Group #33241591 — subgroups

Subgroups — #33241591

Order 18688.

532 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 139 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	#22620582	C₂	1	2	yes	maximal, complemented
2	#22612181	C₂	1	1	yes	maximal, characteristic, complemented
3	#22612174	C₂	1	2	yes	maximal, complemented
4	#22612035	C₂	1	2	yes	maximal, complemented
5	#22612018	C₂	1	2	yes	maximal, complemented
6	#22611806	C₂	1	2	yes	maximal, complemented
7	#22611777	C₂	1	2	yes	maximal, complemented
8	#22611526	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇₃×#2253	C₂	1	1	yes	maximal, characteristic, complemented
10	#17989193	—	2	2	no	—
11	C₂×D₁₁₆₈	C₂²	1	2	yes	—
12	C₂×D₁₁₆₈	C₂²	1	2	yes	—
13	C₂×#14556530	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×D₇₃	C₂²	1	1	yes	characteristic
15	#17988964	C₂²	1	2	yes	—
16	#17988953	—	2	2	no	—
17	#17988841	—	2	2	no	—
18	#17988824	C₂²	1	4	yes	—
19	#17988698	—	2	2	no	—
20	#17988669	C₂²	1	4	yes	—
21	#17988541	C₂²	1	1	yes	characteristic
22	#17988387	C₂²	1	4	yes	—
23	#17988387	C₂²	1	4	yes	—
24	#17988363	C₂²	1	1	yes	characteristic
25	#17988362	C₂²	1	1	yes	characteristic
26	C₁₆×Dic₇₃	C₂²	1	1	yes	characteristic
27	#499×C₇₃	C₂²	1	2	yes	—
28	#367×C₇₃	C₂²	1	2	yes	—
29	#366×C₇₃	C₂²	1	2	yes	—
30	C₄×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
31	C₂×D₅₈₄	—	2	2	no	—
32	C₂×D₅₈₄	C₂³	1	4	yes	—
33	C₂×#11924011	D₄	1	1	yes	characteristic
34	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
35	#14556588	—	2	2	no	—
36	#14556576	—	4	4	no	—
37	#14556566	—	2	4	no	—
38	#14556566	—	4	4	no	—
39	#14556553	—	2	4	no	—
40	#14556548	D₄	1	1	yes	characteristic
41	D₁₁₆₈	—	2	4	no	—
42	D₁₁₆₈	—	2	4	no	—
43	#14556530	—	2	2	no	—
44	C₂×#11924003	C₂³	1	1	yes	characteristic
45	C₂×#11924003	C₂³	1	1	yes	characteristic
46	C₁₆×D₇₃	—	2	2	no	—
47	#14556511	—	2	4	no	—
48	#14556511	—	2	4	no	—
49	#14556502	D₄	1	1	yes	characteristic
50	#14556501	D₄	1	1	yes	characteristic
51	C₈×Dic₇₃	C₂³	1	1	yes	characteristic
52	#125×C₇₃	—	2	2	no	—
53	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
54	C₂×C₁₆×C₇₃	C₂³	1	1	yes	characteristic
55	#107×C₇₃	C₂³	1	4	yes	—
56	#106×C₇₃	—	2	2	no	—
57	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
58	C₂×D₂₉₂	—	2	4	no	—
59	C₂×D₂₉₂	—	4	4	no	—
60	C₂×D₂₉₂	—	4	4	no	—
61	C₂×C₄×D₇₃	—	4	4	no	—
62	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
63	D₅₈₄	—	2	4	no	—
64	D₅₈₄	—	2	4	no	—
