Group #32916620 — subgroups

Subgroups — C₇₃×#7216 #32916620

Order 18688.

276 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 74 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	C₇₃×#1822	C₂	1	1	yes	maximal, characteristic
2	C₇₃×#1750	C₂	1	1	yes	maximal, characteristic
3	C₇₃×#1464	C₂	1	1	yes	maximal, characteristic
4	C₂×#117×C₇₃	C₂²	1	1	yes	characteristic
5	#432×C₇₃	—	2	1	no	—
6	#407×C₇₃	—	2	1	no	—
7	C₂×C₂²⋊C₈×C₇₃	—	2	1	no	—
8	C₂×#97×C₇₃	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₇₃	C₄	1	1	yes	characteristic
10	#343×C₇₃	—	2	1	no	—
11	#343×C₇₃	C₄	1	2	yes	—
12	#336×C₇₃	—	2	1	no	—
13	#324×C₇₃	—	2	1	no	—
14	#323×C₇₃	C₄	1	2	yes	—
15	C₂³×C₄×C₇₃	D₄	1	1	yes	characteristic
16	C₂×M₁₆×C₇₃	—	2	2	no	—
17	C₂²×C₈×C₇₃	—	2	1	no	—
18	C₂²×C₈×C₇₃	—	2	1	no	—
19	#117×C₇₃	—	4	1	no	—
20	#117×C₇₃	—	4	1	no	—
21	C₂×C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄⋊C₄×C₇₃	D₄	1	1	yes	characteristic
23	C₂×C₂²⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₇₃	Q₈	1	1	yes	characteristic
25	C₂×C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
27	C₄⋊C₈×C₇₃	—	4	1	no	—
28	C₂²⋊C₈×C₇₃	—	2	4	no	—
29	C₂²⋊C₈×C₇₃	—	2	2	no	—
30	C₂²⋊C₈×C₇₃	—	4	1	no	—
31	C₂²⋊C₈×C₇₃	—	4	1	no	—
32	#97×C₇₃	—	4	1	no	—
33	#97×C₇₃	—	4	1	no	—
34	C₄×C₈×C₇₃	—	4	1	no	—
35	C₂⁴×C₇₃	C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₄×C₇₃	—	2	1	no	—
37	C₂²×C₄×C₇₃	—	2	1	no	—
38	C₂²×C₄×C₇₃	—	2	2	no	—
39	C₂²×C₄×C₇₃	—	4	1	no	—
40	C₂²×C₄×C₇₃	C₄²	1	1	yes	characteristic
41	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
46	M₁₆×C₇₃	—	4	2	no	—
47	M₁₆×C₇₃	—	4	2	no	—
48	C₂×C₈×C₇₃	—	2	2	no	—
49	C₂×C₈×C₇₃	—	2	2	no	—
50	C₂×C₈×C₇₃	—	4	1	no	—
51	C₂×C₈×C₇₃	—	4	1	no	—
52	C₂×C₈×C₇₃	—	4	1	no	—
53	C₂×C₈×C₇₃	—	4	1	no	—
54	C₂×C₈×C₇₃	—	4	2	no	—
55	C₂×C₈×C₇₃	—	4	2	no	—
56	C₄⋊C₄×C₇₃	—	4	1	no	—
57	C₄⋊C₄×C₇₃	—	4	1	no	—
58	C₂²⋊C₄×C₇₃	—	4	1	no	—
59	C₂²⋊C₄×C₇₃	—	4	1	no	—
60	C₄²×C₇₃	—	2	1	no	—
61	C₄²×C₇₃	—	2	1	no	—
62	C₄²×C₇₃	—	2	1	no	—
63	C₄²×C₇₃	—	2	1	no	—
64	C₂³×C₇₃	—	2	1	no	—
65	C₂³×C₇₃	—	2	1	no	—
66	C₂³×C₇₃	—	2	1	no	—
67	C₂³×C₇₃	—	4	1	no	—
68	C₂³×C₇₃	—	4	1	no	—
69	C₂³×C₇₃	#95	1	1	yes	characteristic
70	C₂×C₄×C₇₃	—	2	1	no	—
71	C₂×C₄×C₇₃	—	2	1	no	—
72	C₂×C₄×C₇₃	—	2	1	no	—
