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

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

		d	ρ	Label	ID
C₂²×C₄×He₃		144		C2^2xC4xHe3	432,401

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×He₃)⋊₁C₂² = C₃⋊S₃⋊D₁₂	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	36	12+	(C4xHe3):1C2^2	432,301
(C₄×He₃)⋊₂C₂² = C₁₂.₈₆S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	36	6+	(C4xHe3):2C2^2	432,302
(C₄×He₃)⋊₃C₂² = D₄×C₃²⋊C₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	36	12+	(C4xHe3):3C2^2	432,360
(C₄×He₃)⋊₄C₂² = D₄×He₃⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	36	6	(C4xHe3):4C2^2	432,390
(C₄×He₃)⋊₅C₂² = C₄×C₃²⋊D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	36	6	(C4xHe3):5C2^2	432,300
(C₄×He₃)⋊₆C₂² = C₂×He₃⋊₄D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72		(C4xHe3):6C2^2	432,350
(C₄×He₃)⋊₇C₂² = C₂×He₃⋊₅D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72		(C4xHe3):7C2^2	432,386
(C₄×He₃)⋊₈C₂² = C₂×C₄×C₃²⋊C₆	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72		(C4xHe3):8C2^2	432,349
(C₄×He₃)⋊₉C₂² = C₂×C₄×He₃⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72		(C4xHe3):9C2^2	432,385
(C₄×He₃)⋊₁₀C₂² = C₂×D₄×He₃	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72		(C4xHe3):10C2^2	432,404

