Group #30774064 — subgroups

Subgroups — #30774064

Order 17152.

590 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 167 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×#16863197	C₂	1	4	yes	maximal, complemented
2	C₂×#16863172	C₂	1	1	yes	maximal, characteristic, complemented
3	#22560373	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#493×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₆₇⋊C₁₆	C₂²	1	2	yes	—
6	C₂×#14523977	C₂²	1	2	yes	—
7	C₂×#14523975	—	2	1	no	—
8	#16863262	—	2	1	no	—
9	#16863197	—	2	8	no	—
10	#16863172	—	2	2	no	—
11	C₂²×D₈×C₆₇	—	2	1	no	—
12	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
13	C₂×#127×C₆₇	—	2	1	no	—
14	#493×C₆₇	—	2	2	no	—
15	#493×C₆₇	C₄	1	4	yes	complemented
16	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Dic₆₇	—	2	2	no	—
18	C₂×C₆₇⋊C₁₆	—	2	2	no	—
19	C₂×C₆₇⋊C₁₆	—	2	2	no	—
20	C₂×C₆₇⋊C₁₆	D₄	1	4	yes	complemented
21	#14523977	—	2	4	no	—
22	#14523975	—	4	2	no	—
23	C₆₇⋊#95	—	4	2	no	—
24	C₂²×D₄×C₆₇	—	2	2	no	—
25	C₂²×D₄×C₆₇	—	4	2	no	—
26	C₂×D₈×C₆₇	—	2	4	no	—
27	C₂×D₈×C₆₇	—	2	4	no	—
28	C₂×D₈×C₆₇	—	2	2	no	—
29	C₂×D₈×C₆₇	—	2	4	no	—
30	C₂×D₈×C₆₇	—	4	2	no	—
31	C₂×D₈×C₆₇	—	4	2	no	—
32	C₂×D₈×C₆₇	C₂×C₄	1	4	yes	—
33	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
34	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
35	#127×C₆₇	—	2	4	no	—
36	#127×C₆₇	—	4	2	no	—
37	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
38	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
39	C₄×C₈×C₆₇	D₄	1	2	yes	—
40	C₂²×Dic₆₇	—	4	2	no	—
41	C₄⋊Dic₆₇	—	4	2	no	—
42	C₄⋊Dic₆₇	—	4	2	no	—
43	C₆₇⋊C₁₆	—	2	4	no	—
44	C₂⁴×C₆₇	—	4	2	no	—
45	C₂×D₄×C₆₇	—	2	4	no	—
46	C₂×D₄×C₆₇	—	4	8	no	—
47	C₂×D₄×C₆₇	—	4	2	no	—
48	C₂×D₄×C₆₇	—	4	2	no	—
49	C₂×D₄×C₆₇	—	4	2	no	—
50	C₂×D₄×C₆₇	—	4	2	no	—
51	C₂×D₄×C₆₇	—	4	2	no	—
52	C₂×D₄×C₆₇	—	8	8	no	—
53	C₂²×C₄×C₆₇	D₈	1	2	yes	—
54	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
55	D₈×C₆₇	—	2	8	no	—
56	D₈×C₆₇	—	4	8	no	—
57	D₈×C₆₇	—	4	4	no	—
58	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
59	C₂×C₈×C₆₇	D₈	1	2	yes	—
60	C₂×C₈×C₆₇	SD₁₆	1	2	yes	—
61	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
62	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
63	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
64	C₂×C₈×C₆₇	#41	1	2	yes	—
65	C₄²×C₆₇	C₂²⋊C₄	1	2	yes	—
66	C₄²×C₆₇	SD₁₆	1	2	yes	—
67	C₂³×C₆₇	—	4	4	no	—
68	C₂³×C₆₇	—	8	2	no	—
69	C₂³×C₆₇	—	8	2	no	—
70	C₂³×C₆₇	—	8	8	no	—
71	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
72	D₄×C₆₇	—	4	4	no	—
73	D₄×C₆₇	—	4	4	no	—
74	D₄×C₆₇	—	8	16	no	—
75	D₄×C₆₇	—	8	2	no	—
76	D₄×C₆₇	—	8	2	no	—
77	C₂×C₄×C₆₇	—	2	4	no	—
78	C₂×C₄×C₆₇	#102	1	4	yes	—
79	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
81	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
82	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
84	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
85	C₂×Dic₆₇	—	8	2	no	—
86	C₂×Dic₆₇	—	8	4	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	—	8	8	no	—
91	C₂²×C₆₇	—	8	4	no	—
92	C₂²×C₆₇	—	16	4	no	—
93	C₂²×C₆₇	—	16	4	no	—
94	C₂²×C₆₇	C₂×#102	1	1	yes	characteristic
95	C₂²×C₆₇	#486	1	1	yes	characteristic
96	C₂²×C₆₇	#493	1	1	yes	characteristic
97	C₂²×C₆₇	#509	1	4	yes	—
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	—	16	4	no	—
106	C₂×C₆₇	#1957	1	1	yes	characteristic
