Group #32922854 — subgroups

Subgroups — C₇₃×#13450 #32922854

Order 18688.

410 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 130 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	C₂²×Q₃₂×C₇₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#358×C₇₃	C₂	1	2	yes	maximal
4	C₇₃×#1969	C₂	1	2	yes	maximal
5	C₇₃×#1380	C₂	1	1	yes	maximal, characteristic
6	C₂²×Q₁₆×C₇₃	C₂²	1	2	yes	—
7	C₂×Q₃₂×C₇₃	—	2	4	no	—
8	C₂×Q₃₂×C₇₃	—	2	2	no	—
9	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
10	C₂²×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
11	C₂×#107×C₇₃	C₂²	1	2	yes	—
12	C₂×#103×C₇₃	—	2	2	no	—
13	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	#391×C₇₃	—	2	2	no	—
15	C₄⋊C₁₆×C₇₃	—	2	2	no	—
16	#358×C₇₃	—	2	4	no	—
17	C₂²×Q₈×C₇₃	—	2	2	no	—
18	C₂×Q₁₆×C₇₃	—	2	2	no	—
19	C₂×Q₁₆×C₇₃	—	2	2	no	—
20	C₂×Q₁₆×C₇₃	—	2	2	no	—
21	C₂×Q₁₆×C₇₃	—	2	2	no	—
22	C₂×Q₁₆×C₇₃	—	2	2	no	—
23	C₂×Q₁₆×C₇₃	D₄	1	4	yes	—
24	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
25	C₂²×C₈×C₇₃	C₂³	1	1	yes	characteristic
26	C₂×C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₂×C₄²×C₇₃	D₄	1	1	yes	characteristic
28	Q₃₂×C₇₃	—	2	8	no	—
29	C₂×C₁₆×C₇₃	—	2	2	no	—
30	C₂×C₁₆×C₇₃	—	2	2	no	—
31	C₂×C₁₆×C₇₃	—	2	1	no	—
32	C₂×C₁₆×C₇₃	D₄	1	2	yes	—
33	#107×C₇₃	—	2	2	no	—
34	#107×C₇₃	—	2	2	no	—
35	#103×C₇₃	—	4	4	no	—
36	C₄×C₈×C₇₃	—	2	1	no	—
37	C₄×C₈×C₇₃	—	2	1	no	—
38	#95×C₇₃	—	4	2	no	—
39	#95×C₇₃	—	4	2	no	—
40	C₂×Q₈×C₇₃	—	2	4	no	—
41	C₂×Q₈×C₇₃	—	4	2	no	—
42	C₂×Q₈×C₇₃	—	4	2	no	—
43	C₂×Q₈×C₇₃	—	4	2	no	—
44	C₂×Q₈×C₇₃	—	4	2	no	—
45	C₂×Q₈×C₇₃	—	4	2	no	—
46	C₂²×C₄×C₇₃	—	4	2	no	—
47	C₂²×C₄×C₇₃	—	4	2	no	—
48	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
49	C₂²×C₄×C₇₃	D₈	1	1	yes	characteristic
50	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
51	Q₁₆×C₇₃	—	2	4	no	—
52	Q₁₆×C₇₃	—	2	4	no	—
53	Q₁₆×C₇₃	—	4	2	no	—
54	Q₁₆×C₇₃	—	4	2	no	—
55	C₂×C₈×C₇₃	—	2	1	no	—
56	C₂×C₈×C₇₃	—	2	2	no	—
57	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
58	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₇₃	#41	1	1	yes	characteristic
60	C₂×C₈×C₇₃	#41	1	2	yes	—
61	C₄⋊C₄×C₇₃	—	4	2	no	—
62	C₄⋊C₄×C₇₃	—	4	2	no	—
63	C₄²×C₇₃	—	2	1	no	—
64	C₄²×C₇₃	—	2	1	no	—
65	C₁₆×C₇₃	—	2	2	no	—
66	C₁₆×C₇₃	—	4	1	no	—
