Group #41006864 — subgroups

Subgroups — #41006864

Order 26973.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688514	C₃	1	1	yes	maximal, characteristic
2	#22582572	C₃	1	1	yes	maximal, characteristic, complemented
3	#22582558	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×#15688502	C₃	1	1	yes	maximal, characteristic, complemented
5	#22582481	C₃	1	1	yes	maximal, characteristic, complemented
6	#22582481	C₃	1	1	yes	maximal, characteristic, complemented
7	3₋¹⁺²⋊#66524	C₃	1	1	yes	maximal, characteristic, complemented
8	3₋¹⁺²⋊#66524	C₃	1	1	yes	maximal, characteristic, complemented
9	#22582475	C₃	1	1	yes	maximal, characteristic, complemented
10	#22582475	C₃	1	1	yes	maximal, characteristic, complemented
11	#22582467	C₃	1	1	yes	maximal, characteristic, complemented
12	#22582467	C₃	1	1	yes	maximal, characteristic, complemented
13	C₃₇×#6894	C₃	1	1	yes	maximal, characteristic, complemented
14	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
15	C₃×#11758608	C₃²	1	1	yes	characteristic
16	C₃×#11758605	—	3	1	no	—
17	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
18	C₃²×#66524	C₃²	1	1	yes	characteristic
19	C₃²×#66524	C₃²	1	1	yes	characteristic
20	#15688514	—	3	3	no	—
21	#15688506	—	3	1	no	—
22	#15688504	—	3	1	no	—
23	#15688504	—	3	1	no	—
24	C₃²⋊#66524	C₃²	1	1	yes	characteristic
25	C₃²⋊#66524	C₃²	1	1	yes	characteristic
26	C₃²⋊#66524	C₃²	1	1	yes	characteristic
27	C₃²⋊#66524	C₃²	1	1	yes	characteristic
28	#15688502	—	3	1	no	—
29	#15688502	—	3	1	no	—
30	#15688502	—	3	1	no	—
31	#15688502	—	3	1	no	—
32	#15688502	—	3	1	no	—
33	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
34	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
35	C₃₇×C₉⋊C₉	—	3	1	no	—
36	C₃₇×C₉⋊C₉	—	3	1	no	—
37	C₃₇×C₉⋊C₉	—	3	1	no	—
38	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
39	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
40	C₃³×C₃₇	C₃³	1	1	yes	characteristic
41	C₃²×C₃₇⋊C₃	—	3	1	no	—
42	C₃²×C₃₇⋊C₃	—	3	2	no	—
43	C₃²×C₃₇⋊C₃	—	3	1	no	—
44	C₃²×C₃₇⋊C₃	—	9	1	no	—
45	C₃²×C₃₇⋊C₃	—	9	1	no	—
46	C₃²×C₃₇⋊C₃	—	9	1	no	—
47	C₃²×C₃₇⋊C₃	3₋¹⁺²	1	3	yes	complemented
48	3₋¹⁺²×C₃₇	—	3	1	no	—
49	3₋¹⁺²×C₃₇	—	3	2	no	—
50	C₃×C₉×C₃₇	—	3	1	no	—
51	C₃×C₉×C₃₇	—	3	1	no	—
52	C₃×C₉×C₃₇	—	3	1	no	—
53	C₃×C₉×C₃₇	—	9	1	no	—
54	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
55	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
56	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
57	C₃²⋊(C₃₇⋊C₃)	—	3	1	no	—
58	C₃²⋊(C₃₇⋊C₃)	—	3	2	no	—
59	#11758608	—	3	1	no	—
60	#11758608	—	3	2	no	—
61	C₃×#66524	—	3	1	no	—
62	C₃×#66524	—	3	1	no	—
63	C₃×#66524	—	3	1	no	—
64	C₃×#66524	—	3	1	no	—
65	C₃×#66524	—	3	1	no	—
66	C₃×#66524	—	3	1	no	—
67	C₃×#66524	—	3	1	no	—
68	C₃×#66524	—	9	1	no	—
69	C₃×#66524	—	9	1	no	—
70	#11758605	—	9	3	no	—
71	#10624788	—	37	1	no	maximal, Sylow
72	C₃²×C₃₇	—	3	1	no	—
73	C₃²×C₃₇	—	3	1	no	—
74	C₃²×C₃₇	—	3	1	no	—
75	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
76	C₃²×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
77	C₃²×C₃₇	#737	1	2	yes	—
78	C₃×C₃₇⋊C₃	—	3	3	no	—
79	C₃×C₃₇⋊C₃	—	9	6	no	—
80	C₃×C₃₇⋊C₃	—	9	1	no	—
81	C₃×C₃₇⋊C₃	—	9	1	no	—
82	C₃×C₃₇⋊C₃	—	9	1	no	—
83	C₃×C₃₇⋊C₃	—	9	3	no	—
84	C₃×C₃₇⋊C₃	—	9	1	no	—
85	C₃×C₃₇⋊C₃	—	9	1	no	—
86	C₃×C₃₇⋊C₃	—	9	1	no	—
87	C₃×C₃₇⋊C₃	—	9	1	no	—
88	C₉×C₃₇	—	3	1	no	—
89	C₉×C₃₇	—	3	1	no	—
90	C₉×C₃₇	—	3	1	no	—
91	C₉×C₃₇	—	9	1	no	—
92	C₉×C₃₇	—	9	1	no	—
93	C₉×C₃₇	—	9	1	no	—
