Group #22573082 — subgroups

Subgroups — #22573082

Order 8576.

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

normal subgroups only

This group has 338 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	#16864125	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864103	C₂	1	1	yes	maximal, characteristic
3	#16863796	C₂	1	2	yes	maximal, complemented
4	#16863794	C₂	1	1	yes	maximal, characteristic, complemented
5	#16863701	C₂	1	2	yes	maximal, complemented
6	#16863698	C₂	1	2	yes	maximal
7	#16863691	C₂	1	1	yes	maximal, characteristic, complemented
8	#16863676	C₂	1	1	yes	maximal, characteristic
9	C₈×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×Dic₆₇	C₂	1	2	yes	maximal
11	C₄×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic
12	#14524043	—	2	1	no	—
13	#14524043	C₂²	1	1	yes	characteristic
14	#14524043	C₂²	1	1	yes	characteristic
15	#14524034	—	2	2	no	—
16	#14524034	C₂²	1	2	yes	—
17	#14524034	C₂²	1	2	yes	—
18	#14524022	—	2	1	no	—
19	#14524020	—	2	2	no	—
20	Q₈×Dic₆₇	C₂²	1	2	yes	—
21	C₄×Dic₁₃₄	—	2	1	no	—
22	C₄×Dic₁₃₄	C₂²	1	1	yes	characteristic
23	D₄×Dic₆₇	C₂²	1	2	yes	—
24	C₂×C₄⋊Dic₆₇	—	2	1	no	—
25	#14523976	C₂²	1	2	yes	—
26	#14523976	C₂²	1	2	yes	—
27	#14523975	C₂²	1	2	yes	—
28	#14523975	C₂²	1	2	yes	—
29	C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
30	Dic₆₇⋊C₈	C₂²	1	2	yes	—
31	#14523967	C₂²	1	2	yes	—
32	#14523964	C₂²	1	2	yes	—
33	C₈×Dic₆₇	C₂²	1	2	yes	—
34	C₂×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
37	#106×C₆₇	C₂²	1	1	yes	characteristic
38	#103×C₆₇	C₂²	1	1	yes	characteristic
39	#102×C₆₇	C₂²	1	1	yes	characteristic
40	C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×Dic₁₃₄	—	2	1	no	—
42	C₂×Dic₁₃₄	—	2	1	no	—
43	C₂×Dic₁₃₄	D₄	1	1	yes	characteristic
44	C₂²×Dic₆₇	—	2	2	no	—
45	C₂×C₆₇⋊C₈	C₂³	1	2	yes	—
46	C₄⋊Dic₆₇	—	2	1	no	—
47	C₄⋊Dic₆₇	—	2	1	no	—
48	C₄⋊Dic₆₇	—	2	2	no	—
49	C₄⋊Dic₆₇	—	2	2	no	—
50	C₄⋊Dic₆₇	—	2	2	no	—
51	C₄⋊Dic₆₇	D₄	1	1	yes	characteristic
52	C₄⋊Dic₆₇	C₂³	1	2	yes	—
53	C₄⋊Dic₆₇	C₂³	1	2	yes	—
54	Dic₆₇⋊C₄	—	2	2	no	—
55	Dic₆₇⋊C₄	—	2	2	no	—
56	Dic₆₇⋊C₄	D₄	1	2	yes	—
57	C₂²⋊Dic₆₇	—	2	2	no	—
58	C₄×Dic₆₇	—	2	2	no	—
59	C₄×Dic₆₇	C₂³	1	2	yes	—
60	C₂×Q₈×C₆₇	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₆₇	C₂³	1	1	yes	characteristic
62	C₂²×C₄×C₆₇	—	2	1	no	—
63	SD₁₆×C₆₇	Q₈	1	4	yes	complemented
64	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×C₈×C₆₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₄×C₆₇	—	2	1	no	—
67	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
69	C₂²⋊C₄×C₆₇	—	2	1	no	—
70	C₄²×C₆₇	—	2	1	no	—
71	C₄²×C₆₇	C₂³	1	1	yes	characteristic
72	C₂³×C₆₇	—	2	1	no	—
73	Q₈×C₆₇	—	2	1	no	—
74	Q₈×C₆₇	C₂×Q₈	1	2	yes	—
75	D₄×C₆₇	—	2	1	no	—
76	D₄×C₆₇	C₂×Q₈	1	2	yes	—
77	C₂×C₄×C₆₇	—	2	1	no	—
78	C₂×C₄×C₆₇	—	2	1	no	—
79	C₂×C₄×C₆₇	—	2	1	no	—
80	C₂×C₄×C₆₇	—	4	2	no	—
81	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
83	C₂×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
84	C₂×Dic₆₇	—	2	2	no	—
85	C₂×Dic₆₇	—	2	2	no	—
86	C₂×Dic₆₇	—	8	2	no	—
87	C₂×Dic₆₇	C₂×D₄	1	2	yes	—
88	C₂×Dic₆₇	C₂×D₄	1	2	yes	—
89	Dic₁₃₄	—	2	2	no	—
90	Dic₁₃₄	—	4	2	no	—
91	Dic₁₃₄	—	8	1	no	—
92	C₈×C₆₇	—	2	1	no	—
93	C₈×C₆₇	C₂×Q₈	1	2	yes	—
94	C₆₇⋊C₈	—	2	2	no	—
95	C₂²×C₆₇	—	2	2	no	—
96	C₂²×C₆₇	—	4	1	no	—
97	C₂²×C₆₇	—	4	1	no	—
98	C₂²×C₆₇	C₂²×D₄	1	1	yes	characteristic
99	C₄×C₆₇	—	2	2	no	—
100	C₄×C₆₇	—	2	1	no	—
101	C₄×C₆₇	—	4	1	no	—
102	C₄×C₆₇	—	4	1	no	—
103	C₄×C₆₇	#135	1	2	yes	—
104	C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
105	C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
106	Dic₆₇	—	2	2	no	—
