Group #22573117 — subgroups

Subgroups — #22573117

Order 8576.

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

normal subgroups only

This group has 340 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	Q₈×Dic₁₃₄	C₂	1	1	yes	maximal, characteristic, complemented
2	#16864103	C₂	1	1	yes	maximal, characteristic
3	#16863803	C₂	1	2	yes	maximal, complemented
4	#16863801	C₂	1	1	yes	maximal, characteristic, complemented
5	#16863705	C₂	1	2	yes	maximal, complemented
6	#16863691	C₂	1	1	yes	maximal, characteristic, complemented
7	#16863686	C₂	1	1	yes	maximal, characteristic
8	#16863674	C₂	1	2	yes	maximal
9	#16863526	C₂	1	1	yes	maximal, characteristic, complemented
10	#16863497	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	#14524042	—	2	2	no	—
16	#14524042	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	#14523977	C₂²	1	2	yes	—
26	#14523977	C₂²	1	2	yes	—
27	#14523976	C₂²	1	2	yes	—
28	#14523974	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	#14523953	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	—	2	2	no	—
44	C₂×Dic₁₃₄	D₄	1	1	yes	characteristic
45	C₂²×Dic₆₇	—	2	2	no	—
46	C₂×C₆₇⋊C₈	C₂³	1	2	yes	—
47	C₄⋊Dic₆₇	—	2	1	no	—
48	C₄⋊Dic₆₇	—	2	1	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	—	8	2	no	—
91	Dic₁₃₄	—	8	1	no	—
92	Dic₁₃₄	—	8	1	no	—
93	C₈×C₆₇	—	2	1	no	—
94	C₈×C₆₇	C₂×Q₈	1	2	yes	—
95	C₆₇⋊C₈	—	2	2	no	—
96	C₂²×C₆₇	—	2	2	no	—
97	C₂²×C₆₇	—	4	1	no	—
98	C₂²×C₆₇	—	4	1	no	—
99	C₂²×C₆₇	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₆₇	—	2	2	no	—
101	C₄×C₆₇	—	2	1	no	—
102	C₄×C₆₇	—	4	1	no	—
103	C₄×C₆₇	—	4	1	no	—
104	C₄×C₆₇	#137	1	2	yes	—
105	C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
106	C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
107	Dic₆₇	—	2	2	no	—
108	Dic₆₇	—	2	2	no	—
109	Dic₆₇	—	4	2	no	—
110	Dic₆₇	—	4	2	no	—
111	C₂×C₆₇	—	4	2	no	—
112	C₂×C₆₇	D₄×Q₈	1	1	yes	characteristic
113	C₂×C₆₇	C₂×#137	1	1	yes	characteristic
114	C₂×C₆₇	#576	1	1	yes	characteristic
115	#3385	—	67	1	no	maximal, Sylow
116	C₆₇	#3385	1	1	yes	characteristic, complemented, Sylow
117	Q₈²	—	67	1	no	—
118	#554	—	67	1	no	—
119	#501	—	67	2	no	—
120	#500	—	67	1	no	—
121	#479	—	67	2	no	—
122	#477	—	67	1	no	—
123	#476	—	67	1	no	—
124	#474	—	67	2	no	—
125	#446	—	67	1	no	—
126	#440	—	67	2	no	—
127	C₄×SD₁₆	D₆₇	1	1	yes	characteristic
128	C₂×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
129	C₄⋊Q₈	—	67	2	no	—
130	C₄⋊Q₈	—	67	1	no	—
131	C₄⋊Q₈	—	67	1	no	—
132	C₄⋊Q₈	—	134	1	no	—
133	C₄⋊Q₈	—	134	2	no	—
134	#125	—	67	2	no	—
135	C₂²⋊Q₈	—	134	2	no	—
136	C₂²⋊Q₈	—	134	1	no	—
137	C₄×Q₈	—	67	1	no	—
138	C₄×Q₈	—	67	2	no	—