94	#66524	—	9	1	no	—
95	#66524	—	9	1	no	—
96	#66524	—	9	1	no	—
97	#66524	—	9	1	no	—
98	#66524	—	9	1	no	—
99	#66524	—	9	1	no	—
100	#66524	—	9	1	no	—
101	C₃×AΣL(1,𝔽₂₇)	—	37	1	no	—
102	#6894	—	37	1	no	—
103	#6894	C₃₇⋊C₃	1	1	yes	characteristic, complemented
104	C₉⋊H(3,𝔽₃)	—	37	1	no	—
105	C₃×C₃²⋊C₉	—	37	1	no	—
106	3₋¹⁺²⋊C₉	—	37	1	no	—
107	3₋¹⁺²⋊C₉	—	37	1	no	—
108	3₋¹⁺²⋊C₉	—	37	1	no	—
109	3₋¹⁺²⋊C₉	—	37	1	no	—
110	H(3,𝔽₃)⋊C₉	—	37	1	no	—
111	H(3,𝔽₃)⋊C₉	—	37	1	no	—
112	#6866	—	37	1	no	—
113	#6866	—	37	1	no	—
114	C₃×C₃₇	—	3	1	no	—
115	C₃×C₃₇	—	3	2	no	—
116	C₃×C₃₇	C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
117	C₃×C₃₇	#6909	1	1	yes	characteristic
118	C₃×C₃₇	#6913	1	1	yes	characteristic
119	C₃×C₃₇	#6913	1	1	yes	characteristic
120	C₃₇⋊C₃	—	9	3	no	—
121	C₃₇⋊C₃	—	27	1	no	—
122	C₃⁴	—	37	1	no	—
123	C₃×3₋¹⁺²	—	37	1	no	—
124	C₃×3₋¹⁺²	—	111	1	no	—
125	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
126	C₃×H(3,𝔽₃)	—	37	1	no	—
127	C₃²×C₉	—	37	1	no	—
128	C₃²×C₉	—	37	1	no	—
129	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
130	AΣL(1,𝔽₂₇)	—	111	3	no	—
131	C₉⋊C₉	—	3	1	no	—
132	C₉⋊C₉	—	3	1	no	—
133	C₉⋊C₉	—	3	1	no	—
134	C₉⋊C₉	—	111	1	no	—
135	C₉⋊C₉	—	111	1	no	—
136	C₉⋊C₉	—	111	1	no	—
137	C₃²⋊C₉	—	37	1	no	—
138	C₃²⋊C₉	—	37	1	no	—
139	C₃²⋊C₉	—	37	1	no	—
140	C₃²⋊C₉	—	37	1	no	—
141	C₃²⋊C₉	—	111	1	no	—
142	C₃²⋊C₉	—	111	1	no	—
143	C₃²⋊C₉	—	111	1	no	—
144	C₃²⋊C₉	—	111	1	no	—
145	C₃²⋊C₉	—	111	1	no	—
146	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
147	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
148	C₃₇	#10624788	1	1	yes	characteristic, complemented, Sylow
149	C₃³	—	37	3	no	—
150	C₃³	—	333	1	no	—
151	C₃³	—	333	1	no	—
152	C₃³	—	333	1	no	—
153	C₃³	—	111	1	no	—
154	C₃³	—	111	1	no	—
155	C₃³	—	111	2	no	—
156	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
157	3₋¹⁺²	—	3	1	no	—
158	3₋¹⁺²	—	3	2	no	—
159	3₋¹⁺²	—	333	3	no	—
160	3₋¹⁺²	—	111	1	no	—
161	3₋¹⁺²	—	111	2	no	—
162	H(3,𝔽₃)	—	111	1	no	—
163	H(3,𝔽₃)	—	111	2	no	—
164	C₃×C₉	—	3	1	no	—
165	C₃×C₉	—	3	1	no	—
166	C₃×C₉	—	3	1	no	—
167	C₃×C₉	—	9	1	no	—
168	C₃×C₉	—	333	1	no	—
169	C₃×C₉	—	333	1	no	—
170	C₃×C₉	—	111	1	no	—
171	C₃×C₉	—	111	1	no	—
172	C₃×C₉	—	111	1	no	—
173	C₃×C₉	—	111	1	no	—
174	C₃×C₉	—	111	1	no	—
175	C₃×C₉	—	111	1	no	—
176	C₃×C₉	—	111	1	no	—
177	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
178	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
179	C₃×C₉	C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
180	C₃²	—	3	1	no	—
181	C₃²	—	3	1	no	—
182	C₃²	—	3	1	no	—
183	C₃²	—	333	3	no	—
184	C₃²	—	333	6	no	—
185	C₃²	—	333	1	no	—
186	C₃²	—	333	1	no	—
187	C₃²	—	333	1	no	—
188	C₃²	—	333	1	no	—
189	C₃²	—	333	1	no	—
190	C₃²	—	333	1	no	—
191	C₃²	—	333	1	no	—
192	C₃²	—	111	3	no	—
193	C₃²	C₃×C₃²⋊(C₃₇⋊C₃)	1	1	yes	characteristic
194	C₃²	3₋¹⁺²×C₃₇⋊C₃	1	1	yes	characteristic
195	C₃²	#15688532	1	2	yes	—
196	C₉	—	3	1	no	—
197	C₉	—	3	1	no	—
198	C₉	—	3	1	no	—
199	C₉	—	9	1	no	—
200	C₉	—	9	1	no	—
201	C₉	—	9	1	no	—
202	C₉	—	333	1	no	—
203	C₉	—	333	1	no	—
204	C₉	—	333	1	no	—
205	C₉	—	333	1	no	—
206	C₉	—	333	1	no	—
207	C₉	—	333	1	no	—
208	C₉	—	333	1	no	—
209	C₃	—	3	1	no	—
210	C₃	—	3	2	no	—
211	C₃	—	333	3	no	—
212	C₃	—	999	1	no	—
213	C₃	#22582555	1	1	yes	characteristic
214	C₃	#22582639	1	1	yes	characteristic
215	C₃	#22582655	1	1	yes	characteristic
216	C₃	#22582656	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#15688514