73	C₂×C₄×C₇₃	—	2	1	no	—
74	C₂×C₄×C₇₃	—	2	1	no	—
75	C₂×C₄×C₇₃	—	2	1	no	—
76	C₂×C₄×C₇₃	—	2	1	no	—
77	C₂×C₄×C₇₃	—	2	1	no	—
78	C₂×C₄×C₇₃	—	4	2	no	—
79	C₂×C₄×C₇₃	—	4	2	no	—
80	C₂×C₄×C₇₃	—	4	1	no	—
81	C₂×C₄×C₇₃	—	4	1	no	—
82	C₂×C₄×C₇₃	—	4	1	no	—
83	C₂×C₄×C₇₃	—	4	1	no	—
84	C₂×C₄×C₇₃	#99	1	1	yes	characteristic
85	C₂×C₄×C₇₃	#99	1	1	yes	characteristic
86	C₂×C₄×C₇₃	#104	1	2	yes	—
87	C₈×C₇₃	—	4	2	no	—
88	C₈×C₇₃	—	4	2	no	—
89	C₈×C₇₃	—	8	2	no	—
90	C₈×C₇₃	—	8	2	no	—
91	C₂²×C₇₃	—	2	1	no	—
92	C₂²×C₇₃	—	2	1	no	—
93	C₂²×C₇₃	—	4	2	no	—
94	C₂²×C₇₃	—	4	1	no	—
95	C₂²×C₇₃	—	4	1	no	—
96	C₂²×C₇₃	—	4	1	no	—
97	C₂²×C₇₃	—	8	1	no	—
98	C₂²×C₇₃	H(3,ℤ/4)	1	1	yes	characteristic
99	C₂²×C₇₃	#339	1	1	yes	characteristic
100	C₂²×C₇₃	#342	1	1	yes	characteristic
101	C₄×C₇₃	—	2	1	no	—
102	C₄×C₇₃	—	2	1	no	—
103	C₄×C₇₃	—	2	2	no	—
104	C₄×C₇₃	—	4	1	no	—
105	C₄×C₇₃	—	4	1	no	—
106	C₄×C₇₃	—	4	1	no	—
107	C₄×C₇₃	—	4	1	no	—
108	#7216	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
109	C₂×C₇₃	—	2	1	no	—
110	C₂×C₇₃	—	2	1	no	—
111	C₂×C₇₃	—	8	1	no	—
112	C₂×C₇₃	#1284	1	1	yes	characteristic
113	C₂×C₇₃	#1392	1	1	yes	characteristic
114	C₂×C₇₃	#1395	1	1	yes	characteristic
115	#1822	C₂×C₇₃	1	1	yes	characteristic
116	#1750	C₂×C₇₃	1	1	yes	characteristic
117	#1464	C₂×C₇₃	1	1	yes	characteristic
118	C₇₃	#7216	1	1	yes	characteristic, direct product factor, Sylow
119	C₂×#117	C₂²×C₇₃	1	1	yes	characteristic
120	#432	—	2	1	no	—
121	#407	—	2	1	no	—
122	C₂×C₂²⋊C₈	—	2	1	no	—
123	C₂×#97	C₄×C₇₃	1	1	yes	characteristic
124	C₂×C₄×C₈	C₄×C₇₃	1	1	yes	characteristic
125	#343	—	2	1	no	—
126	#343	C₄×C₇₃	1	2	yes	—
127	#336	—	2	1	no	—
128	#324	—	2	1	no	—
129	#323	C₄×C₇₃	1	2	yes	—
130	C₂³×C₄	D₄×C₇₃	1	1	yes	characteristic
131	C₂×M₁₆	—	2	2	no	—
132	C₂²×C₈	—	2	1	no	—
133	C₂²×C₈	—	2	1	no	—
134	#117	—	4	1	no	—
135	#117	—	4	1	no	—
136	C₂×C₄⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
137	C₂×C₄⋊C₄	D₄×C₇₃	1	1	yes	characteristic
138	C₂×C₂²⋊C₄	C₂×C₄×C₇₃	1	1	yes	characteristic
139	C₂×C₂²⋊C₄	Q₈×C₇₃	1	1	yes	characteristic
140	C₂×C₄²	C₂×C₄×C₇₃	1	1	yes	characteristic
141	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
142	C₄⋊C₈	—	4	1	no	—
143	C₂²⋊C₈	—	2	4	no	—
144	C₂²⋊C₈	—	2	2	no	—
145	C₂²⋊C₈	—	4	1	no	—
