Group #22559977 — subgroups

Subgroups — #22559977

Order 8576.

336 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14524002	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊(C₆₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
3	C₂×#14523953	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₈×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#16863150	C₂	1	1	yes	maximal, characteristic, complemented
6	#16863150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂²⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
10	#14524002	—	2	2	no	—
11	#14524002	—	2	2	no	—
12	C₂×C₄⋊Dic₆₇	C₄	1	2	yes	—
13	C₂×C₂²⋊Dic₆₇	C₄	1	2	yes	—
14	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₆₇	C₂²	1	1	yes	characteristic
16	C₂²⋊(C₆₇⋊C₈)	C₄	1	4	yes	complemented
17	#14523953	—	2	2	no	—
18	C₈×Dic₆₇	—	2	2	no	—
19	C₂³×C₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×C₈×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×C₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²⋊C₈×C₆₇	C₄	1	4	yes	complemented
23	C₂²×Dic₆₇	C₂×C₄	1	2	yes	—
24	C₂²×Dic₆₇	C₂×C₄	1	2	yes	—
25	C₂×C₆₇⋊C₈	—	2	1	no	—
26	C₂×C₆₇⋊C₈	—	2	1	no	—
27	C₂×C₆₇⋊C₈	—	2	1	no	—
28	C₂×C₆₇⋊C₈	—	2	1	no	—
29	C₂×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
30	C₂×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
31	C₄⋊Dic₆₇	—	2	4	no	—
32	C₂²⋊Dic₆₇	—	2	4	no	—
33	C₄×Dic₆₇	—	2	1	no	—
34	C₄×Dic₆₇	—	2	1	no	—
35	C₄×Dic₆₇	D₄	1	2	yes	—
36	C₄×Dic₆₇	D₄	1	2	yes	—
37	C₂⁴×C₆₇	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₆₇	—	2	1	no	—
39	C₂²×C₄×C₆₇	—	2	1	no	—
40	C₂²×C₄×C₆₇	—	2	1	no	—
41	C₂²×C₄×C₆₇	—	2	1	no	—
42	C₂²×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×C₆₇	C₂×C₄	1	2	yes	—
44	C₂²×C₄×C₆₇	C₂×C₄	1	2	yes	—
45	C₂²×C₄×C₆₇	C₂³	1	1	yes	characteristic
46	C₂×C₈×C₆₇	—	2	1	no	—
47	C₂×C₈×C₆₇	—	2	1	no	—
48	C₂×C₈×C₆₇	—	2	1	no	—
49	C₂×C₈×C₆₇	—	2	1	no	—
50	C₂×C₈×C₆₇	C₂×C₄	1	2	yes	—
51	C₂×C₈×C₆₇	C₂×C₄	1	2	yes	—
52	C₂³×C₆₇	—	2	1	no	—
53	C₂³×C₆₇	—	2	1	no	—
54	C₂³×C₆₇	—	2	2	no	—
55	C₂³×C₆₇	—	2	2	no	—
56	C₂³×C₆₇	C₄²	1	2	yes	—
57	C₂³×C₆₇	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₄×C₆₇	—	2	1	no	—
59	C₂×C₄×C₆₇	—	2	1	no	—
60	C₂×C₄×C₆₇	—	2	2	no	—
61	C₂×C₄×C₆₇	—	2	2	no	—
