Group #30869721 — subgroups

Subgroups — #30869721

Order 17152.

810 conjugacy classes of subgroups; only the 211 normal subgroups are shown.

normal subgroups only

This group has 810 conjugacy classes of subgroups — too many to draw. Only its 211 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	#22570637	C₂	1	1	yes	maximal, characteristic
2	#22568928	C₂	1	2	yes	maximal, complemented
3	#22561041	C₂	1	2	yes	maximal, complemented
4	#22560535	C₂	1	8	yes	maximal, complemented
5	#22560347	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1746	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#14524065	C₂²	1	4	yes	—
8	C₂×#14524049	C₂²	1	4	yes	—
9	#16863946	C₂²	1	2	yes	—
10	#16863780	C₄	1	4	yes	complemented
11	#16863776	C₄	1	1	yes	characteristic, complemented
12	#16863773	C₄	1	1	yes	characteristic, complemented
13	#16863769	C₄	1	2	yes	complemented
14	#16863469	—	2	8	no	—
15	#16863420	C₂²	1	2	yes	—
16	C₂×#14523971	C₂²	1	8	yes	—
17	#16863362	C₂²	1	4	yes	—
18	#16863161	C₂²	1	4	yes	—
19	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
21	#376×C₆₇	C₂²	1	1	yes	characteristic
22	#336×C₆₇	C₂²	1	4	yes	—
23	C₂×#11761628	C₂³	1	4	yes	—
24	#14524065	—	4	8	no	—
25	C₂×Dic₂₆₈	C₂×C₄	1	4	yes	—
26	C₂×#11761617	C₂×C₄	1	8	yes	—
27	C₂×D₅₃₆	C₂×C₄	1	4	yes	—
28	#14524049	—	4	8	no	—
29	C₂×#11761612	C₂³	1	4	yes	—
30	C₂×#11761611	—	2	4	no	—
31	C₂×C₈×D₆₇	—	2	4	no	—
32	#14524043	C₂×C₄	1	2	yes	—
33	#14524040	C₂×C₄	1	2	yes	—
34	#14524031	C₂×C₄	1	4	yes	—
35	#14524017	—	2	4	no	—
36	C₄×D₂₆₈	—	2	4	no	—
37	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
38	#14523971	—	4	8	no	—
39	(C₂×D₆₇)⋊C₈	—	2	8	no	—
40	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
41	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
42	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
43	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
44	#97×C₆₇	D₄	1	4	yes	—
45	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
46	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
47	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
48	#95×C₆₇	—	2	2	no	—
49	#11761628	—	2	8	no	—
50	#11761628	—	2	8	no	—
51	C₂×Dic₁₃₄	C₂²×C₄	1	4	yes	—
52	C₂×D₂₆₈	—	2	4	no	—
53	C₂×D₂₆₈	C₂²×C₄	1	4	yes	—
54	C₂×C₂²⋊D₆₇	—	2	4	no	—
55	C₂×C₄×D₆₇	—	2	4	no	—
56	Dic₂₆₈	—	4	4	no	—
57	#11761617	—	4	8	no	—
58	D₅₃₆	—	4	4	no	—
59	#11761612	—	2	8	no	—
60	#11761611	—	4	8	no	—
61	C₂×C₆₇⋊C₈	—	2	4	no	—
62	C₈×D₆₇	—	4	8	no	—
63	C₄⋊Dic₆₇	—	2	4	no	—
64	(C₂×D₆₇)⋊C₄	—	2	8	no	—
65	C₂²×C₄×C₆₇	—	2	2	no	—
66	C₂²×C₄×C₆₇	#41	1	2	yes	—
67	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
68	C₂×C₈×C₆₇	—	2	4	no	—
69	C₂×C₈×C₆₇	—	2	4	no	—
70	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
71	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
72	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
73	C₄²×C₆₇	—	2	4	no	—
74	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
75	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
76	C₄²×C₆₇	C₂×D₄	1	2	yes	—
77	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
78	C₂²×D₆₇	—	2	4	no	—
79	C₂×C₄×C₆₇	—	4	2	no	—
80	C₂×C₄×C₆₇	—	4	4	no	—
81	C₂×C₄×C₆₇	—	4	2	no	—
82	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
84	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
85	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
86	C₂×C₄×C₆₇	H(5,𝔽₂)	1	4	yes	—
87	C₂²⋊D₆₇	—	4	8	no	—
88	C₂×Dic₆₇	—	2	4	no	—
89	D₂₆₈	—	2	8	no	—
90	D₂₆₈	—	8	4	no	—
91	C₄×D₆₇	—	4	4	no	—
92	C₄×D₆₇	—	4	4	no	—
93	Dic₁₃₄	—	2	8	no	—
94	C₈×C₆₇	—	2	2	no	—
95	C₈×C₆₇	—	2	2	no	—
96	C₈×C₆₇	—	2	4	no	—
97	C₆₇⋊C₈	—	4	4	no	—
98	C₂²×C₆₇	—	2	2	no	—
99	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
100	C₂²×C₆₇	#540	1	2	yes	—
