Group #30767400 — subgroups

Subgroups — #30767400

Order 17152.

270 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 115 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	#22561963	C₂	1	2	yes	maximal
2	C₈²×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#22558279	C₂	1	1	yes	maximal, characteristic, complemented
4	#22558278	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1370	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14523982	—	2	2	no	—
7	C₄×C₈×D₆₇	C₄	1	1	yes	characteristic
8	C₄×C₈×D₆₇	C₄	1	1	yes	characteristic
9	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
10	C₄⋊(C₆₇⋊C₁₆)	C₂²	1	2	yes	—
11	Dic₆₇⋊C₁₆	—	2	2	no	—
12	C₈×C₆₇⋊C₈	C₄	1	1	yes	characteristic
13	C₈×C₆₇⋊C₈	C₄	1	1	yes	characteristic
14	C₈×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	—
16	C₈²×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×C₈×D₆₇	—	2	1	no	—
18	C₂×C₈×D₆₇	C₈	1	1	yes	characteristic
19	C₂×C₈×D₆₇	C₈	1	1	yes	characteristic
20	C₂×C₈×D₆₇	D₄	1	1	yes	characteristic
21	C₂×C₈×D₆₇	Q₈	1	1	yes	characteristic
22	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
23	#14523982	—	4	4	no	—
24	C₂×C₆₇⋊C₁₆	—	2	2	no	—
25	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
26	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₈×Dic₆₇	—	2	1	no	—
29	C₈×Dic₆₇	C₈	1	1	yes	characteristic
30	C₈×Dic₆₇	C₈	1	1	yes	characteristic
31	C₈×Dic₆₇	D₄	1	1	yes	characteristic
32	C₈×Dic₆₇	Q₈	1	1	yes	characteristic
33	C₂×C₁₆×C₆₇	—	2	2	no	—
34	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
37	C₂×C₄×D₆₇	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₄×D₆₇	C₂×C₈	1	1	yes	characteristic
39	C₂×C₄×D₆₇	M₁₆	1	1	yes	characteristic
40	C₂×C₆₇⋊C₈	—	2	1	no	—
41	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
42	C₂×C₆₇⋊C₈	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₆₇⋊C₈	C₂×C₈	1	1	yes	characteristic
44	C₂×C₆₇⋊C₈	C₂×C₈	1	1	yes	characteristic
45	C₈×D₆₇	—	2	4	no	—
46	C₈×D₆₇	—	2	2	no	—
47	C₈×D₆₇	—	2	2	no	—
48	C₈×D₆₇	—	2	2	no	—
49	C₈×D₆₇	D₈	1	2	yes	—
50	C₈×D₆₇	Q₁₆	1	2	yes	—
51	C₄×Dic₆₇	C₄⋊C₄	1	1	yes	characteristic
52	C₄×Dic₆₇	C₂×C₈	1	1	yes	characteristic
53	C₄×Dic₆₇	M₁₆	1	1	yes	characteristic
54	C₆₇⋊C₁₆	—	4	2	no	—
55	C₂×C₈×C₆₇	—	2	1	no	—
56	C₂×C₈×C₆₇	C₂×C₈	1	1	yes	characteristic