C₃

yes

maximal, characteristic

#22582572

C₃

yes

maximal, characteristic, complemented

#22582558

C₃

yes

maximal, characteristic, complemented

C₃×#15688502

C₃

yes

maximal, characteristic, complemented

#22582481

C₃

yes

maximal, characteristic, complemented

#22582481

C₃

yes

maximal, characteristic, complemented

3₋¹⁺²⋊#66524

C₃

yes

maximal, characteristic, complemented

3₋¹⁺²⋊#66524

C₃

yes

maximal, characteristic, complemented

#22582475

C₃

yes

maximal, characteristic, complemented

#22582475

C₃

yes

maximal, characteristic, complemented

#22582467

C₃

yes

maximal, characteristic, complemented

#22582467

C₃

yes

maximal, characteristic, complemented

C₃₇×#6894

C₃

yes

maximal, characteristic, complemented

C₃³×C₃₇⋊C₃

C₃²

yes

characteristic

C₃×#11758608

C₃²

yes

characteristic

C₃×#11758605

—

C₃×C₃²⋊(C₃₇⋊C₃)

C₃²

yes

characteristic

C₃²×#66524

C₃²

yes

characteristic

C₃²×#66524

C₃²

yes

—

—

—

—

C₃²

yes

characteristic

C₃²⋊#66524

C₃²

yes

characteristic

C₃²⋊#66524

C₃²

yes

characteristic

C₃²⋊#66524

C₃²

yes

—

—

—

—

—

C₃×3₋¹⁺²×C₃₇

C₃²

yes

characteristic

C₃²×C₉×C₃₇

C₃²

yes

characteristic

C₃₇×C₉⋊C₉

—

C₃₇×C₉⋊C₉

—

C₃₇×C₉⋊C₉

—

C₃₇×C₃²⋊C₉

C₃²

yes

characteristic

C₃₇×C₃²⋊C₉

C₃²

yes

characteristic

C₃³×C₃₇

C₃³

yes

characteristic

C₃²×C₃₇⋊C₃

—

C₃²×C₃₇⋊C₃

—

C₃²×C₃₇⋊C₃

—

C₃²×C₃₇⋊C₃

—

C₃²×C₃₇⋊C₃

—

C₃²×C₃₇⋊C₃

—

C₃²×C₃₇⋊C₃

3₋¹⁺²

yes

complemented

3₋¹⁺²×C₃₇

—

3₋¹⁺²×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

—

C₃×C₉×C₃₇

yes

C₃×C₉×C₃₇

yes

C₃×C₉×C₃₇

yes

C₃²⋊(C₃₇⋊C₃)

