Group #22571864 — subgroups

Subgroups — #22571864

Order 8576.

476 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 121 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×#14524072	C₂	1	2	yes	maximal, complemented
2	#16864054	C₂	1	2	yes	maximal, complemented
3	#16863639	C₂	1	2	yes	maximal, complemented
4	#16863615	C₂	1	2	yes	maximal, complemented
5	#16863550	C₂	1	2	yes	maximal, complemented
6	#16863538	C₂	1	2	yes	maximal, complemented
7	C₄×Dic₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#16863475	C₂	1	1	yes	maximal, characteristic, complemented
9	#495×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#11761627	C₂²	1	2	yes	—
11	C₂×Q₈×D₆₇	C₂²	1	2	yes	—
12	#14524072	—	2	8	no	—
13	C₂×Dic₂₆₈	C₂²	1	1	yes	characteristic
14	C₂×#11761618	C₂²	1	2	yes	—
15	C₂×#11761616	C₂²	1	2	yes	—
16	C₂×#11761611	C₂²	1	2	yes	—
17	#14524029	—	2	2	no	—
18	#14524020	—	2	2	no	—
19	#14524019	C₂²	1	2	yes	—
20	#14524016	—	2	2	no	—
21	#14524014	C₂²	1	2	yes	—
22	C₄×Dic₁₃₄	C₂²	1	2	yes	—
23	C₄×D₂₆₈	C₂²	1	1	yes	characteristic
24	(C₂²⋊D₆₇)⋊C₄	—	2	2	no	—
25	#14523977	C₂²	1	1	yes	characteristic
26	C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
27	#14523968	C₂²	1	2	yes	—
28	#14523967	C₂²	1	2	yes	—
29	#14523964	C₂²	1	2	yes	—
30	(C₂×D₆₇)⋊C₈	C₂²	1	2	yes	—
31	C₂×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×SD₁₆×C₆₇	C₂²	1	2	yes	—
33	C₂×D₈×C₆₇	C₂²	1	1	yes	characteristic
34	#124×C₆₇	C₂²	1	2	yes	—
35	C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
36	#11761627	—	2	4	no	—
37	#11761627	—	4	2	no	—
38	C₂×Dic₁₃₄	—	2	2	no	—
39	C₂×Dic₁₃₄	C₂³	1	2	yes	—
40	Q₈×D₆₇	—	2	4	no	—
41	Q₈×D₆₇	—	4	2	no	—
42	C₂×D₂₆₈	D₄	1	1	yes	characteristic
43	C₂×C₂²⋊D₆₇	—	2	2	no	—
44	C₂×C₂²⋊D₆₇	—	2	2	no	—
45	C₂²×Dic₆₇	—	2	2	no	—
46	C₂×C₄×D₆₇	—	2	2	no	—
47	C₂×C₄×D₆₇	C₂³	1	2	yes	—
48	Dic₂₆₈	D₄	1	4	yes	complemented
49	#11761618	—	2	4	no	—
50	#11761616	—	2	4	no	—
51	#11761611	—	2	4	no	—
52	C₂×C₆₇⋊C₈	C₂³	1	2	yes	—
53	C₄⋊Dic₆₇	D₄	1	1	yes	characteristic
54	C₄⋊Dic₆₇	C₂³	1	2	yes	—
55	Dic₆₇⋊C₄	—	2	2	no	—
56	Dic₆₇⋊C₄	—	2	2	no	—
57	C₂²⋊Dic₆₇	—	2	2	no	—
58	(C₂×D₆₇)⋊C₄	—	2	2	no	—
59	(C₂×D₆₇)⋊C₄	D₄	1	2	yes	—
60	C₄×Dic₆₇	—	2	2	no	—
61	C₂×Q₈×C₆₇	C₂³	1	2	yes	—
62	C₂×D₄×C₆₇	C₂³	1	2	yes	—
63	Q₁₆×C₆₇	—	4	1	no	—
64	SD₁₆×C₆₇	—	2	4	no	—
65	D₈×C₆₇	—	4	1	no	—