65	D₅₈₄	—	4	4	no	—
66	#11924011	—	2	2	no	—
67	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
68	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
69	C₈×D₇₃	—	2	1	no	—
70	C₈×D₇₃	—	2	1	no	—
71	#11924007	D₈	1	2	yes	—
72	#11924005	—	4	4	no	—
73	#11924005	—	4	4	no	—
74	#11924005	D₈	1	2	yes	—
75	C₄×Dic₇₃	C₂×D₄	1	1	yes	characteristic
76	#11924003	—	2	1	no	—
77	#11924003	—	2	1	no	—
78	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
79	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
80	C₄⋊C₄×C₇₃	—	2	4	no	—
81	C₄⋊C₄×C₇₃	—	4	4	no	—
82	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
83	C₁₆×C₇₃	#41	1	2	yes	—
84	C₁₆×C₇₃	#41	1	2	yes	—
85	C₂²×D₇₃	—	4	4	no	—
86	C₂²×D₇₃	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₇₃	—	4	4	no	—
88	C₂×C₄×C₇₃	C₂×D₈	1	2	yes	—
89	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
90	C₂×Dic₇₃	C₂×D₈	1	2	yes	—
91	C₂×Dic₇₃	C₂×D₈	1	1	yes	characteristic
92	D₂₉₂	—	4	4	no	—
93	D₂₉₂	—	4	4	no	—
94	D₂₉₂	—	16	4	no	—
95	D₂₉₂	—	16	4	no	—
96	C₄×D₇₃	—	2	1	no	—
97	C₄×D₇₃	—	2	1	no	—
98	C₄×D₇₃	—	16	4	no	—
99	C₈×C₇₃	#135	1	2	yes	—
100	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
101	C₈×C₇₃	C₂×#41	1	1	yes	characteristic
102	#10596831	—	2	1	no	—
103	#10596831	—	2	1	no	—
104	C₂²×C₇₃	C₂²×D₈	1	1	yes	characteristic
105	C₂×D₇₃	—	2	2	no	—
106	C₂×D₇₃	—	2	1	no	—
107	C₂×D₇₃	—	8	4	no	—
108	C₂×D₇₃	—	8	4	no	—
109	C₂×D₇₃	—	8	4	no	—
110	C₄×C₇₃	—	2	2	no	—
111	C₄×C₇₃	—	8	4	no	—
112	C₄×C₇₃	#532	1	1	yes	characteristic
113	C₄×C₇₃	C₂×#135	1	1	yes	characteristic
114	Dic₇₃	—	2	2	no	—
115	Dic₇₃	—	2	1	no	—
116	#33740	—	73	1	no	maximal, Sylow
117	C₂×C₇₃	#3169	1	1	yes	characteristic
118	C₂×C₇₃	#3415	1	2	yes	—
119	D₇₃	—	4	1	no	—
120	D₇₃	—	16	4	no	—
121	#3176	—	73	2	no	—
122	#2253	D₇₃	1	1	yes	characteristic, complemented
123	#2246	—	73	1	no	—
124	#2244	—	73	2	no	—
125	#2218	—	73	2	no	—
126	#2215	—	73	2	no	—
127	#2177	—	73	2	no	—
128	C₄×D₁₆	—	73	2	no	—
129	#2108	—	73	1	no	—
130	C₇₃	#33740	1	1	yes	characteristic, complemented, Sylow
131	#540	—	146	2	no	—
132	C₂×D₁₆	—	73	2	no	—
133	C₂×D₁₆	—	73	2	no	—
134	C₂×M₃₂	—	73	1	no	—
135	C₂²×C₁₆	—	73	1	no	—
136	#499	C₂×D₇₃	1	2	yes	—
137	#493	—	73	2	no	—
138	#490	—	146	2	no	—
139	#469	—	146	2	no	—
140	#466	—	73	4	no	—
141	#442	—	146	2	no	—
142	C₄×D₈	—	73	4	no	—
143	#405	—	73	1	no	—
144	#367	C₂×D₇₃	1	2	yes	—
145	#366	C₂×D₇₃	1	2	yes	—
146	#357	—	73	4	no	—
147	#357	—	73	4	no	—
148	#346	—	73	1	no	—