57	C₂×C₈×C₆₇	C₂×C₈	1	1	yes	characteristic
58	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
59	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
60	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
61	C₁₆×C₆₇	—	4	2	no	—
62	C₂²×D₆₇	C₄⋊C₈	1	1	yes	characteristic
63	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
64	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
65	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
66	C₂×Dic₆₇	C₄⋊C₈	1	1	yes	characteristic
67	C₂×Dic₆₇	C₄⋊C₈	1	1	yes	characteristic
68	C₂×Dic₆₇	C₄⋊C₈	1	1	yes	characteristic
69	C₄×D₆₇	—	2	1	no	—
70	C₄×D₆₇	—	2	1	no	—
71	C₄×D₆₇	—	2	2	no	—
72	C₄×D₆₇	#107	1	2	yes	—
73	C₄×D₆₇	#108	1	2	yes	—
74	C₈×C₆₇	—	2	2	no	—
75	C₈×C₆₇	—	2	1	no	—
76	C₈×C₆₇	—	2	1	no	—
77	C₈×C₆₇	M₃₂	1	2	yes	complemented
78	C₈×C₆₇	C₂×D₈	1	1	yes	characteristic
79	C₈×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
80	C₆₇⋊C₈	—	2	2	no	—
81	C₆₇⋊C₈	—	2	1	no	—
82	C₆₇⋊C₈	—	2	1	no	—
83	C₆₇⋊C₈	#107	1	2	yes	—
84	C₆₇⋊C₈	M₃₂	1	2	yes	complemented
85	C₂²×C₆₇	C₂×C₄⋊C₈	1	1	yes	characteristic
86	C₂×D₆₇	—	2	1	no	—
87	C₂×D₆₇	—	2	1	no	—
88	C₂×D₆₇	#335	1	2	yes	—
89	C₄×C₆₇	—	2	1	no	—
90	C₄×C₆₇	C₂×#107	1	1	yes	characteristic
91	C₄×C₆₇	C₂×#108	1	1	yes	characteristic
92	C₄×C₆₇	C₂×M₃₂	1	1	yes	characteristic
93	C₄×C₆₇	C₂×M₃₂	1	1	yes	characteristic
94	Dic₆₇	—	2	1	no	—
95	Dic₆₇	#335	1	2	yes	—
96	Dic₆₇	#364	1	2	yes	—
97	#12004	—	67	1	no	maximal, Sylow
98	C₂×C₆₇	C₂×#335	1	1	yes	characteristic
99	C₂×C₆₇	#2150	1	1	yes	characteristic
100	C₂×C₆₇	C₂×#364	1	1	yes	characteristic
101	D₆₇	—	2	2	no	—
102	#2150	—	67	2	no	—
103	C₂×C₈²	—	67	1	no	—
104	#1370	—	67	2	no	—
105	#1370	—	67	1	no	—
106	#1370	D₆₇	1	1	yes	characteristic, complemented
107	C₆₇	#12004	1	1	yes	characteristic, complemented, Sylow
108	C₂×M₃₂	—	134	2	no	—
109	C₂×C₄×C₈	—	67	1	no	—
110	C₂×C₄×C₈	—	67	1	no	—
111	C₂×C₄×C₈	—	67	1	no	—
112	C₄⋊C₁₆	—	67	2	no	—
113	C₄⋊C₁₆	—	134	2	no	—
114	C₄⋊C₁₆	C₂×D₆₇	1	2	yes	—
115	C₈²	—	67	1	no	—
116	C₈²	—	67	1	no	—
117	C₈²	—	67	1	no	—
118	C₈²	C₂×D₆₇	1	1	yes	characteristic
119	C₂²×C₈	—	67	1	no	—
120	C₂²×C₈	—	67	1	no	—
121	C₂²×C₈	—	67	1	no	—
122	C₂²×C₈	—	67	1	no	—
123	C₂²×C₈	—	134	1	no	—
124	C₂×C₄²	—	67	1	no	—
125	M₃₂	—	268	4	no	—
126	C₂×C₁₆	—	2	2	no	—
