Group #16952697 — subgroups

Subgroups — #16952697

Order 4352.

438 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 135 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×Dic₁₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#11762612	C₂	1	2	yes	maximal
3	C₂×C₁₆×Dic₁₇	C₂	1	1	yes	maximal, characteristic
4	#14529643	C₂	1	2	yes	maximal
5	C₂×C₁₇×#366	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₆₈	C₂²	1	2	yes	—
7	C₂×Dic₁₃₆	—	2	2	no	—
8	C₂×Dic₁₃₆	—	2	2	no	—
9	C₂×Dic₁₃₆	C₄	1	4	yes	complemented
10	C₂²×#63214	C₂²	1	1	yes	characteristic
11	C₂×#10587481	—	2	2	no	—
12	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
13	#11762714	—	2	2	no	—
14	#11762612	—	2	4	no	—
15	C₁₆×Dic₁₇	—	2	2	no	—
16	C₂²×C₁₆×C₁₇	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×#107	C₂²	1	2	yes	—
18	C₁₇×#366	—	2	2	no	—
19	C₂²×Dic₃₄	—	2	2	no	—
20	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
21	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
22	C₂×C₄×Dic₁₇	D₄	1	1	yes	characteristic
23	C₂²×#3622	D₄	1	1	yes	characteristic
24	C₂×Dic₆₈	—	2	2	no	—
25	C₂×Dic₆₈	—	2	2	no	—
26	C₂×Dic₆₈	—	2	2	no	—
27	C₂×Dic₆₈	—	2	2	no	—
28	C₂×Dic₆₈	—	2	2	no	—
29	C₂×Dic₆₈	C₂×C₄	1	4	yes	—
30	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
31	C₂×C₁₆×C₁₇	D₄	1	2	yes	—
32	C₂×C₁₆×C₁₇	D₄	1	2	yes	—
33	C₁₇×#107	—	2	2	no	—
34	C₁₇×#107	—	2	2	no	—
35	#10587502	—	4	4	no	—
36	C₈×Dic₁₇	—	2	1	no	—
37	C₈×Dic₁₇	—	2	1	no	—
38	C₂×#63214	—	2	1	no	—
39	C₂×#63214	—	2	1	no	—
40	C₂×#63214	D₄	1	2	yes	—
41	#10587481	—	4	4	no	—
42	Dic₁₃₆	—	2	8	no	—
43	C₂²×C₄×C₁₇	—	4	2	no	—
44	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
45	C₂²×Dic₁₇	—	4	2	no	—
46	C₂²×Dic₁₇	D₈	1	2	yes	—
47	C₂×Dic₃₄	—	2	4	no	—
48	C₂×Dic₃₄	—	4	2	no	—
49	C₂×Dic₃₄	—	4	2	no	—
50	C₂×Dic₃₄	—	4	2	no	—
51	C₂×Dic₃₄	—	4	2	no	—
52	C₂×Dic₃₄	—	4	2	no	—
53	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
54	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
55	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
58	C₂×C₈×C₁₇	#41	1	1	yes	characteristic
59	C₄⋊C₄×C₁₇	—	4	2	no	—
60	C₄⋊C₄×C₁₇	—	4	2	no	—
61	C₄×Dic₁₇	—	2	1	no	—
62	C₄×Dic₁₇	—	2	1	no	—
63	C₂×#3622	—	2	1	no	—
64	C₂×#3622	—	2	1	no	—
65	C₂×#3622	D₈	1	2	yes	—
66	Dic₆₈	—	2	4	no	—
67	Dic₆₈	—	2	4	no	—
68	Dic₆₈	—	4	2	no	—
69	Dic₆₈	—	4	2	no	—
70	C₁₆×C₁₇	C₂²⋊C₄	1	4	yes	—
71	#63214	—	2	2	no	—
72	#13236	—	17	1	no	maximal, Sylow