67	C₂³×C₇₃	C₂×D₈	1	1	yes	characteristic
68	Q₈×C₇₃	—	4	4	no	—
69	Q₈×C₇₃	—	4	4	no	—
70	Q₈×C₇₃	—	8	2	no	—
71	Q₈×C₇₃	—	8	2	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	2	no	—
76	C₂×C₄×C₇₃	—	4	4	no	—
77	C₂×C₄×C₇₃	—	8	2	no	—
78	C₂×C₄×C₇₃	—	8	2	no	—
79	C₂×C₄×C₇₃	—	8	2	no	—
80	C₂×C₄×C₇₃	—	8	2	no	—
81	C₂×C₄×C₇₃	—	8	2	no	—
82	C₂×C₄×C₇₃	Q₃₂	1	2	yes	complemented
83	C₂×C₄×C₇₃	#121	1	2	yes	—
84	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
85	C₂×C₄×C₇₃	#135	1	1	yes	characteristic
86	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
87	C₈×C₇₃	—	4	1	no	—
88	C₈×C₇₃	#120	1	1	yes	characteristic
89	C₈×C₇₃	#123	1	2	yes	—
90	C₈×C₇₃	#124	1	1	yes	characteristic
91	C₂²×C₇₃	#459	1	2	yes	—
92	C₂²×C₇₃	#466	1	1	yes	characteristic
93	C₂²×C₇₃	C₂×Q₃₂	1	1	yes	characteristic
94	C₂²×C₇₃	#508	1	1	yes	characteristic
95	C₂²×C₇₃	#510	1	2	yes	—
96	C₄×C₇₃	—	2	2	no	—
97	C₄×C₇₃	—	4	1	no	—
98	C₄×C₇₃	—	8	4	no	—
99	C₄×C₇₃	—	16	2	no	—
100	C₄×C₇₃	#394	1	1	yes	characteristic
101	C₄×C₇₃	#463	1	2	yes	—
102	C₄×C₇₃	#469	1	1	yes	characteristic
103	#13450	C₇₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
104	C₂×C₇₃	#2054	1	1	yes	characteristic
105	C₂×C₇₃	#2209	1	2	yes	—
106	C₂×C₇₃	#2211	1	2	yes	—
107	C₂×C₇₃	#2216	1	1	yes	characteristic
108	C₂×C₇₃	#2219	1	1	yes	characteristic
109	C₂²×Q₃₂	C₂×C₇₃	1	1	yes	characteristic
110	C₂×C₄⋊C₁₆	C₂×C₇₃	1	1	yes	characteristic
111	C₂×#358	C₂×C₇₃	1	2	yes	—
112	#1969	C₂×C₇₃	1	2	yes	—
113	#1380	C₂×C₇₃	1	1	yes	characteristic
114	C₇₃	#13450	1	1	yes	characteristic, direct product factor, Sylow
115	C₂²×Q₁₆	C₂²×C₇₃	1	2	yes	—
116	C₂×Q₃₂	—	2	4	no	—
117	C₂×Q₃₂	—	2	2	no	—
118	C₂²×C₁₆	C₂²×C₇₃	1	1	yes	characteristic
119	C₂²×C₁₆	C₂²×C₇₃	1	1	yes	characteristic
120	C₂×#107	C₂²×C₇₃	1	2	yes	—
121	C₂×#103	—	2	2	no	—
122	C₂×C₄×C₈	C₂²×C₇₃	1	1	yes	characteristic
123	#391	—	2	2	no	—
124	C₄⋊C₁₆	—	2	2	no	—
125	#358	—	2	4	no	—
126	C₂²×Q₈	—	2	2	no	—
127	C₂×Q₁₆	—	2	2	no	—
128	C₂×Q₁₆	—	2	2	no	—
129	C₂×Q₁₆	—	2	2	no	—
130	C₂×Q₁₆	—	2	2	no	—
131	C₂×Q₁₆	—	2	2	no	—
132	C₂×Q₁₆	D₄×C₇₃	1	4	yes	—
133	C₂²×C₈	D₄×C₇₃	1	1	yes	characteristic
134	C₂²×C₈	C₂³×C₇₃	1	1	yes	characteristic
135	C₂×C₄⋊C₄	—	2	2	no	—
136	C₂×C₄²	D₄×C₇₃	1	1	yes	characteristic
137	Q₃₂	—	2	8	no	—
