Group #30748662 — subgroups

Subgroups — #30748662

Order 17152.

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

normal subgroups only

This group has 476 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	#22560326	C₂	1	2	yes	maximal
2	C₂×#16863145	C₂	1	2	yes	maximal
3	#22558092	C₂	1	2	yes	maximal
4	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	4	yes	—
6	#16863151	—	2	2	no	—
7	#16863151	—	2	2	no	—
8	#16863145	—	2	4	no	—
9	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₆₇	C₄	1	2	yes	—
11	#391×C₆₇	C₄	1	2	yes	—
12	#389×C₆₇	—	2	2	no	—
13	#384×C₆₇	C₂²	1	1	yes	characteristic
14	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
15	C₄³×C₆₇	C₂²	1	1	yes	characteristic
16	C₂²×C₆₇⋊C₈	—	2	4	no	—
17	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
18	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
19	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
20	C₄⋊Q₈×C₆₇	—	2	2	no	—
21	C₄⋊Q₈×C₆₇	D₄	1	2	yes	—
22	C₄⋊Q₈×C₆₇	Q₈	1	2	yes	—
23	C₄×Q₈×C₆₇	—	4	4	no	—
24	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
25	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
26	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
27	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
28	C₂×C₄²×C₆₇	—	2	2	no	—
29	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₆₇	D₄	1	2	yes	—
32	C₂×C₄²×C₆₇	D₄	1	2	yes	—
33	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
34	#95×C₆₇	—	2	4	no	—
35	C₂×C₆₇⋊C₈	—	4	4	no	—
36	C₂×C₆₇⋊C₈	—	4	4	no	—
37	C₂×C₆₇⋊C₈	—	4	4	no	—
38	C₂×Q₈×C₆₇	—	2	2	no	—
39	C₂×Q₈×C₆₇	—	4	2	no	—
40	C₂×Q₈×C₆₇	—	4	2	no	—
41	C₂×Q₈×C₆₇	C₄⋊C₄	1	4	yes	—
42	C₂²×C₄×C₆₇	—	2	2	no	—
43	C₂²×C₄×C₆₇	—	2	2	no	—
44	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₆₇	C₂²⋊C₄	1	2	yes	—
46	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
49	C₄⋊C₄×C₆₇	—	2	4	no	—
50	C₄⋊C₄×C₆₇	—	2	4	no	—
51	C₄⋊C₄×C₆₇	—	4	2	no	—
52	C₄⋊C₄×C₆₇	—	4	4	no	—
53	C₄⋊C₄×C₆₇	—	4	4	no	—
54	C₄²×C₆₇	—	2	2	no	—
55	C₄²×C₆₇	—	2	4	no	—
56	C₄²×C₆₇	—	2	4	no	—
57	C₄²×C₆₇	—	4	1	no	—
58	C₄²×C₆₇	—	4	4	no	—
59	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
60	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
61	C₄²×C₆₇	#41	1	2	yes	—
62	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
63	Q₈×C₆₇	—	4	4	no	—
64	Q₈×C₆₇	—	4	4	no	—
65	C₂×C₄×C₆₇	—	2	1	no	—
66	C₂×C₄×C₆₇	—	2	1	no	—
67	C₂×C₄×C₆₇	—	2	2	no	—
68	C₂×C₄×C₆₇	—	2	4	no	—
69	C₂×C₄×C₆₇	—	2	1	no	—
70	C₂×C₄×C₆₇	—	2	2	no	—
71	C₂×C₄×C₆₇	—	2	2	no	—
72	C₂×C₄×C₆₇	—	2	2	no	—
73	C₂×C₄×C₆₇	—	2	2	no	—
74	C₂×C₄×C₆₇	—	4	2	no	—
75	C₂×C₄×C₆₇	—	4	2	no	—
76	C₂×C₄×C₆₇	—	4	2	no	—
77	C₂×C₄×C₆₇	—	4	4	no	—
78	C₂×C₄×C₆₇	#100	1	2	yes	—
79	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
81	C₂×C₄×C₆₇	#121	1	2	yes	—
82	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
83	C₂×C₄×C₆₇	#135	1	4	yes	—
84	C₂×C₄×C₆₇	#137	1	4	yes	—