149	#346	—	73	1	no	—
150	C₄×C₁₆	—	73	1	no	—
151	C₄×C₁₆	C₂×D₇₃	1	1	yes	characteristic
152	C₂×D₈	—	73	4	no	—
153	C₂×D₈	—	146	2	no	—
154	C₂×M₁₆	—	73	1	no	—
155	C₂²×C₈	—	73	1	no	—
156	#127	—	146	2	no	—
157	#125	—	2	2	no	—
158	#123	—	292	4	no	—
159	#121	—	292	4	no	—
160	#121	—	146	4	no	—
161	C₄×D₄	—	146	4	no	—
162	#117	—	73	1	no	—
163	D₁₆	—	146	4	no	—
164	D₁₆	—	146	4	no	—
165	M₃₂	—	146	2	no	—
166	C₂×C₁₆	—	73	1	no	—
167	C₂×C₁₆	—	73	1	no	—
168	C₂×C₁₆	—	146	2	no	—
169	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
170	C₂×C₁₆	C₂²×D₇₃	1	1	yes	characteristic
171	#107	C₂²×D₇₃	1	4	yes	—
172	#106	—	2	2	no	—
173	#102	—	146	4	no	—
174	#102	—	146	4	no	—
175	#97	—	73	1	no	—
176	#97	—	73	1	no	—
177	C₄×C₈	—	73	1	no	—
178	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
179	C₂×D₄	—	292	4	no	—
180	C₂×D₄	—	292	4	no	—
181	C₂×D₄	—	146	4	no	—
182	C₂²×C₄	—	292	4	no	—
183	C₂²×C₄	—	73	1	no	—
184	D₈	—	292	4	no	—
185	D₈	—	146	4	no	—
186	D₈	—	146	4	no	—
187	M₁₆	—	146	2	no	—
188	C₂×C₈	—	73	1	no	—
189	C₂×C₈	—	73	1	no	—
190	C₂×C₈	—	146	1	no	—
191	C₂×C₈	—	146	1	no	—
192	C₂×C₈	D₄×D₇₃	1	1	yes	characteristic
193	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	4	4	no	—
196	C₄⋊C₄	—	73	2	no	—
197	C₂²⋊C₄	—	292	4	no	—
198	C₂²⋊C₄	—	292	4	no	—
199	C₂²⋊C₄	—	73	2	no	—
200	C₄²	—	73	1	no	—
201	C₄²	D₄×D₇₃	1	1	yes	characteristic
202	C₁₆	—	146	1	no	—
203	C₁₆	—	146	1	no	—
204	C₁₆	#11924029	1	2	yes	—
205	C₁₆	#11924029	1	2	yes	—
206	C₂³	—	292	4	no	—
207	C₂³	—	73	1	no	—
208	D₄	—	292	4	no	—
209	D₄	—	292	4	no	—
210	D₄	—	1168	4	no	—
211	D₄	—	1168	4	no	—
212	C₂×C₄	—	4	4	no	—
213	C₂×C₄	—	73	2	no	—
214	C₂×C₄	—	73	1	no	—
215	C₂×C₄	—	1168	4	no	—
216	C₂×C₄	—	146	1	no	—
217	C₂×C₄	—	146	1	no	—
218	C₂×C₄	D₈×D₇₃	1	2	yes	—
219	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
220	C₈	—	146	1	no	—
221	C₈	—	146	1	no	—
222	C₈	#14556614	1	2	yes	—
223	C₈	C₂×#11924029	1	1	yes	characteristic
224	C₈	C₂×#11924029	1	1	yes	characteristic
225	C₂²	—	584	4	no	—
226	C₂²	—	584	4	no	—
227	C₂²	—	584	4	no	—
228	C₂²	—	146	2	no	—
229	C₂²	—	146	1	no	—
230	C₂²	C₂×D₈×D₇₃	1	1	yes	characteristic
231	C₄	—	2	2	no	—
232	C₄	—	8	4	no	—
233	C₄	—	146	2	no	—
234	C₄	—	146	1	no	—
235	C₄	#17989138	1	1	yes	characteristic
236	C₄	C₂×#14556614	1	1	yes	characteristic
237	C₂	—	292	1	no	—
238	C₂	—	1168	4	no	—
239	C₂	#22620511	1	1	yes	characteristic
240	C₂	#22623069	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22620582

