Group #30774063 — subgroups

Subgroups — #30774063

Order 17152.

590 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 163 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×#16863773	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863198	C₂	1	4	yes	maximal, complemented
3	#22560373	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#346×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₅₃₆	—	2	1	no	—
6	C₂²×D₅₃₆	C₂²	1	2	yes	—
7	C₂×#14524040	—	2	1	no	—
8	#16863773	—	2	2	no	—
9	#16863773	C₄	1	4	yes	complemented
10	C₂×#14523977	C₂²	1	2	yes	—
11	C₂×#14523975	—	2	1	no	—
12	#16863262	—	2	1	no	—
13	#16863198	—	2	8	no	—
14	C₂²×C₁₆×C₆₇	C₂²	1	2	yes	—
15	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
16	#346×C₆₇	—	2	2	no	—
17	C₂²×D₂₆₈	—	2	2	no	—
18	C₂²×D₂₆₈	—	4	2	no	—
19	C₂×D₅₃₆	—	2	4	no	—
20	C₂×D₅₃₆	—	2	4	no	—
21	C₂×D₅₃₆	—	2	2	no	—
22	C₂×D₅₃₆	—	2	4	no	—
23	C₂×D₅₃₆	—	4	2	no	—
24	C₂×D₅₃₆	—	4	2	no	—
25	C₂×D₅₃₆	C₂×C₄	1	4	yes	—
26	#14524040	—	2	4	no	—
27	#14524040	—	4	2	no	—
28	C₂×C₄⋊Dic₆₇	—	2	2	no	—
29	#14523977	—	2	4	no	—
30	#14523975	—	4	2	no	—
31	C₆₇⋊#95	—	4	2	no	—
32	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
33	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
35	C₂×C₁₆×C₆₇	—	2	2	no	—
36	C₂×C₁₆×C₆₇	—	2	2	no	—
37	C₂×C₁₆×C₆₇	D₄	1	4	yes	complemented
38	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₆₇	D₄	1	2	yes	—
40	C₂³×D₆₇	—	4	2	no	—
41	C₂×D₂₆₈	—	2	4	no	—
42	C₂×D₂₆₈	—	4	2	no	—
43	C₂×D₂₆₈	—	4	2	no	—
44	C₂×D₂₆₈	—	4	2	no	—
45	C₂×D₂₆₈	—	4	2	no	—
46	C₂×D₂₆₈	—	4	8	no	—
47	C₂×D₂₆₈	—	4	2	no	—
48	C₂×D₂₆₈	—	8	8	no	—
49	C₂²×Dic₆₇	—	4	2	no	—
50	D₅₃₆	—	2	8	no	—
51	D₅₃₆	—	4	8	no	—
52	D₅₃₆	—	4	4	no	—
53	C₄⋊Dic₆₇	—	4	2	no	—
54	C₄⋊Dic₆₇	—	4	2	no	—
55	C₂²×C₄×C₆₇	D₈	1	2	yes	—
56	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
58	C₂×C₈×C₆₇	D₈	1	2	yes	—
59	C₂×C₈×C₆₇	SD₁₆	1	2	yes	—
60	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
61	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
62	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₆₇	#41	1	2	yes	—
64	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
65	C₄²×C₆₇	SD₁₆	1	2	yes	—
66	C₁₆×C₆₇	—	2	4	no	—
67	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
68	C₂²×D₆₇	—	4	4	no	—
69	C₂²×D₆₇	—	8	2	no	—
70	C₂²×D₆₇	—	8	2	no	—
71	C₂²×D₆₇	—	8	8	no	—