127	C₂×C₁₆	—	134	2	no	—
128	C₄×C₈	—	67	1	no	—
129	C₄×C₈	—	67	1	no	—
130	C₄×C₈	—	67	1	no	—
131	C₄×C₈	—	67	1	no	—
132	C₄×C₈	—	67	1	no	—
133	C₄×C₈	—	67	1	no	—
134	C₄×C₈	—	67	1	no	—
135	C₄×C₈	—	134	1	no	—
136	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
137	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
138	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
139	C₂²×C₄	—	67	1	no	—
140	C₂²×C₄	—	67	1	no	—
141	C₂²×C₄	—	67	1	no	—
142	C₂×C₈	—	2	1	no	—
143	C₂×C₈	—	67	1	no	—
144	C₂×C₈	—	67	1	no	—
145	C₂×C₈	—	67	2	no	—
146	C₂×C₈	—	67	2	no	—
147	C₂×C₈	—	67	1	no	—
148	C₂×C₈	—	67	1	no	—
149	C₂×C₈	—	134	2	no	—
150	C₂×C₈	—	134	2	no	—
151	C₂×C₈	—	134	4	no	—
152	C₂×C₈	—	134	1	no	—
153	C₂×C₈	—	134	2	no	—
154	C₂×C₈	C₈×D₆₇	1	1	yes	characteristic
155	C₂×C₈	C₈×D₆₇	1	1	yes	characteristic
156	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
157	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
158	C₄²	—	67	1	no	—
159	C₄²	—	67	1	no	—
160	C₄²	—	67	1	no	—
161	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
162	C₁₆	—	4	2	no	—
163	C₁₆	—	268	2	no	—
164	C₂³	—	67	1	no	—
165	C₂×C₄	—	67	1	no	—
166	C₂×C₄	—	67	1	no	—
167	C₂×C₄	—	67	2	no	—
168	C₂×C₄	—	67	2	no	—
169	C₂×C₄	—	67	1	no	—
170	C₂×C₄	—	134	2	no	—
171	C₂×C₄	—	134	1	no	—
172	C₂×C₄	—	134	1	no	—
173	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
174	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
175	C₂×C₄	M₁₆×D₆₇	1	1	yes	characteristic
176	C₈	—	2	2	no	—
177	C₈	—	2	1	no	—
178	C₈	—	2	1	no	—
179	C₈	—	67	2	no	—
180	C₈	—	67	2	no	—
181	C₈	—	134	2	no	—
182	C₈	—	134	1	no	—
183	C₈	—	134	1	no	—
184	C₈	#14523982	1	2	yes	complemented
185	C₈	D₈×D₆₇	1	1	yes	characteristic
186	C₈	Q₁₆×D₆₇	1	1	yes	characteristic
187	C₂²	—	67	2	no	—
188	C₂²	—	134	1	no	—
189	C₂²	—	134	1	no	—
190	C₂²	C₄⋊C₈×D₆₇	1	1	yes	characteristic
191	C₄	—	2	1	no	—
192	C₄	—	67	2	no	—
193	C₄	—	67	2	no	—
194	C₄	—	134	1	no	—
195	C₄	#107×D₆₇	1	1	yes	characteristic
196	C₄	#108×D₆₇	1	1	yes	characteristic
197	C₄	M₃₂×D₆₇	1	1	yes	characteristic
198	C₄	C₂×#14523982	1	1	yes	characteristic
199	C₂	—	134	2	no	—
200	C₂	#335×D₆₇	1	1	yes	characteristic
201	C₂	#22561963	1	1	yes	characteristic
202	C₂	#364×D₆₇	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22561963