73	C₂³×C₁₇	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₁₇	—	8	2	no	—
75	C₂×C₄×C₁₇	—	8	4	no	—
76	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
77	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
78	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
79	C₂×C₄×C₁₇	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₁₇	#135	1	1	yes	characteristic
81	C₂×C₄×C₁₇	#135	1	1	yes	characteristic
82	C₂×Dic₁₇	—	2	2	no	—
83	C₂×Dic₁₇	—	2	2	no	—
84	C₂×Dic₁₇	—	4	4	no	—
85	C₂×Dic₁₇	—	8	2	no	—
86	C₂×Dic₁₇	—	8	2	no	—
87	C₂×Dic₁₇	Q₃₂	1	4	yes	complemented
88	Dic₃₄	—	4	4	no	—
89	Dic₃₄	—	4	4	no	—
90	Dic₃₄	—	8	2	no	—
91	Dic₃₄	—	8	2	no	—
92	C₈×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
93	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
94	C₈×C₁₇	#121	1	1	yes	characteristic
95	C₈×C₁₇	#124	1	1	yes	characteristic
96	#3622	—	2	2	no	—
97	C₂²×Q₃₂	—	17	1	no	—
98	C₂×#366	D₁₇	1	1	yes	characteristic
99	C₂×#358	—	17	2	no	—
100	C₂×C₄×C₁₆	—	17	1	no	—
101	#1969	—	17	2	no	—
102	C₂²×C₁₇	C₄×D₈	1	1	yes	characteristic
103	C₂²×C₁₇	#466	1	1	yes	characteristic
104	C₂²×C₁₇	#493	1	1	yes	characteristic
105	C₂²×C₁₇	C₂×Q₃₂	1	2	yes	—
106	C₂²×C₁₇	#508	1	2	yes	—
107	C₄×C₁₇	—	16	2	no	—
108	C₄×C₁₇	#390	1	1	yes	characteristic
109	C₄×C₁₇	C₄×D₈	1	1	yes	characteristic
110	C₄×C₁₇	#466	1	1	yes	characteristic
111	C₄×C₁₇	#495	1	1	yes	characteristic
112	Dic₁₇	—	2	4	no	—
113	Dic₁₇	—	8	4	no	—
114	C₂²×Q₁₆	—	17	2	no	—
115	C₂×Q₃₂	—	17	4	no	—
116	C₂×Q₃₂	—	34	2	no	—
117	C₂×Q₃₂	—	34	2	no	—
118	C₂²×C₁₆	—	17	1	no	—
119	C₂²×C₁₆	C₂×D₁₇	1	1	yes	characteristic
120	C₂×#107	C₂×D₁₇	1	2	yes	—
121	C₂×#103	—	34	2	no	—
122	C₂×C₄×C₈	—	17	1	no	—
123	#391	—	34	2	no	—
124	#366	—	2	2	no	—
125	#358	—	34	4	no	—
126	C₄×C₁₆	—	34	2	no	—
127	C₂×C₁₇	#1970	1	1	yes	characteristic
128	C₂×C₁₇	C₄×Q₃₂	1	2	yes	—
129	C₂×C₁₇	#2216	1	2	yes	—
130	C₂×C₁₇	#2247	1	1	yes	characteristic
131	C₂×C₁₇	#2249	1	1	yes	characteristic
132	C₂²×Q₈	—	34	2	no	—
133	C₂×Q₁₆	—	17	4	no	—
134	C₂×Q₁₆	—	34	2	no	—
135	C₂×Q₁₆	—	34	2	no	—
136	C₂×Q₁₆	—	34	2	no	—
137	C₂×Q₁₆	—	34	2	no	—
138	C₂×Q₁₆	—	34	2	no	—
139	C₂²×C₈	—	17	1	no	—
140	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
141	C₂×C₄⋊C₄	—	2	2	no	—
142	C₂×C₄²	—	17	1	no	—
143	Q₃₂	—	34	8	no	—
144	C₂×C₁₆	—	17	2	no	—
145	C₂×C₁₆	—	34	1	no	—
146	C₂×C₁₆	—	34	1	no	—
147	C₂×C₁₆	C₄×D₁₇	1	2	yes	—
148	C₂×C₁₆	D₆₈	1	2	yes	—
149	C₂×C₁₆	C₂²⋊D₁₇	1	2	yes	—