66	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
67	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
68	C₂²⋊C₄×C₆₇	—	2	2	no	—
69	C₂²⋊C₄×C₆₇	—	2	2	no	—
70	C₄²×C₆₇	C₂³	1	1	yes	characteristic
71	C₂³×C₆₇	—	2	2	no	—
72	C₂²×D₆₇	C₂×D₄	1	2	yes	—
73	Q₈×C₆₇	—	2	2	no	—
74	Q₈×C₆₇	—	2	2	no	—
75	D₄×C₆₇	—	2	2	no	—
76	D₄×C₆₇	—	2	2	no	—
77	C₂×C₄×C₆₇	—	2	2	no	—
78	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
81	C₂²⋊D₆₇	—	4	4	no	—
82	C₂²⋊D₆₇	—	4	4	no	—
83	C₂×Dic₆₇	—	2	2	no	—
84	C₂×Dic₆₇	—	2	2	no	—
85	C₂×Dic₆₇	—	4	4	no	—
86	C₂×Dic₆₇	C₂×D₄	1	2	yes	—
87	D₂₆₈	—	4	1	no	—
88	C₄×D₆₇	—	2	2	no	—
89	C₄×D₆₇	—	2	2	no	—
90	C₄×D₆₇	—	4	4	no	—
91	Dic₁₃₄	—	2	2	no	—
92	Dic₁₃₄	—	4	4	no	—
93	Dic₁₃₄	C₂×D₄	1	4	yes	—
94	C₈×C₆₇	—	2	1	no	—
95	C₈×C₆₇	C₂×D₄	1	2	yes	—
96	C₆₇⋊C₈	—	2	2	no	—
97	C₂²×C₆₇	—	4	2	no	—
98	C₂²×C₆₇	—	4	2	no	—
99	C₂²×C₆₇	—	4	2	no	—
100	C₂²×C₆₇	C₂²×D₄	1	1	yes	characteristic
101	C₂×D₆₇	—	2	2	no	—
102	C₂×D₆₇	—	2	2	no	—
103	C₂×D₆₇	—	2	2	no	—
104	C₄×C₆₇	—	2	1	no	—
105	C₄×C₆₇	—	2	1	no	—
106	C₄×C₆₇	—	4	2	no	—
107	C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
108	C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
109	Dic₆₇	—	2	4	no	—
110	Dic₆₇	—	2	2	no	—
111	Dic₆₇	—	4	2	no	—
112	C₂×C₆₇	—	8	2	no	—
113	C₂×C₆₇	D₄²	1	1	yes	characteristic
114	C₂×C₆₇	#575	1	1	yes	characteristic
115	C₂×C₆₇	#578	1	1	yes	characteristic
116	D₆₇	—	4	2	no	—
117	#3277	—	67	1	no	maximal, Sylow
118	C₆₇	#3277	1	1	yes	characteristic, complemented, Sylow
119	C₂×#137	—	67	2	no	—
120	#548	—	67	2	no	—
121	#495	D₆₇	1	1	yes	characteristic, complemented
122	#468	—	67	2	no	—
123	#464	—	67	2	no	—
124	#451	—	67	2	no	—
125	#449	—	67	2	no	—
126	C₄×Q₁₆	—	67	1	no	—
127	#436	—	67	1	no	—
128	C₂×#41	—	67	2	no	—
129	C₂²×Q₈	—	67	2	no	—
130	#137	—	134	8	no	—
131	C₂×Q₁₆	—	67	2	no	—
132	C₂×Q₁₆	—	67	1	no	—
133	C₂×Q₁₆	C₂×D₆₇	1	1	yes	characteristic
134	C₂×SD₁₆	—	67	2	no	—
135	C₂×SD₁₆	C₂×D₆₇	1	2	yes	—
136	C₂×D₈	C₂×D₆₇	1	1	yes	characteristic
137	C₂×M₁₆	—	67	2	no	—
138	#124	—	134	2	no	—
139	#124	C₂×D₆₇	1	2	yes	—
140	C₂²⋊Q₈	—	67	2	no	—
141	C₂²⋊Q₈	—	134	2	no	—
142	#121	—	67	2	no	—
143	#121	—	134	2	no	—
144	C₄×Q₈	—	67	2	no	—
145	C₄×D₄	—	67	1	no	—
146	C₄×D₄	—	134	2	no	—
147	#107	—	67	1	no	—
148	C₄⋊C₈	—	67	1	no	—
149	#103	—	67	2	no	—
150	#103	—	67	2	no	—