101	C₂×D₆₇	—	4	4	no	—
102	C₂×D₆₇	—	4	8	no	—
103	C₄×C₆₇	—	2	2	no	—
104	C₄×C₆₇	—	2	2	no	—
105	C₄×C₆₇	—	8	2	no	—
106	C₄×C₆₇	#518	1	2	yes	—
107	C₄×C₆₇	#535	1	2	yes	—
108	Dic₆₇	—	4	4	no	—
109	#22282	—	67	1	no	maximal, Sylow
110	C₂×C₆₇	—	2	2	no	—
111	C₂×C₆₇	#2328	1	1	yes	characteristic
112	C₂×C₆₇	#2957	1	2	yes	—
113	D₆₇	—	8	4	no	—
114	#3147	—	67	1	no	—
115	#2932	—	67	2	no	—
116	#1963	—	67	2	no	—
117	#1876	—	67	8	no	—
118	#1837	—	67	1	no	—
119	#1746	D₆₇	1	1	yes	characteristic, complemented
120	C₆₇	#22282	1	1	yes	characteristic, complemented, Sylow
121	C₂×#135	—	67	4	no	—
122	C₂×#131	—	67	4	no	—
123	#532	—	67	2	no	—
124	#495	—	67	4	no	—
125	#494	—	67	1	no	—
126	#493	—	67	1	no	—
127	#492	—	67	2	no	—
128	#435	—	134	8	no	—
129	#423	—	67	2	no	—
130	C₂×#104	—	67	8	no	—
131	#408	—	67	4	no	—
132	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
133	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
134	#376	C₂×D₆₇	1	1	yes	characteristic
135	#341	—	67	4	no	—
136	#336	C₂×D₆₇	1	4	yes	—
137	C₂×#41	—	67	4	no	—
138	#135	—	268	8	no	—
139	C₂×Q₁₆	—	67	4	no	—
140	C₂×SD₁₆	—	67	8	no	—
141	C₂×D₈	—	67	4	no	—
142	#131	—	268	8	no	—
143	C₂×M₁₆	—	67	4	no	—
144	C₂×M₁₆	—	134	4	no	—
145	C₂²×C₈	—	134	4	no	—
146	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
147	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
148	C₄⋊Q₈	—	67	2	no	—
149	#127	—	67	2	no	—
150	#124	—	67	4	no	—
151	#121	—	134	4	no	—
152	C₄×D₄	—	134	4	no	—
153	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
154	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
155	C₄⋊C₈	—	134	4	no	—
156	#104	—	268	8	no	—
157	C₂²⋊C₈	—	134	8	no	—
158	#97	D₂₆₈	1	4	yes	—
159	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
160	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
161	C₄×C₈	C₄×D₆₇	1	2	yes	—
162	#95	—	2	2	no	—
163	#41	—	134	8	no	—
164	#41	—	134	8	no	—
165	C₂×Q₈	—	67	4	no	—
166	C₂×D₄	—	67	4	no	—
167	C₂×D₄	—	134	4	no	—
168	C₂×D₄	—	134	4	no	—
169	C₂²×C₄	—	2	2	no	—
170	C₂²×C₄	—	134	4	no	—
171	C₂²×C₄	#11761628	1	2	yes	—
172	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
173	Q₁₆	—	268	4	no	—
174	SD₁₆	—	268	8	no	—
175	D₈	—	268	4	no	—
176	M₁₆	—	268	8	no	—
177	M₁₆	—	134	8	no	—
178	C₂×C₈	—	2	4	no	—
179	C₂×C₈	—	2	4	no	—
180	C₂×C₈	—	268	8	no	—
181	C₂×C₈	—	134	4	no	—
182	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
183	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
184	C₂×C₈	C₂×D₂₆₈	1	4	yes	—
185	C₄⋊C₄	—	134	4	no	—
186	C₂²⋊C₄	—	134	8	no	—
187	C₄²	—	2	4	no	—
188	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
189	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
190	C₄²	C₂×D₂₆₈	1	2	yes	—
191	C₂³	—	134	4	no	—
192	C₂³	C₂×#11761628	1	1	yes	characteristic
193	Q₈	—	134	8	no	—
194	D₄	—	268	8	no	—
195	D₄	—	536	4	no	—
196	D₄	—	134	8	no	—
197	C₂×C₄	—	4	2	no	—
198	C₂×C₄	—	4	4	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	—	268	4	no	—
201	C₂×C₄	—	268	4	no	—
202	C₂×C₄	—	134	4	no	—
203	C₂×C₄	C₄×D₂₆₈	1	2	yes	—
204	C₂×C₄	C₄×D₂₆₈	1	2	yes	—
205	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
206	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
207	C₂×C₄	#14524089	1	4	yes	—
208	C₈	—	2	2	no	—
209	C₈	—	2	2	no	—
210	C₈	—	2	4	no	—
211	C₈	—	268	4	no	—
212	C₂²	—	2	2	no	—
213	C₂²	—	268	4	no	—
214	C₂²	—	268	8	no	—
215	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
216	C₂²	#16864001	1	2	yes	—
217	C₄	—	2	2	no	—
218	C₄	—	2	2	no	—
219	C₄	—	8	2	no	—
220	C₄	—	268	4	no	—
221	C₄	#16863870	1	2	yes	—
222	C₄	#16863965	1	2	yes	—
223	C₂	—	2	2	no	—
224	C₂	—	536	4	no	—
225	C₂	#22562934	1	1	yes	characteristic
226	C₂	#22569127	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22570637