C₂

yes

maximal, complemented

#22612181

C₂

yes

maximal, characteristic, complemented

#22612174

C₂

yes

maximal, complemented

#22612035

C₂

yes

maximal, complemented

#22612018

C₂

yes

maximal, complemented

#22611806

C₂

yes

maximal, complemented

#22611777

C₂

yes

maximal, complemented

#22611526

C₂

yes

maximal, characteristic, complemented

C₇₃×#2253

C₂

yes

maximal, characteristic, complemented

#17989193

—

C₂×D₁₁₆₈

C₂²

yes

—

C₂×D₁₁₆₈

C₂²

yes

—

C₂×#14556530

C₂²

yes

characteristic

C₂×C₁₆×D₇₃

C₂²

yes

characteristic

#17988964

C₂²

yes

—

#17988953

—

#17988841

—

#17988824

C₂²

yes

—

#17988698

—

#17988669

C₂²

yes

—

#17988541

C₂²

yes

characteristic

#17988387

C₂²

yes

—

#17988387

C₂²

yes

—

#17988363

C₂²

yes

characteristic

#17988362

C₂²

yes

characteristic

C₁₆×Dic₇₃

C₂²

yes

characteristic

#499×C₇₃

C₂²

yes

—

#367×C₇₃

C₂²

yes

—

#366×C₇₃

C₂²

yes

—

C₄×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×D₅₈₄

—

C₂×D₅₈₄

C₂³

yes

—

C₂×#11924011

D₄

yes

characteristic

C₂×C₈×D₇₃

C₂³

yes

—

—

—

—

—

D₄

yes

characteristic

D₁₁₆₈

—

D₁₁₆₈

—

#14556530

—

C₂×#11924003

C₂³

yes

characteristic

C₂×#11924003

C₂³

yes

characteristic

C₁₆×D₇₃

—

#14556511

—

#14556511

—

#14556502

D₄

yes

characteristic

#14556501

D₄

yes

characteristic

C₈×Dic₇₃

C₂³

yes

characteristic

#125×C₇₃

—

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

C₂×C₁₆×C₇₃

C₂³

yes

characteristic

#107×C₇₃

C₂³

yes

—

#106×C₇₃

—

C₄×C₈×C₇₃

C₂³

yes

characteristic

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×D₄

yes

characteristic

D₅₈₄

—

D₅₈₄

—

D₅₈₄

—

#11924011

—

C₂×#10596831

C₂×D₄

yes

characteristic

C₂×#10596831

C₂×D₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

#11924007

D₈

yes

—

#11924005

—

#11924005

—

#11924005

D₈

yes

—

C₄×Dic₇₃

C₂×D₄

yes

characteristic

#11924003

—

#11924003

—

C₂×C₈×C₇₃

C₂×D₄

yes

characteristic

C₂×C₈×C₇₃

C₂⁴

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂×D₄

yes

characteristic

C₁₆×C₇₃

#41

yes

—

C₁₆×C₇₃

#41

yes

—

C₂²×D₇₃

—

C₂²×D₇₃

C₂×D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

characteristic

C₂×Dic₇₃

C₂×D₈

yes

—

C₂×Dic₇₃

C₂×D₈

yes

characteristic

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

#135

yes

—

100

C₈×C₇₃

C₂×#41

yes

characteristic

101

C₈×C₇₃

C₂×#41

yes

characteristic

102

#10596831

—

103

#10596831

—

104

C₂²×C₇₃

C₂²×D₈

yes

characteristic

105

C₂×D₇₃

—

106

C₂×D₇₃

—

107

C₂×D₇₃

—

108

C₂×D₇₃

—

109

C₂×D₇₃

—

110

C₄×C₇₃

—

111

C₄×C₇₃

—

112

C₄×C₇₃

#532

yes

characteristic

113

C₄×C₇₃

C₂×#135

yes

characteristic

114

Dic₇₃

—

115

Dic₇₃

—

116

#33740

—

maximal, Sylow

117

C₂×C₇₃

#3169

yes

characteristic

118

C₂×C₇₃

#3415

yes

—

119

D₇₃

—

120

D₇₃

—

121

#3176

—

122

#2253

D₇₃

yes

characteristic, complemented

123

#2246

—

124

#2244

—

125

#2218

—

126

#2215

—

127

#2177

—

128

C₄×D₁₆

—

129

#2108

—

130

C₇₃

#33740

yes

characteristic, complemented, Sylow

131

#540

—

146

—

132

C₂×D₁₆

—

133

C₂×D₁₆

—

134

C₂×M₃₂

—

135

C₂²×C₁₆

—

136

#499

C₂×D₇₃

yes

—

137

#493

—

138

#490

—

146

—

139

#469

—

146

—

140

#466

—

141

#442

—

146

—

142

C₄×D₈

—

143

#405

—

144

#367

C₂×D₇₃

yes

—

145

#366

C₂×D₇₃

yes

—

146

#357

—

147

#357

—

148

#346

—

149

#346

—

150

C₄×C₁₆

—

151

C₄×C₁₆

C₂×D₇₃