138	C₂×C₁₆	—	2	2	no	—
139	C₂×C₁₆	—	2	2	no	—
140	C₂×C₁₆	—	2	1	no	—
141	C₂×C₁₆	D₄×C₇₃	1	2	yes	—
142	#107	—	2	2	no	—
143	#107	—	2	2	no	—
144	#103	—	4	4	no	—
145	C₄×C₈	—	2	1	no	—
146	C₄×C₈	—	2	1	no	—
147	#95	—	4	2	no	—
148	#95	—	4	2	no	—
149	C₂×Q₈	—	2	4	no	—
150	C₂×Q₈	—	4	2	no	—
151	C₂×Q₈	—	4	2	no	—
152	C₂×Q₈	—	4	2	no	—
153	C₂×Q₈	—	4	2	no	—
154	C₂×Q₈	—	4	2	no	—
155	C₂²×C₄	—	4	2	no	—
156	C₂²×C₄	—	4	2	no	—
157	C₂²×C₄	D₈×C₇₃	1	1	yes	characteristic
158	C₂²×C₄	D₈×C₇₃	1	1	yes	characteristic
159	C₂²×C₄	C₂×D₄×C₇₃	1	1	yes	characteristic
160	Q₁₆	—	2	4	no	—
161	Q₁₆	—	2	4	no	—
162	Q₁₆	—	4	2	no	—
163	Q₁₆	—	4	2	no	—
164	C₂×C₈	—	2	1	no	—
165	C₂×C₈	—	2	2	no	—
166	C₂×C₈	C₂×D₄×C₇₃	1	2	yes	—
167	C₂×C₈	C₂×D₄×C₇₃	1	1	yes	characteristic
168	C₂×C₈	#41×C₇₃	1	1	yes	characteristic
169	C₂×C₈	#41×C₇₃	1	2	yes	—
170	C₄⋊C₄	—	4	2	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄²	—	2	1	no	—
173	C₄²	—	2	1	no	—
174	C₁₆	—	2	2	no	—
175	C₁₆	—	4	1	no	—
176	C₂³	C₂×D₈×C₇₃	1	1	yes	characteristic
177	Q₈	—	4	4	no	—
178	Q₈	—	4	4	no	—
179	Q₈	—	8	2	no	—
180	Q₈	—	8	2	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	2	1	no	—
183	C₂×C₄	—	2	1	no	—
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	4	4	no	—
186	C₂×C₄	—	8	2	no	—
187	C₂×C₄	—	8	2	no	—
188	C₂×C₄	—	8	2	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	2	no	—
191	C₂×C₄	Q₃₂×C₇₃	1	2	yes	complemented
192	C₂×C₄	#121×C₇₃	1	2	yes	—
193	C₂×C₄	#121×C₇₃	1	1	yes	characteristic
194	C₂×C₄	#135×C₇₃	1	1	yes	characteristic
195	C₂×C₄	AGL(1,ℤ/8)×C₇₃	1	2	yes	—
196	C₈	—	4	1	no	—
197	C₈	#120×C₇₃	1	1	yes	characteristic
198	C₈	#123×C₇₃	1	2	yes	—
199	C₈	#124×C₇₃	1	1	yes	characteristic
200	C₂²	#459×C₇₃	1	2	yes	—
201	C₂²	#466×C₇₃	1	1	yes	characteristic
202	C₂²	C₂×Q₃₂×C₇₃	1	1	yes	characteristic
203	C₂²	#508×C₇₃	1	1	yes	characteristic
204	C₂²	#510×C₇₃	1	2	yes	—
205	C₄	—	2	2	no	—
206	C₄	—	4	1	no	—
207	C₄	—	8	4	no	—
208	C₄	—	16	2	no	—
209	C₄	#394×C₇₃	1	1	yes	characteristic
210	C₄	#463×C₇₃	1	2	yes	—
211	C₄	#469×C₇₃	1	1	yes	characteristic
212	C₂	C₇₃×#2054	1	1	yes	characteristic
213	C₂	C₇₃×#2209	1	2	yes	—
214	C₂	C₇₃×#2211	1	2	yes	—
215	C₂	C₇₃×#2216	1	1	yes	characteristic
216	C₂	C₇₃×#2219	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Q₃₂×C₇₃