107	Dic₆₇	—	2	2	no	—
108	Dic₆₇	—	4	2	no	—
109	Dic₆₇	—	4	2	no	—
110	C₂×C₆₇	—	4	2	no	—
111	C₂×C₆₇	D₄×Q₈	1	1	yes	characteristic
112	C₂×C₆₇	C₂×#135	1	1	yes	characteristic
113	C₂×C₆₇	#577	1	1	yes	characteristic
114	#3381	—	67	1	no	maximal, Sylow
115	C₆₇	#3381	1	1	yes	characteristic, complemented, Sylow
116	#557	—	67	1	no	—
117	#554	—	67	1	no	—
118	#499	—	67	2	no	—
119	#498	—	67	1	no	—
120	#479	—	67	2	no	—
121	#478	—	67	2	no	—
122	#477	—	67	1	no	—
123	#474	—	67	1	no	—
124	C₈×Q₈	—	67	1	no	—
125	C₄×SD₁₆	—	67	2	no	—
126	C₄×SD₁₆	D₆₇	1	1	yes	characteristic
127	C₂×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
128	C₄⋊Q₈	—	67	1	no	—
129	C₄⋊Q₈	—	67	1	no	—
130	C₄⋊Q₈	—	134	1	no	—
131	#125	—	67	2	no	—
132	#125	—	67	2	no	—
133	#125	—	134	2	no	—
134	C₂²⋊Q₈	—	134	2	no	—
135	C₂²⋊Q₈	—	134	1	no	—
136	C₄×Q₈	—	67	1	no	—
137	C₄×Q₈	—	67	2	no	—
138	C₄×Q₈	—	134	1	no	—
139	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
140	C₄×D₄	—	67	2	no	—
141	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
142	C₂×C₄⋊C₄	—	134	1	no	—
143	#107	—	67	2	no	—
144	#107	—	67	2	no	—
145	#106	—	67	2	no	—
146	#106	—	67	2	no	—
147	#106	C₂×D₆₇	1	1	yes	characteristic
148	C₄⋊C₈	—	67	2	no	—
149	C₄⋊C₈	—	67	1	no	—
150	#103	—	67	2	no	—
151	#103	C₂×D₆₇	1	1	yes	characteristic
152	#102	—	67	2	no	—
153	#102	C₂×D₆₇	1	1	yes	characteristic
154	C₄×C₈	—	67	2	no	—
155	C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
156	C₂×Q₈	—	67	1	no	—
157	C₂×Q₈	—	134	1	no	—
158	C₂×Q₈	—	134	1	no	—
159	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
160	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
161	C₂²×C₄	—	2	1	no	—
162	C₂²×C₄	—	134	2	no	—
163	SD₁₆	Dic₁₃₄	1	4	yes	complemented
164	C₂×C₈	—	67	2	no	—
165	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
166	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
167	C₄⋊C₄	—	2	1	no	—
168	C₄⋊C₄	—	67	1	no	—
169	C₄⋊C₄	—	67	2	no	—
170	C₄⋊C₄	—	67	2	no	—
171	C₄⋊C₄	—	67	2	no	—
172	C₄⋊C₄	—	134	2	no	—
173	C₄⋊C₄	—	134	2	no	—
174	C₄⋊C₄	—	134	2	no	—
175	C₄⋊C₄	—	134	2	no	—
176	C₄⋊C₄	—	134	2	no	—
177	C₄⋊C₄	—	134	1	no	—
178	C₄⋊C₄	—	134	1	no	—
179	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
180	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
181	C₂²⋊C₄	—	2	1	no	—
182	C₂²⋊C₄	—	134	2	no	—
183	C₄²	—	2	1	no	—
184	C₄²	—	67	2	no	—
185	C₄²	—	134	2	no	—
186	C₄²	C₂²×D₆₇	1	1	yes	characteristic
187	C₂³	—	2	1	no	—
188	Q₈	—	2	1	no	—
189	Q₈	—	268	2	no	—
190	Q₈	—	536	1	no	—
191	Q₈	—	134	2	no	—
192	Q₈	C₂×Dic₁₃₄	1	2	yes	—
193	D₄	—	2	1	no	—
194	D₄	C₂×Dic₁₃₄	1	2	yes	—
195	C₂×C₄	—	2	1	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	4	2	no	—
199	C₂×C₄	—	536	2	no	—
200	C₂×C₄	—	67	2	no	—
201	C₂×C₄	—	67	2	no	—
202	C₂×C₄	—	134	2	no	—
203	C₂×C₄	—	134	2	no	—
204	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
205	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
206	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
207	C₈	—	2	1	no	—
208	C₈	—	134	2	no	—
209	C₈	C₂×Dic₁₃₄	1	2	yes	—
210	C₂²	—	2	2	no	—
211	C₂²	—	4	1	no	—
212	C₂²	—	4	1	no	—
213	C₂²	C₂×D₄×D₆₇	1	1	yes	characteristic
214	C₄	—	2	2	no	—
215	C₄	—	2	1	no	—
216	C₄	—	4	1	no	—
217	C₄	—	4	1	no	—
218	C₄	—	268	2	no	—
219	C₄	—	268	2	no	—
220	C₄	—	134	2	no	—
221	C₄	—	134	2	no	—
222	C₄	#14524064	1	2	yes	—
223	C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
224	C₄	#14524090	1	1	yes	characteristic
225	C₂	—	4	2	no	—
226	C₂	D₄×Dic₁₃₄	1	1	yes	characteristic
227	C₂	C₂×#14524064	1	1	yes	characteristic
228	C₂	#16864203	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#16864125

