Extensions 1→N→G→Q→1 with N=Dic₁₅ and Q=C₂³

Direct product G=N×Q with N=Dic₁₅ and Q=C₂³

		d	ρ	Label	ID
C₂³×Dic₁₅		480		C2^3xDic15	480,1178

Semidirect products G=N:Q with N=Dic₁₅ and Q=C₂³

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₅⋊₁C₂³ = S₃×D₄×D₅	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	60	8+	Dic15:1C2^3	480,1097
Dic₁₅⋊₂C₂³ = C₂×D₅×C₃⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120		Dic15:2C2^3	480,1122
Dic₁₅⋊₃C₂³ = C₂×S₃×C₅⋊D₄	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120		Dic15:3C2^3	480,1123
Dic₁₅⋊₄C₂³ = C₂×D₄×D₁₅	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120		Dic15:4C2^3	480,1169
Dic₁₅⋊₅C₂³ = C₂²×C₁₅⋊₇D₄	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15:5C2^3	480,1179
Dic₁₅⋊₆C₂³ = S₃×C₂×C₄×D₅	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120		Dic15:6C2^3	480,1086
Dic₁₅⋊₇C₂³ = C₂×C₂₀⋊D₆	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120		Dic15:7C2^3	480,1089
Dic₁₅⋊₈C₂³ = C₂²×D₅×Dic₃	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15:8C2^3	480,1112
Dic₁₅⋊₉C₂³ = C₂²×S₃×Dic₅	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15:9C2^3	480,1115
Dic₁₅⋊₁₀C₂³ = C₂²×C₁₅⋊D₄	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15:10C2^3	480,1118
Dic₁₅⋊₁₁C₂³ = C₂²×C₄×D₁₅	φ: trivial image	240		Dic15:11C2^3	480,1166

