Extensions 1→N→G→Q→1 with N=C₇⋊Q₁₆ and Q=C₂²

Direct product G=N×Q with N=C₇⋊Q₁₆ and Q=C₂²

		d	ρ	Label	ID
C₂²×C₇⋊Q₁₆		448		C2^2xC7:Q16	448,1262

Semidirect products G=N:Q with N=C₇⋊Q₁₆ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₇⋊Q₁₆⋊₁C₂² = D₂₈.₂₉D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₇⋊Q₁₆	112	4	C7:Q16:1C2^2	448,1215
C₇⋊Q₁₆⋊₂C₂² = D₈⋊₁₁D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₇⋊Q₁₆	112	4	C7:Q16:2C2^2	448,1223
C₇⋊Q₁₆⋊₃C₂² = SD₁₆⋊D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₇⋊Q₁₆	112	8-	C7:Q16:3C2^2	448,1226
C₇⋊Q₁₆⋊₄C₂² = D₇×C₈.C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₇⋊Q₁₆	112	8-	C7:Q16:4C2^2	448,1229
C₇⋊Q₁₆⋊₅C₂² = D₅₆⋊C₂²	φ: C₂²/C₁ → C₂² ⊆ Out C₇⋊Q₁₆	112	8+	C7:Q16:5C2^2	448,1230
C₇⋊Q₁₆⋊₆C₂² = C₂×SD₁₆⋊D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	224		C7:Q16:6C2^2	448,1213
C₇⋊Q₁₆⋊₇C₂² = C₂×SD₁₆⋊₃D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	224		C7:Q16:7C2^2	448,1214
C₇⋊Q₁₆⋊₈C₂² = C₂×D₇×Q₁₆	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	224		C7:Q16:8C2^2	448,1216
C₇⋊Q₁₆⋊₉C₂² = C₂×Q₁₆⋊D₇	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	224		C7:Q16:9C2^2	448,1217
C₇⋊Q₁₆⋊₁₀C₂² = D₇×C₄○D₈	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	112	4	C7:Q16:10C2^2	448,1220
C₇⋊Q₁₆⋊₁₁C₂² = D₈⋊₁₀D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	112	4	C7:Q16:11C2^2	448,1221
C₇⋊Q₁₆⋊₁₂C₂² = D₈⋊₅D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	112	8+	C7:Q16:12C2^2	448,1227
C₇⋊Q₁₆⋊₁₃C₂² = D₈⋊₆D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	112	8-	C7:Q16:13C2^2	448,1228
C₇⋊Q₁₆⋊₁₄C₂² = C₅₆.C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	112	8+	C7:Q16:14C2^2	448,1231
C₇⋊Q₁₆⋊₁₅C₂² = C₂×C₂₈.C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	224		C7:Q16:15C2^2	448,1261
C₇⋊Q₁₆⋊₁₆C₂² = C₂₈.C₂⁴	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	112	4	C7:Q16:16C2^2	448,1275
C₇⋊Q₁₆⋊₁₇C₂² = C₂×D₄.₉D₁₄	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	224		C7:Q16:17C2^2	448,1276
C₇⋊Q₁₆⋊₁₈C₂² = D₂₈.₃₃C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	112	8-	C7:Q16:18C2^2	448,1289
C₇⋊Q₁₆⋊₁₉C₂² = D₂₈.₃₄C₂³	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	112	8+	C7:Q16:19C2^2	448,1290
C₇⋊Q₁₆⋊₂₀C₂² = C₂×D₄.₈D₁₄	φ: trivial image	224		C7:Q16:20C2^2	448,1274
C₇⋊Q₁₆⋊₂₁C₂² = D₂₈.₃₂C₂³	φ: trivial image	112	8+	C7:Q16:21C2^2	448,1288

Non-split extensions G=N.Q with N=C₇⋊Q₁₆ and Q=C₂²

extension	φ:Q→Out N	d	ρ	Label	ID
C₇⋊Q₁₆.₁C₂² = D₂₈.₃₀D₄	φ: C₂²/C₁ → C₂² ⊆ Out C₇⋊Q₁₆	224	4	C7:Q16.1C2^2	448,1219
C₇⋊Q₁₆.₂C₂² = D₈.₁₀D₁₄	φ: C₂²/C₁ → C₂² ⊆ Out C₇⋊Q₁₆	224	4-	C7:Q16.2C2^2	448,1224
C₇⋊Q₁₆.₃C₂² = D₂₈.₄₄D₄	φ: C₂²/C₂ → C₂ ⊆ Out C₇⋊Q₁₆	224	8-	C7:Q16.3C2^2	448,1232
C₇⋊Q₁₆.₄C₂² = D₂₈.₃₅C₂³	φ: trivial image	224	8-	C7:Q16.4C2^2	448,1291

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Extensions 1→N→G→Q→1 with N=C7⋊Q16 and Q=C22

Extensions 1→N→G→Q→1 with N=C₇⋊Q₁₆ and Q=C₂²