C₂

yes

maximal, characteristic, complemented

#16864103

C₂

yes

maximal, characteristic

#16863796

C₂

yes

maximal, complemented

#16863794

C₂

yes

maximal, characteristic, complemented

#16863701

C₂

yes

maximal, complemented

#16863698

C₂

yes

maximal

#16863691

C₂

yes

maximal, characteristic, complemented

#16863676

C₂

yes

maximal, characteristic

C₈×Dic₁₃₄

C₂

yes

maximal, characteristic, complemented

SD₁₆×Dic₆₇

C₂

yes

maximal

C₄×SD₁₆×C₆₇

C₂

yes

maximal, characteristic

#14524043

—

#14524043

C₂²

yes

characteristic

#14524043

C₂²

yes

characteristic

#14524034

—

#14524034

C₂²

yes

—

#14524034

C₂²

yes

—

#14524022

—

#14524020

—

Q₈×Dic₆₇

C₂²

yes

—

C₄×Dic₁₃₄

—

C₄×Dic₁₃₄

C₂²

yes

characteristic

D₄×Dic₆₇

C₂²

yes

—

C₂×C₄⋊Dic₆₇

—

#14523976

C₂²

yes

—

#14523976

C₂²

yes

—

#14523975

C₂²

yes

—

#14523975

C₂²

yes

—

C₄⋊(C₆₇⋊C₈)