72	C₂×C₄×C₆₇	—	2	4	no	—
73	C₂×C₄×C₆₇	#102	1	4	yes	—
74	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
75	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
76	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
77	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
78	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
79	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
80	C₂×Dic₆₇	—	8	2	no	—
81	C₂×Dic₆₇	—	8	4	no	—
82	D₂₆₈	—	4	4	no	—
83	D₂₆₈	—	4	4	no	—
84	D₂₆₈	—	8	16	no	—
85	D₂₆₈	—	8	2	no	—
86	D₂₆₈	—	8	2	no	—
87	C₈×C₆₇	#102	1	4	yes	—
88	C₈×C₆₇	C₄×D₄	1	2	yes	—
89	C₈×C₆₇	#121	1	2	yes	—
90	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
91	C₂²×C₆₇	#486	1	1	yes	characteristic
92	C₂²×C₆₇	#493	1	1	yes	characteristic
93	C₂²×C₆₇	#509	1	4	yes	—
94	C₂×D₆₇	—	8	8	no	—
95	C₂×D₆₇	—	8	4	no	—
96	C₂×D₆₇	—	16	4	no	—
97	C₂×D₆₇	—	16	4	no	—
98	C₄×C₆₇	—	2	4	no	—
99	C₄×C₆₇	#390	1	1	yes	characteristic
100	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
101	C₄×C₆₇	#486	1	1	yes	characteristic
102	C₄×C₆₇	#492	1	1	yes	characteristic
103	Dic₆₇	—	16	2	no	—
104	#13206	—	67	1	no	maximal, Sylow
105	C₂×C₆₇	#1957	1	1	yes	characteristic
106	C₂×C₆₇	#2140	1	2	yes	—
107	C₂×C₆₇	#2244	1	2	yes	—
108	C₂×C₆₇	#2250	1	2	yes	—
109	D₆₇	—	16	4	no	—
110	C₂×#493	—	67	1	no	—
111	C₂×#357	—	67	4	no	—
112	C₂×#346	D₆₇	1	1	yes	characteristic, complemented
113	#1846	—	67	1	no	—
114	C₆₇	#13206	1	1	yes	characteristic, complemented, Sylow
115	C₂²×D₈	—	67	2	no	—
116	C₂²×D₈	—	134	1	no	—
117	C₂×#127	—	134	1	no	—
118	C₂²×C₁₆	C₂×D₆₇	1	2	yes	—
119	#493	—	67	4	no	—
120	#493	—	134	2	no	—
121	C₂×#107	—	67	2	no	—
122	C₂×#106	—	134	1	no	—
123	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
124	#382	—	134	1	no	—
125	#357	—	134	8	no	—
126	#346	—	2	2	no	—
127	C₂²×D₄	—	268	2	no	—
128	C₂²×D₄	—	134	2	no	—
129	C₂×D₈	—	268	2	no	—
130	C₂×D₈	—	268	2	no	—
131	C₂×D₈	—	67	4	no	—
132	C₂×D₈	—	134	4	no	—
133	C₂×D₈	—	134	2	no	—
134	C₂×D₈	—	134	4	no	—
135	C₂×D₈	—	134	4	no	—
136	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
137	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
138	#127	—	268	2	no	—
139	#127	—	134	4	no	—
140	C₂×C₄⋊C₄	—	134	2	no	—
141	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
142	C₂×C₁₆	—	2	2	no	—
143	C₂×C₁₆	—	2	2	no	—
144	C₂×C₁₆	D₂₆₈	1	4	yes	complemented
