Group #26111587 — subgroups

Subgroups — #26111587

Order 12032.

444 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 103 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	#20253710	C₂	1	1	yes	maximal, characteristic
2	#20252455	C₂	1	1	yes	maximal, characteristic
3	#20241810	C₂	1	2	yes	maximal, complemented
4	#20241226	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1525	C₂	1	1	yes	maximal, characteristic
6	#15689680	C₂²	1	1	yes	characteristic
7	#15689477	—	2	2	no	—
8	#15689473	C₄	1	2	yes	—
9	#15689469	C₄	1	2	yes	—
10	#15689201	—	2	2	no	—
11	D₄×C₄₇⋊C₈	—	2	2	no	—
12	#15689176	C₂²	1	2	yes	—
13	#15689119	—	2	2	no	—
14	#15689090	—	2	2	no	—
15	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	#15688855	—	2	2	no	—
17	#15688855	—	2	2	no	—
18	C₄₇×#532	C₂²	1	1	yes	characteristic
19	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#329	—	2	2	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	#13094024	C₂×C₄	1	2	yes	—
25	#13094016	—	2	1	no	—
26	#13094003	—	2	2	no	—
27	C₄×Dic₉₄	—	2	2	no	—
28	#13093983	—	2	1	no	—
29	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
30	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
31	#13093948	—	2	4	no	—
32	#13093945	—	2	4	no	—
33	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
34	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
35	C₄×C₄₇⋊C₈	—	2	1	no	—
36	C₄×C₄₇⋊C₈	—	2	2	no	—
37	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
38	C₂×#41×C₄₇	D₄	1	2	yes	—
39	C₂×M₁₆×C₄₇	—	2	2	no	—
40	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
41	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
42	#124×C₄₇	D₄	1	2	yes	—
43	#121×C₄₇	—	2	2	no	—
44	C₄×D₄×C₄₇	—	2	2	no	—
45	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
46	#97×C₄₇	—	2	2	no	—
47	C₄×C₈×C₄₇	—	2	2	no	—
48	#41×C₄₇	—	4	2	no	—
49	#41×C₄₇	—	4	2	no	—
50	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
51	C₂×D₄×C₄₇	—	2	2	no	—
52	C₂×D₄×C₄₇	—	2	2	no	—
53	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
54	C₂²×C₄×C₄₇	—	2	2	no	—
55	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	#41	1	2	yes	—
57	C₂×Dic₉₄	—	2	2	no	—
58	M₁₆×C₄₇	—	2	4	no	—
59	M₁₆×C₄₇	—	4	2	no	—
60	C₂×C₈×C₄₇	—	4	2	no	—
61	C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂²⋊C₄×C₄₇	—	2	4	no	—