62	C₂×C₄×C₆₇	—	2	2	no	—
63	C₂×C₄×C₆₇	—	2	2	no	—
64	C₂×C₄×C₆₇	C₄²	1	2	yes	—
65	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
66	C₂×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
68	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₆₇	#41	1	1	yes	characteristic
70	C₂×C₄×C₆₇	#41	1	1	yes	characteristic
71	C₂×Dic₆₇	—	2	2	no	—
72	C₂×Dic₆₇	—	2	2	no	—
73	C₂×Dic₆₇	—	2	2	no	—
74	C₂×Dic₆₇	—	2	2	no	—
75	C₂×Dic₆₇	—	2	2	no	—
76	C₂×Dic₆₇	C₂²⋊C₄	1	4	yes	—
77	C₈×C₆₇	—	2	2	no	—
78	C₈×C₆₇	—	2	2	no	—
79	C₆₇⋊C₈	—	2	2	no	—
80	C₆₇⋊C₈	—	2	2	no	—
81	C₂²×C₆₇	—	2	2	no	—
82	C₂²×C₆₇	—	2	2	no	—
83	C₂²×C₆₇	—	2	2	no	—
84	C₂²×C₆₇	—	4	2	no	—
85	C₂²×C₆₇	—	4	2	no	—
86	C₂²×C₆₇	C₂×C₄²	1	1	yes	characteristic
87	C₂²×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×C₆₇	#117	1	1	yes	characteristic
89	C₂²×C₆₇	#131	1	2	yes	—
90	C₂²×C₆₇	#131	1	2	yes	—
91	C₄×C₆₇	—	2	2	no	—
92	C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
93	C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
94	C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
95	C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
96	Dic₆₇	—	2	4	no	—
97	Dic₆₇	—	4	2	no	—
98	C₂×C₆₇	—	4	2	no	—
99	C₂×C₆₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₆₇	#405	1	1	yes	characteristic
101	C₂×C₆₇	#405	1	1	yes	characteristic
102	C₂×C₆₇	#408	1	2	yes	—
103	C₂×C₆₇	#433	1	2	yes	—
104	#1750	—	67	1	no	maximal, Sylow
105	C₆₇	#1750	1	1	yes	characteristic, complemented, Sylow
106	C₂×#117	—	67	1	no	—
107	C₂×C₂²⋊C₈	—	67	1	no	—
108	C₂×C₂²⋊C₈	D₆₇	1	1	yes	characteristic
109	C₂×#97	—	67	1	no	—
110	C₂×C₄×C₈	—	67	1	no	—
111	#336	—	67	1	no	—
112	#336	—	67	1	no	—
113	C₂³×C₄	C₂×D₆₇	1	1	yes	characteristic
114	C₂²×C₈	—	67	1	no	—
115	C₂²×C₈	—	67	1	no	—
116	C₂²×C₈	C₂×D₆₇	1	1	yes	characteristic
117	C₂²×C₈	C₂×D₆₇	1	1	yes	characteristic
118	#117	—	134	2	no	—
119	#117	—	134	2	no	—
120	C₂×C₄⋊C₄	—	67	2	no	—
121	C₂×C₂²⋊C₄	—	67	2	no	—
122	C₂×C₄²	—	67	1	no	—
123	C₂×C₄²	—	67	1	no	—
124	C₂²⋊C₈	—	67	4	no	—
125	C₂²⋊C₈	Dic₆₇	1	4	yes	complemented
126	#97	—	134	2	no	—
127	C₄×C₈	—	134	2	no	—
128	C₂⁴	C₄×D₆₇	1	1	yes	characteristic
129	C₂²×C₄	—	2	1	no	—
130	C₂²×C₄	—	2	1	no	—
131	C₂²×C₄	—	2	1	no	—
132	C₂²×C₄	—	2	1	no	—
133	C₂²×C₄	—	67	2	no	—
134	C₂²×C₄	—	67	2	no	—