151	#102	—	67	2	no	—
152	C₂²⋊C₈	—	67	2	no	—
153	C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
154	#41	—	268	2	no	—
155	#41	—	134	4	no	—
156	C₂×Q₈	—	268	2	no	—
157	C₂×Q₈	—	67	2	no	—
158	C₂×Q₈	—	134	2	no	—
159	C₂×Q₈	—	134	4	no	—
160	C₂×Q₈	C₂²×D₆₇	1	2	yes	—
161	C₂×D₄	—	67	1	no	—
162	C₂×D₄	—	134	2	no	—
163	C₂×D₄	—	134	2	no	—
164	C₂×D₄	C₂²×D₆₇	1	2	yes	—
165	C₂²×C₄	—	67	2	no	—
166	C₂²×C₄	—	134	2	no	—
167	C₂²×C₄	—	134	2	no	—
168	Q₁₆	—	4	1	no	—
169	Q₁₆	—	67	4	no	—
170	Q₁₆	—	134	4	no	—
171	SD₁₆	—	2	4	no	—
172	SD₁₆	—	134	4	no	—
173	D₈	—	4	1	no	—
174	M₁₆	—	134	4	no	—
175	C₂×C₈	—	67	2	no	—
176	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
177	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
178	C₄⋊C₄	—	67	1	no	—
179	C₄⋊C₄	—	67	2	no	—
180	C₄⋊C₄	—	134	2	no	—
181	C₄⋊C₄	—	134	2	no	—
182	C₂²⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	2	2	no	—
184	C₂²⋊C₄	—	67	2	no	—
185	C₂²⋊C₄	—	134	2	no	—
186	C₂²⋊C₄	—	134	2	no	—
187	C₄²	—	134	2	no	—
188	C₄²	C₂²×D₆₇	1	1	yes	characteristic
189	C₂³	—	2	2	no	—
190	C₂³	—	67	2	no	—
191	Q₈	—	2	2	no	—
192	Q₈	—	2	2	no	—
193	Q₈	—	268	4	no	—
194	Q₈	—	67	4	no	—
195	Q₈	—	134	2	no	—
196	D₄	—	2	2	no	—
197	D₄	—	2	2	no	—
198	D₄	—	268	1	no	—
199	D₄	—	268	4	no	—
200	D₄	—	268	4	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	268	4	no	—
203	C₂×C₄	—	268	4	no	—
204	C₂×C₄	—	67	2	no	—
205	C₂×C₄	—	134	2	no	—
206	C₂×C₄	—	134	2	no	—
207	C₂×C₄	—	134	2	no	—
208	C₂×C₄	—	134	2	no	—
209	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
210	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
211	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
212	C₈	—	2	1	no	—
213	C₈	—	134	2	no	—
214	C₈	D₄×D₆₇	1	2	yes	—
215	C₂²	—	4	2	no	—
216	C₂²	—	4	2	no	—
217	C₂²	—	4	2	no	—
218	C₂²	—	134	2	no	—
219	C₂²	—	134	2	no	—
220	C₂²	—	134	2	no	—
221	C₂²	C₂×D₄×D₆₇	1	1	yes	characteristic
222	C₄	—	2	1	no	—
223	C₄	—	2	1	no	—
224	C₄	—	4	2	no	—
225	C₄	—	268	2	no	—
226	C₄	—	134	2	no	—
227	C₄	—	134	4	no	—
228	C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
229	C₄	#14524088	1	1	yes	characteristic
230	C₂	—	8	2	no	—
231	C₂	—	268	2	no	—
232	C₂	#16864031	1	1	yes	characteristic
233	C₂	#16864193	1	1	yes	characteristic
234	C₂	#16864210	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14524072