139	C₄×Q₈	—	134	1	no	—
140	C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
141	C₄×D₄	—	67	2	no	—
142	C₄×D₄	C₂×D₆₇	1	1	yes	characteristic
143	C₂×C₄⋊C₄	—	134	1	no	—
144	#107	—	67	2	no	—
145	#107	—	67	2	no	—
146	#107	—	67	2	no	—
147	#106	—	67	2	no	—
148	#106	C₂×D₆₇	1	1	yes	characteristic
149	C₄⋊C₈	—	67	2	no	—
150	C₄⋊C₈	—	67	1	no	—
151	#103	—	67	2	no	—
152	#103	C₂×D₆₇	1	1	yes	characteristic
153	#102	—	67	2	no	—
154	#102	C₂×D₆₇	1	1	yes	characteristic
155	#97	—	67	2	no	—
156	C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
157	C₂×Q₈	—	67	1	no	—
158	C₂×Q₈	—	134	2	no	—
159	C₂×Q₈	—	134	1	no	—
160	C₂×Q₈	—	134	1	no	—
161	C₂×Q₈	C₂²×D₆₇	1	1	yes	characteristic
162	C₂×D₄	C₂²×D₆₇	1	1	yes	characteristic
163	C₂²×C₄	—	2	1	no	—
164	C₂²×C₄	—	134	2	no	—
165	SD₁₆	Dic₁₃₄	1	4	yes	complemented
166	C₂×C₈	—	67	2	no	—
167	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
168	C₂×C₈	C₂²×D₆₇	1	1	yes	characteristic
169	C₄⋊C₄	—	2	1	no	—
170	C₄⋊C₄	—	67	1	no	—
171	C₄⋊C₄	—	67	2	no	—
172	C₄⋊C₄	—	67	2	no	—
173	C₄⋊C₄	—	67	2	no	—
174	C₄⋊C₄	—	134	2	no	—
175	C₄⋊C₄	—	134	2	no	—
176	C₄⋊C₄	—	134	2	no	—
177	C₄⋊C₄	—	134	2	no	—
178	C₄⋊C₄	—	134	1	no	—
179	C₄⋊C₄	—	134	1	no	—
180	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
181	C₄⋊C₄	C₂²×D₆₇	1	1	yes	characteristic
182	C₂²⋊C₄	—	2	1	no	—
183	C₂²⋊C₄	—	134	2	no	—
184	C₄²	—	2	1	no	—
185	C₄²	—	67	2	no	—
186	C₄²	—	134	2	no	—
187	C₄²	C₂²×D₆₇	1	1	yes	characteristic
188	C₂³	—	2	1	no	—
189	Q₈	—	2	1	no	—
190	Q₈	—	536	1	no	—
191	Q₈	—	536	1	no	—
192	Q₈	—	536	2	no	—
193	Q₈	—	134	2	no	—
194	Q₈	C₂×Dic₁₃₄	1	2	yes	—
195	D₄	—	2	1	no	—
196	D₄	C₂×Dic₁₃₄	1	2	yes	—
197	C₂×C₄	—	2	1	no	—
198	C₂×C₄	—	2	1	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	4	2	no	—
201	C₂×C₄	—	536	2	no	—
202	C₂×C₄	—	67	2	no	—
203	C₂×C₄	—	67	2	no	—
204	C₂×C₄	—	134	2	no	—
205	C₂×C₄	—	134	2	no	—
206	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
207	C₂×C₄	D₄×D₆₇	1	1	yes	characteristic
208	C₂×C₄	C₂³×D₆₇	1	1	yes	characteristic
209	C₈	—	2	1	no	—
210	C₈	—	134	2	no	—
211	C₈	C₂×Dic₁₃₄	1	2	yes	—
212	C₂²	—	2	2	no	—
213	C₂²	—	4	1	no	—
214	C₂²	—	4	1	no	—
215	C₂²	C₂×D₄×D₆₇	1	1	yes	characteristic
216	C₄	—	2	2	no	—
217	C₄	—	2	1	no	—
218	C₄	—	4	1	no	—
219	C₄	—	4	1	no	—
220	C₄	—	268	2	no	—
221	C₄	—	268	2	no	—
222	C₄	—	134	2	no	—
223	C₄	—	134	2	no	—
224	C₄	#14524072	1	2	yes	—
225	C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
226	C₄	#14524090	1	1	yes	characteristic
227	C₂	—	4	2	no	—
228	C₂	D₄×Dic₁₃₄	1	1	yes	characteristic
229	C₂	C₂×#14524072	1	1	yes	characteristic
230	C₂	#16864198	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