107	C₂×C₆₇	#2140	1	2	yes	—
108	C₂×C₆₇	#2244	1	2	yes	—
109	C₂×C₆₇	#2250	1	2	yes	—
110	C₂×#493	D₆₇	1	1	yes	characteristic
111	C₂×#357	—	67	4	no	—
112	C₂×#346	—	67	1	no	—
113	#1846	—	67	1	no	—
114	C₆₇	#13206	1	1	yes	characteristic, complemented, Sylow
115	C₂²×D₈	—	2	1	no	—
116	C₂²×D₈	C₂×D₆₇	1	2	yes	—
117	C₂×#127	—	2	1	no	—
118	C₂²×C₁₆	—	67	2	no	—
119	#493	—	2	2	no	—
120	#493	Dic₆₇	1	4	yes	complemented
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	—	134	2	no	—
127	C₂²×D₄	—	2	2	no	—
128	C₂²×D₄	—	4	2	no	—
129	C₂×D₈	—	2	4	no	—
130	C₂×D₈	—	2	4	no	—
131	C₂×D₈	—	2	2	no	—
132	C₂×D₈	—	2	4	no	—
133	C₂×D₈	—	4	2	no	—
134	C₂×D₈	—	4	2	no	—
135	C₂×D₈	C₂×Dic₆₇	1	4	yes	—
136	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
137	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
138	#127	—	2	4	no	—
139	#127	—	4	2	no	—
140	C₂×C₄⋊C₄	—	134	2	no	—
141	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
142	C₂×C₁₆	—	67	4	no	—
143	C₂×C₁₆	—	134	2	no	—
144	C₂×C₁₆	—	134	2	no	—
145	#107	—	134	4	no	—
146	#106	—	268	2	no	—
147	C₄×C₈	C₂×Dic₆₇	1	2	yes	—
148	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
149	#95	—	268	2	no	—
150	C₂⁴	—	4	2	no	—
151	C₂×D₄	—	2	4	no	—
152	C₂×D₄	—	4	8	no	—
153	C₂×D₄	—	4	2	no	—
154	C₂×D₄	—	4	2	no	—
155	C₂×D₄	—	4	2	no	—
156	C₂×D₄	—	4	2	no	—
157	C₂×D₄	—	4	2	no	—
158	C₂×D₄	—	8	8	no	—
159	C₂²×C₄	—	268	2	no	—
160	C₂²×C₄	#11761613	1	2	yes	—
161	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
162	D₈	—	2	8	no	—
163	D₈	—	4	8	no	—
164	D₈	—	4	4	no	—
165	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
166	C₂×C₈	#11761613	1	2	yes	—
167	C₂×C₈	#11761616	1	2	yes	—
168	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
169	C₂×C₈	D₄×D₆₇	1	2	yes	—
170	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
171	C₂×C₈	#11761627	1	2	yes	—
172	C₄⋊C₄	—	268	2	no	—
173	C₄⋊C₄	—	268	2	no	—
174	C₄²	C₂²⋊Dic₆₇	1	2	yes	—
175	C₄²	#11761616	1	2	yes	—
176	C₁₆	—	134	4	no	—
177	C₂³	—	4	4	no	—
178	C₂³	—	8	2	no	—
179	C₂³	—	8	8	no	—
180	C₂³	—	8	2	no	—
181	C₂³	C₂×#11761613	1	1	yes	characteristic
182	D₄	—	4	4	no	—
183	D₄	—	4	4	no	—
184	D₄	—	8	16	no	—
185	D₄	—	8	2	no	—
186	D₄	—	8	2	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	536	2	no	—
189	C₂×C₄	—	536	4	no	—
190	C₂×C₄	#14523964	1	4	yes	—
191	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
192	C₂×C₄	#14524030	1	1	yes	characteristic
193	C₂×C₄	#14524039	1	1	yes	characteristic
194	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
195	C₂×C₄	C₂×#11761616	1	1	yes	characteristic
196	C₂×C₄	C₂×#11761616	1	1	yes	characteristic
197	C₈	#14523964	1	4	yes	—
198	C₈	D₄×Dic₆₇	1	2	yes	—
199	C₈	#14524014	1	2	yes	—
200	C₂²	—	8	8	no	—
201	C₂²	—	8	4	no	—
202	C₂²	—	16	4	no	—
203	C₂²	—	16	4	no	—
204	C₂²	C₂×#14523964	1	1	yes	characteristic
205	C₂²	#16863742	1	1	yes	characteristic
206	C₂²	#16863772	1	1	yes	characteristic
207	C₂²	#16863832	1	4	yes	—
208	C₄	—	2	4	no	—
209	C₄	—	1072	2	no	—
210	C₄	#16863299	1	1	yes	characteristic
211	C₄	C₂×#14523964	1	1	yes	characteristic
212	C₄	#16863742	1	1	yes	characteristic
213	C₄	#16863768	1	1	yes	characteristic
214	C₂	—	16	4	no	—
215	C₂	#22561016	1	1	yes	characteristic
216	C₂	#22561925	1	2	yes	—
217	C₂	#22562450	1	2	yes	—
218	C₂	#22562473	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16863197