150	#107	—	2	2	no	—
151	#107	—	2	2	no	—
152	#103	—	68	4	no	—
153	C₄×C₈	—	34	1	no	—
154	C₄×C₈	—	34	1	no	—
155	#95	—	68	4	no	—
156	C₁₇	#13236	1	1	yes	characteristic, complemented, Sylow
157	C₂×Q₈	—	34	4	no	—
158	C₂×Q₈	—	68	2	no	—
159	C₂×Q₈	—	68	2	no	—
160	C₂×Q₈	—	68	2	no	—
161	C₂×Q₈	—	68	2	no	—
162	C₂×Q₈	—	68	2	no	—
163	C₂²×C₄	—	4	2	no	—
164	C₂²×C₄	—	17	2	no	—
165	C₂²×C₄	—	68	2	no	—
166	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
167	Q₁₆	—	34	4	no	—
168	Q₁₆	—	34	4	no	—
169	Q₁₆	—	68	2	no	—
170	Q₁₆	—	68	2	no	—
171	C₂×C₈	—	17	2	no	—
172	C₂×C₈	—	34	1	no	—
173	C₂×C₈	—	34	1	no	—
174	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
175	C₂×C₈	C₂×D₆₈	1	1	yes	characteristic
176	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
177	C₂×C₈	#63256	1	1	yes	characteristic
178	C₂×C₈	#63256	1	1	yes	characteristic
179	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
180	C₄⋊C₄	—	4	2	no	—
181	C₄⋊C₄	—	4	2	no	—
182	C₄²	—	34	1	no	—
183	C₄²	—	34	1	no	—
184	C₁₆	—	34	2	no	—
185	C₁₆	#63227	1	4	yes	—
186	C₂³	D₈×D₁₇	1	1	yes	characteristic
187	Q₈	—	68	4	no	—
188	Q₈	—	68	4	no	—
189	Q₈	—	136	2	no	—
190	Q₈	—	136	2	no	—
191	C₂×C₄	—	8	4	no	—
192	C₂×C₄	—	8	2	no	—
193	C₂×C₄	—	17	4	no	—
194	C₂×C₄	—	34	2	no	—
195	C₂×C₄	—	34	2	no	—
196	C₂×C₄	—	68	4	no	—
197	C₂×C₄	—	136	2	no	—
198	C₂×C₄	—	136	2	no	—
199	C₂×C₄	#10587579	1	1	yes	characteristic
200	C₂×C₄	#10587581	1	1	yes	characteristic
201	C₂×C₄	D₈×D₁₇	1	1	yes	characteristic
202	C₂×C₄	#10587605	1	1	yes	characteristic
203	C₂×C₄	#10587605	1	1	yes	characteristic
204	C₂×C₄	#10587626	1	1	yes	characteristic
205	C₈	—	34	2	no	—
206	C₈	#10587579	1	1	yes	characteristic
207	C₈	#10587581	1	1	yes	characteristic
208	C₈	C₂×#63227	1	1	yes	characteristic
209	C₈	#10587633	1	1	yes	characteristic
210	C₂²	#11762891	1	1	yes	characteristic
211	C₂²	#11763046	1	1	yes	characteristic
212	C₂²	#11763184	1	1	yes	characteristic
213	C₂²	Q₃₂×D₁₇	1	2	yes	—
214	C₂²	#11763238	1	2	yes	—
215	C₄	—	16	2	no	—
216	C₄	—	34	4	no	—
217	C₄	—	136	4	no	—
218	C₄	#11762710	1	1	yes	characteristic
219	C₄	#11762891	1	1	yes	characteristic
220	C₄	#11763046	1	1	yes	characteristic
221	C₄	#11763194	1	1	yes	characteristic
222	C₂	#14529648	1	1	yes	characteristic
223	C₂	#14530642	1	2	yes	—
224	C₂	#14530876	1	2	yes	—
225	C₂	#14531035	1	1	yes	characteristic
226	C₂	#14531042	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₁₃₆