Q₈×Dic₁₃₄

C₂

yes

maximal, characteristic, complemented

#16864103

C₂

yes

maximal, characteristic

#16863803

C₂

yes

maximal, complemented

#16863801

C₂

yes

maximal, characteristic, complemented

#16863705

C₂

yes

maximal, complemented

#16863691

C₂

yes

maximal, characteristic, complemented

#16863686

C₂

yes

maximal, characteristic

#16863674

C₂

yes

maximal

#16863526

C₂

yes

maximal, characteristic, complemented

#16863497

C₂

yes

maximal

C₄×SD₁₆×C₆₇

C₂

yes

maximal, characteristic

#14524043

—

#14524043

C₂²

yes

characteristic

#14524043

C₂²

yes

characteristic

#14524042

—

#14524042

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

—

#14523977

C₂²

yes

—

#14523977

C₂²

yes

—

#14523976

C₂²

yes

—

#14523974

C₂²

yes

—

C₄⋊(C₆₇⋊C₈)

C₂²

yes

characteristic

Dic₆₇⋊C₈

C₂²

yes

—

#14523967

C₂²

yes

—

#14523964

C₂²

yes

—

#14523953

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

—

C₂×Dic₁₃₄

D₄

yes

characteristic

C₂²×Dic₆₇

—

C₂×C₆₇⋊C₈

C₂³

yes

—

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

—

Dic₁₃₄

—

C₈×C₆₇

—

C₈×C₆₇

C₂×Q₈

yes

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

C₂²×D₄

yes

characteristic

100

C₄×C₆₇

—

101

C₄×C₆₇

—

102

C₄×C₆₇

—

103

C₄×C₆₇

—

104

C₄×C₆₇

#137

yes

—

105

C₄×C₆₇

C₂²×Q₈

yes

characteristic

106

C₄×C₆₇

2₋¹⁺⁴

yes

characteristic

107

Dic₆₇

—

108

Dic₆₇

—

109

Dic₆₇

—

110

Dic₆₇

—

111

C₂×C₆₇

—

112

C₂×C₆₇

D₄×Q₈

yes

characteristic

113

C₂×C₆₇

C₂×#137

yes

characteristic

114

C₂×C₆₇

yes

115

—

116

C₆₇

#3385

yes

characteristic, complemented, Sylow

117

Q₈²

—

118

#554

—

119

#501

—

120

#500

—

121

#479

—

122

#477

—

123

#476

—

124

#474

—

125

#446

—

126

#440

—

127

C₄×SD₁₆

D₆₇

yes

characteristic

128

C₂×SD₁₆

C₂×D₆₇

yes

characteristic

129

C₄⋊Q₈

—

130

C₄⋊Q₈

—

131

C₄⋊Q₈

—

132

C₄⋊Q₈

—

134

—

133

C₄⋊Q₈

—

134

—

134

#125

—

135

C₂²⋊Q₈

—

134

—

136

C₂²⋊Q₈

—

134

—

137

C₄×Q₈

—

138

C₄×Q₈

—

139

C₄×Q₈

—

134

—

140

C₄×Q₈

C₂×D₆₇

yes

characteristic

141

C₄×D₄

—

142

C₄×D₄

C₂×D₆₇

yes

characteristic

143

C₂×C₄⋊C₄

—

134

—

144

#107

—

145

#107

—

146

#107

—

147

#106

—

148

#106

C₂×D₆₇

yes

characteristic

149

C₄⋊C₈

—

150

C₄⋊C₈

—

151

#103

—

152

#103

C₂×D₆₇

yes

characteristic

153

#102

—

154

#102

C₂×D₆₇

yes

characteristic

155

#97

—

156

C₄×C₈

C₂×D₆₇

yes

characteristic

157

