Group #33238954 — subgroups

Subgroups — #33238954

Order 18688.

1102 conjugacy classes of subgroups; only the 351 normal subgroups are shown.

normal subgroups only

This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 351 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	C₂×#17989404	C₂	1	1	yes	maximal, characteristic
2	#22623034	C₂	1	1	yes	maximal, characteristic, complemented
3	#22611678	C₂	1	6	yes	maximal, complemented
4	C₂×#17988402	C₂	1	6	yes	maximal, complemented
5	C₇₃×#2916	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14556638	—	2	1	no	—
7	#17989404	—	2	4	no	—
8	#17989404	C₄	1	8	yes	—
9	C₂×#14556624	—	2	3	no	—
10	C₂×#14556613	C₂²	1	3	yes	—
11	C₂²×Dic₂₉₂	C₂²	1	3	yes	—
12	#17989004	—	2	4	no	—
13	C₂×#14556531	C₂²	1	6	yes	—
14	#17988402	C₂²	1	12	yes	—
15	#17988399	C₂²	1	4	yes	—
16	#568×C₇₃	—	2	1	no	—
17	C₂×#131×C₇₃	C₂²	1	1	yes	characteristic
18	#430×C₇₃	—	2	3	no	—
19	C₂×#108×C₇₃	C₂²	1	6	yes	—
20	#14556638	—	2	8	no	—
21	#14556638	—	4	4	no	—
22	C₂×#11924028	—	2	3	no	—
23	C₂×#11924027	—	4	3	no	—
24	C₂²×Dic₁₄₆	—	2	3	no	—
25	C₂×Q₈×D₇₃	—	4	1	no	—
26	#14556624	—	2	24	no	—
27	#14556613	—	2	6	no	—
28	#14556613	C₂×C₄	1	12	yes	—
29	C₂×Dic₂₉₂	—	2	3	no	—
30	C₂×Dic₂₉₂	—	2	6	no	—
31	C₂×Dic₂₉₂	C₂×C₄	1	12	yes	—
32	C₂×Dic₂₉₂	C₂³	1	3	yes	—
33	C₂×#11924017	—	2	3	no	—
34	C₂×D₅₈₄	C₂³	1	1	yes	characteristic
35	#14556531	—	2	6	no	—
36	#14556531	C₂³	1	4	yes	—
37	C₂×#11924003	—	2	6	no	—
38	C₂×#41×C₇₃	D₄	1	1	yes	characteristic
39	#131×C₇₃	—	4	4	no	—
40	#131×C₇₃	C₂×C₄	1	4	yes	—
41	#131×C₇₃	D₄	1	4	yes	—
42	C₂×M₁₆×C₇₃	—	2	6	no	—
43	C₂×M₁₆×C₇₃	D₄	1	3	yes	—
44	C₂²×C₈×C₇₃	C₂³	1	3	yes	—
45	#108×C₇₃	—	2	6	no	—
46	#108×C₇₃	C₂³	1	4	yes	—
47	#11924028	—	2	12	no	—
48	#11924028	—	4	6	no	—
49	#11924027	—	4	24	no	—
50	C₂×Dic₁₄₆	—	2	12	no	—
51	C₂×Dic₁₄₆	—	2	3	no	—
52	C₂×Dic₁₄₆	—	4	6	no	—
53	C₂×Dic₁₄₆	—	4	3	no	—
54	Q₈×D₇₃	—	4	8	no	—
55	C₂×D₂₉₂	—	2	1	no	—
56	C₂×C₂²⋊D₇₃	—	4	3	no	—
57	C₂²×Dic₇₃	—	4	3	no	—
58	C₂×C₄×D₇₃	—	4	3	no	—
59	Dic₂₉₂	—	2	12	no	—
60	Dic₂₉₂	—	2	3	no	—
61	Dic₂₉₂	C₂²×C₄	1	6	yes	—
62	#11924017	—	2	12	no	—
63	D₅₈₄	—	2	1	no	—
64	D₅₈₄	C₂²×C₄	1	2	yes	—
65	#11924003	—	2	4	no	—
66	#41×C₇₃	C₂²⋊C₄	1	4	yes	—
67	#41×C₇₃	D₈	1	4	yes	—
68	C₂×Q₈×C₇₃	SD₁₆	1	1	yes	characteristic