C₂

yes

maximal, characteristic

#22568928

C₂

yes

maximal, complemented

#22561041

C₂

yes

maximal, complemented

#22560535

C₂

yes

maximal, complemented

#22560347

C₂

yes

maximal, characteristic, complemented

C₆₇×#1746

C₂

yes

maximal, characteristic, complemented

C₂×#14524065

C₂²

yes

—

C₂×#14524049

C₂²

yes

—

#16863946

C₂²

yes

—

#16863780

C₄

yes

complemented

#16863776

C₄

yes

characteristic, complemented

#16863773

C₄

yes

characteristic, complemented

#16863769

C₄

yes

complemented

#16863469

—

#16863420

C₂²

yes

—

C₂×#14523971

C₂²

yes

—

#16863362

C₂²

yes

—

#16863161

C₂²

yes

—

C₂×#97×C₆₇

C₂²

yes

characteristic

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

#376×C₆₇

C₂²

yes

characteristic

#336×C₆₇

C₂²

yes

—

C₂×#11761628

C₂³

yes

—

#14524065

—

C₂×Dic₂₆₈

C₂×C₄

yes

—

C₂×#11761617

C₂×C₄

yes

—

C₂×D₅₃₆

C₂×C₄

yes

—

#14524049

—

C₂×#11761612

C₂³

yes

—

C₂×#11761611

—

C₂×C₈×D₆₇

—

#14524043

C₂×C₄

yes

—

#14524040

C₂×C₄

yes

—

#14524031

C₂×C₄

yes

—

#14524017

—

C₄×D₂₆₈

—

C₄⋊(C₆₇⋊C₈)