135	C₂²×C₄	C₄×D₆₇	1	1	yes	characteristic
136	C₂²×C₄	C₄×D₆₇	1	2	yes	—
137	C₂²×C₄	C₂×Dic₆₇	1	2	yes	—
138	C₂²×C₄	C₂²×D₆₇	1	1	yes	characteristic
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	—	2	1	no	—
141	C₂×C₈	—	2	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	67	2	no	—
144	C₂×C₈	—	67	2	no	—
145	C₂×C₈	—	134	1	no	—
146	C₂×C₈	—	134	1	no	—
147	C₂×C₈	—	134	1	no	—
148	C₂×C₈	—	134	1	no	—
149	C₂×C₈	C₂×Dic₆₇	1	2	yes	—
150	C₂×C₈	C₂×Dic₆₇	1	2	yes	—
151	C₄⋊C₄	—	134	4	no	—
152	C₂²⋊C₄	—	134	4	no	—
153	C₄²	—	67	2	no	—
154	C₄²	—	67	2	no	—
155	C₄²	—	134	1	no	—
156	C₄²	—	134	1	no	—
157	C₂³	—	2	1	no	—
158	C₂³	—	2	1	no	—
159	C₂³	—	2	2	no	—
160	C₂³	—	2	2	no	—
161	C₂³	C₄×Dic₆₇	1	2	yes	—
162	C₂³	C₂×C₄×D₆₇	1	1	yes	characteristic
163	C₂×C₄	—	2	1	no	—
164	C₂×C₄	—	2	1	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	2	2	no	—
169	C₂×C₄	—	67	4	no	—
170	C₂×C₄	—	134	2	no	—
171	C₂×C₄	—	134	2	no	—
172	C₂×C₄	—	134	2	no	—
173	C₂×C₄	—	134	2	no	—
174	C₂×C₄	—	134	2	no	—
175	C₂×C₄	C₄×Dic₆₇	1	2	yes	—
176	C₂×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
177	C₂×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
178	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
179	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
180	C₂×C₄	#11761627	1	1	yes	characteristic
181	C₂×C₄	#11761627	1	1	yes	characteristic
182	C₈	—	2	2	no	—
183	C₈	—	2	2	no	—
184	C₈	—	134	2	no	—
185	C₈	—	134	2	no	—
186	C₂²	—	2	2	no	—
187	C₂²	—	2	2	no	—
188	C₂²	—	2	2	no	—
189	C₂²	—	4	2	no	—
190	C₂²	—	4	2	no	—
191	C₂²	C₂×C₄×Dic₆₇	1	1	yes	characteristic
192	C₂²	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
193	C₂²	#14523999	1	1	yes	characteristic
194	C₂²	#14524049	1	2	yes	—
195	C₂²	#14524051	1	2	yes	—
196	C₄	—	2	2	no	—
197	C₄	—	268	2	no	—
198	C₄	—	134	4	no	—
199	C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
200	C₄	(C₂²⋊D₆₇)⋊C₄	1	1	yes	characteristic
201	C₄	D₄×Dic₆₇	1	1	yes	characteristic
202	C₄	D₄×Dic₆₇	1	1	yes	characteristic
203	C₂	—	4	2	no	—
204	C₂	C₂²⋊C₄×Dic₆₇	1	1	yes	characteristic
205	C₂	#16863351	1	1	yes	characteristic
206	C₂	#16863354	1	1	yes	characteristic
207	C₂	#16863361	1	2	yes	—
208	C₂	#16863454	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14524002