69	C₂×D₄×C₇₃	SD₁₆	1	3	yes	—
70	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
71	M₁₆×C₇₃	—	2	4	no	—
72	M₁₆×C₇₃	—	4	6	no	—
73	M₁₆×C₇₃	C₂²⋊C₄	1	12	yes	—
74	C₂×C₈×C₇₃	—	4	6	no	—
75	C₂×C₈×C₇₃	C₂²×C₄	1	6	yes	—
76	C₂×C₈×C₇₃	C₂×D₄	1	3	yes	—
77	C₂×C₈×C₇₃	C₂×D₄	1	6	yes	—
78	C₂×C₈×C₇₃	C₂⁴	1	1	yes	characteristic
79	C₂³×C₇₃	C₂×SD₁₆	1	3	yes	—
80	C₂²×D₇₃	—	4	1	no	—
81	Q₈×C₇₃	#102	1	4	yes	—
82	D₄×C₇₃	#102	1	12	yes	—
83	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	6	yes	—
84	C₂×C₄×C₇₃	C₂×D₈	1	6	yes	—
85	C₂×C₄×C₇₃	C₂×SD₁₆	1	3	yes	—
86	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
87	C₂²⋊D₇₃	—	4	12	no	—
88	C₂×Dic₇₃	—	4	3	no	—
89	C₂×Dic₇₃	—	4	12	no	—
90	D₂₉₂	—	2	2	no	—
91	D₂₉₂	—	4	1	no	—
92	C₄×D₇₃	—	4	12	no	—
93	Dic₁₄₆	—	2	6	no	—
94	Dic₁₄₆	—	4	3	no	—
95	Dic₁₄₆	—	4	12	no	—
96	C₈×C₇₃	—	4	4	no	—
97	C₈×C₇₃	C₂×C₂²⋊C₄	1	6	yes	—
98	C₈×C₇₃	C₂³×C₄	1	1	yes	characteristic
99	C₈×C₇₃	C₂²×D₄	1	1	yes	characteristic
100	C₂²×C₇₃	—	4	3	no	—
101	C₂²×C₇₃	C₂×#102	1	6	yes	—
102	C₂²×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
103	C₂×D₇₃	—	4	2	no	—
104	C₂×D₇₃	—	8	2	no	—
105	C₄×C₇₃	C₂×#102	1	6	yes	—
106	C₄×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
107	C₄×C₇₃	C₂²×D₈	1	1	yes	characteristic
108	Dic₇₃	—	4	6	no	—
109	#33393	—	73	1	no	maximal, Sylow
110	C₂×C₇₃	—	2	1	no	—
111	C₂×C₇₃	—	2	6	no	—
112	C₂×C₇₃	C₂²×#102	1	1	yes	characteristic
113	D₇₃	—	8	2	no	—
114	C₂×#578	—	73	1	no	—
115	#3407	—	73	1	no	—
116	#2916	D₇₃	1	1	yes	characteristic, complemented
117	#2148	—	73	6	no	—
118	C₂×#362	—	73	6	no	—
119	C₇₃	#33393	1	1	yes	characteristic, complemented, Sylow
120	C₂×2₋¹⁺⁴	—	146	1	no	—
121	#578	—	73	8	no	—
122	#578	—	146	4	no	—
123	C₂×#137	—	146	3	no	—
124	C₂×#135	—	73	3	no	—
125	C₂²×Q₁₆	—	73	3	no	—
126	#568	—	2	1	no	—
127	C₂×#131	C₂×D₇₃	1	1	yes	characteristic
128	#504	—	146	4	no	—
129	C₂×M₃₂	—	73	6	no	—
130	#430	—	2	3	no	—
131	C₂×#108	C₂×D₇₃	1	6	yes	—
132	#362	—	73	12	no	—
133	#361	—	73	4	no	—
134	2₋¹⁺⁴	—	292	4	no	—
135	2₋¹⁺⁴	—	146	8	no	—
136	C₂×#41	—	292	3	no	—
137	C₂×#41	—	146	3	no	—
138	C₂×#41	C₂²⋊D₇₃	1	1	yes	characteristic
139	C₂²×Q₈	—	292	1	no	—
140	C₂²×Q₈	—	146	3	no	—
141	#137	—	146	24	no	—
142	#135	—	73	12	no	—
143	#135	—	146	6	no	—
144	C₂×Q₁₆	—	73	12	no	—
145	C₂×Q₁₆	—	73	3	no	—