C₂

yes

maximal, characteristic

C₂×C₄⋊C₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂×#358×C₇₃

C₂

yes

maximal

C₇₃×#1969

C₂

yes

maximal

C₇₃×#1380

C₂

yes

maximal, characteristic

C₂²×Q₁₆×C₇₃

C₂²

yes

—

C₂×Q₃₂×C₇₃

—

C₂×Q₃₂×C₇₃

—

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂²×C₁₆×C₇₃

C₂²

yes

characteristic

C₂×#107×C₇₃

C₂²

yes

—

C₂×#103×C₇₃

—

C₂×C₄×C₈×C₇₃

C₂²

yes

characteristic

#391×C₇₃

—

C₄⋊C₁₆×C₇₃

—

#358×C₇₃

—

C₂²×Q₈×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

—

C₂×Q₁₆×C₇₃

D₄

yes

—

C₂²×C₈×C₇₃

D₄

yes

characteristic

C₂²×C₈×C₇₃

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

C₂×C₄²×C₇₃

D₄

yes

characteristic

Q₃₂×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

D₄

yes

—

#107×C₇₃

—

#107×C₇₃

—

#103×C₇₃

—

C₄×C₈×C₇₃

—

C₄×C₈×C₇₃

—

#95×C₇₃

—

#95×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

D₈

yes

characteristic

C₂²×C₄×C₇₃

C₂×D₄

yes

characteristic

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

Q₁₆×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×D₄

yes

—

C₂×C₈×C₇₃

C₂×D₄

yes

C₂×C₈×C₇₃

yes

C₂×C₈×C₇₃

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

—

C₁₆×C₇₃

—

C₁₆×C₇₃

—

C₂³×C₇₃

C₂×D₈

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×C₇₃

—

Q₈×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

Q₃₂

yes

complemented

C₂×C₄×C₇₃

#121

yes

—

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

C₂×C₄×C₇₃

yes

—

C₈×C₇₃

—

C₈×C₇₃

#120

yes

characteristic

C₈×C₇₃

#123

yes

—

C₈×C₇₃

#124

yes

characteristic

C₂²×C₇₃

#459

yes

—

C₂²×C₇₃

#466

yes

characteristic

C₂²×C₇₃

C₂×Q₃₂

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

100

C₄×C₇₃

#394

yes

characteristic

101

C₄×C₇₃

#463

yes

—

102

C₄×C₇₃

#469

yes

characteristic

103

#13450

C₇₃

yes

maximal, characteristic, direct product factor, Sylow

104

C₂×C₇₃

#2054

yes

characteristic

105

C₂×C₇₃

#2209

yes

—

106

C₂×C₇₃

#2211

yes

—

107

C₂×C₇₃

#2216

yes

characteristic

108

C₂×C₇₃

#2219

yes

characteristic

109

C₂²×Q₃₂

C₂×C₇₃

yes

characteristic

110

C₂×C₄⋊C₁₆

C₂×C₇₃

yes

characteristic

111

C₂×#358

C₂×C₇₃

yes

—

112

#1969

C₂×C₇₃

yes

—

113

#1380

C₂×C₇₃

yes

characteristic

114

C₇₃

#13450

yes

characteristic, direct product factor, Sylow

115

C₂²×Q₁₆

C₂²×C₇₃

yes

—

116

C₂×Q₃₂

—

117

C₂×Q₃₂

—

118

C₂²×C₁₆

C₂²×C₇₃

yes

characteristic

119

C₂²×C₁₆

C₂²×C₇₃

yes

characteristic

120

C₂×#107

C₂²×C₇₃

yes

—

121

C₂×#103

—

122

C₂×C₄×C₈

C₂²×C₇₃

yes

characteristic

123

#391

—

124

C₄⋊C₁₆

—

125

#358

—

126

C₂²×Q₈

—

127

C₂×Q₁₆

—

128

C₂×Q₁₆

—

129

C₂×Q₁₆

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

D₄×C₇₃

yes

—

133

C₂²×C₈

D₄×C₇₃

yes

characteristic

134

C₂²×C₈

C₂³×C₇₃

yes

characteristic

135

C₂×C₄⋊C₄

—