C₂

yes

maximal, characteristic

C₂×C₂²⋊(C₆₇⋊C₈)

C₂

yes

maximal, characteristic

C₂×#14523953

C₂

yes

maximal, characteristic, complemented

C₂×C₈×Dic₆₇

C₂

yes

maximal, characteristic, complemented

#16863150

C₂

yes

maximal, characteristic, complemented

#16863150

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊C₈×C₆₇

C₂

yes

maximal, characteristic

C₂²×C₆₇⋊C₈

C₂²

yes

characteristic

C₂²×C₆₇⋊C₈

C₂²

yes

characteristic

#14524002

—

#14524002

—

C₂×C₄⋊Dic₆₇

C₄

yes

—

C₂×C₂²⋊Dic₆₇

C₄

yes

—

C₂×C₄×Dic₆₇

C₂²

yes

characteristic

C₂×C₄×Dic₆₇

C₂²

yes

characteristic

C₂²⋊(C₆₇⋊C₈)

C₄

yes

complemented

#14523953

—

C₈×Dic₆₇

—

C₂³×C₄×C₆₇

C₂²

yes

characteristic

C₂²×C₈×C₆₇

C₂²

yes

characteristic

C₂²×C₈×C₆₇

C₂²

yes

characteristic

C₂²⋊C₈×C₆₇

C₄

yes

complemented

C₂²×Dic₆₇

C₂×C₄

yes

—

C₂²×Dic₆₇

C₂×C₄

yes

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

C₂×C₄

yes

—

C₂×C₆₇⋊C₈

C₂×C₄

yes

—

C₄⋊Dic₆₇

—

C₂²⋊Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

D₄

yes

—

C₄×Dic₆₇

D₄

yes

—

C₂⁴×C₆₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×C₄

yes

—

C₂²×C₄×C₆₇

C₂×C₄

yes

—

C₂²×C₄×C₆₇

C₂³

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂×C₄

yes

—

C₂×C₈×C₆₇

C₂×C₄

yes

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

C₄²

yes

—

C₂³×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₄²

yes

—

C₂×C₄×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₄×C₆₇

C₂×D₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

C₂²⋊C₄

yes

—

C₈×C₆₇

—

C₈×C₆₇

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

C₂×C₄²

yes

characteristic

C₂²×C₆₇

C₂×C₂²⋊C₄

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

—

C₂²×C₆₇

#131

yes

—

C₄×C₆₇

—

C₄×C₆₇

C₄×D₄

yes

characteristic

C₄×C₆₇

C₄×D₄

yes

characteristic

C₄×C₆₇

C₄×D₄

yes

characteristic

C₄×C₆₇

C₄×D₄

yes

characteristic

Dic₆₇

—

Dic₆₇

—

C₂×C₆₇

—

C₂×C₆₇

C₄×C₂²⋊C₄

yes

characteristic

100

C₂×C₆₇

#405

yes

characteristic

101

C₂×C₆₇

#405

yes

characteristic

102

C₂×C₆₇

#408

yes

—

103

C₂×C₆₇

#433

yes

—

104

#1750

—

maximal, Sylow

105

C₆₇

#1750

yes

characteristic, complemented, Sylow

106

C₂×#117

—

107

C₂×C₂²⋊C₈

—

108

C₂×C₂²⋊C₈

D₆₇

yes

characteristic

109

C₂×#97

—

110

C₂×C₄×C₈

—

111

#336

—

112

#336

—

113

C₂³×C₄

C₂×D₆₇

yes

characteristic

114

C₂²×C₈

—

115

C₂²×C₈

—

116

C₂²×C₈

C₂×D₆₇

yes

characteristic

117

C₂²×C₈

C₂×D₆₇

yes

characteristic

118

#117

—

134

—

119

#117

—

134

—

120

C₂×C₄⋊C₄

—

121

C₂×C₂²⋊C₄

—

122

C₂×C₄²

—

123

C₂×C₄²

—

124

C₂²⋊C₈

—

125

C₂²⋊C₈

Dic₆₇

yes

complemented

126

#97

—

134

—

127

C₄×C₈

—

134

—

128

C₂⁴

C₄×D₆₇

yes

characteristic

129

C₂²×C₄

—

130

C₂²×C₄

—

131

C₂²×C₄

—

132

C₂²×C₄

—

133

C₂²×C₄