146	C₂²⋊C₈	—	4	1	no	—
147	#97	—	4	1	no	—
148	#97	—	4	1	no	—
149	C₄×C₈	—	4	1	no	—
150	C₂⁴	C₄⋊C₄×C₇₃	1	1	yes	characteristic
151	C₂²×C₄	—	2	1	no	—
152	C₂²×C₄	—	2	1	no	—
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	4	1	no	—
155	C₂²×C₄	C₄²×C₇₃	1	1	yes	characteristic
156	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
157	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
158	C₂²×C₄	C₂²⋊C₄×C₇₃	1	1	yes	characteristic
159	C₂²×C₄	C₄⋊C₄×C₇₃	1	1	yes	characteristic
160	C₂²×C₄	C₄⋊C₄×C₇₃	1	1	yes	characteristic
161	M₁₆	—	4	2	no	—
162	M₁₆	—	4	2	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	2	2	no	—
165	C₂×C₈	—	4	1	no	—
166	C₂×C₈	—	4	1	no	—
167	C₂×C₈	—	4	1	no	—
168	C₂×C₈	—	4	1	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	4	2	no	—
171	C₄⋊C₄	—	4	1	no	—
172	C₄⋊C₄	—	4	1	no	—
173	C₂²⋊C₄	—	4	1	no	—
174	C₂²⋊C₄	—	4	1	no	—
175	C₄²	—	2	1	no	—
176	C₄²	—	2	1	no	—
177	C₄²	—	2	1	no	—
178	C₄²	—	2	1	no	—
179	C₂³	—	2	1	no	—
180	C₂³	—	2	1	no	—
181	C₂³	—	2	1	no	—
182	C₂³	—	4	1	no	—
183	C₂³	—	4	1	no	—
184	C₂³	#95×C₇₃	1	1	yes	characteristic
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	2	1	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	1	no	—
191	C₂×C₄	—	2	1	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	4	2	no	—
194	C₂×C₄	—	4	2	no	—
195	C₂×C₄	—	4	1	no	—
196	C₂×C₄	—	4	1	no	—
197	C₂×C₄	—	4	1	no	—
198	C₂×C₄	—	4	1	no	—
199	C₂×C₄	#99×C₇₃	1	1	yes	characteristic
200	C₂×C₄	#99×C₇₃	1	1	yes	characteristic
201	C₂×C₄	#104×C₇₃	1	2	yes	—
202	C₈	—	4	2	no	—
203	C₈	—	4	2	no	—
204	C₈	—	8	2	no	—
205	C₈	—	8	2	no	—
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	—	4	2	no	—
209	C₂²	—	4	1	no	—
210	C₂²	—	4	1	no	—
211	C₂²	—	4	1	no	—
212	C₂²	—	8	1	no	—
213	C₂²	H(3,ℤ/4)×C₇₃	1	1	yes	characteristic
214	C₂²	#339×C₇₃	1	1	yes	characteristic
215	C₂²	#342×C₇₃	1	1	yes	characteristic
216	C₄	—	2	1	no	—
217	C₄	—	2	1	no	—
218	C₄	—	2	2	no	—
219	C₄	—	4	1	no	—
220	C₄	—	4	1	no	—
221	C₄	—	4	1	no	—
222	C₄	—	4	1	no	—
223	C₂	—	2	1	no	—
224	C₂	—	2	1	no	—
225	C₂	—	8	1	no	—
226	C₂	C₇₃×#1284	1	1	yes	characteristic
227	C₂	C₇₃×#1392	1	1	yes	characteristic
228	C₂	C₇₃×#1395	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₇₃×#1822