C₂

yes

maximal, complemented

C₂×#16863172

C₂

yes

maximal, characteristic, complemented

#22560373

C₂

yes

maximal, characteristic, complemented

C₂×#493×C₆₇

C₂

yes

maximal, characteristic

C₂²×C₆₇⋊C₁₆

C₂²

yes

—

C₂×#14523977

C₂²

yes

—

—

—

—

—

C₂²×D₈×C₆₇

—

C₂²×D₈×C₆₇

C₂²

yes

—

C₂×#127×C₆₇

—

#493×C₆₇

—

#493×C₆₇

C₄

yes

complemented

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

C₂×C₄⋊Dic₆₇

—

C₂×C₆₇⋊C₁₆

—

C₂×C₆₇⋊C₁₆

—

C₂×C₆₇⋊C₁₆

D₄

yes

complemented

#14523977

—

#14523975

—

C₆₇⋊#95

—

C₂²×D₄×C₆₇

—

C₂²×D₄×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

—

C₂×D₈×C₆₇

C₂×C₄

yes

—

C₂²×C₈×C₆₇

D₄

yes

characteristic

C₂²×C₈×C₆₇

C₂³

yes

characteristic

#127×C₆₇

—

#127×C₆₇

—

C₂×C₄²×C₆₇

D₄

yes

characteristic

C₄×C₈×C₆₇

C₂×C₄

yes

—

C₄×C₈×C₆₇

D₄

yes

—

C₂²×Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₆₇⋊C₁₆

—

C₂⁴×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂×D₄×C₆₇

—

C₂²×C₄×C₆₇

D₈

yes

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

D₈×C₆₇

—

D₈×C₆₇

—

D₈×C₆₇

—

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

—

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

#41

yes

—

C₄²×C₆₇

C₂²⋊C₄

yes

—

C₄²×C₆₇

SD₁₆

yes

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

C₂×D₈

yes

characteristic

D₄×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

D₄×C₆₇

—

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

—

C₈×C₆₇

#102

yes

—

C₈×C₆₇

C₄×D₄

yes

—

C₈×C₆₇

#121

yes

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

—

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

—

106

C₂×C₆₇

#1957

yes

characteristic

107

C₂×C₆₇

#2140

yes

—

108

C₂×C₆₇

#2244

yes

—

109

C₂×C₆₇

#2250

yes

—

110

C₂×#493

D₆₇

yes

characteristic

111

C₂×#357

—

112

C₂×#346

—

113

#1846

—

114

C₆₇

#13206

yes

characteristic, complemented, Sylow

115

C₂²×D₈

—

116

C₂²×D₈

C₂×D₆₇

yes

—

117

C₂×#127

—

118

C₂²×C₁₆

—

119

#493

—

120

#493

Dic₆₇

yes

complemented

121

C₂×#107

—

122

C₂×#106

—

134

—

123

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

124

#382

—

134

—

125

#357

—

134

—

126

#346

—

134

—

127

C₂²×D₄

—

128

C₂²×D₄

—

129

C₂×D₈

—

130

C₂×D₈

—

131

C₂×D₈

—

132

C₂×D₈

—

133

C₂×D₈

—

134

C₂×D₈

—

135

C₂×D₈

C₂×Dic₆₇

yes

—

136

C₂²×C₈

C₂²⋊D₆₇

yes

characteristic

137

C₂²×C₈

C₂²×D₆₇

yes

characteristic

138

#127

—

139

#127

—

140

C₂×C₄⋊C₄

—

134

—

141

C₂×C₄²

C₂²⋊D₆₇

yes

characteristic

142

C₂×C₁₆

—

143

C₂×C₁₆

—

134

—

144

C₂×C₁₆

—

134

—

145

#107

—

134

—

146

#106

—

268

—

147

C₄×C₈

C₂×Dic₆₇

yes

—

148

C₄×C₈

C₂²⋊D₆₇

yes

—

149

#95

—

268

—

150

C₂⁴

—

151

C₂×D₄

—

152

C₂×D₄

—

153

C₂×D₄

—

154

C₂×D₄

—

155

C₂×D₄

—

156

C₂×D₄

—

157

C₂×D₄

—

158

C₂×D₄

—

159

C₂²×C₄

—

268

—

160