yes

characteristic

152

C₂×D₈

—

153

C₂×D₈

—

146

—

154

C₂×M₁₆

—

155

C₂²×C₈

—

156

#127

—

146

—

157

#125

—

158

#123

—

292

—

159

#121

—

292

—

160

#121

—

146

—

161

C₄×D₄

—

146

—

162

#117

—

163

D₁₆

—

146

—

164

D₁₆

—

146

—

165

M₃₂

—

146

—

166

C₂×C₁₆

—

167

C₂×C₁₆

—

168

C₂×C₁₆

—

146

—

169

C₂×C₁₆

C₂²×D₇₃

yes

characteristic

170

C₂×C₁₆

C₂²×D₇₃

yes

characteristic

171

#107

C₂²×D₇₃

yes

—

172

#106

—

173

#102

—

146

—

174

#102

—

146

—

175

#97

—

176

#97

—

177

C₄×C₈

—

178

C₄×C₈

C₂²×D₇₃

yes

characteristic

179

C₂×D₄

—

292

—

180

C₂×D₄

—

292

—

181

C₂×D₄

—

146

—

182

C₂²×C₄

—

292

—

183

C₂²×C₄

—

184

D₈

—

292

—

185

D₈

—

146

—

186

D₈

—

146

—

187

M₁₆

—

146

—

188

C₂×C₈

—

189

C₂×C₈

—

190

C₂×C₈

—

146

—

191

C₂×C₈

—

146

—

192

C₂×C₈

D₄×D₇₃

yes

characteristic

193

C₂×C₈

C₂³×D₇₃

yes

characteristic

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₂²⋊C₄

—

292

—

198

C₂²⋊C₄

—

292

—

199

C₂²⋊C₄

—

200

C₄²

—

201

C₄²

D₄×D₇₃

yes

characteristic

202

C₁₆

—

146

—

203

C₁₆

—

146

—

204

C₁₆

#11924029

yes

—

205

C₁₆

#11924029

yes

—

206

C₂³

—

292

—

207

C₂³

—

208

D₄

—

292

—

209

D₄

—

292

—

210

D₄

—

1168

—

211

D₄

—

1168

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

1168

—

216

C₂×C₄

—

146

—

217

C₂×C₄

—

146

—

218

C₂×C₄

D₈×D₇₃

yes

—

219

C₂×C₄

C₂×D₄×D₇₃

yes

characteristic

220

C₈

—

146

—

221

C₈

—

146

—

222

C₈

#14556614

yes

—

223

C₈

C₂×#11924029

yes

characteristic

224

C₈

C₂×#11924029

yes

characteristic

225

C₂²

—

584

—

226

C₂²

—

584

—

227

C₂²

—

584

—

228

C₂²

—

146

—

229

C₂²

—

146

—

230

C₂²

C₂×D₈×D₇₃

yes

characteristic

231

C₄

—

232

C₄

—

233

C₄

—

146

—

234

C₄

—

146

—

235

C₄

#17989138

yes

characteristic

236

C₄

C₂×#14556614

yes

characteristic

237

C₂

—

292

—

238

C₂

—

1168

—

239

C₂

#22620511

yes

characteristic

240

C₂

#22623069

yes

—

	subgroup	G/H
center	C₂²	C₂×D₈×D₇₃
commutator, cosocle	C₂×C₈×C₇₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2253	C₂
socle	C₂²×C₇₃	C₂²×D₈
hypercenter	#2253	D₇₃
hypocenter	C₇₃	#33740
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2253

subgroup

G/H

center

C₂²

C₂×D₈×D₇₃

commutator, cosocle

C₂×C₈×C₇₃

C₂⁴

Frattini

C₂×C₈

C₂³×D₇₃

Fitting

C₇₃×#2253

C₂

socle

C₂²×C₇₃

C₂²×D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2253

N	H ≅ G/N	type
1. #22620582	C₂	semidirect
2. #22612181	C₂	semidirect
3. #22612174	C₂	semidirect
4. #22612035	C₂	semidirect
5. #22612018	C₂	semidirect
6. #22611806	C₂	semidirect
7. #22611777	C₂	semidirect
8. #22611526	C₂	semidirect
9. C₇₃×#2253	C₂	semidirect
122. #2253	D₇₃	semidirect
130. C₇₃	#33740	semidirect

H ≅ G/N

type

1. #22620582

C₂

semidirect

2. #22612181

C₂

semidirect

3. #22612174

C₂

semidirect

4. #22612035

C₂

semidirect

5. #22612018

C₂

semidirect

6. #22611806

C₂

semidirect

7. #22611777

C₂

semidirect

8. #22611526

C₂

semidirect

9. C₇₃×#2253

C₂

semidirect

122. #2253

D₇₃

semidirect

130. C₇₃

#33740

semidirect

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

subgroup	index
#22620582	2
#22612181	2
#22612174	2
#22612035	2
#22612018	2
#22611806	2
#22611777	2
#22611526	2
C₇₃×#2253	2
#33740	73

subgroup

index

C₇₃×#2253

Subgroups — #33241591

Conjugacy classes of subgroups

Complements

Maximal subgroups