C₂

yes

maximal

C₈²×D₆₇

C₂

yes

maximal, characteristic

#22558279

C₂

yes

maximal, characteristic, complemented

#22558278

C₂

yes

maximal, complemented

C₆₇×#1370

C₂

yes

maximal, characteristic, complemented

C₂×#14523982

—

C₄×C₈×D₆₇

C₄

yes

characteristic

C₄×C₈×D₆₇

C₄

yes

characteristic

C₄×C₈×D₆₇

C₂²

yes

characteristic

C₄⋊(C₆₇⋊C₁₆)

C₂²

yes

—

Dic₆₇⋊C₁₆

—

C₈×C₆₇⋊C₈

C₄

yes

characteristic

C₈×C₆₇⋊C₈

C₄

yes

characteristic

C₈×C₆₇⋊C₈

C₂²

yes

characteristic

C₄⋊C₁₆×C₆₇

C₂²

yes

—

C₈²×C₆₇

C₂²

yes

characteristic

C₂×C₈×D₆₇

—

C₂×C₈×D₆₇

C₈

yes

characteristic

C₂×C₈×D₆₇

C₈

yes

characteristic

C₂×C₈×D₆₇

D₄

yes

characteristic

C₂×C₈×D₆₇

Q₈

yes

characteristic

C₄²×D₆₇

C₂×C₄

yes

characteristic

#14523982

—

C₂×C₆₇⋊C₁₆

—

C₄×C₆₇⋊C₈

C₂×C₄

yes

characteristic

C₄×C₆₇⋊C₈

C₂×C₄

yes

characteristic

C₄×C₆₇⋊C₈

C₂×C₄

yes

characteristic

C₈×Dic₆₇

—

C₈×Dic₆₇

C₈

yes

characteristic

C₈×Dic₆₇

C₈

yes

characteristic

C₈×Dic₆₇

D₄

yes

characteristic

C₈×Dic₆₇

Q₈

yes

characteristic

C₂×C₁₆×C₆₇

—

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

C₂³

yes

characteristic

C₂×C₄×D₆₇

C₄⋊C₄

yes

characteristic

C₂×C₄×D₆₇

C₂×C₈

yes

characteristic

C₂×C₄×D₆₇

M₁₆

yes

characteristic

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₆₇⋊C₈

C₄⋊C₄

yes

characteristic

C₂×C₆₇⋊C₈

C₂×C₈

yes

characteristic

C₂×C₆₇⋊C₈

C₂×C₈

yes

characteristic

C₈×D₆₇

—

C₈×D₆₇

—

C₈×D₆₇

—

C₈×D₆₇

—

C₈×D₆₇

D₈

yes

—

C₈×D₆₇

Q₁₆

yes

—

C₄×Dic₆₇

C₄⋊C₄

yes

characteristic

C₄×Dic₆₇

C₂×C₈

yes

characteristic

C₄×Dic₆₇

M₁₆

yes

characteristic

C₆₇⋊C₁₆

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂×C₈

yes

characteristic

C₂×C₈×C₆₇

C₂×C₈

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂×Q₈

yes

characteristic

C₄²×C₆₇

C₂²×C₄

yes

characteristic

C₁₆×C₆₇

—

C₂²×D₆₇

C₄⋊C₈

yes

characteristic

C₂×C₄×C₆₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₂²×C₈

yes

characteristic

C₂×C₄×C₆₇

C₂×M₁₆

yes

characteristic

C₂×Dic₆₇

C₄⋊C₈

yes

characteristic

C₂×Dic₆₇

C₄⋊C₈

yes

characteristic

C₂×Dic₆₇

C₄⋊C₈

yes

characteristic

C₄×D₆₇

—

C₄×D₆₇

—

C₄×D₆₇

—

C₄×D₆₇

#107

yes

—

C₄×D₆₇

#108

yes

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

M₃₂

yes

complemented

C₈×C₆₇

C₂×D₈

yes

characteristic

C₈×C₆₇

C₂×Q₁₆

yes

characteristic

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₆₇⋊C₈

#107

yes

—

C₆₇⋊C₈

M₃₂

yes

complemented

C₂²×C₆₇

C₂×C₄⋊C₈

yes

characteristic

C₂×D₆₇

—

C₂×D₆₇

—

C₂×D₆₇

#335

yes

—

C₄×C₆₇

—

C₄×C₆₇

yes

C₄×C₆₇

yes

C₄×C₆₇

C₂×M₃₂

yes

characteristic

C₄×C₆₇

C₂×M₃₂

yes

characteristic

Dic₆₇

—

Dic₆₇

#335

yes

—

Dic₆₇

#364

yes

—

—

C₂×C₆₇

yes

C₂×C₆₇

yes

100

C₂×C₆₇

C₂×#364

yes

characteristic

101

D₆₇

—

102

#2150

—

103

C₂×C₈²

—

104

#1370

—

105

#1370

—

106

#1370

D₆₇

yes

characteristic, complemented

107

C₆₇

#12004

yes

characteristic, complemented, Sylow

108

C₂×M₃₂

—

134

—

109

C₂×C₄×C₈

—

110

C₂×C₄×C₈

—

111

C₂×C₄×C₈

—

112

C₄⋊C₁₆

—

113

C₄⋊C₁₆

—

134

—

114

C₄⋊C₁₆

C₂×D₆₇

yes

—

115

C₈²

—

116

C₈²

—