C₂²

yes

characteristic

Dic₆₇⋊C₈

C₂²

yes

—

#14523967

C₂²

yes

—

#14523964

C₂²

yes

—

C₈×Dic₆₇

C₂²

yes

—

C₂×SD₁₆×C₆₇

C₂²

yes

characteristic

C₄×Q₈×C₆₇

C₂²

yes

characteristic

C₄×D₄×C₆₇

C₂²

yes

characteristic

#106×C₆₇

C₂²

yes

characteristic

#103×C₆₇

C₂²

yes

characteristic

#102×C₆₇

C₂²

yes

characteristic

C₄×C₈×C₆₇

C₂²

yes

characteristic

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

D₄

yes

characteristic

C₂²×Dic₆₇

—

C₂×C₆₇⋊C₈

C₂³

yes

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

D₄

yes

characteristic

C₄⋊Dic₆₇

C₂³

yes

—

C₄⋊Dic₆₇

C₂³

yes

—

Dic₆₇⋊C₄

—

Dic₆₇⋊C₄

—

Dic₆₇⋊C₄

D₄

yes

—

C₂²⋊Dic₆₇

—

C₄×Dic₆₇

—

C₄×Dic₆₇

C₂³

yes

—

C₂×Q₈×C₆₇

C₂³

yes

characteristic

C₂×D₄×C₆₇

C₂³

yes

characteristic

C₂²×C₄×C₆₇

—

SD₁₆×C₆₇

Q₈

yes

complemented

C₂×C₈×C₆₇

C₂³

yes

characteristic

C₂×C₈×C₆₇

C₂³

yes

characteristic

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

C₂³

yes

characteristic

C₄⋊C₄×C₆₇

C₂³

yes

characteristic

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

C₂³

yes

characteristic

C₂³×C₆₇

—

Q₈×C₆₇

—

Q₈×C₆₇

C₂×Q₈

yes

—

D₄×C₆₇

—

D₄×C₆₇

C₂×Q₈

yes

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₄×C₆₇

C₂⁴

yes

characteristic

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

C₂×D₄

yes

—

C₂×Dic₆₇

C₂×D₄

yes

—

Dic₁₃₄

—

Dic₁₃₄

—

Dic₁₃₄

—

C₈×C₆₇

—

C₈×C₆₇

C₂×Q₈

yes

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

C₂²×D₄

yes

characteristic

C₄×C₆₇

—

100

C₄×C₆₇

—

101

C₄×C₆₇

—

102

C₄×C₆₇

—

103

C₄×C₆₇

#135

yes

—

104

C₄×C₆₇

C₂²×Q₈

yes

characteristic

105

C₄×C₆₇

2₋¹⁺⁴

yes

characteristic

106

Dic₆₇

—

107

Dic₆₇

—

108

Dic₆₇

—

109

Dic₆₇

—

110

C₂×C₆₇

—

111

C₂×C₆₇

D₄×Q₈

yes

characteristic

112

C₂×C₆₇

C₂×#135

yes

characteristic

113

C₂×C₆₇

yes

114

—

115

C₆₇

#3381

yes

characteristic, complemented, Sylow

116

#557

—

117

#554

—

118

#499

—

119

#498

—

120

#479

—

121

#478

—

122

#477

—

123

#474

—

124

C₈×Q₈

—

125

C₄×SD₁₆

—

126

C₄×SD₁₆

D₆₇

yes

characteristic

127

C₂×SD₁₆

C₂×D₆₇

yes

characteristic

128

C₄⋊Q₈

—

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

134

—

131

#125

—

132

#125

—

133

#125

—

134

—

134

C₂²⋊Q₈

—

134

—

135

C₂²⋊Q₈

—

134

—

136

C₄×Q₈

—

137

C₄×Q₈

—

138

C₄×Q₈

—

134

—

139

C₄×Q₈

C₂×D₆₇

yes

characteristic

140

C₄×D₄

—

141

C₄×D₄

C₂×D₆₇

yes

characteristic

142

C₂×C₄⋊C₄

—

134

—

143

#107

—

144

#107

—

145

#106

—

146

#106

—

147

#106

C₂×D₆₇

yes

characteristic

148

C₄⋊C₈

—

149

C₄⋊C₈

—

150

#103

—

151

#103

C₂×D₆₇

yes

characteristic

152

#102

—

153

#102

C₂×D₆₇

yes

characteristic

154

C₄×C₈

—

155

C₄×C₈

C₂×D₆₇

yes