63	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₄²×C₄₇	C₂×D₄	1	2	yes	—
66	C₂²⋊Dic₄₇	—	4	1	no	—
67	C₄⋊Dic₄₇	—	2	2	no	—
68	C₄⋊Dic₄₇	—	2	2	no	—
69	Dic₄₇⋊C₄	—	4	2	no	—
70	C₄×Dic₄₇	—	4	1	no	—
71	#10625329	—	8	2	no	—
72	C₂×C₄₇⋊C₈	—	2	2	no	—
73	C₂×C₄₇⋊C₈	—	2	2	no	—
74	C₂×C₄₇⋊C₈	—	2	2	no	—
75	C₂×C₄₇⋊C₈	—	4	1	no	—
76	C₂×C₄₇⋊C₈	—	4	1	no	—
77	C₂×C₄₇⋊C₈	—	8	2	no	—
78	C₂³×C₄₇	—	2	2	no	—
79	C₂³×C₄₇	#123	1	1	yes	characteristic
80	Q₈×C₄₇	—	4	2	no	—
81	D₄×C₄₇	—	4	2	no	—
82	D₄×C₄₇	—	4	2	no	—
83	D₄×C₄₇	—	4	2	no	—
84	D₄×C₄₇	—	8	2	no	—
85	C₂×C₄×C₄₇	—	2	2	no	—
86	C₂×C₄×C₄₇	—	2	2	no	—
87	C₂×C₄×C₄₇	—	2	1	no	—
88	C₂×C₄×C₄₇	—	2	1	no	—
89	C₂×C₄×C₄₇	—	2	2	no	—
90	C₂×C₄×C₄₇	—	4	2	no	—
91	C₂×C₄×C₄₇	—	4	2	no	—
92	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
95	C₂×C₄×C₄₇	#121	1	2	yes	—
96	C₂×Dic₄₇	—	4	2	no	—
97	Dic₉₄	—	4	2	no	—
98	Dic₉₄	—	4	2	no	—
99	C₈×C₄₇	—	4	4	no	—
100	C₄₇⋊C₈	—	4	2	no	—
101	C₄₇⋊C₈	—	4	2	no	—
102	C₄₇⋊C₈	—	4	2	no	—
103	#9067	—	47	1	no	maximal, Sylow
104	C₂²×C₄₇	—	2	2	no	—
105	C₂²×C₄₇	—	2	1	no	—
106	C₂²×C₄₇	—	4	4	no	—
107	C₂²×C₄₇	—	4	2	no	—
108	C₂²×C₄₇	#386	1	1	yes	characteristic
109	C₄×C₄₇	—	2	2	no	—
110	C₄×C₄₇	—	2	1	no	—
111	C₄×C₄₇	—	4	2	no	—
112	C₄×C₄₇	#443	1	2	yes	—
113	C₄×C₄₇	#444	1	2	yes	—
114	C₄×C₄₇	#455	1	1	yes	characteristic
115	C₄×C₄₇	#455	1	1	yes	characteristic
116	Dic₄₇	—	8	2	no	—
117	#3131	—	47	1	no	—
118	#2979	—	47	1	no	—
119	#1525	D₄₇	1	1	yes	characteristic
120	#1485	—	47	2	no	—
121	#1278	—	47	2	no	—
122	C₂×C₄₇	—	4	1	no	—
123	C₂×C₄₇	—	8	2	no	—
124	C₂×C₄₇	#1876	1	2	yes	—
125	C₂×C₄₇	#1885	1	1	yes	characteristic
126	#533	—	47	1	no	—
127	#532	C₂×D₄₇	1	1	yes	characteristic
128	#488	—	94	2	no	—
129	#487	—	47	2	no	—
130	#486	—	47	2	no	—
131	#436	—	94	2	no	—
132	C₈×D₄	—	94	2	no	—
133	#431	—	47	2	no	—
134	#416	—	94	2	no	—
135	#408	—	94	2	no	—
136	C₄×M₁₆	C₂×D₄₇	1	2	yes	—
137	C₂×C₄×C₈	—	47	1	no	—
138	#329	—	2	2	no	—
139	Q₈⋊C₈	—	94	2	no	—
140	Q₈⋊C₈	—	94	2	no	—
141	C₄₇	#9067	1	1	yes	characteristic, complemented, Sylow
142	C₂×#41	D₁₈₈	1	2	yes	—
143	C₂×M₁₆	—	2	2	no	—
144	C₂×M₁₆	—	94	2	no	—
145	C₂²×C₈	—	94	2	no	—
146	C₂²×C₈	—	94	1	no	—
147	C₄⋊Q₈	—	47	2	no	—
148	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
149	#127	C₄×D₄₇	1	1	yes	characteristic
150	#125	—	94	1	no	—
151	#124	C₂²⋊D₄₇	1	2	yes	—