—

#14523971

—

(C₂×D₆₇)⋊C₈

—

C₂²×C₈×C₆₇

C₂³

yes

—

C₂²×C₈×C₆₇

C₂³

yes

—

C₂×C₄²×C₆₇

C₂³

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

#97×C₆₇

D₄

yes

—

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

C₂×C₄

yes

characteristic

C₄×C₈×C₆₇

C₂×C₄

yes

—

#95×C₆₇

—

#11761628

—

#11761628

—

C₂×Dic₁₃₄

C₂²×C₄

yes

—

C₂×D₂₆₈

—

C₂×D₂₆₈

C₂²×C₄

yes

—

C₂×C₂²⋊D₆₇

—

C₂×C₄×D₆₇

—

Dic₂₆₈

—

#11761617

—

D₅₃₆

—

#11761612

—

#11761611

—

C₂×C₆₇⋊C₈

—

C₈×D₆₇

—

C₄⋊Dic₆₇

—

(C₂×D₆₇)⋊C₄

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

#41

yes

—

C₂²×C₄×C₆₇

C₂⁴

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²×C₄

yes

—

C₂×C₈×C₆₇

C₂²×C₄

yes

—

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₄²×C₆₇

—

C₄²×C₆₇

C₂²×C₄

yes

characteristic

C₄²×C₆₇

C₂²×C₄

yes

characteristic

C₄²×C₆₇

C₂×D₄

yes

—

C₂³×C₆₇

C₂×#41

yes

characteristic

C₂²×D₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₄×D₄

yes

—

C₂×C₄×C₆₇

C₄×D₄

yes

—

C₂×C₄×C₆₇

C₂³×C₄

yes

characteristic

C₂×C₄×C₆₇

C₂²×D₄

yes

characteristic

C₂×C₄×C₆₇

H(5,𝔽₂)