146	C₂×Q₁₆	—	146	3	no	—
147	C₂×Q₁₆	—	146	6	no	—
148	C₂×SD₁₆	—	146	3	no	—
149	C₂×D₈	—	73	1	no	—
150	#131	—	4	4	no	—
151	#131	C₄×D₇₃	1	4	yes	—
152	#131	D₂₉₂	1	4	yes	—
153	C₂×M₁₆	—	2	6	no	—
154	C₂×M₁₆	C₂²⋊D₇₃	1	3	yes	—
155	C₂²×C₈	C₂²×D₇₃	1	3	yes	—
156	M₃₂	—	73	4	no	—
157	M₃₂	—	146	6	no	—
158	C₂×C₁₆	—	146	6	no	—
159	#108	—	2	6	no	—
160	#108	C₂²×D₇₃	1	4	yes	—
161	#41	—	292	24	no	—
162	#41	—	292	6	no	—
163	#41	—	146	12	no	—
164	#41	#11924005	1	4	yes	—
165	#41	#11924013	1	4	yes	—
166	C₂×Q₈	—	292	8	no	—
167	C₂×Q₈	—	292	6	no	—
168	C₂×Q₈	—	292	3	no	—
169	C₂×Q₈	—	146	12	no	—
170	C₂×Q₈	—	146	3	no	—
171	C₂×Q₈	#11924015	1	1	yes	characteristic
172	C₂×D₄	—	292	3	no	—
173	C₂×D₄	—	146	1	no	—
174	C₂×D₄	#11924015	1	3	yes	—
175	C₂²×C₄	—	292	3	no	—
176	C₂²×C₄	—	292	3	no	—
177	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
178	Q₁₆	—	73	6	no	—
179	Q₁₆	—	146	12	no	—
180	Q₁₆	—	146	3	no	—
181	SD₁₆	—	146	12	no	—
182	D₈	—	73	2	no	—
183	D₈	—	146	1	no	—
184	M₁₆	—	2	4	no	—
185	M₁₆	—	4	6	no	—
186	M₁₆	#11924005	1	12	yes	—
187	C₂×C₈	—	4	6	no	—
188	C₂×C₈	C₂×C₄×D₇₃	1	6	yes	—
189	C₂×C₈	C₂×C₂²⋊D₇₃	1	3	yes	—
190	C₂×C₈	C₂×D₂₉₂	1	6	yes	—
191	C₂×C₈	C₂³×D₇₃	1	1	yes	characteristic
192	C₁₆	—	146	4	no	—
193	C₂³	—	292	1	no	—
194	C₂³	C₂×#11924015	1	3	yes	—
195	Q₈	—	292	12	no	—
196	Q₈	—	292	3	no	—
197	Q₈	—	146	6	no	—
198	Q₈	#14556511	1	4	yes	—
199	D₄	—	292	12	no	—
200	D₄	—	292	1	no	—
201	D₄	—	146	2	no	—
202	D₄	#14556511	1	12	yes	—
203	C₂×C₄	—	292	12	no	—
204	C₂×C₄	—	292	3	no	—
205	C₂×C₄	—	292	12	no	—
206	C₂×C₄	C₂×#11924005	1	6	yes	—
207	C₂×C₄	C₂×#11924013	1	6	yes	—
208	C₂×C₄	C₂×#11924015	1	3	yes	—
209	C₂×C₄	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
210	C₈	—	4	4	no	—
211	C₈	C₂×#11924005	1	6	yes	—
212	C₈	C₂²×C₄×D₇₃	1	1	yes	characteristic
213	C₈	C₂²×D₂₉₂	1	1	yes	characteristic
214	C₂²	—	4	3	no	—
215	C₂²	—	292	2	no	—
216	C₂²	—	584	2	no	—
217	C₂²	C₂×#14556511	1	6	yes	—
218	C₂²	C₂²×#11924015	1	1	yes	characteristic
219	C₄	—	292	6	no	—
220	C₄	C₂×#14556511	1	6	yes	—
221	C₄	C₂²×#11924005	1	1	yes	characteristic
222	C₄	C₂²×#11924013	1	1	yes	characteristic
223	C₂	—	2	1	no	—
224	C₂	—	2	6	no	—
225	C₂	—	584	2	no	—
226	C₂	C₂²×#14556511	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#17989404