152	C₂²⋊Q₈	—	94	2	no	—
153	#121	—	2	2	no	—
154	C₄×Q₈	—	94	2	no	—
155	C₄×D₄	—	2	2	no	—
156	#117	—	94	1	no	—
157	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
158	C₄⋊C₈	—	47	2	no	—
159	C₄⋊C₈	—	47	2	no	—
160	#103	—	94	4	no	—
161	#102	—	94	4	no	—
162	C₂²⋊C₈	—	94	4	no	—
163	C₂²⋊C₈	—	94	2	no	—
164	#97	—	2	2	no	—
165	C₄×C₈	—	2	2	no	—
166	C₄×C₈	—	47	2	no	—
167	C₄×C₈	—	94	2	no	—
168	C₄×C₈	—	94	1	no	—
169	#41	—	4	2	no	—
170	#41	—	4	2	no	—
171	C₂×Q₈	—	94	2	no	—
172	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	2	yes	—
173	C₂×D₄	—	2	2	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
176	C₂²×C₄	—	2	2	no	—
177	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
178	C₂²×C₄	#10625352	1	2	yes	—
179	M₁₆	—	2	4	no	—
180	M₁₆	—	4	2	no	—
181	M₁₆	—	376	2	no	—
182	C₂×C₈	—	4	2	no	—
183	C₂×C₈	—	94	2	no	—
184	C₂×C₈	—	94	2	no	—
185	C₂×C₈	—	94	2	no	—
186	C₂×C₈	—	376	2	no	—
187	C₂×C₈	—	188	1	no	—
188	C₂×C₈	—	188	1	no	—
189	C₄⋊C₄	—	2	2	no	—
190	C₄⋊C₄	—	94	2	no	—
191	C₄⋊C₄	—	94	2	no	—
192	C₄⋊C₄	—	188	2	no	—
193	C₂²⋊C₄	—	2	4	no	—
194	C₂²⋊C₄	—	188	1	no	—
195	C₄²	—	188	1	no	—
196	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
197	C₄²	D₄×D₄₇	1	2	yes	—
198	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
199	C₂³	—	2	2	no	—
200	C₂³	#13094008	1	1	yes	characteristic
201	Q₈	—	4	2	no	—
202	Q₈	—	188	2	no	—
203	Q₈	—	188	2	no	—
204	D₄	—	4	2	no	—
205	D₄	—	4	2	no	—
206	D₄	—	4	2	no	—
207	D₄	—	8	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	188	2	no	—
216	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
217	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
218	C₂×C₄	#13093994	1	1	yes	characteristic
219	C₂×C₄	#13093996	1	2	yes	—
220	C₈	—	4	4	no	—
221	C₈	—	188	2	no	—
222	C₈	—	188	2	no	—
223	C₈	—	188	2	no	—
224	C₂²	—	2	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	4	4	no	—
227	C₂²	—	4	2	no	—
228	C₂²	#15689000	1	1	yes	characteristic
229	C₄	—	2	2	no	—
230	C₄	—	2	1	no	—
231	C₄	—	4	2	no	—
232	C₄	—	376	2	no	—
233	C₄	#15689237	1	2	yes	—
234	C₄	#15689242	1	2	yes	—
235	C₄	#15689303	1	1	yes	characteristic
236	C₄	#15689303	1	1	yes	characteristic
237	C₂	—	4	1	no	—
238	C₂	—	8	2	no	—
239	C₂	#20243713	1	2	yes	—
240	C₂	#20243774	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#20253710

