Extensions 1→N→G→Q→1 with N=C₈×D₇ and Q=C₂²

Direct product G=N×Q with N=C₈×D₇ and Q=C₂²

		d	ρ	Label	ID
D₇×C₂²×C₈		224		D7xC2^2xC8	448,1189

Semidirect products G=N:Q with N=C₈×D₇ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₈×D₇)⋊₁C₂² = D₇×C₈⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	56	8+	(C8xD7):1C2^2	448,1225
(C₈×D₇)⋊₂C₂² = SD₁₆⋊D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	8-	(C8xD7):2C2^2	448,1226
(C₈×D₇)⋊₃C₂² = D₈⋊₅D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	8+	(C8xD7):3C2^2	448,1227
(C₈×D₇)⋊₄C₂² = D₈⋊₆D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	8-	(C8xD7):4C2^2	448,1228
(C₈×D₇)⋊₅C₂² = D₅₆⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	8+	(C8xD7):5C2^2	448,1230
(C₈×D₇)⋊₆C₂² = C₅₆.C₂³	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	8+	(C8xD7):6C2^2	448,1231
(C₈×D₇)⋊₇C₂² = D₈⋊₁₃D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	4	(C8xD7):7C2^2	448,1210
(C₈×D₇)⋊₈C₂² = D₈⋊₁₅D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	4+	(C8xD7):8C2^2	448,1222
(C₈×D₇)⋊₉C₂² = D₂₈.₂₉D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	4	(C8xD7):9C2^2	448,1215
(C₈×D₇)⋊₁₀C₂² = D₈⋊₁₁D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	4	(C8xD7):10C2^2	448,1223
(C₈×D₇)⋊₁₁C₂² = C₂₈.₇₀C₂⁴	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	4	(C8xD7):11C2^2	448,1198
(C₈×D₇)⋊₁₂C₂² = C₅₆.₄₉C₂³	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	4	(C8xD7):12C2^2	448,1203
(C₈×D₇)⋊₁₃C₂² = C₂×D₇×D₈	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	112		(C8xD7):13C2^2	448,1207
(C₈×D₇)⋊₁₄C₂² = C₂×D₈⋊₃D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224		(C8xD7):14C2^2	448,1209
(C₈×D₇)⋊₁₅C₂² = C₂×Q₈.D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224		(C8xD7):15C2^2	448,1218
(C₈×D₇)⋊₁₆C₂² = D₇×C₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	112	4	(C8xD7):16C2^2	448,1220
(C₈×D₇)⋊₁₇C₂² = C₂×D₇×SD₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	112		(C8xD7):17C2^2	448,1211
(C₈×D₇)⋊₁₈C₂² = C₂×SD₁₆⋊₃D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224		(C8xD7):18C2^2	448,1214
(C₈×D₇)⋊₁₉C₂² = C₂×D₂₈.₂C₄	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224		(C8xD7):19C2^2	448,1191
(C₈×D₇)⋊₂₀C₂² = D₇×C₈○D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	112	4	(C8xD7):20C2^2	448,1202
(C₈×D₇)⋊₂₁C₂² = C₂×D₇×M₄(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	112		(C8xD7):21C2^2	448,1196
(C₈×D₇)⋊₂₂C₂² = C₂×D₂₈.C₄	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224		(C8xD7):22C2^2	448,1197

Non-split extensions G=N.Q with N=C₈×D₇ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
(C₈×D₇).₁C₂² = D₇×C₈.C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	8-	(C8xD7).1C2^2	448,1229
(C₈×D₇).₂C₂² = D₂₈.₄₄D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	224	8-	(C8xD7).2C2^2	448,1232
(C₈×D₇).₃C₂² = D₈⋊D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	4	(C8xD7).3C2^2	448,445
(C₈×D₇).₄C₂² = D₁₁₂⋊C₂	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	112	4+	(C8xD7).4C2^2	448,448
(C₈×D₇).₅C₂² = SD₃₂⋊D₇	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	224	4-	(C8xD7).5C2^2	448,449
(C₈×D₇).₆C₂² = Q₃₂⋊D₇	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	224	4	(C8xD7).6C2^2	448,452
(C₈×D₇).₇C₂² = D₂₈.₃₀D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	224	4	(C8xD7).7C2^2	448,1219
(C₈×D₇).₈C₂² = D₈.₁₀D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₈×D₇	224	4-	(C8xD7).8C2^2	448,1224
(C₈×D₇).₉C₂² = D₇×D₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	112	4+	(C8xD7).9C2^2	448,444
(C₈×D₇).₁₀C₂² = D₁₆⋊₃D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224	4-	(C8xD7).10C2^2	448,446
(C₈×D₇).₁₁C₂² = D₇×SD₃₂	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	112	4	(C8xD7).11C2^2	448,447
(C₈×D₇).₁₂C₂² = SD₃₂⋊₃D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224	4	(C8xD7).12C2^2	448,450
(C₈×D₇).₁₃C₂² = D₇×Q₃₂	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224	4-	(C8xD7).13C2^2	448,451
(C₈×D₇).₁₄C₂² = Q₃₂⋊₃D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224	4+	(C8xD7).14C2^2	448,453
(C₈×D₇).₁₅C₂² = C₂×D₇×Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224		(C8xD7).15C2^2	448,1216
(C₈×D₇).₁₆C₂² = C₂×C₁₆⋊D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224		(C8xD7).16C2^2	448,434
(C₈×D₇).₁₇C₂² = D₂₈.₄C₈	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224	2	(C8xD7).17C2^2	448,435
(C₈×D₇).₁₈C₂² = D₇×M₅(2)	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	112	4	(C8xD7).18C2^2	448,440
(C₈×D₇).₁₉C₂² = C₁₆.₁₂D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₈×D₇	224	4	(C8xD7).19C2^2	448,441
(C₈×D₇).₂₀C₂² = D₇×C₂×C₁₆	φ: trivial image	224		(C8xD7).20C2^2	448,433

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=C8×D7 and Q=C22

Extensions 1→N→G→Q→1 with N=C₈×D₇ and Q=C₂²