136

C₂×C₄²

D₄×C₇₃

yes

characteristic

137

Q₃₂

—

138

C₂×C₁₆

—

139

C₂×C₁₆

—

140

C₂×C₁₆

—

141

C₂×C₁₆

D₄×C₇₃

yes

—

142

#107

—

143

#107

—

144

#103

—

145

C₄×C₈

—

146

C₄×C₈

—

147

#95

—

148

#95

—

149

C₂×Q₈

—

150

C₂×Q₈

—

151

C₂×Q₈

—

152

C₂×Q₈

—

153

C₂×Q₈

—

154

C₂×Q₈

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

D₈×C₇₃

yes

characteristic

158

C₂²×C₄

D₈×C₇₃

yes

characteristic

159

C₂²×C₄

C₂×D₄×C₇₃

yes

characteristic

160

Q₁₆

—

161

Q₁₆

—

162

Q₁₆

—

163

Q₁₆

—

164

C₂×C₈

—

165

C₂×C₈

—

166

C₂×C₈

C₂×D₄×C₇₃

yes

—

167

C₂×C₈

C₂×D₄×C₇₃

yes

characteristic

168

C₂×C₈

#41×C₇₃

yes

characteristic

169

C₂×C₈

#41×C₇₃

yes

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄²

—

173

C₄²

—

174

C₁₆

—

175

C₁₆

—

176

C₂³

C₂×D₈×C₇₃

yes

characteristic

177

Q₈

—

178

Q₈

—

179

Q₈

—

180

Q₈

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

Q₃₂×C₇₃

yes

complemented

192

C₂×C₄

#121×C₇₃

yes

—

193

C₂×C₄

#121×C₇₃

yes

characteristic

194

C₂×C₄

#135×C₇₃

yes

characteristic

195

C₂×C₄

AGL(1,ℤ/8)×C₇₃

yes

—

196

C₈

—

197

C₈

#120×C₇₃

yes

characteristic

198

C₈

#123×C₇₃

yes

—

199

C₈

#124×C₇₃

yes

characteristic

200

C₂²

#459×C₇₃

yes

—

201

C₂²

#466×C₇₃

yes

characteristic

202

C₂²

C₂×Q₃₂×C₇₃

yes

characteristic

203

C₂²

#508×C₇₃

yes

characteristic

204

C₂²

#510×C₇₃

yes

—

205

C₄

—

206

C₄

—

207

C₄

—

208

C₄

—

209

C₄

#394×C₇₃

yes

characteristic

210

C₄

#463×C₇₃

yes

—

211

C₄

#469×C₇₃

yes

characteristic

212

C₂

C₇₃×#2054

yes

characteristic

213

C₂

C₇₃×#2209

yes

—

214

C₂

C₇₃×#2211

yes

—

215

C₂

C₇₃×#2216

yes

characteristic

216

C₂

C₇₃×#2219

yes

characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₇₃	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₇₃
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ C₂×C₄×C₈×C₇₃ ◁ G

subgroup

G/H

center, socle, prime radical

C₂³×C₇₃

C₂×D₈

commutator, Frattini, cosocle

C₂²×C₈

C₂³×C₇₃

LCS

G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁

UCS

C₁ ◁ C₂³×C₇₃ ◁ C₂×C₄²×C₇₃ ◁ C₂×C₄×C₈×C₇₃ ◁ G

N	H ≅ G/N	type
82. C₂×C₄×C₇₃	Q₃₂	semidirect
103. #13450	C₇₃	direct (N × H)
114. C₇₃	#13450	direct (N × H)
191. C₂×C₄	Q₃₂×C₇₃	semidirect

H ≅ G/N

type

82. C₂×C₄×C₇₃

Q₃₂

semidirect

103. #13450

C₇₃

direct (N × H)

114. C₇₃

#13450

direct (N × H)

191. C₂×C₄

Q₃₂×C₇₃

semidirect

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

subgroup	index
C₂²×Q₃₂×C₇₃	2
C₂×C₄⋊C₁₆×C₇₃	2
C₂×#358×C₇₃	2
C₇₃×#1969	2
C₇₃×#1380	2
#13450	73

subgroup

index

C₂²×Q₃₂×C₇₃

C₂×C₄⋊C₁₆×C₇₃

C₂×#358×C₇₃

C₇₃×#1969

C₇₃×#1380

#13450

Subgroups — C₇₃×#13450 #32922854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C73×#13450 #32922854

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇₃×#13450 #32922854