C₂

yes

maximal, characteristic

C₇₃×#1750

C₂

yes

maximal, characteristic

C₇₃×#1464

C₂

yes

maximal, characteristic

C₂×#117×C₇₃

C₂²

yes

characteristic

#432×C₇₃

—

#407×C₇₃

—

C₂×C₂²⋊C₈×C₇₃

—

C₂×#97×C₇₃

C₄

yes

characteristic

C₂×C₄×C₈×C₇₃

C₄

yes

characteristic

#343×C₇₃

—

#343×C₇₃

C₄

yes

—

#336×C₇₃

—

#324×C₇₃

—

#323×C₇₃

C₄

yes

—

C₂³×C₄×C₇₃

D₄

yes

characteristic

C₂×M₁₆×C₇₃

—

C₂²×C₈×C₇₃

—

C₂²×C₈×C₇₃

—

#117×C₇₃

—

#117×C₇₃

—

C₂×C₄⋊C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₇₃

D₄

yes

characteristic

C₂×C₂²⋊C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₇₃

Q₈

yes

characteristic

C₂×C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂×C₄²×C₇₃

D₄

yes

characteristic

C₄⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

C₂²⋊C₈×C₇₃

—

#97×C₇₃

—

#97×C₇₃

—

C₄×C₈×C₇₃

—

C₂⁴×C₇₃

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₄²

yes

characteristic

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₇₃

C₄⋊C₄

yes

characteristic

M₁₆×C₇₃

—

M₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

#95

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₈×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