145	#107	—	134	4	no	—
146	#106	—	268	2	no	—
147	C₄×C₈	C₄×D₆₇	1	2	yes	—
148	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
149	#95	—	268	2	no	—
150	C₂⁴	—	268	2	no	—
151	C₂×D₄	—	268	8	no	—
152	C₂×D₄	—	268	2	no	—
153	C₂×D₄	—	268	2	no	—
154	C₂×D₄	—	268	2	no	—
155	C₂×D₄	—	268	2	no	—
156	C₂×D₄	—	268	2	no	—
157	C₂×D₄	—	536	8	no	—
158	C₂×D₄	—	134	4	no	—
159	C₂²×C₄	—	268	2	no	—
160	C₂²×C₄	D₅₃₆	1	2	yes	—
161	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
162	D₈	—	268	8	no	—
163	D₈	—	268	4	no	—
164	D₈	—	134	8	no	—
165	C₂×C₈	(C₂×D₆₇)⋊C₄	1	2	yes	—
166	C₂×C₈	D₅₃₆	1	2	yes	—
167	C₂×C₈	#11761617	1	2	yes	—
168	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
169	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
170	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
171	C₂×C₈	#11761628	1	2	yes	—
172	C₄⋊C₄	—	268	2	no	—
173	C₄⋊C₄	—	268	2	no	—
174	C₄²	(C₂×D₆₇)⋊C₄	1	2	yes	—
175	C₄²	#11761617	1	2	yes	—
176	C₁₆	—	2	4	no	—
177	C₂³	—	268	4	no	—
178	C₂³	—	536	2	no	—
179	C₂³	—	536	8	no	—
180	C₂³	—	536	2	no	—
181	C₂³	C₂×D₅₃₆	1	1	yes	characteristic
182	D₄	—	268	4	no	—
183	D₄	—	268	4	no	—
184	D₄	—	536	16	no	—
185	D₄	—	536	2	no	—
186	D₄	—	536	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	536	2	no	—
189	C₂×C₄	—	536	4	no	—
190	C₂×C₄	#14523965	1	4	yes	—
191	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
192	C₂×C₄	#14524031	1	1	yes	characteristic
193	C₂×C₄	#14524040	1	1	yes	characteristic
194	C₂×C₄	C₂×D₅₃₆	1	1	yes	characteristic
195	C₂×C₄	C₂×#11761617	1	1	yes	characteristic
196	C₂×C₄	C₂×#11761617	1	1	yes	characteristic
197	C₈	#14523965	1	4	yes	—
198	C₈	C₄×D₂₆₈	1	2	yes	—
199	C₈	#14524017	1	2	yes	—
200	C₂²	—	536	8	no	—
201	C₂²	—	536	4	no	—
202	C₂²	—	1072	4	no	—
203	C₂²	—	1072	4	no	—
204	C₂²	C₂×#14523965	1	1	yes	characteristic
205	C₂²	#16863743	1	1	yes	characteristic
206	C₂²	#16863773	1	1	yes	characteristic
207	C₂²	#16863834	1	4	yes	—
208	C₄	—	2	4	no	—
209	C₄	—	1072	2	no	—
210	C₄	#16863298	1	1	yes	characteristic
211	C₄	C₂×#14523965	1	1	yes	characteristic
212	C₄	#16863743	1	1	yes	characteristic
213	C₄	#16863769	1	1	yes	characteristic
214	C₂	—	1072	4	no	—
215	C₂	#22561015	1	1	yes	characteristic
216	C₂	#22561926	1	2	yes	—
217	C₂	#22562451	1	2	yes	—
218	C₂	#22562475	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16863773