C₂

yes

maximal, complemented

#16864054

C₂

yes

maximal, complemented

#16863639

C₂

yes

maximal, complemented

#16863615

C₂

yes

maximal, complemented

#16863550

C₂

yes

maximal, complemented

#16863538

C₂

yes

maximal, complemented

C₄×Dic₂₆₈

C₂

yes

maximal, characteristic, complemented

#16863475

C₂

yes

maximal, characteristic, complemented

#495×C₆₇

C₂

yes

maximal, characteristic, complemented

C₂×#11761627

C₂²

yes

—

C₂×Q₈×D₆₇

C₂²

yes

—

#14524072

—

C₂×Dic₂₆₈

C₂²

yes

characteristic

C₂×#11761618

C₂²

yes

—

C₂×#11761616

C₂²

yes

—

C₂×#11761611

C₂²

yes

—

#14524029

—

#14524020

—

#14524019

C₂²

yes

—

#14524016

—

#14524014

C₂²

yes

—

C₄×Dic₁₃₄

C₂²

yes

—

C₄×D₂₆₈

C₂²

yes

characteristic

(C₂²⋊D₆₇)⋊C₄

—

#14523977

C₂²

yes

characteristic

C₄⋊(C₆₇⋊C₈)

C₂²

yes

characteristic

#14523968

C₂²

yes

—

#14523967

C₂²

yes

—

#14523964

C₂²

yes

—

(C₂×D₆₇)⋊C₈

C₂²

yes

—

C₂×Q₁₆×C₆₇

C₂²

yes

characteristic

C₂×SD₁₆×C₆₇

C₂²

yes

—

C₂×D₈×C₆₇

C₂²

yes

characteristic

#124×C₆₇

C₂²

yes

—

C₄×C₈×C₆₇

C₂²

yes

characteristic

#11761627

—

#11761627

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

C₂³

yes

—

Q₈×D₆₇

—

Q₈×D₆₇

—

C₂×D₂₆₈

D₄

yes

characteristic

C₂×C₂²⋊D₆₇

—

C₂×C₂²⋊D₆₇

—

C₂²×Dic₆₇

—

C₂×C₄×D₆₇

—

C₂×C₄×D₆₇

C₂³

yes

—

Dic₂₆₈

D₄

yes

—

—

—

C₂×C₆₇⋊C₈

C₂³

yes

—

C₄⋊Dic₆₇

D₄

yes

characteristic

C₄⋊Dic₆₇

C₂³

yes

—

Dic₆₇⋊C₄

—

Dic₆₇⋊C₄

—

C₂²⋊Dic₆₇

—

(C₂×D₆₇)⋊C₄

—

(C₂×D₆₇)⋊C₄

D₄

yes

—

C₄×Dic₆₇

—

C₂×Q₈×C₆₇

C₂³

yes

—

C₂×D₄×C₆₇

C₂³

yes

—

Q₁₆×C₆₇

—

SD₁₆×C₆₇

—

D₈×C₆₇

—

C₂×C₈×C₆₇

C₂³

yes

characteristic

C₂×C₈×C₆₇

C₂³

yes

characteristic

C₂²⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

C₂³

yes

characteristic

C₂³×C₆₇

—

C₂²×D₆₇

C₂×D₄

yes

—

Q₈×C₆₇

—

Q₈×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₄×C₆₇

C₂⁴

yes

characteristic

C₂²⋊D₆₇

—

C₂²⋊D₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

C₂×D₄

yes

—

D₂₆₈

—

C₄×D₆₇

—

C₄×D₆₇

—

C₄×D₆₇

—

Dic₁₃₄

—

Dic₁₃₄

—

Dic₁₃₄

C₂×D₄

yes

—

C₈×C₆₇

—

C₈×C₆₇

C₂×D₄

yes

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

100

C₂²×C₆₇

C₂²×D₄

yes

characteristic

101

C₂×D₆₇

—

102

C₂×D₆₇

—

103

C₂×D₆₇

—

104

C₄×C₆₇

—

105

C₄×C₆₇

—

106

C₄×C₆₇

—

107

C₄×C₆₇

C₂²×D₄

yes

characteristic

108

C₄×C₆₇

H(5,𝔽₂)