—

134

C₂²×C₄

—

135

C₂²×C₄

C₄×D₆₇

yes

characteristic

136

C₂²×C₄

C₄×D₆₇

yes

—

137

C₂²×C₄

C₂×Dic₆₇

yes

—

138

C₂²×C₄

C₂²×D₆₇

yes

characteristic

139

C₂×C₈

—

140

C₂×C₈

—

141

C₂×C₈

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

134

—

146

C₂×C₈

—

134

—

147

C₂×C₈

—

134

—

148

C₂×C₈

—

134

—

149

C₂×C₈

C₂×Dic₆₇

yes

—

150

C₂×C₈

C₂×Dic₆₇

yes

—

151

C₄⋊C₄

—

134

—

152

C₂²⋊C₄

—

134

—

153

C₄²

—

154

C₄²

—

155

C₄²

—

134

—

156

C₄²

—

134

—

157

C₂³

—

158

C₂³

—

159

C₂³

—

160

C₂³

—

161

C₂³

C₄×Dic₆₇

yes

—

162

C₂³

C₂×C₄×D₆₇

yes

characteristic

163

C₂×C₄

—

164

C₂×C₄

—

165

C₂×C₄

—

166

C₂×C₄

—

167

C₂×C₄

—

168

C₂×C₄

—

169

C₂×C₄

—

170

C₂×C₄

—

134

—

171

C₂×C₄

—

134

—

172

C₂×C₄

—

134

—

173

C₂×C₄

—

134

—

174

C₂×C₄

—

134

—

175

C₂×C₄

C₄×Dic₆₇

yes

—

176

C₂×C₄

C₂×C₄×D₆₇

yes

characteristic

177

C₂×C₄

C₂²×Dic₆₇

yes

characteristic

178

C₂×C₄

D₄×D₆₇

yes

characteristic

179

C₂×C₄

D₄×D₆₇

yes

characteristic

180

C₂×C₄

#11761627

yes

characteristic

181

C₂×C₄

#11761627

yes

characteristic

182

C₈

—

183

C₈

—

184

C₈

—

134

—

185

C₈

—

134

—

186

C₂²

—

187

C₂²

—

188

C₂²

—

189

C₂²

—

190

C₂²

—

191

C₂²

C₂×C₄×Dic₆₇

yes

characteristic

192

C₂²

C₂²⋊C₄×D₆₇

yes

characteristic

193

C₂²

#14523999

yes

characteristic

194

C₂²

#14524049

yes

—

195

C₂²

#14524051

yes

—

196

C₄

—

197

C₄

—

268

—

198

C₄

—

134

—

199

C₄

(C₂²⋊D₆₇)⋊C₄

yes

characteristic

200

C₄

(C₂²⋊D₆₇)⋊C₄

yes

characteristic

201

C₄

D₄×Dic₆₇

yes

characteristic

202

C₄

D₄×Dic₆₇

yes

characteristic

203

C₂

—

204

C₂

C₂²⋊C₄×Dic₆₇

yes

characteristic

205

C₂

#16863351

yes

characteristic

206

C₂

#16863354

yes

characteristic

207

C₂

#16863361

yes

—

208

C₂

#16863454

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₆₇
commutator	C₂²×C₆₇	C₂×C₄²
Fitting	C₂×C₂²⋊C₈×C₆₇	C₂
socle	C₂³×C₆₇	C₂²×C₄
hypercenter	C₂×C₂²⋊C₈	D₆₇
hypocenter	C₆₇	#1750
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₆₇

commutator

C₂²×C₆₇

C₂×C₄²

Fitting

C₂×C₂²⋊C₈×C₆₇

C₂

socle

C₂³×C₆₇

C₂²×C₄

hypercenter

C₂×C₂²⋊C₈

D₆₇

C₆₇

G ▷ C₂²×C₆₇ ▷ C₆₇

C₁ ◁ C₂²×C₄ ◁ C₂×C₂²⋊C₈

N	H ≅ G/N	type
3. C₂×#14523953	C₂	semidirect
4. C₂×C₈×Dic₆₇	C₂	semidirect
5. #16863150	C₂	semidirect
6. #16863150	C₂	semidirect
16. C₂²⋊(C₆₇⋊C₈)	C₄	semidirect
22. C₂²⋊C₈×C₆₇	C₄	semidirect
105. C₆₇	#1750	semidirect
125. C₂²⋊C₈	Dic₆₇	semidirect

H ≅ G/N

type

3. C₂×#14523953

C₂

semidirect

4. C₂×C₈×Dic₆₇

C₂

semidirect

5. #16863150

C₂

semidirect

6. #16863150

C₂

semidirect

16. C₂²⋊(C₆₇⋊C₈)

C₄

semidirect

22. C₂²⋊C₈×C₆₇

C₄

semidirect

105. C₆₇

#1750

semidirect

125. C₂²⋊C₈

Dic₆₇

semidirect

Subgroups — #22559977

Conjugacy classes of subgroups

Complements