C₂

yes

maximal, characteristic

#20252455

C₂

yes

maximal, characteristic

#20241810

C₂

yes

maximal, complemented

#20241226

C₂

yes

maximal, complemented

C₄₇×#1525

C₂

yes

maximal, characteristic

#15689680

C₂²

yes

characteristic

#15689477

—

#15689473

C₄

yes

—

#15689469

C₄

yes

—

#15689201

—

D₄×C₄₇⋊C₈

—

#15689176

C₂²

yes

—

#15689119

—

#15689090

—

C₂×C₄×C₄₇⋊C₈

C₂²

yes

characteristic

#15688855

—

#15688855

—

C₄₇×#532

C₂²

yes

characteristic

C₄×M₁₆×C₄₇

C₂²

yes

—

C₄₇×#329

—

C₂×#10625329

—

C₂²×C₄₇⋊C₈

—

C₂²×C₄₇⋊C₈

—

#13094024

C₂×C₄

yes

—

#13094016

—

#13094003

—

C₄×Dic₉₄

—

#13093983

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

C₄⋊(C₄₇⋊C₈)

D₄

yes

—

#13093948

—

#13093945

—

C₂²⋊(C₄₇⋊C₈)

—

C₂²⋊(C₄₇⋊C₈)

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

—

C₄×C₄₇⋊C₈

C₂×C₄

yes

—

C₂×#41×C₄₇

D₄

yes

—

C₂×M₁₆×C₄₇

—

C₄⋊Q₈×C₄₇

C₂×C₄

yes

characteristic

#127×C₄₇

C₂×C₄

yes

characteristic

#124×C₄₇

D₄

yes

—

#121×C₄₇

—

C₄×D₄×C₄₇

—

C₂×C₄²×C₄₇

C₂³

yes

characteristic

#97×C₄₇

—

C₄×C₈×C₄₇

—

#41×C₄₇

—

#41×C₄₇

—

C₂×Q₈×C₄₇

C₂²⋊C₄

yes

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

—

C₂×D₄×C₄₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₄₇

—

C₂²×C₄×C₄₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₄₇

#41

yes

—

C₂×Dic₉₄

—

M₁₆×C₄₇

—

M₁₆×C₄₇

—

C₂×C₈×C₄₇

—

C₄⋊C₄×C₄₇

—

C₂²⋊C₄×C₄₇

—

C₄²×C₄₇

C₂²×C₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

characteristic

C₄²×C₄₇

C₂×D₄

yes

—

C₂²⋊Dic₄₇

—

C₄⋊Dic₄₇

—

C₄⋊Dic₄₇

—

Dic₄₇⋊C₄

—

C₄×Dic₄₇

—

#10625329

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂×C₄₇⋊C₈

—

C₂³×C₄₇

—

C₂³×C₄₇

#123

yes

characteristic

Q₈×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

D₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

—

C₂×C₄×C₄₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₄₇

C₄×D₄

yes

—

C₂×C₄×C₄₇

#120

yes

characteristic

C₂×C₄×C₄₇

#121

yes

—

C₂×Dic₄₇

—

Dic₉₄

—

Dic₉₄

—

C₈×C₄₇

—

100

C₄₇⋊C₈

—

101

C₄₇⋊C₈

—

102

C₄₇⋊C₈

—

103

#9067

—

maximal, Sylow

104

C₂²×C₄₇

—

105

C₂²×C₄₇

—

106

C₂²×C₄₇

—

107

C₂²×C₄₇

—

108

C₂²×C₄₇

#386

yes

characteristic

109

C₄×C₄₇

—

110

C₄×C₄₇

—

111

C₄×C₄₇

—

112

C₄×C₄₇

#443

yes

—

113

C₄×C₄₇

#444

yes

—

114

C₄×C₄₇

#455

yes

characteristic

115

C₄×C₄₇

#455

yes

characteristic

116

Dic₄₇

—

117

#3131

—

118

#2979

—

119

#1525

D₄₇

yes

characteristic

120

#1485

—

121

#1278

—

122

C₂×C₄₇

—

123

C₂×C₄₇

—

124

C₂×C₄₇

#1876

yes

—

125

C₂×C₄₇

#1885

yes

characteristic

126

#533

—

127

#532

C₂×D₄₇

yes

characteristic

128

#488

—

129

#487

—

130

#486

—

131

#436

—

132

C₈×D₄

—

133

#431

—

134

#416

—

135

#408

—

136

C₄×M₁₆

C₂×D₄₇

yes

—

137

C₂×C₄×C₈

—

138

#329

—

139

Q₈⋊C₈

—

140

Q₈⋊C₈

—

141

C₄₇

#9067

yes

characteristic, complemented, Sylow

142

C₂×#41

D₁₈₈

yes

—

143

C₂×M₁₆