117

C₈²

—

118

C₈²

C₂×D₆₇

yes

characteristic

119

C₂²×C₈

—

120

C₂²×C₈

—

121

C₂²×C₈

—

122

C₂²×C₈

—

123

C₂²×C₈

—

134

—

124

C₂×C₄²

—

125

M₃₂

—

268

—

126

C₂×C₁₆

—

127

C₂×C₁₆

—

134

—

128

C₄×C₈

—

129

C₄×C₈

—

130

C₄×C₈

—

131

C₄×C₈

—

132

C₄×C₈

—

133

C₄×C₈

—

134

C₄×C₈

—

135

C₄×C₈

—

134

—

136

C₄×C₈

C₄×D₆₇

yes

characteristic

137

C₄×C₈

C₄×D₆₇

yes

characteristic

138

C₄×C₈

C₂²×D₆₇

yes

characteristic

139

C₂²×C₄

—

140

C₂²×C₄

—

141

C₂²×C₄

—

142

C₂×C₈

—

143

C₂×C₈

—

144

C₂×C₈

—

145

C₂×C₈

—

146

C₂×C₈

—

147

C₂×C₈

—

148

C₂×C₈

—

149

C₂×C₈

—

134

—

150

C₂×C₈

—

134

—

151

C₂×C₈

—

134

—

152

C₂×C₈

—

134

—

153

C₂×C₈

—

134

—

154

C₂×C₈

C₈×D₆₇

yes

characteristic

155

C₂×C₈

C₈×D₆₇

yes

characteristic

156

C₂×C₈

D₄×D₆₇

yes

characteristic

157

C₂×C₈

Q₈×D₆₇

yes

characteristic

158

C₄²

—

159

C₄²

—

160

C₄²

—

161

C₄²

C₂×C₄×D₆₇

yes

characteristic

162

C₁₆

—

163

C₁₆

—

268

—

164

C₂³

—

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

C₄⋊C₄×D₆₇

yes

characteristic

174

C₂×C₄

C₂×C₈×D₆₇

yes

characteristic

175

C₂×C₄

M₁₆×D₆₇

yes

characteristic

176

C₈

—

177

C₈

—

178

C₈

—

179

C₈

—

180

C₈

—

181

C₈

—

134

—

182

C₈

—

134

—

183

C₈

—

134

—

184

C₈

#14523982

yes

complemented

185

C₈

D₈×D₆₇

yes

characteristic

186

C₈

Q₁₆×D₆₇

yes

characteristic

187

C₂²

—

188

C₂²

—

134

—

189

C₂²

—

134

—

190

C₂²

C₄⋊C₈×D₆₇

yes

characteristic

191

C₄

—

192

C₄

—

193

C₄

—

194

C₄

—

134

—

195

C₄

#107×D₆₇

yes

characteristic

196

C₄

#108×D₆₇

yes

characteristic

197

C₄

M₃₂×D₆₇

yes

characteristic

198

C₄

C₂×#14523982

yes

characteristic

199

C₂

—

134

—

200

C₂

#335×D₆₇

yes

characteristic

201

C₂

#22561963

yes

characteristic

202

C₂

#364×D₆₇

yes

characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂²×C₈
Frattini	C₄×C₈	C₂²×D₆₇
Fitting	C₆₇×#1370	C₂
socle	C₂²×C₆₇	C₂×C₄⋊C₈
prime radical	C₂²×D₆₇	C₄⋊C₈
cosocle	C₄×C₈×C₆₇	C₂³
hypercenter	#1370	D₆₇
hypocenter	C₆₇	#12004
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

subgroup

G/H

center

C₂×C₈

D₄×D₆₇

commutator

C₂×C₄×C₆₇

C₂²×C₈

Frattini

C₄×C₈

C₂²×D₆₇

Fitting

C₆₇×#1370

C₂

socle

C₂²×C₆₇

C₂×C₄⋊C₈

prime radical

C₂²×D₆₇

C₄⋊C₈

cosocle

C₄×C₈×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #1370

N	H ≅ G/N	type
3. #22558279	C₂	semidirect
4. #22558278	C₂	semidirect
5. C₆₇×#1370	C₂	semidirect
77. C₈×C₆₇	M₃₂	semidirect
84. C₆₇⋊C₈	M₃₂	semidirect
106. #1370	D₆₇	semidirect
107. C₆₇	#12004	semidirect
184. C₈	#14523982	semidirect

H ≅ G/N

type

3. #22558279

C₂

semidirect

4. #22558278

C₂

semidirect

5. C₆₇×#1370

C₂

semidirect

77. C₈×C₆₇

M₃₂

semidirect

84. C₆₇⋊C₈

M₃₂

semidirect

106. #1370

D₆₇

semidirect

107. C₆₇

#12004

semidirect

184. C₈

#14523982

semidirect

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

subgroup	index
#22561963	2
C₈²×D₆₇	2
#22558279	2
#22558278	2
C₆₇×#1370	2
#12004	67

subgroup

index

C₈²×D₆₇

C₆₇×#1370

Subgroups — #30767400

Conjugacy classes of subgroups

Complements

Maximal subgroups