C₂

yes

maximal, characteristic

C₂×#11762612

C₂

yes

maximal

C₂×C₁₆×Dic₁₇

C₂

yes

maximal, characteristic

#14529643

C₂

yes

maximal

C₂×C₁₇×#366

C₂

yes

maximal, characteristic

C₂²×Dic₆₈

C₂²

yes

—

C₂×Dic₁₃₆

—

C₂×Dic₁₃₆

—

C₂×Dic₁₃₆

C₄

yes

complemented

C₂²×#63214

C₂²

yes

characteristic

C₂×#10587481

—

C₂×C₈×Dic₁₇

C₂²

yes

characteristic

#11762714

—

#11762612

—

C₁₆×Dic₁₇

—

C₂²×C₁₆×C₁₇

C₂²

yes

characteristic

C₂×C₁₇×#107

C₂²

yes

—

C₁₇×#366

—

C₂²×Dic₃₄

—

C₂²×C₈×C₁₇

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₁₇

—

C₂×C₄×Dic₁₇

D₄

yes

characteristic

C₂²×#3622

D₄

yes

characteristic

C₂×Dic₆₈

—

C₂×Dic₆₈

—

C₂×Dic₆₈

—

C₂×Dic₆₈

—

C₂×Dic₆₈

—

C₂×Dic₆₈

C₂×C₄

yes

—

C₂×C₁₆×C₁₇

C₂×C₄

yes

—

C₂×C₁₆×C₁₇

D₄

yes

—

C₂×C₁₆×C₁₇

D₄

yes

—

C₁₇×#107

—

C₁₇×#107

—

#10587502

—

C₈×Dic₁₇

—

C₈×Dic₁₇

—

C₂×#63214

—

C₂×#63214

—

C₂×#63214

D₄

yes

—

#10587481

—

Dic₁₃₆

—

C₂²×C₄×C₁₇

—

C₂²×C₄×C₁₇

C₂×D₄

yes

characteristic

C₂²×Dic₁₇

—

C₂²×Dic₁₇

D₈

yes

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×Dic₃₄

—

C₂×C₈×C₁₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

characteristic

C₂×C₈×C₁₇

C₂×D₄

yes

C₂×C₈×C₁₇

yes

C₂×C₈×C₁₇

yes

C₄⋊C₄×C₁₇

—

C₄⋊C₄×C₁₇

—

C₄×Dic₁₇

—

C₄×Dic₁₇

—

C₂×#3622

—

C₂×#3622

—

C₂×#3622

D₈

yes

—

Dic₆₈

—

Dic₆₈

—

Dic₆₈

—

Dic₆₈

—

C₁₆×C₁₇

C₂²⋊C₄

yes

—

#63214

—

#13236

—

maximal, Sylow

C₂³×C₁₇

C₂×D₈

yes

characteristic

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

C₄×D₄

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

C₂×D₈

yes

C₂×C₄×C₁₇

yes

C₂×C₄×C₁₇

yes

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

Q₃₂

yes

complemented

Dic₃₄

—

Dic₃₄

—

Dic₃₄

—

Dic₃₄

—

C₈×C₁₇

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₁₇

C₄×D₄

yes

C₈×C₁₇

yes

C₈×C₁₇

yes

—

C₂²×Q₃₂

—

C₂×#366

D₁₇

yes

characteristic

C₂×#358

—

100

C₂×C₄×C₁₆

—

101

#1969

—

102

C₂²×C₁₇

C₄×D₈

yes

characteristic

103

C₂²×C₁₇

#466

yes

characteristic

104

C₂²×C₁₇

#493

yes

characteristic

105

C₂²×C₁₇

C₂×Q₃₂

yes

—

106

C₂²×C₁₇

#508

yes

—

107

C₄×C₁₇

—

108

C₄×C₁₇

#390

yes

characteristic

109

C₄×C₁₇

C₄×D₈

yes

characteristic

110

C₄×C₁₇

#466

yes

characteristic

111

C₄×C₁₇

#495

yes

characteristic

112

Dic₁₇

—

113

Dic₁₇

—

114

C₂²×Q₁₆

—

115

C₂×Q₃₂

—

116

C₂×Q₃₂

—

117

C₂×Q₃₂

—

118

C₂²×C₁₆

—

119

C₂²×C₁₆

C₂×D₁₇

yes

characteristic

120

C₂×#107

C₂×D₁₇

yes

—

121

C₂×#103

—

122

C₂×C₄×C₈

—

123

#391

—

124

#366

—

125

#358

—

126

C₄×C₁₆

—

127

C₂×C₁₇

#1970

yes

characteristic

128

C₂×C₁₇

C₄×Q₃₂

yes

—

129

C₂×C₁₇

#2216

yes

—

130

C₂×C₁₇

#2247

yes

characteristic

131

C₂×C₁₇

#2249

yes

characteristic

132

C₂²×Q₈

—

133

C₂×Q₁₆

—

134

C₂×Q₁₆

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

137

C₂×Q₁₆

—

138

C₂×Q₁₆

—

139

C₂²×C₈

—

140

C₂²×C₈

C₂²×D₁₇

yes

characteristic

141

C₂×C₄⋊C₄

—

142

C₂×C₄²

—

143

Q₃₂

—

144

C₂×C₁₆

—

145

C₂×C₁₆

—

146

C₂×C₁₆

—

147

C₂×C₁₆

C₄×D₁₇

yes

—