—

C₃²⋊(C₃₇⋊C₃)

—

—

—

—

—

—

—

—

—

—

—

—

—

—

C₃²×C₃₇

—

C₃²×C₃₇

—

C₃²×C₃₇

—

C₃²×C₃₇

C₃×H(3,𝔽₃)

yes

characteristic

C₃²×C₃₇

C₃×3₋¹⁺²

yes

characteristic

C₃²×C₃₇

#737

yes

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₃×C₃₇⋊C₃

—

C₉×C₃₇

—

C₉×C₃₇

—

C₉×C₃₇

—

C₉×C₃₇

—

C₉×C₃₇

—

C₉×C₃₇

—

—

—

—

—

—

—

100

#66524

—

101

C₃×AΣL(1,𝔽₂₇)

—

102

#6894

—

103

#6894

C₃₇⋊C₃

yes

characteristic, complemented

104

C₉⋊H(3,𝔽₃)

—

105

C₃×C₃²⋊C₉

—

106

3₋¹⁺²⋊C₉

—

107

3₋¹⁺²⋊C₉

—

108

3₋¹⁺²⋊C₉

—

109

3₋¹⁺²⋊C₉

—

110

H(3,𝔽₃)⋊C₉

—

111

H(3,𝔽₃)⋊C₉

—

112

#6866

—

113

#6866

—

114

C₃×C₃₇

—

115

C₃×C₃₇

—

116

C₃×C₃₇

C₉⋊H(3,𝔽₃)

yes

characteristic

117

C₃×C₃₇

#6909

yes

characteristic

118

C₃×C₃₇

#6913

yes

characteristic

119

C₃×C₃₇

#6913

yes

characteristic

120

C₃₇⋊C₃

—

121

C₃₇⋊C₃

—

122

C₃⁴

—

123

C₃×3₋¹⁺²

—

124

C₃×3₋¹⁺²

—

111

—

125

C₃×3₋¹⁺²

C₃×C₃₇⋊C₃

yes

characteristic

126

C₃×H(3,𝔽₃)

—

127

C₃²×C₉

—

128

C₃²×C₉

—

129

C₃²×C₉

C₃×C₃₇⋊C₃

yes

characteristic

130

AΣL(1,𝔽₂₇)

—

111

—

131

C₉⋊C₉

—

132

C₉⋊C₉

—

133

C₉⋊C₉

—

134

C₉⋊C₉

—

111

—

135

C₉⋊C₉

—

111

—

136

C₉⋊C₉

—

111

—

137

C₃²⋊C₉

—

138

C₃²⋊C₉

—

139

C₃²⋊C₉

—

140

C₃²⋊C₉

—

141

C₃²⋊C₉

—

111

—

142

C₃²⋊C₉

—

111

—

143

C₃²⋊C₉

—

111

—

144

C₃²⋊C₉

—

111

—

145

C₃²⋊C₉

—

111

—

146

C₃²⋊C₉

C₃×C₃₇⋊C₃

yes

characteristic

147

C₃²⋊C₉

C₃×C₃₇⋊C₃

yes

characteristic

148

C₃₇

#10624788

yes

characteristic, complemented, Sylow

149

C₃³

—

150

C₃³

—

333

—

151

C₃³

—

333

—

152

C₃³

—

333

—

153

C₃³

—

111

—

154

C₃³

—

111

—

155

C₃³

—

111

—

156

C₃³

C₃²×C₃₇⋊C₃

yes

characteristic

157

3₋¹⁺²

—

158

3₋¹⁺²

—

159

3₋¹⁺²

—

333

—

160

3₋¹⁺²

—

111

—

161

3₋¹⁺²

—

111

—

162

H(3,𝔽₃)

—

111

—

163

H(3,𝔽₃)