C₂

yes

maximal, characteristic

C₂×#16863198

C₂

yes

maximal, complemented

#22560373

C₂

yes

maximal, characteristic, complemented

C₂×#346×C₆₇

C₂

yes

maximal, characteristic, complemented

C₂²×D₅₃₆

—

C₂²×D₅₃₆

C₂²

yes

—

C₂×#14524040

—

#16863773

—

#16863773

C₄

yes

complemented

C₂×#14523977

C₂²

yes

—

C₂×#14523975

—

#16863262

—

#16863198

—

C₂²×C₁₆×C₆₇

C₂²

yes

—

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

#346×C₆₇

—

C₂²×D₂₆₈

—

C₂²×D₂₆₈

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

—

C₂×D₅₃₆

C₂×C₄

yes

—

#14524040

—

#14524040

—

C₂×C₄⋊Dic₆₇

—

#14523977

—

#14523975

—

C₆₇⋊#95

—

C₂²×C₈×C₆₇

D₄

yes

characteristic

C₂²×C₈×C₆₇

C₂³

yes

characteristic

C₂×C₄²×C₆₇

D₄

yes

characteristic

C₂×C₁₆×C₆₇

—

C₂×C₁₆×C₆₇

—

C₂×C₁₆×C₆₇

D₄

yes

complemented

C₄×C₈×C₆₇

C₂×C₄

yes

—

C₄×C₈×C₆₇

D₄

yes

—

C₂³×D₆₇

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂×D₂₆₈

—

C₂²×Dic₆₇

—

D₅₃₆

—

D₅₃₆

—

D₅₃₆

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₂²×C₄×C₆₇

D₈

yes

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₂×C₈×C₆₇

D₈

yes

—

C₂×C₈×C₆₇

SD₁₆

yes

—

C₂×C₈×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

#41

yes

—

C₄²×C₆₇

C₂²⋊C₄

yes

—

C₄²×C₆₇

SD₁₆

yes

—

C₁₆×C₆₇

—

C₂³×C₆₇

C₂×D₈

yes

characteristic

C₂²×D₆₇

—

C₂²×D₆₇

—

C₂²×D₆₇

—

C₂²×D₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#102

yes

—

C₂×C₄×C₆₇

C₂×C₂²⋊C₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

C₂×D₈

yes

characteristic

C₂×C₄×C₆₇

C₂×SD₁₆

yes

characteristic

C₂×C₄×C₆₇

C₂×SD₁₆

yes

characteristic

C₂×Dic₆₇

—

C₂×Dic₆₇

—

D₂₆₈

—

D₂₆₈

—

D₂₆₈

—

D₂₆₈

—

D₂₆₈

—

C₈×C₆₇

#102

yes

—

C₈×C₆₇

C₄×D₄

yes

—

C₈×C₆₇

#121

yes

—

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

—

C₂×D₆₇

—

C₂×D₆₇

—

C₂×D₆₇

—

C₂×D₆₇

—

C₄×C₆₇

—

C₄×C₆₇

#390

yes

characteristic

100

C₄×C₆₇

C₂×#102

yes

characteristic

101

C₄×C₆₇

#486

yes

characteristic

102

C₄×C₆₇

#492

yes

characteristic

103

Dic₆₇

—

104

#13206

—

maximal, Sylow

105

C₂×C₆₇

#1957

yes

characteristic

106

C₂×C₆₇

#2140

yes

—

107

C₂×C₆₇

#2244

yes

—

108

C₂×C₆₇

#2250

yes

—

109

D₆₇

—

110

C₂×#493

—

111

C₂×#357

—

112

C₂×#346

D₆₇

yes

characteristic, complemented

113

#1846

—

114

C₆₇

#13206

yes

characteristic, complemented, Sylow

115

C₂²×D₈

—

116

C₂²×D₈

—

134

—

117

C₂×#127

—

134

—

118

C₂²×C₁₆

C₂×D₆₇

yes

—

119

#493

—

120

#493

—

134

—

121

C₂×#107

—

122

C₂×#106

—

134

—

123

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

124

#382

—

134

—

125

#357

—

134

—

126

#346

—

127

C₂²×D₄

—

268

—

128

C₂²×D₄

—

134

—

129

C₂×D₈

—

268

—

130

C₂×D₈

—

268

—

131

C₂×D₈

—

132

C₂×D₈

—

134

—

133

C₂×D₈

—

134

—

134

C₂×D₈

—

134

—

135

C₂×D₈

—

134

—

136

C₂²×C₈

D₂₆₈

yes

characteristic

137

C₂²×C₈

C₂²×D₆₇

yes

characteristic

138

#127

—

268

—

139

#127

—

134

—

140

C₂×C₄⋊C₄

—

134

—

141

C₂×C₄²

D₂₆₈

yes

characteristic

142

C₂×C₁₆

—

143

C₂×C₁₆

—

144

C₂×C₁₆

D₂₆₈

yes

complemented

145

#107

—

134

—

146

#106

—

268

—

147

C₄×C₈

C₄×D₆₇

yes

—

148

C₄×C₈

C₂²⋊D₆₇

yes

—

149

#95

—

268

—

150

C₂⁴

—

268

—

151