148

C₂×C₁₆

D₆₈

yes

—

149

C₂×C₁₆

C₂²⋊D₁₇

yes

—

150

#107

—

151

#107

—

152

#103

—

153

C₄×C₈

—

154

C₄×C₈

—

155

#95

—

156

C₁₇

#13236

yes

characteristic, complemented, Sylow

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂×Q₈

—

162

C₂×Q₈

—

163

C₂²×C₄

—

164

C₂²×C₄

—

165

C₂²×C₄

—

166

C₂²×C₄

D₄×D₁₇

yes

characteristic

167

Q₁₆

—

168

Q₁₆

—

169

Q₁₆

—

170

Q₁₆

—

171

C₂×C₈

—

172

C₂×C₈

—

173

C₂×C₈

—

174

C₂×C₈

C₂×C₄×D₁₇

yes

characteristic

175

C₂×C₈

C₂×D₆₈

yes

characteristic

176

C₂×C₈

D₄×D₁₇

yes

characteristic

177

C₂×C₈

#63256

yes

characteristic

178

C₂×C₈

#63256

yes

characteristic

179

C₂×C₈

C₂×C₂²⋊D₁₇

yes

characteristic

180

C₄⋊C₄

—

181

C₄⋊C₄

—

182

C₄²

—

183

C₄²

—

184

C₁₆

—

185

C₁₆

#63227

yes

—

186

C₂³

D₈×D₁₇

yes

characteristic

187

Q₈

—

188

Q₈

—

189

Q₈

—

136

—

190

Q₈

—

136

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

136

—

198

C₂×C₄

—

136

—

199

C₂×C₄

#10587579

yes

characteristic

200

C₂×C₄

#10587581

yes

characteristic

201

C₂×C₄

D₈×D₁₇

yes

characteristic

202

C₂×C₄

#10587605

yes

characteristic

203

C₂×C₄

#10587605

yes

characteristic

204

C₂×C₄

#10587626

yes

characteristic

205

C₈

—

206

C₈

#10587579

yes

characteristic

207

C₈

#10587581

yes

characteristic

208

C₈

C₂×#63227

yes

characteristic

209

C₈

#10587633

yes

characteristic

210

C₂²

#11762891

yes

characteristic

211

C₂²

#11763046

yes

characteristic

212

C₂²

#11763184

yes

characteristic

213

C₂²

Q₃₂×D₁₇

yes

—

214

C₂²

#11763238

yes

—

215

C₄

—

216

C₄

—

217

C₄

—

136

—

218

C₄

#11762710

yes

characteristic

219

C₄

#11762891

yes

characteristic

220

C₄

#11763046

yes

characteristic

221

C₄

#11763194

yes

characteristic

222

C₂

#14529648

yes

characteristic

223

C₂

#14530642

yes

—

224

C₂

#14530876

yes

—

225

C₂

#14531035

yes

characteristic

226

C₂

#14531042

yes

characteristic

	subgroup	G/H
center	C₂³	D₈×D₁₇
commutator	C₂×C₈×C₁₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₇
Fitting	C₂×C₁₇×#366	C₂
socle, prime radical	C₂³×C₁₇	C₂×D₈
cosocle	C₂²×C₈×C₁₇	C₂³
hypercenter	C₂×#366	D₁₇
hypocenter	C₁₇	#13236
LCS	G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

subgroup

G/H

center

C₂³

D₈×D₁₇

commutator

C₂×C₈×C₁₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₇

Fitting

C₂×C₁₇×#366

C₂

socle, prime radical

C₂³×C₁₇

C₂×D₈

cosocle

C₂²×C₈×C₁₇

C₂³

D₁₇

C₁₇

G ▷ C₂×C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

N	H ≅ G/N	type
9. C₂×Dic₁₃₆	C₄	semidirect
87. C₂×Dic₁₇	Q₃₂	semidirect
156. C₁₇	#13236	semidirect

H ≅ G/N

type

9. C₂×Dic₁₃₆

C₄

semidirect

87. C₂×Dic₁₇

Q₃₂

semidirect

156. C₁₇

#13236

semidirect

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

subgroup	index
C₂²×Dic₁₃₆	2
C₂×#11762612	2
C₂×C₁₆×Dic₁₇	2
#14529643	2
C₂×C₁₇×#366	2
#13236	17

subgroup

index

C₂²×Dic₁₃₆

C₂×#11762612

C₂×C₁₆×Dic₁₇

#14529643

C₂×C₁₇×#366

#13236

Subgroups — #16952697

Conjugacy classes of subgroups

Complements

Maximal subgroups