—

144

C₂×M₁₆

—

145

C₂²×C₈

—

146

C₂²×C₈

—

147

C₄⋊Q₈

—

148

C₄⋊Q₈

C₄×D₄₇

yes

characteristic

149

#127

C₄×D₄₇

yes

characteristic

150

#125

—

151

#124

C₂²⋊D₄₇

yes

—

152

C₂²⋊Q₈

—

153

#121

—

154

C₄×Q₈

—

155

C₄×D₄

—

156

#117

—

157

C₂×C₄²

C₂²×D₄₇

yes

characteristic

158

C₄⋊C₈

—

159

C₄⋊C₈

—

160

#103

—

161

#102

—

162

C₂²⋊C₈

—

163

C₂²⋊C₈

—

164

#97

—

165

C₄×C₈

—

166

C₄×C₈

—

167

C₄×C₈

—

168

C₄×C₈

—

169

#41

—

170

#41

—

171

C₂×Q₈

—

172

C₂×Q₈

(C₂×D₄₇)⋊C₄

yes

—

173

C₂×D₄

—

174

C₂×D₄

—

175

C₂×D₄

(C₂×D₄₇)⋊C₄

yes

—

176

C₂²×C₄

—

177

C₂²×C₄

C₂×D₁₈₈

yes

characteristic

178

C₂²×C₄

#10625352

yes

—

179

M₁₆

—

180

M₁₆

—

181

M₁₆

—

376

—

182

C₂×C₈

—

183

C₂×C₈

—

184

C₂×C₈

—

185

C₂×C₈

—

186

C₂×C₈

—

376

—

187

C₂×C₈

—

188

—

188

C₂×C₈

—

188

—

189

C₄⋊C₄

—

190

C₄⋊C₄

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

188

—

193

C₂²⋊C₄

—

194

C₂²⋊C₄

—

188

—

195

C₄²

—

188

—

196

C₄²

C₂×C₄×D₄₇

yes

characteristic

197

C₄²

D₄×D₄₇

yes

—

198

C₄²

C₂×C₂²⋊D₄₇

yes

characteristic

199

C₂³

—

200

C₂³

#13094008

yes

characteristic

201

Q₈

—

202

Q₈

—

188

—

203

Q₈

—

188

—

204

D₄

—

205

D₄

—

206

D₄

—

207

D₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

188

—

216

C₂×C₄

C₂×(C₂×D₄₇)⋊C₄

yes

characteristic

217

C₂×C₄

(C₂²⋊D₄₇)⋊C₄

yes

—

218

C₂×C₄

#13093994

yes

characteristic

219

C₂×C₄

#13093996

yes

—

220

C₈

—

221

C₈

—

188

—

222

C₈

—

188

—

223

C₈

—

188

—

224

C₂²

—

225

C₂²

—

226

C₂²

—

227

C₂²

—

228

C₂²

#15689000

yes

characteristic

229

C₄

—

230

C₄

—

231

C₄

—

232

C₄

—

376

—

233

C₄

#15689237

yes

—

234

C₄

#15689242

yes

—

235

C₄

#15689303

yes

characteristic

236

C₄

#15689303

yes

characteristic

237

C₂

—

238

C₂

—

239

C₂

#20243713

yes

—

240

C₂

#20243774

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#13093994
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1525	C₂
socle	C₂²×C₄₇	#386
prime radical	C₄₇×#532	C₂²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1525	D₄₇
hypocenter	C₄₇	#9067
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1525

subgroup

G/H

center

C₂×C₄

#13093994

commutator

C₄²×C₄₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₄₇

Fitting

C₄₇×#1525

C₂

socle

C₂²×C₄₇

#386

prime radical

C₄₇×#532

C₂²

cosocle

C₂×C₄²×C₄₇

C₂³

D₄₇

C₄₇

G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1525

N	H ≅ G/N	type
3. #20241810	C₂	semidirect
4. #20241226	C₂	semidirect
141. C₄₇	#9067	semidirect

H ≅ G/N

type

3. #20241810

C₂

semidirect

4. #20241226

C₂

semidirect

141. C₄₇

#9067

semidirect

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

subgroup	index
#20253710	2
#20252455	2
#20241810	2
#20241226	2
C₄₇×#1525	2
#9067	47

subgroup

index

C₄₇×#1525

Subgroups — #26111587

Conjugacy classes of subgroups

Complements

Maximal subgroups