yes

C₂²×C₇₃

yes

100

C₂²×C₇₃

#342

yes

characteristic

101

C₄×C₇₃

—

102

C₄×C₇₃

—

103

C₄×C₇₃

—

104

C₄×C₇₃

—

105

C₄×C₇₃

—

106

C₄×C₇₃

—

107

C₄×C₇₃

—

108

#7216

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

109

C₂×C₇₃

—

110

C₂×C₇₃

—

111

C₂×C₇₃

—

112

C₂×C₇₃

#1284

yes

characteristic

113

C₂×C₇₃

#1392

yes

characteristic

114

C₂×C₇₃

#1395

yes

characteristic

115

#1822

C₂×C₇₃

yes

characteristic

116

#1750

C₂×C₇₃

yes

characteristic

117

#1464

C₂×C₇₃

yes

characteristic

118

C₇₃

#7216

yes

characteristic, direct product factor, Sylow

119

C₂×#117

C₂²×C₇₃

yes

characteristic

120

#432

—

121

#407

—

122

C₂×C₂²⋊C₈

—

123

C₂×#97

C₄×C₇₃

yes

characteristic

124

C₂×C₄×C₈

C₄×C₇₃

yes

characteristic

125

#343

—

126

#343

C₄×C₇₃

yes

—

127

#336

—

128

#324

—

129

#323

C₄×C₇₃

yes

—

130

C₂³×C₄

D₄×C₇₃

yes

characteristic

131

C₂×M₁₆

—

132

C₂²×C₈

—

133

C₂²×C₈

—

134

#117

—

135

#117

—

136

C₂×C₄⋊C₄

C₂×C₄×C₇₃

yes

characteristic

137

C₂×C₄⋊C₄

D₄×C₇₃

yes

characteristic

138

C₂×C₂²⋊C₄

C₂×C₄×C₇₃

yes

characteristic

139

C₂×C₂²⋊C₄

Q₈×C₇₃

yes

characteristic

140

C₂×C₄²

C₂×C₄×C₇₃

yes

characteristic

141

C₂×C₄²

D₄×C₇₃

yes

characteristic

142

C₄⋊C₈

—

143

C₂²⋊C₈

—

144

C₂²⋊C₈

—

145

C₂²⋊C₈

—

146

C₂²⋊C₈

—

147

#97

—

148

#97

—

149

C₄×C₈

—

150

C₂⁴

C₄⋊C₄×C₇₃

yes

characteristic

151

C₂²×C₄

—

152

C₂²×C₄

—

153

C₂²×C₄

—

154

C₂²×C₄

—

155

C₂²×C₄

C₄²×C₇₃

yes

characteristic

156

C₂²×C₄

C₂²⋊C₄×C₇₃

yes

characteristic

157

C₂²×C₄

C₂²⋊C₄×C₇₃

yes

characteristic

158

C₂²×C₄

C₂²⋊C₄×C₇₃

yes

characteristic

159

C₂²×C₄

C₄⋊C₄×C₇₃

yes

characteristic

160

C₂²×C₄

C₄⋊C₄×C₇₃

yes

characteristic

161

M₁₆

—

162

M₁₆

—

163

C₂×C₈

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

—

167

C₂×C₈

—

168

C₂×C₈

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₂²⋊C₄

—

174

C₂²⋊C₄

—

175

C₄²

—

176

C₄²

—

177

C₄²

—

178

C₄²

—

179

C₂³

—

180

C₂³

—

181

C₂³

—

182

C₂³

—

183

C₂³

—

184

C₂³

#95×C₇₃

yes

characteristic

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

#99×C₇₃

yes

characteristic

200

C₂×C₄

#99×C₇₃

yes

characteristic

201

C₂×C₄

#104×C₇₃

yes

—

202

C₈

—

203

C₈

—

204

C₈

—

205

C₈

—

206

C₂²

—

207

C₂²

—

208

C₂²

—

209

C₂²

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

H(3,ℤ/4)×C₇₃

yes

characteristic

214

C₂²

#339×C₇₃

yes

characteristic

215

C₂²

#342×C₇₃

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

—

222

C₄

—

223

C₂

—

224

C₂

—

225

C₂

—

226

C₂

C₇₃×#1284

yes

characteristic

227

C₂

C₇₃×#1392

yes

characteristic

228

C₂

C₇₃×#1395

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₇₃	#342
commutator	C₂²×C₄	C₄²×C₇₃
Frattini, cosocle	C₂×#117	C₂²×C₇₃
prime radical	C₂⁴×C₇₃	C₄⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

subgroup

G/H

center, socle

C₂²×C₇₃

#342

commutator

C₂²×C₄

C₄²×C₇₃

Frattini, cosocle

C₂×#117

C₂²×C₇₃

prime radical

C₂⁴×C₇₃

C₄⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂²×C₇₃ ◁ C₂²×C₄×C₇₃ ◁ C₂×#117×C₇₃ ◁ G

N	H ≅ G/N	type
108. #7216	C₇₃	direct (N × H)
118. C₇₃	#7216	direct (N × H)

H ≅ G/N

type

108. #7216

C₇₃

direct (N × H)

118. C₇₃

#7216

direct (N × H)

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

subgroup	index
C₇₃×#1822	2
C₇₃×#1750	2
C₇₃×#1464	2
#7216	73

subgroup

index

C₇₃×#1822

C₇₃×#1750

C₇₃×#1464

#7216

Subgroups — C₇₃×#7216 #32916620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#7216 #32916620

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#7216 #32916620