yes

—

C₂²⋊D₆₇

—

C₂×Dic₆₇

—

D₂₆₈

—

D₂₆₈

—

C₄×D₆₇

—

C₄×D₆₇

—

Dic₁₃₄

—

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

C₂×C₄×D₄

yes

characteristic

100

C₂²×C₆₇

#540

yes

—

101

C₂×D₆₇

—

102

C₂×D₆₇

—

103

C₄×C₆₇

—

104

C₄×C₆₇

—

105

C₄×C₆₇

—

106

C₄×C₆₇

#518

yes

—

107

C₄×C₆₇

#535

yes

—

108

Dic₆₇

—

109

#22282

—

maximal, Sylow

110

C₂×C₆₇

—

111

C₂×C₆₇

#2328

yes

characteristic

112

C₂×C₆₇

#2957

yes

—

113

D₆₇

—

114

#3147

—

115

#2932

—

116

#1963

—

117

#1876

—

118

#1837

—

119

#1746

D₆₇

yes

characteristic, complemented

120

C₆₇

#22282

yes

characteristic, complemented, Sylow

121

C₂×#135

—

122

C₂×#131

—

123

#532

—

124

#495

—

125

#494

—

126

#493

—

127

#492

—

128

#435

—

134

—

129

#423

—

130

C₂×#104

—

131

#408

—

132

C₂×#97

C₂×D₆₇

yes

characteristic

133

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

134

#376

C₂×D₆₇

yes

characteristic

135

#341

—

136

#336

C₂×D₆₇

yes

—

137

C₂×#41

—

138

#135

—

268

—

139

C₂×Q₁₆

—

140

C₂×SD₁₆

—

141

C₂×D₈

—

142

#131

—

268

—

143

C₂×M₁₆

—

144

C₂×M₁₆

—

134

—

145

C₂²×C₈

—

134

—

146

C₂²×C₈

C₂²×D₆₇

yes

—

147

C₂²×C₈

C₂²×D₆₇

yes

—

148

C₄⋊Q₈

—

149

#127

—

150

#124

—

151

#121

—

134

—

152

C₄×D₄

—

134

—

153

C₂×C₄²

C₂²×D₆₇

yes

—

154

C₂×C₄²

C₂²×D₆₇

yes

characteristic

155

C₄⋊C₈

—

134

—

156

#104

—

268

—

157

C₂²⋊C₈

—

134

—

158

#97

D₂₆₈

yes

—

159

C₄×C₈

C₄×D₆₇

yes

characteristic

160

C₄×C₈

C₄×D₆₇

yes

characteristic

161

C₄×C₈

C₄×D₆₇

yes

—

162

#95

—

163

#41

—

134

—

164

#41

—

134

—

165

C₂×Q₈

—

166

C₂×D₄

—

167

C₂×D₄

—

134

—

168

C₂×D₄

—

134

—

169

C₂²×C₄

—

170

C₂²×C₄

—

134

—

171

C₂²×C₄

#11761628

yes

—

172

C₂²×C₄

C₂³×D₆₇

yes

characteristic

173

Q₁₆

—

268

—

174

SD₁₆

—

268

—

175

D₈

—

268

—

176

M₁₆

—

268

—

177

M₁₆

—

134

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

—

268

—

181

C₂×C₈

—

134

—

182

C₂×C₈

C₂×C₄×D₆₇

yes

—

183

C₂×C₈

C₂×C₄×D₆₇

yes

—

184

C₂×C₈

C₂×D₂₆₈

yes

—

185

C₄⋊C₄

—

134

—

186

C₂²⋊C₄

—

134

—

187

C₄²

—

188

C₄²

C₂×C₄×D₆₇

yes

characteristic

189

C₄²

C₂×C₄×D₆₇

yes

characteristic

190

C₄²

C₂×D₂₆₈

yes

—

191

C₂³

—

134

—

192

C₂³

C₂×#11761628

yes

characteristic

193

Q₈

—

134

—

194

D₄

—

268

—

195

D₄

—

536

—

196

D₄

—

134

—

197

C₂×C₄

—

198

C₂×C₄

—

199

C₂×C₄

—

200

C₂×C₄

—

268

—

201

C₂×C₄

—

268

—

202

C₂×C₄

—

134

—

203

C₂×C₄

C₄×D₂₆₈

yes

—

204

C₂×C₄

C₄×D₂₆₈

yes

—

205

C₂×C₄

C₂²×C₄×D₆₇

yes

characteristic

206

C₂×C₄

C₂²×D₂₆₈

yes

characteristic

207

C₂×C₄

#14524089

yes

—

208

C₈

—

209

C₈

—

210

C₈

—

211

C₈

—

268

—

212

C₂²

—

213

C₂²

—

268

—

214

C₂²

—

268

—

215

C₂²

C₂×C₄×D₂₆₈

yes

characteristic

216

C₂²

#16864001

yes

—

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

268

—

221

C₄

#16863870

yes

—

222

C₄

#16863965

yes

—

223

C₂

—

224

C₂

—

536

—

225

C₂

#22562934

yes

characteristic

226

C₂

#22569127

yes

—

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#1746	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#22570637	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#1746	D₆₇
hypocenter	C₆₇	#22282
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1746

subgroup

G/H

center

C₂×C₄

C₂²×D₂₆₈

commutator

C₂×C₄×C₆₇

C₂³×C₄

Frattini

C₂²×C₄

C₂³×D₆₇

Fitting

C₆₇×#1746

C₂

socle

C₂²×C₆₇

C₂×C₄×D₄

prime radical

#22570637

C₂

cosocle

C₂²×C₄×C₆₇

C₂⁴

D₆₇

C₆₇

G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #1746

N	H ≅ G/N	type
2. #22568928	C₂	semidirect
3. #22561041	C₂	semidirect
4. #22560535	C₂	semidirect
5. #22560347	C₂	semidirect
6. C₆₇×#1746	C₂	semidirect
10. #16863780	C₄	semidirect
11. #16863776	C₄	semidirect
12. #16863773	C₄	semidirect
13. #16863769	C₄	semidirect
119. #1746	D₆₇	semidirect
120. C₆₇	#22282	semidirect

H ≅ G/N

type

2. #22568928

C₂

semidirect

3. #22561041

C₂

semidirect

4. #22560535

C₂

semidirect

5. #22560347

C₂

semidirect

6. C₆₇×#1746

C₂

semidirect

10. #16863780

C₄

semidirect

11. #16863776

C₄

semidirect

12. #16863773

C₄

semidirect

13. #16863769

C₄

semidirect

119. #1746

D₆₇

semidirect

120. C₆₇

#22282

semidirect

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

subgroup	index
#22570637	2
#22568928	2
#22561041	2
#22560535	2
#22560347	2
C₆₇×#1746	2
#22282	67

subgroup

index

C₆₇×#1746

Subgroups — #30869721

Conjugacy classes of subgroups

Complements

Maximal subgroups