C₂×Q₈

—

158

C₂×Q₈

—

134

—

159

C₂×Q₈

—

134

—

160

C₂×Q₈

—

134

—

161

C₂×Q₈

C₂²×D₆₇

yes

characteristic

162

C₂×D₄

C₂²×D₆₇

yes

characteristic

163

C₂²×C₄

—

164

C₂²×C₄

—

134

—

165

SD₁₆

Dic₁₃₄

yes

complemented

166

C₂×C₈

—

167

C₂×C₈

C₂²×D₆₇

yes

characteristic

168

C₂×C₈

C₂²×D₆₇

yes

characteristic

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

174

C₄⋊C₄

—

134

—

175

C₄⋊C₄

—

134

—

176

C₄⋊C₄

—

134

—

177

C₄⋊C₄

—

134

—

178

C₄⋊C₄

—

134

—

179

C₄⋊C₄

—

134

—

180

C₄⋊C₄

C₂²×D₆₇

yes

characteristic

181

C₄⋊C₄

C₂²×D₆₇

yes

characteristic

182

C₂²⋊C₄

—

183

C₂²⋊C₄

—

134

—

184

C₄²

—

185

C₄²

—

186

C₄²

—

134

—

187

C₄²

C₂²×D₆₇

yes

characteristic

188

C₂³

—

189

Q₈

—

190

Q₈

—

536

—

191

Q₈

—

536

—

192

Q₈

—

536

—

193

Q₈

—

134

—

194

Q₈

C₂×Dic₁₃₄

yes

—

195

D₄

—

196

D₄

C₂×Dic₁₃₄

yes

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

536

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

134

—

205

C₂×C₄

—

134

—

206

C₂×C₄

D₄×D₆₇

yes

characteristic

207

C₂×C₄

D₄×D₆₇

yes

characteristic

208

C₂×C₄

C₂³×D₆₇

yes

characteristic

209

C₈

—

210

C₈

—

134

—

211

C₈

C₂×Dic₁₃₄

yes

—

212

C₂²

—

213

C₂²

—

214

C₂²

—

215

C₂²

C₂×D₄×D₆₇

yes

characteristic

216

C₄

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

268

—

221

C₄

—

268

—

222

C₄

—

134

—

223

C₄

—

134

—

224

C₄

#14524072

yes

—

225

C₄

C₂²×Dic₁₃₄

yes

characteristic

226

C₄

#14524090

yes

characteristic

227

C₂

—

228

C₂

D₄×Dic₁₃₄

yes

characteristic

229

C₂

C₂×#14524072

yes

characteristic

230

C₂

#16864198

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	#3385
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

#3385

LCS

G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×SD₁₆

N	H ≅ G/N	type
1. Q₈×Dic₁₃₄	C₂	semidirect
3. #16863803	C₂	semidirect
4. #16863801	C₂	semidirect
5. #16863705	C₂	semidirect
6. #16863691	C₂	semidirect
9. #16863526	C₂	semidirect
63. SD₁₆×C₆₇	Q₈	semidirect
116. C₆₇	#3385	semidirect
165. SD₁₆	Dic₁₃₄	semidirect

H ≅ G/N

type

1. Q₈×Dic₁₃₄

C₂

semidirect

3. #16863803

C₂

semidirect

4. #16863801

C₂

semidirect

5. #16863705

C₂

semidirect

6. #16863691

C₂

semidirect

9. #16863526

C₂

semidirect

63. SD₁₆×C₆₇

Q₈

semidirect

116. C₆₇

#3385

semidirect

165. SD₁₆

Dic₁₃₄

semidirect

Subgroups — #22573117

Conjugacy classes of subgroups

Complements