characteristic

156

C₂×Q₈

—

157

C₂×Q₈

—

134

—

158

C₂×Q₈

—

134

—

159

C₂×Q₈

C₂²×D₆₇

yes

characteristic

160

C₂×D₄

C₂²×D₆₇

yes

characteristic

161

C₂²×C₄

—

162

C₂²×C₄

—

134

—

163

SD₁₆

Dic₁₃₄

yes

complemented

164

C₂×C₈

—

165

C₂×C₈

C₂²×D₆₇

yes

characteristic

166

C₂×C₈

C₂²×D₆₇

yes

characteristic

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

134

—

173

C₄⋊C₄

—

134

—

174

C₄⋊C₄

—

134

—

175

C₄⋊C₄

—

134

—

176

C₄⋊C₄

—

134

—

177

C₄⋊C₄

—

134

—

178

C₄⋊C₄

—

134

—

179

C₄⋊C₄

C₂²×D₆₇

yes

characteristic

180

C₄⋊C₄

C₂²×D₆₇

yes

characteristic

181

C₂²⋊C₄

—

182

C₂²⋊C₄

—

134

—

183

C₄²

—

184

C₄²

—

185

C₄²

—

134

—

186

C₄²

C₂²×D₆₇

yes

characteristic

187

C₂³

—

188

Q₈

—

189

Q₈

—

268

—

190

Q₈

—

536

—

191

Q₈

—

134

—

192

Q₈

C₂×Dic₁₃₄

yes

—

193

D₄

—

194

D₄

C₂×Dic₁₃₄

yes

—

195

C₂×C₄

—

196

C₂×C₄

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

536

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

134

—

203

C₂×C₄

—

134

—

204

C₂×C₄

D₄×D₆₇

yes

characteristic

205

C₂×C₄

D₄×D₆₇

yes

characteristic

206

C₂×C₄

C₂³×D₆₇

yes

characteristic

207

C₈

—

208

C₈

—

134

—

209

C₈

C₂×Dic₁₃₄

yes

—

210

C₂²

—

211

C₂²

—

212

C₂²

—

213

C₂²

C₂×D₄×D₆₇

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

—

268

—

219

C₄

—

268

—

220

C₄

—

134

—

221

C₄

—

134

—

222

C₄

#14524064

yes

—

223

C₄

C₂²×Dic₁₃₄

yes

characteristic

224

C₄

#14524090

yes

characteristic

225

C₂

—

226

C₂

D₄×Dic₁₃₄

yes

characteristic

227

C₂

C₂×#14524064

yes

characteristic

228

C₂

#16864203

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂⁴
Frattini	C₂×C₄	C₂³×D₆₇
Fitting	C₄×SD₁₆×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×D₄
hypercenter	C₄×SD₁₆	D₆₇
hypocenter	C₆₇	#3381
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

subgroup

G/H

center

C₂²

C₂×D₄×D₆₇

commutator

C₂×C₄×C₆₇

C₂⁴

Frattini

C₂×C₄

C₂³×D₆₇

Fitting

C₄×SD₁₆×C₆₇

C₂

socle

C₂²×C₆₇

C₂²×D₄

hypercenter

C₄×SD₁₆

D₆₇

hypocenter

C₆₇

#3381

LCS

G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

N	H ≅ G/N	type
1. #16864125	C₂	semidirect
3. #16863796	C₂	semidirect
4. #16863794	C₂	semidirect
5. #16863701	C₂	semidirect
7. #16863691	C₂	semidirect
9. C₈×Dic₁₃₄	C₂	semidirect
63. SD₁₆×C₆₇	Q₈	semidirect
115. C₆₇	#3381	semidirect
163. SD₁₆	Dic₁₃₄	semidirect

H ≅ G/N

type

1. #16864125

C₂

semidirect

3. #16863796

C₂

semidirect

4. #16863794

C₂

semidirect

5. #16863701

C₂

semidirect

7. #16863691

C₂

semidirect

9. C₈×Dic₁₃₄

C₂

semidirect

63. SD₁₆×C₆₇

Q₈

semidirect

115. C₆₇

#3381

semidirect

163. SD₁₆

Dic₁₃₄

semidirect

Subgroups — #22573082

Conjugacy classes of subgroups

Complements