C₂

yes

maximal, characteristic

#22623034

C₂

yes

maximal, characteristic, complemented

#22611678

C₂

yes

maximal, complemented

C₂×#17988402

C₂

yes

maximal, complemented

C₇₃×#2916

C₂

yes

maximal, characteristic, complemented

C₂×#14556638

—

#17989404

—

#17989404

C₄

yes

—

C₂×#14556624

—

C₂×#14556613

C₂²

yes

—

C₂²×Dic₂₉₂

C₂²

yes

—

#17989004

—

C₂×#14556531

C₂²

yes

—

#17988402

C₂²

yes

—

#17988399

C₂²

yes

—

#568×C₇₃

—

C₂×#131×C₇₃

C₂²

yes

characteristic

#430×C₇₃

—

C₂×#108×C₇₃

C₂²

yes

—

—

—

—

—

C₂²×Dic₁₄₆

—

C₂×Q₈×D₇₃

—

#14556624

—

#14556613

—

#14556613

C₂×C₄

yes

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₂×C₄

yes

—

C₂×Dic₂₉₂

C₂³

yes

—

C₂×#11924017

—

C₂×D₅₈₄

C₂³

yes

characteristic

#14556531

—

#14556531

C₂³

yes

—

C₂×#11924003

—

C₂×#41×C₇₃

D₄

yes

characteristic

#131×C₇₃

—

#131×C₇₃

C₂×C₄

yes

—

#131×C₇₃

D₄

yes

—

C₂×M₁₆×C₇₃

—

C₂×M₁₆×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

C₂³

yes

—

#108×C₇₃

—

#108×C₇₃

C₂³

yes

—

#11924028

—

#11924028

—

#11924027

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

Q₈×D₇₃

—

C₂×D₂₉₂

—

C₂×C₂²⋊D₇₃

—

C₂²×Dic₇₃

—

C₂×C₄×D₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

C₂²×C₄

yes

—

#11924017

—

D₅₈₄

—

D₅₈₄

C₂²×C₄

yes

—

#11924003

—

#41×C₇₃

C₂²⋊C₄

yes

—

#41×C₇₃

D₈

yes

—

C₂×Q₈×C₇₃

SD₁₆

yes

characteristic

C₂×D₄×C₇₃

SD₁₆

yes

—

C₂²×C₄×C₇₃

C₂×D₄

yes

—

M₁₆×C₇₃

—

M₁₆×C₇₃

—

M₁₆×C₇₃

C₂²⋊C₄

yes

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²×C₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂⁴

