×He₃).₁₅C₂² = C₄○D₄×He₃	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).15C2^2	432,410
(C₂²×He₃).₁₆C₂² = C₄×C₃²⋊C₁₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).16C2^2	432,138
(C₂²×He₃).₁₇C₂² = C₆².₁₉D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).17C2^2	432,139
(C₂²×He₃).₁₈C₂² = C₆².₂₀D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).18C2^2	432,140
(C₂²×He₃).₁₉C₂² = C₆².₂₁D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).19C2^2	432,141
(C₂²×He₃).₂₀C₂² = C₆²⋊₃C₁₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).20C2^2	432,166
(C₂²×He₃).₂₁C₂² = C₄×He₃⋊₃C₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).21C2^2	432,186
(C₂²×He₃).₂₂C₂² = C₆².₂₉D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).22C2^2	432,187
(C₂²×He₃).₂₃C₂² = C₆².₃₀D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).23C2^2	432,188
(C₂²×He₃).₂₄C₂² = C₆².₃₁D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).24C2^2	432,189
(C₂²×He₃).₂₅C₂² = C₆²⋊₄Dic₃	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).25C2^2	432,199
(C₂²×He₃).₂₆C₂² = C₂×He₃⋊₃Q₈	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).26C2^2	432,348
(C₂²×He₃).₂₇C₂² = C₂×C₄×C₃²⋊C₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).27C2^2	432,349
(C₂²×He₃).₂₈C₂² = C₂×He₃⋊₄D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).28C2^2	432,350
(C₂²×He₃).₂₉C₂² = C₆².₃₆D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).29C2^2	432,351
(C₂²×He₃).₃₀C₂² = C₂²×C₃²⋊C₁₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).30C2^2	432,376
(C₂²×He₃).₃₁C₂² = C₂×He₃⋊₄Q₈	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).31C2^2	432,384
(C₂²×He₃).₃₂C₂² = C₂×C₄×He₃⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).32C2^2	432,385
(C₂²×He₃).₃₃C₂² = C₂×He₃⋊₅D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72		(C2^2xHe3).33C2^2	432,386
(C₂²×He₃).₃₄C₂² = C₆².₄₇D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	72	6	(C2^2xHe3).34C2^2	432,387
(C₂²×He₃).₃₅C₂² = C₂²×He₃⋊₃C₄	φ: C₂²/C₂ → C₂ ⊆ Out C₂²×He₃	144		(C2^2xHe3).35C2^2	432,398
(C₂²×He₃).₃₆C₂² = C₄²×He₃	φ: trivial image	144		(C2^2xHe3).36C2^2	432,201
(C₂²×He₃).₃₇C₂² = C₂²⋊C₄×He₃	φ: trivial image	72		(C2^2xHe3).37C2^2	432,204
(C₂²×He₃).₃₈C₂² = C₄⋊C₄×He₃	φ: trivial image	144		(C2^2xHe3).38C2^2	432,207
(C₂²×He₃).₃₉C₂² = C₂²×C₄×He₃	φ: trivial image	144		(C2^2xHe3).39C2^2	432,401
(C₂²×He₃).₄₀C₂² = C₂×Q₈×He₃	φ: trivial image	144		(C2^2xHe3).40C2^2	432,407

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C22×He3 and Q=C22

Extensions 1→N→G→Q→1 with N=C₂²×He₃ and Q=C₂²