—

111

—

164

C₃×C₉

—

165

C₃×C₉

—

166

C₃×C₉

—

167

C₃×C₉

—

168

C₃×C₉

—

333

—

169

C₃×C₉

—

333

—

170

C₃×C₉

—

111

—

171

C₃×C₉

—

111

—

172

C₃×C₉

—

111

—

173

C₃×C₉

—

111

—

174

C₃×C₉

—

111

—

175

C₃×C₉

—

111

—

176

C₃×C₉

—

111

—

177

C₃×C₉

C₃²⋊(C₃₇⋊C₃)

yes

characteristic

178

C₃×C₉

C₃²⋊(C₃₇⋊C₃)

yes

characteristic

179

C₃×C₉

C₃²⋊(C₃₇⋊C₃)

yes

characteristic

180

C₃²

—

181

C₃²

—

182

C₃²

—

183

C₃²

—

333

—

184

C₃²

—

333

—

185

C₃²

—

333

—

186

C₃²

—

333

—

187

C₃²

—

333

—

188

C₃²

—

333

—

189

C₃²

—

333

—

190

C₃²

—

333

—

191

C₃²

—

333

—

192

C₃²

—

111

—

193

C₃²

C₃×C₃²⋊(C₃₇⋊C₃)

yes

characteristic

194

C₃²

3₋¹⁺²×C₃₇⋊C₃

yes

characteristic

195

C₃²

#15688532

yes

—

196

C₉

—

197

C₉

—

198

C₉

—

199

C₉

—

200

C₉

—

201

C₉

—

202

C₉

—

333

—

203

C₉

—

333

—

204

C₉

—

333

—

205

C₉

—

333

—

206

C₉

—

333

—

207

C₉

—

333

—

208

C₉

—

333

—

209

C₃

—

210

C₃

—

211

C₃

—

333

—

212

C₃

—

999

—

213

C₃

#22582555

yes

characteristic

214

C₃

#22582639

yes

characteristic

215

C₃

#22582655

yes

characteristic

216

C₃

#22582656

yes

characteristic

	subgroup	G/H
center	C₃²	C₃×C₃²⋊(C₃₇⋊C₃)
commutator, cosocle	C₃³×C₃₇	C₃³
Frattini	C₃³	C₃²×C₃₇⋊C₃
Fitting	C₃₇×#6894	C₃
socle	C₃²×C₃₇	C₃×H(3,𝔽₃)
prime radical	C₃×#15688514	C₃
hypercenter	#6894	C₃₇⋊C₃
hypocenter	C₃₇	#10624788
LCS	G ▷ C₃³×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₃²×C₉ ◁ #6894

subgroup

G/H

center

C₃²

C₃×C₃²⋊(C₃₇⋊C₃)

commutator, cosocle

C₃³×C₃₇

C₃³

Frattini

C₃³

C₃²×C₃₇⋊C₃

Fitting

C₃₇×#6894

C₃

socle

C₃²×C₃₇

C₃×H(3,𝔽₃)

C₃

C₃₇⋊C₃

C₃₇

G ▷ C₃³×C₃₇ ▷ C₃×C₃₇ ▷ C₃₇

UCS

C₁ ◁ C₃² ◁ C₃²×C₉ ◁ #6894

N	H ≅ G/N	type
2. #22582572	C₃	semidirect
3. #22582558	C₃	semidirect
4. C₃×#15688502	C₃	semidirect
5. #22582481	C₃	semidirect
6. #22582481	C₃	semidirect
7. 3₋¹⁺²⋊#66524	C₃	semidirect
8. 3₋¹⁺²⋊#66524	C₃	semidirect
9. #22582475	C₃	semidirect
10. #22582475	C₃	semidirect
11. #22582467	C₃	semidirect
12. #22582467	C₃	semidirect
13. C₃₇×#6894	C₃	semidirect
47. C₃²×C₃₇⋊C₃	3₋¹⁺²	semidirect
103. #6894	C₃₇⋊C₃	semidirect
148. C₃₇	#10624788	semidirect

H ≅ G/N

type

2. #22582572

C₃

semidirect

3. #22582558

C₃

semidirect

4. C₃×#15688502

C₃

semidirect

5. #22582481

C₃

semidirect

6. #22582481

C₃

semidirect

7. 3₋¹⁺²⋊#66524

C₃

semidirect

8. 3₋¹⁺²⋊#66524

C₃

semidirect

9. #22582475

C₃

semidirect

10. #22582475

C₃

semidirect

11. #22582467

C₃

semidirect

12. #22582467

C₃

semidirect

13. C₃₇×#6894

C₃

semidirect

47. C₃²×C₃₇⋊C₃

3₋¹⁺²

semidirect

103. #6894

C₃₇⋊C₃

semidirect

148. C₃₇

#10624788

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#15688514	3
#22582572	3
#22582558	3
C₃×#15688502	3
#22582481	3
3₋¹⁺²⋊#66524	3
#22582475	3
#22582467	3
C₃₇×#6894	3
#10624788	37

subgroup

index

C₃₇×#6894

Subgroups — #41006864

Conjugacy classes of subgroups

Complements

Maximal subgroups