C₂²×C₄

#11761613

yes

—

161

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

162

D₈

—

163

D₈

—

164

D₈

—

165

C₂×C₈

C₂²⋊Dic₆₇

yes

—

166

C₂×C₈

#11761613

yes

—

167

C₂×C₈

#11761616

yes

—

168

C₂×C₈

C₂²×Dic₆₇

yes

characteristic

169

C₂×C₈

D₄×D₆₇

yes

—

170

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

171

C₂×C₈

#11761627

yes

—

172

C₄⋊C₄

—

268

—

173

C₄⋊C₄

—

268

—

174

C₄²

C₂²⋊Dic₆₇

yes

—

175

C₄²

#11761616

yes

—

176

C₁₆

—

134

—

177

C₂³

—

178

C₂³

—

179

C₂³

—

180

C₂³

—

181

C₂³

C₂×#11761613

yes

characteristic

182

D₄

—

183

D₄

—

184

D₄

—

185

D₄

—

186

D₄

—

187

C₂×C₄

—

188

C₂×C₄

—

536

—

189

C₂×C₄

—

536

—

190

C₂×C₄

#14523964

yes

—

191

C₂×C₄

C₂×C₂²⋊Dic₆₇

yes

characteristic

192

C₂×C₄

#14524030

yes

characteristic

193

C₂×C₄

#14524039

yes

characteristic

194

C₂×C₄

C₂×#11761613

yes

characteristic

195

C₂×C₄

C₂×#11761616

yes

characteristic

196

C₂×C₄

C₂×#11761616

yes

characteristic

197

C₈

#14523964

yes

—

198

C₈

D₄×Dic₆₇

yes

—

199

C₈

#14524014

yes

—

200

C₂²

—

201

C₂²

—

202

C₂²

—

203

C₂²

—

204

C₂²

C₂×#14523964

yes

characteristic

205

C₂²

#16863742

yes

characteristic

206

C₂²

#16863772

yes

characteristic

207

C₂²

#16863832

yes

—

208

C₄

—

209

C₄

—

1072

—

210

C₄

#16863299

yes

characteristic

211

C₄

C₂×#14523964

yes

characteristic

212

C₄

#16863742

yes

characteristic

213

C₄

#16863768

yes

characteristic

214

C₂

—

215

C₂

#22561016

yes

characteristic

216

C₂

#22561925

yes

—

217

C₂

#22562450

yes

—

218

C₂

#22562473

yes

—

	subgroup	G/H
center	C₂³	C₂×#11761613
commutator	C₂×C₈×C₆₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting, prime radical	C₂×#493×C₆₇	C₂
socle	C₂³×C₆₇	C₂×D₈
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	C₂×#493	D₆₇
hypocenter	C₆₇	#13206
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#493

subgroup

G/H

center

C₂³

C₂×#11761613

commutator

C₂×C₈×C₆₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting, prime radical

C₂×#493×C₆₇

C₂

socle

C₂³×C₆₇

C₂×D₈

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×#493

N	H ≅ G/N	type
1. C₂×#16863197	C₂	semidirect
2. C₂×#16863172	C₂	semidirect
3. #22560373	C₂	semidirect
15. #493×C₆₇	C₄	semidirect
20. C₂×C₆₇⋊C₁₆	D₄	semidirect
114. C₆₇	#13206	semidirect
120. #493	Dic₆₇	semidirect

H ≅ G/N

type

1. C₂×#16863197

C₂

semidirect

2. C₂×#16863172

C₂

semidirect

3. #22560373

C₂

semidirect

15. #493×C₆₇

C₄

semidirect

20. C₂×C₆₇⋊C₁₆

D₄

semidirect

114. C₆₇

#13206

semidirect

120. #493

Dic₆₇

semidirect

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

subgroup	index
C₂×#16863197	2
C₂×#16863172	2
#22560373	2
C₂×#493×C₆₇	2
#13206	67

subgroup

index

C₂×#493×C₆₇

Subgroups — #30774064

Conjugacy classes of subgroups

Complements

Maximal subgroups