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

extension	φ:Q→Out N	d	ρ	Label	ID
(C₄×He₃).₁C₂² = He₃⋊₃SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).1C2^2	432,78
(C₄×He₃).₂C₂² = He₃⋊₂D₈	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6+	(C4xHe3).2C2^2	432,79
(C₄×He₃).₃C₂² = He₃⋊₂Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	144	6-	(C4xHe3).3C2^2	432,80
(C₄×He₃).₄C₂² = He₃⋊₃D₈	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12+	(C4xHe3).4C2^2	432,83
(C₄×He₃).₅C₂² = He₃⋊₄SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12-	(C4xHe3).5C2^2	432,84
(C₄×He₃).₆C₂² = He₃⋊₅SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12+	(C4xHe3).6C2^2	432,85
(C₄×He₃).₇C₂² = He₃⋊₃Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	144	12-	(C4xHe3).7C2^2	432,86
(C₄×He₃).₈C₂² = He₃⋊₈SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12-	(C4xHe3).8C2^2	432,152
(C₄×He₃).₉C₂² = He₃⋊₆D₈	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12+	(C4xHe3).9C2^2	432,153
(C₄×He₃).₁₀C₂² = He₃⋊₆Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	144	12-	(C4xHe3).10C2^2	432,160
(C₄×He₃).₁₁C₂² = He₃⋊₁₀SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12+	(C4xHe3).11C2^2	432,161
(C₄×He₃).₁₂C₂² = He₃⋊₇D₈	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).12C2^2	432,192
(C₄×He₃).₁₃C₂² = He₃⋊₉SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).13C2^2	432,193
(C₄×He₃).₁₄C₂² = He₃⋊₁₁SD₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).14C2^2	432,196
(C₄×He₃).₁₅C₂² = He₃⋊₇Q₁₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	144	6	(C4xHe3).15C2^2	432,197
(C₄×He₃).₁₆C₂² = C₃⋊S₃⋊Dic₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12-	(C4xHe3).16C2^2	432,294
(C₄×He₃).₁₇C₂² = C₁₂⋊S₃⋊S₃	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12+	(C4xHe3).17C2^2	432,295
(C₄×He₃).₁₈C₂² = C₁₂.₈₄S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).18C2^2	432,296
(C₄×He₃).₁₉C₂² = C₁₂.₈₅S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6-	(C4xHe3).19C2^2	432,298
(C₄×He₃).₂₀C₂² = C₁₂.S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12-	(C4xHe3).20C2^2	432,299
(C₄×He₃).₂₁C₂² = C₆².₁₃D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12-	(C4xHe3).21C2^2	432,361
(C₄×He₃).₂₂C₂² = Q₈×C₃²⋊C₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12-	(C4xHe3).22C2^2	432,368
(C₄×He₃).₂₃C₂² = (Q₈×He₃)⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	12+	(C4xHe3).23C2^2	432,369
(C₄×He₃).₂₄C₂² = C₆².₁₆D₆	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).24C2^2	432,391
(C₄×He₃).₂₅C₂² = Q₈×He₃⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).25C2^2	432,394
(C₄×He₃).₂₆C₂² = He₃⋊₅D₄⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).26C2^2	432,395
(C₄×He₃).₂₇C₂² = C₃²⋊C₆⋊C₈	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).27C2^2	432,76
(C₄×He₃).₂₈C₂² = He₃⋊M₄(2)	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).28C2^2	432,77
(C₄×He₃).₂₉C₂² = C₁₂.₈₉S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).29C2^2	432,81
(C₄×He₃).₃₀C₂² = He₃⋊₃M₄(2)	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).30C2^2	432,82
(C₄×He₃).₃₁C₂² = C₁₂.₉₁S₃²	φ: C₂²/C₁ → C₂² ⊆ Out C₄×He₃	72	6	(C4xHe3).31C2^2	432,297
(C₄×He₃).₃₂C₂² = He₃⋊₄Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	144	6-	(C4xHe3).32C2^2	432,114
(C₄×He₃).₃₃C₂² = He₃⋊₆SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).33C2^2	432,117
(C₄×He₃).₃₄C₂² = He₃⋊₄D₈	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6+	(C4xHe3).34C2^2	432,118
(C₄×He₃).₃₅C₂² = He₃⋊₇SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).35C2^2	432,175
(C₄×He₃).₃₆C₂² = He₃⋊₅D₈	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).36C2^2	432,176
(C₄×He₃).₃₇C₂² = He₃⋊₅Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	144	6	(C4xHe3).37C2^2	432,177
(C₄×He₃).₃₈C₂² = C₂×He₃⋊₃Q₈	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3).38C2^2	432,348
(C₄×He₃).₃₉C₂² = C₂×He₃⋊₄Q₈	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3).39C2^2	432,384
(C₄×He₃).₄₀C₂² = C₆².₄₇D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).40C2^2	432,387
(C₄×He₃).₄₁C₂² = C₈×C₃²⋊C₆	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).41C2^2	432,115
(C₄×He₃).₄₂C₂² = He₃⋊₅M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).42C2^2	432,116
(C₄×He₃).₄₃C₂² = C₂×He₃⋊₃C₈	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3).43C2^2	432,136
(C₄×He₃).₄₄C₂² = He₃⋊₇M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).44C2^2	432,137
(C₄×He₃).₄₅C₂² = C₈×He₃⋊C₂	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	3	(C4xHe3).45C2^2	432,173
(C₄×He₃).₄₆C₂² = He₃⋊₆M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).46C2^2	432,174
(C₄×He₃).₄₇C₂² = C₂×He₃⋊₄C₈	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3).47C2^2	432,184
(C₄×He₃).₄₈C₂² = He₃⋊₈M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).48C2^2	432,185
(C₄×He₃).₄₉C₂² = C₆².₃₆D₆	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).49C2^2	432,351
(C₄×He₃).₅₀C₂² = D₈×He₃	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).50C2^2	432,216
(C₄×He₃).₅₁C₂² = SD₁₆×He₃	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	72	6	(C4xHe3).51C2^2	432,219
(C₄×He₃).₅₂C₂² = Q₁₆×He₃	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	144	6	(C4xHe3).52C2^2	432,222
(C₄×He₃).₅₃C₂² = C₂×Q₈×He₃	φ: C₂²/C₂ → C₂ ⊆ Out C₄×He₃	144		(C4xHe3).53C2^2	432,407
(C₄×He₃).₅₄C₂² = C₂×C₈×He₃	φ: trivial image	144		(C4xHe3).54C2^2	432,210
(C₄×He₃).₅₅C₂² = M₄(2)×He₃	φ: trivial image	72	6	(C4xHe3).55C2^2	432,213
(C₄×He₃).₅₆C₂² = C₄○D₄×He₃	φ: trivial image	72	6	(C4xHe3).56C2^2	432,410

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

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