C₂×D₄

—

268

—

152

C₂×D₄

—

268

—

153

C₂×D₄

—

268

—

154

C₂×D₄

—

268

—

155

C₂×D₄

—

268

—

156

C₂×D₄

—

268

—

157

C₂×D₄

—

536

—

158

C₂×D₄

—

134

—

159

C₂²×C₄

—

268

—

160

C₂²×C₄

D₅₃₆

yes

—

161

C₂²×C₄

C₂×D₂₆₈

yes

characteristic

162

D₈

—

268

—

163

D₈

—

268

—

164

D₈

—

134

—

165

C₂×C₈

(C₂×D₆₇)⋊C₄

yes

—

166

C₂×C₈

D₅₃₆

yes

—

167

C₂×C₈

#11761617

yes

—

168

C₂×C₈

C₂×C₄×D₆₇

yes

characteristic

169

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

170

C₂×C₈

C₂×D₂₆₈

yes

—

171

C₂×C₈

#11761628

yes

—

172

C₄⋊C₄

—

268

—

173

C₄⋊C₄

—

268

—

174

C₄²

(C₂×D₆₇)⋊C₄

yes

—

175

C₄²

#11761617

yes

—

176

C₁₆

—

177

C₂³

—

268

—

178

C₂³

—

536

—

179

C₂³

—

536

—

180

C₂³

—

536

—

181

C₂³

C₂×D₅₃₆

yes

characteristic

182

D₄

—

268

—

183

D₄

—

268

—

184

D₄

—

536

—

185

D₄

—

536

—

186

D₄

—

536

—

187

C₂×C₄

—

188

C₂×C₄

—

536

—

189

C₂×C₄

—

536

—

190

C₂×C₄

#14523965

yes

—

191

C₂×C₄

C₂×(C₂×D₆₇)⋊C₄

yes

characteristic

192

C₂×C₄

#14524031

yes

characteristic

193

C₂×C₄

#14524040

yes

characteristic

194

C₂×C₄

C₂×D₅₃₆

yes

characteristic

195

C₂×C₄

C₂×#11761617

yes

characteristic

196

C₂×C₄

C₂×#11761617

yes

characteristic

197

C₈

#14523965

yes

—

198

C₈

C₄×D₂₆₈

yes

—

199

C₈

#14524017

yes

—

200

C₂²

—

536

—

201

C₂²

—

536

—

202

C₂²

—

1072

—

203

C₂²

—

1072

—

204

C₂²

C₂×#14523965

yes

characteristic

205

C₂²

#16863743

yes

characteristic

206

C₂²

#16863773

yes

characteristic

207

C₂²

#16863834

yes

—

208

C₄

—

209

C₄

—

1072

—

210

C₄

#16863298

yes

characteristic

211

C₄

C₂×#14523965

yes

characteristic

212

C₄

#16863743

yes

characteristic

213

C₄

#16863769

yes

characteristic

214

C₂

—

1072

—

215

C₂

#22561015

yes

characteristic

216

C₂

#22561926

yes

—

217

C₂

#22562451

yes

—

218

C₂

#22562475

yes

—

	subgroup	G/H
center	C₂³	C₂×D₅₃₆
commutator	C₂×C₈×C₆₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₂×#346×C₆₇	C₂
socle	C₂³×C₆₇	C₂×D₈
prime radical	C₂×#16863773	C₂
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	C₂×#346	D₆₇
hypocenter	C₆₇	#13206
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

subgroup

G/H

center

C₂³

C₂×D₅₃₆

commutator

C₂×C₈×C₆₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₂×#346×C₆₇

C₂

socle

C₂³×C₆₇

C₂×D₈

prime radical

C₂×#16863773

C₂

cosocle

C₂²×C₈×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

N	H ≅ G/N	type
2. C₂×#16863198	C₂	semidirect
3. #22560373	C₂	semidirect
4. C₂×#346×C₆₇	C₂	semidirect
9. #16863773	C₄	semidirect
37. C₂×C₁₆×C₆₇	D₄	semidirect
112. C₂×#346	D₆₇	semidirect
114. C₆₇	#13206	semidirect
144. C₂×C₁₆	D₂₆₈	semidirect

H ≅ G/N

type

2. C₂×#16863198

C₂

semidirect

3. #22560373

C₂

semidirect

4. C₂×#346×C₆₇

C₂

semidirect

9. #16863773

C₄

semidirect

37. C₂×C₁₆×C₆₇

D₄

semidirect

112. C₂×#346

D₆₇

semidirect

114. C₆₇

#13206

semidirect

144. C₂×C₁₆

D₂₆₈

semidirect

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

subgroup	index
C₂×#16863773	2
C₂×#16863198	2
#22560373	2
C₂×#346×C₆₇	2
#13206	67

subgroup

index

C₂×#346×C₆₇

Subgroups — #30774063

Conjugacy classes of subgroups

Complements

Maximal subgroups