Non-split extensions G=N.Q with N=Dic₁₅ and Q=C₂³

extension	φ:Q→Out N	d	ρ	Label	ID
Dic₁₅.₁C₂³ = C₂×D₅×Dic₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240		Dic15.1C2^3	480,1073
Dic₁₅.₂C₂³ = C₂×D₂₀⋊₅S₃	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240		Dic15.2C2^3	480,1074
Dic₁₅.₃C₂³ = D₂₀.₃₈D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240	4	Dic15.3C2^3	480,1076
Dic₁₅.₄C₂³ = D₂₀.₃₉D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240	4-	Dic15.4C2^3	480,1077
Dic₁₅.₅C₂³ = C₂×S₃×Dic₁₀	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240		Dic15.5C2^3	480,1078
Dic₁₅.₆C₂³ = C₃₀.C₂⁴	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240	4	Dic15.6C2^3	480,1080
Dic₁₅.₇C₂³ = C₂×D₁₂⋊₅D₅	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240		Dic15.7C2^3	480,1084
Dic₁₅.₈C₂³ = D₅×C₄○D₁₂	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	4	Dic15.8C2^3	480,1090
Dic₁₅.₉C₂³ = S₃×C₄○D₂₀	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	4	Dic15.9C2^3	480,1091
Dic₁₅.₁₀C₂³ = D₂₀⋊₂₅D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	4	Dic15.10C2^3	480,1093
Dic₁₅.₁₁C₂³ = D₂₀⋊₂₆D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	4	Dic15.11C2^3	480,1094
Dic₁₅.₁₂C₂³ = C₁₅⋊2_-¹⁺⁴	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240	8-	Dic15.12C2^3	480,1096
Dic₁₅.₁₃C₂³ = D₅×D₄⋊₂S₃	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	8-	Dic15.13C2^3	480,1098
Dic₁₅.₁₄C₂³ = S₃×D₄⋊₂D₅	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	8-	Dic15.14C2^3	480,1099
Dic₁₅.₁₅C₂³ = D₃₀.C₂³	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	8+	Dic15.15C2^3	480,1100
Dic₁₅.₁₆C₂³ = D₂₀⋊₁₃D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	8-	Dic15.16C2^3	480,1101
Dic₁₅.₁₇C₂³ = D₂₀⋊₁₄D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	8+	Dic15.17C2^3	480,1102
Dic₁₅.₁₈C₂³ = D₁₂⋊₁₄D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	8+	Dic15.18C2^3	480,1103
Dic₁₅.₁₉C₂³ = D₂₀.₂₉D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240	8-	Dic15.19C2^3	480,1104
Dic₁₅.₂₀C₂³ = D₁₂.₂₉D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240	8-	Dic15.20C2^3	480,1106
Dic₁₅.₂₁C₂³ = S₃×Q₈×D₅	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	8-	Dic15.21C2^3	480,1107
Dic₁₅.₂₂C₂³ = D₂₀⋊₁₆D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	8-	Dic15.22C2^3	480,1110
Dic₁₅.₂₃C₂³ = C₂×Dic₅.D₆	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240		Dic15.23C2^3	480,1113
Dic₁₅.₂₄C₂³ = C₂×Dic₃.D₁₀	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	240		Dic15.24C2^3	480,1116
Dic₁₅.₂₅C₂³ = C₁₅⋊2₊¹⁺⁴	φ: C₂³/C₂ → C₂² ⊆ Out Dic₁₅	120	4	Dic15.25C2^3	480,1125
Dic₁₅.₂₆C₂³ = C₂²×Dic₃₀	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	480		Dic15.26C2^3	480,1165
Dic₁₅.₂₇C₂³ = C₂×D₆₀⋊₁₁C₂	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15.27C2^3	480,1168
Dic₁₅.₂₈C₂³ = D₄⋊₆D₃₀	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120	4	Dic15.28C2^3	480,1171
Dic₁₅.₂₉C₂³ = C₂×Q₈×D₁₅	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15.29C2^3	480,1172
Dic₁₅.₃₀C₂³ = Q₈.₁₅D₃₀	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240	4	Dic15.30C2^3	480,1174
Dic₁₅.₃₁C₂³ = C₄○D₄×D₁₅	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120	4	Dic15.31C2^3	480,1175
Dic₁₅.₃₂C₂³ = D₄⋊₈D₃₀	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120	4+	Dic15.32C2^3	480,1176
Dic₁₅.₃₃C₂³ = D₄.₁₀D₃₀	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240	4-	Dic15.33C2^3	480,1177
Dic₁₅.₃₄C₂³ = C₂×D₂₀⋊S₃	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15.34C2^3	480,1075
Dic₁₅.₃₅C₂³ = C₂×D₁₂⋊D₅	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15.35C2^3	480,1079
Dic₁₅.₃₆C₂³ = C₂×D₁₅⋊Q₈	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15.36C2^3	480,1082
Dic₁₅.₃₇C₂³ = C₂×D₆.D₁₀	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15.37C2^3	480,1083
Dic₁₅.₃₈C₂³ = D₂₀⋊₂₄D₆	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120	4	Dic15.38C2^3	480,1092
Dic₁₅.₃₉C₂³ = C₃₀.₃₃C₂⁴	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240	8+	Dic15.39C2^3	480,1105
Dic₁₅.₄₀C₂³ = D₅×Q₈⋊₃S₃	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120	8+	Dic15.40C2^3	480,1108
Dic₁₅.₄₁C₂³ = S₃×Q₈⋊₂D₅	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120	8+	Dic15.41C2^3	480,1109
Dic₁₅.₄₂C₂³ = D₂₀⋊₁₇D₆	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	120	8+	Dic15.42C2^3	480,1111
Dic₁₅.₄₃C₂³ = C₂×C₃₀.C₂³	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	240		Dic15.43C2^3	480,1114
Dic₁₅.₄₄C₂³ = C₂²×C₁₅⋊Q₈	φ: C₂³/C₂² → C₂ ⊆ Out Dic₁₅	480		Dic15.44C2^3	480,1121
Dic₁₅.₄₅C₂³ = C₂×D₄⋊₂D₁₅	φ: trivial image	240		Dic15.45C2^3	480,1170
Dic₁₅.₄₆C₂³ = C₂×Q₈⋊₃D₁₅	φ: trivial image	240		Dic15.46C2^3	480,1173

⋊

ℤ

𝔽

○

≀

ℚ

◁

Extensions 1→N→G→Q→1 with N=Dic15 and Q=C23

Extensions 1→N→G→Q→1 with N=Dic₁₅ and Q=C₂³