yes

characteristic

109

Dic₆₇

—

110

Dic₆₇

—

111

Dic₆₇

—

112

C₂×C₆₇

—

113

C₂×C₆₇

D₄²

yes

characteristic

114

C₂×C₆₇

#575

yes

characteristic

115

C₂×C₆₇

#578

yes

characteristic

116

D₆₇

—

117

#3277

—

maximal, Sylow

118

C₆₇

#3277

yes

characteristic, complemented, Sylow

119

C₂×#137

—

120

#548

—

121

#495

D₆₇

yes

characteristic, complemented

122

#468

—

123

#464

—

124

#451

—

125

#449

—

126

C₄×Q₁₆

—

127

#436

—

128

C₂×#41

—

129

C₂²×Q₈

—

130

#137

—

134

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

C₂×D₆₇

yes

characteristic

134

C₂×SD₁₆

—

135

C₂×SD₁₆

C₂×D₆₇

yes

—

136

C₂×D₈

C₂×D₆₇

yes

characteristic

137

C₂×M₁₆

—

138

#124

—

134

—

139

#124

C₂×D₆₇

yes

—

140

C₂²⋊Q₈

—

141

C₂²⋊Q₈

—

134

—

142

#121

—

143

#121

—

134

—

144

C₄×Q₈

—

145

C₄×D₄

—

146

C₄×D₄

—

134

—

147

#107

—

148

C₄⋊C₈

—

149

#103

—

150

#103

—

151

#102

—

152

C₂²⋊C₈

—

153

C₄×C₈

C₂×D₆₇

yes

characteristic

154

#41

—

268

—

155

#41

—

134

—

156

C₂×Q₈

—

268

—

157

C₂×Q₈

—

158

C₂×Q₈

—

134

—

159

C₂×Q₈

—

134

—

160

C₂×Q₈

C₂²×D₆₇

yes

—

161

C₂×D₄

—

162

C₂×D₄

—

134

—

163

C₂×D₄

—

134

—

164

C₂×D₄

C₂²×D₆₇

yes

—

165

C₂²×C₄

—

166

C₂²×C₄

—

134

—

167

C₂²×C₄

—

134

—

168

Q₁₆

—

169

Q₁₆

—

170

Q₁₆

—

134

—

171

SD₁₆

—

172

SD₁₆

—

134

—

173

D₈

—

174

M₁₆

—

134

—

175

C₂×C₈

—

176

C₂×C₈

C₂²×D₆₇

yes

characteristic

177

C₂×C₈

C₂²×D₆₇

yes

characteristic

178

C₄⋊C₄

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

134

—

181

C₄⋊C₄

—

134

—

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

184

C₂²⋊C₄

—

185

C₂²⋊C₄

—

134

—

186

C₂²⋊C₄

—

134

—

187

C₄²

—

134

—

188

C₄²

C₂²×D₆₇

yes

characteristic

189

C₂³

—

190

C₂³

—

191

Q₈

—

192

Q₈

—

193

Q₈

—

268

—

194

Q₈

—

195

Q₈

—

134

—

196

D₄

—

197

D₄

—

198

D₄

—

268

—

199

D₄

—

268

—

200

D₄

—

268

—

201

C₂×C₄

—

202

C₂×C₄

—

268

—

203

C₂×C₄

—

268

—

204

C₂×C₄

—

205

C₂×C₄

—

134

—

206

C₂×C₄

—

134

—

207

C₂×C₄

—

134

—

208

C₂×C₄

—

134

—

209

C₂×C₄

D₄×D₆₇

yes

characteristic

210

C₂×C₄

D₄×D₆₇

yes

characteristic

211

C₂×C₄

C₂³×D₆₇

yes

characteristic

212

C₈

—

213

C₈

—

134

—

214

C₈

D₄×D₆₇

yes

—

215

C₂²

—

216

C₂²

—

217

C₂²

—

218

C₂²

—

134

—

219

C₂²

—

134

—

220

C₂²

—

134

—

221

C₂²

C₂×D₄×D₆₇

yes

characteristic

222

C₄

—

223

C₄

—

224

C₄

—

225

C₄

—

268

—

226

C₄

—

134

—

227

C₄

—

134

—

228

C₄

C₂×D₄×D₆₇

yes

characteristic

229

C₄

#14524088

yes

characteristic

230

C₂

—

231

C₂

—

268

—

232

C₂

#16864031

yes

characteristic

233

C₂

#16864193

yes

characteristic

234

C₂

#16864210

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₆₇
Fitting	#495×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×D₄
hypercenter	#495	D₆₇
hypocenter	C₆₇	#3277
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #495

subgroup

G/H

center

C₂²

C₂×D₄×D₆₇

commutator

C₂×C₄×C₆₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₆₇

Fitting

#495×C₆₇

C₂

socle

C₂²×C₆₇

C₂²×D₄

D₆₇

C₆₇

G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #495

N	H ≅ G/N	type
1. C₂×#14524072	C₂	semidirect
2. #16864054	C₂	semidirect
3. #16863639	C₂	semidirect
4. #16863615	C₂	semidirect
5. #16863550	C₂	semidirect
6. #16863538	C₂	semidirect
7. C₄×Dic₂₆₈	C₂	semidirect
8. #16863475	C₂	semidirect
9. #495×C₆₇	C₂	semidirect
48. Dic₂₆₈	D₄	semidirect
118. C₆₇	#3277	semidirect
121. #495	D₆₇	semidirect

H ≅ G/N

type

1. C₂×#14524072

C₂

semidirect

2. #16864054

C₂

semidirect

3. #16863639

C₂

semidirect

4. #16863615

C₂

semidirect

5. #16863550

C₂

semidirect

6. #16863538

C₂

semidirect

7. C₄×Dic₂₆₈

C₂

semidirect

8. #16863475

C₂

semidirect

9. #495×C₆₇

C₂

semidirect

48. Dic₂₆₈

D₄

semidirect

118. C₆₇

#3277

semidirect

121. #495

D₆₇

semidirect

Subgroups — #22571864

Conjugacy classes of subgroups

Complements