yes

characteristic

C₂³×C₇₃

C₂×SD₁₆

yes

—

C₂²×D₇₃

—

Q₈×C₇₃

#102

yes

—

D₄×C₇₃

#102

yes

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×D₈

yes

—

C₂×C₄×C₇₃

C₂×SD₁₆

yes

—

C₂×C₄×C₇₃

C₂²×D₄

yes

characteristic

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

C₈×C₇₃

C₂×C₂²⋊C₄

yes

—

C₈×C₇₃

C₂³×C₄

yes

characteristic

C₈×C₇₃

C₂²×D₄

yes

characteristic

100

C₂²×C₇₃

—

101

C₂²×C₇₃

C₂×#102

yes

—

102

C₂²×C₇₃

C₂²×SD₁₆

yes

characteristic

103

C₂×D₇₃

—

104

C₂×D₇₃

—

105

C₄×C₇₃

C₂×#102

yes

—

106

C₄×C₇₃

C₂²×C₂²⋊C₄

yes

characteristic

107

C₄×C₇₃

C₂²×D₈

yes

characteristic

108

Dic₇₃

—

109

#33393

—

maximal, Sylow

110

C₂×C₇₃

—

111

C₂×C₇₃

—

112

C₂×C₇₃

C₂²×#102

yes

characteristic

113

D₇₃

—

114

C₂×#578

—

115

#3407

—

116

#2916

D₇₃

yes

characteristic, complemented

117

#2148

—

118

C₂×#362

—

119

C₇₃

#33393

yes

characteristic, complemented, Sylow

120

C₂×2₋¹⁺⁴

—

146

—

121

#578

—

122

#578

—

146

—

123

C₂×#137

—

146

—

124

C₂×#135

—

125

C₂²×Q₁₆

—

126

#568

—

127

C₂×#131

C₂×D₇₃

yes

characteristic

128

#504

—

146

—

129

C₂×M₃₂

—

130

#430

—

131

C₂×#108

C₂×D₇₃

yes

—

132

#362

—

133

#361

—

134

2₋¹⁺⁴

—

292

—

135

2₋¹⁺⁴

—

146

—

136

C₂×#41

—

292

—

137

C₂×#41

—

146

—

138

C₂×#41

C₂²⋊D₇₃

yes

characteristic

139

C₂²×Q₈

—

292

—

140

C₂²×Q₈

—

146

—

141

#137

—

146

—

142

#135

—

143

#135

—

146

—

144

C₂×Q₁₆

—

145

C₂×Q₁₆

—

146

C₂×Q₁₆

—

146

—

147

C₂×Q₁₆

—

146

—

148

C₂×SD₁₆

—

146

—

149

C₂×D₈

—

150

#131

—

151

#131

C₄×D₇₃

yes

—

152

#131

D₂₉₂

yes

—

153

C₂×M₁₆

—

154

C₂×M₁₆

C₂²⋊D₇₃

yes

—

155

C₂²×C₈

C₂²×D₇₃

yes

—

156

M₃₂

—

157

M₃₂

—

146

—

158

C₂×C₁₆

—

146

—

159

#108

—

160

#108

C₂²×D₇₃

yes

—

161

#41

—

292

—

162

#41

—

292

—

163

#41

—

146

—

164

#41

#11924005

yes

—

165

#41

#11924013

yes

—

166

C₂×Q₈

—

292

—

167

C₂×Q₈

—

292

—

168

C₂×Q₈

—

292

—

169

C₂×Q₈

—

146

—

170

C₂×Q₈

—

146

—

171

C₂×Q₈

#11924015

yes

characteristic

172

C₂×D₄

—

292

—

173

C₂×D₄

—

146

—

174

C₂×D₄

#11924015

yes

—

175

C₂²×C₄

—

292

—

176

C₂²×C₄

—

292

—

177

C₂²×C₄

C₂×C₂²⋊D₇₃

yes

—

178

Q₁₆

—

179

Q₁₆

—

146

—

180

Q₁₆

—

146

—

181

SD₁₆

—

146

—

182

D₈

—

183

D₈

—

146

—

184

M₁₆

—

185

M₁₆

—

186

M₁₆

#11924005

yes

—

187

C₂×C₈

—

188

C₂×C₈

C₂×C₄×D₇₃

yes

—

189

C₂×C₈

C₂×C₂²⋊D₇₃

yes

—

190

C₂×C₈

C₂×D₂₉₂

yes

—

191

C₂×C₈

C₂³×D₇₃

yes

characteristic

192

C₁₆

—

146

—

193

C₂³

—

292

—

194

C₂³

C₂×#11924015

yes

—

195

Q₈

—

292

—

196

Q₈

—

292

—

197

Q₈

—

146

—

198

Q₈

#14556511

yes

—

199

D₄

—

292

—

200

D₄

—

292

—

201

D₄

—

146

—

202

D₄

#14556511

yes

—

203

C₂×C₄

—

292

—

204

C₂×C₄

—

292

—

205

C₂×C₄

—

292

—

206

C₂×C₄

C₂×#11924005

yes

—

207

C₂×C₄

C₂×#11924013

yes

—

208

C₂×C₄

C₂×#11924015

yes

—

209

C₂×C₄

C₂²×C₂²⋊D₇₃

yes

characteristic

210

C₈

—

211

C₈

C₂×#11924005

yes

—

212

C₈

C₂²×C₄×D₇₃

yes

characteristic

213

C₈

C₂²×D₂₉₂

yes

characteristic

214

C₂²

—

215

C₂²

—

292

—

216

C₂²

—

584

—

217

C₂²

C₂×#14556511

yes

—

218

C₂²

C₂²×#11924015

yes

characteristic

219

C₄

—

292

—

220

C₄

C₂×#14556511

yes

—

221

C₄

C₂²×#11924005

yes

characteristic

222

C₄

C₂²×#11924013

yes

characteristic

223

C₂

—

224

C₂

—

225

C₂

—

584

—

226

C₂

C₂²×#14556511

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×#14556511
commutator	C₈×C₇₃	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₇₃
Fitting	C₇₃×#2916	C₂
socle	C₂×C₇₃	C₂²×#102
prime radical	C₂×#17989404	C₂
cosocle	C₂×C₈×C₇₃	C₂⁴
hypercenter	#2916	D₇₃
hypocenter	C₇₃	#33393
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#131 ◁ #2916

subgroup

G/H

center

C₂

C₂²×#14556511

commutator

C₈×C₇₃

C₂³×C₄

Frattini

C₂×C₈

C₂³×D₇₃

Fitting

C₇₃×#2916

C₂

socle

C₂×C₇₃

C₂²×#102

prime radical

C₂×#17989404

C₂

cosocle

C₂×C₈×C₇₃

C₂⁴

D₇₃

C₇₃

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂×#41 ◁ C₂×#131 ◁ #2916

N	H ≅ G/N	type
2. #22623034	C₂	semidirect
3. #22611678	C₂	semidirect
4. C₂×#17988402	C₂	semidirect
5. C₇₃×#2916	C₂	semidirect
116. #2916	D₇₃	semidirect
119. C₇₃	#33393	semidirect

H ≅ G/N

type

2. #22623034

C₂

semidirect

3. #22611678

C₂

semidirect

4. C₂×#17988402

C₂

semidirect

5. C₇₃×#2916

C₂

semidirect

116. #2916

D₇₃

semidirect

119. C₇₃

#33393

semidirect

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

subgroup	index
C₂×#17989404	2
#22623034	2
#22611678	2
C₂×#17988402	2
C₇₃×#2916	2
#33393	73

subgroup

index

C₇₃×#2916

Subgroups — #33238954

Conjugacy classes of subgroups

Complements

Maximal subgroups