85	C₆₇⋊C₈	—	8	4	no	—
86	C₂²×C₆₇	#380	1	1	yes	characteristic
87	C₂²×C₆₇	C₂×#100	1	1	yes	characteristic
88	C₂²×C₆₇	#413	1	1	yes	characteristic
89	C₂²×C₆₇	#416	1	2	yes	—
90	C₂²×C₆₇	#419	1	2	yes	—
91	C₄×C₆₇	—	2	1	no	—
92	C₄×C₆₇	—	2	1	no	—
93	C₄×C₆₇	—	2	2	no	—
94	C₄×C₆₇	—	4	1	no	—
95	C₄×C₆₇	—	4	4	no	—
96	C₄×C₆₇	—	4	2	no	—
97	C₄×C₆₇	—	8	2	no	—
98	C₄×C₆₇	#464	1	4	yes	—
99	C₄×C₆₇	#479	1	4	yes	—
100	#8594	—	67	1	no	maximal, Sylow
101	C₂×C₆₇	#1543	1	1	yes	characteristic
102	C₂×C₆₇	#1554	1	2	yes	—
103	C₂×C₆₇	#1558	1	1	yes	characteristic
104	C₂×C₆₇	#1800	1	1	yes	characteristic
105	C₂×C₆₇	#1805	1	2	yes	—
106	C₄×C₄⋊Q₈	D₆₇	1	1	yes	characteristic
107	#1831	—	67	2	no	—
108	C₂×#333	—	67	2	no	—
109	#1296	—	67	2	no	—
110	C₆₇	#8594	1	1	yes	characteristic, complemented, Sylow
111	C₂×C₄⋊Q₈	C₂×D₆₇	1	1	yes	characteristic
112	C₂×C₄×Q₈	Dic₆₇	1	2	yes	—
113	C₂×C₄⋊C₈	—	67	4	no	—
114	#391	Dic₆₇	1	2	yes	—
115	#389	—	2	2	no	—
116	#384	C₂×D₆₇	1	1	yes	characteristic
117	C₄×C₄⋊C₄	—	2	2	no	—
118	C₄³	C₂×D₆₇	1	1	yes	characteristic
119	#336	—	134	2	no	—
120	#336	—	134	2	no	—
121	#333	—	134	4	no	—
122	C₂²×Q₈	C₂×Dic₆₇	1	2	yes	—
123	C₂²×C₈	—	134	4	no	—
124	C₄⋊Q₈	—	2	2	no	—
125	C₄⋊Q₈	Dic₁₃₄	1	2	yes	—
126	C₄⋊Q₈	D₂₆₈	1	2	yes	—
127	C₄×Q₈	—	4	4	no	—
128	C₂×C₄⋊C₄	—	2	2	no	—
129	C₂×C₄⋊C₄	—	2	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
132	C₂×C₄²	—	2	2	no	—
133	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
134	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
135	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
136	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
137	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
138	C₄⋊C₈	—	134	4	no	—
139	C₄⋊C₈	—	134	4	no	—
140	#95	—	2	4	no	—
141	C₂×Q₈	—	2	2	no	—
142	C₂×Q₈	—	4	2	no	—
143	C₂×Q₈	—	4	2	no	—
144	C₂×Q₈	C₄⋊Dic₆₇	1	4	yes	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	C₂²⋊Dic₆₇	1	2	yes	—
148	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
149	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
150	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₂²⋊D₆₇	1	2	yes	—
152	C₂×C₈	—	268	4	no	—
153	C₂×C₈	—	268	4	no	—
154	C₂×C₈	—	268	4	no	—
155	C₄⋊C₄	—	2	4	no	—
156	C₄⋊C₄	—	2	4	no	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	—	4	4	no	—
159	C₄⋊C₄	—	4	4	no	—
160	C₄²	—	2	2	no	—
161	C₄²	—	2	4	no	—
162	C₄²	—	2	4	no	—
163	C₄²	—	4	1	no	—
164	C₄²	—	4	4	no	—
165	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
166	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
167	C₄²	#11761628	1	2	yes	—
168	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
169	Q₈	—	4	4	no	—
170	Q₈	—	4	4	no	—
171	C₂×C₄	—	2	1	no	—
172	C₂×C₄	—	2	1	no	—
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	4	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	4	2	no	—
181	C₂×C₄	—	4	2	no	—
182	C₂×C₄	—	4	2	no	—
183	C₂×C₄	—	4	4	no	—
184	C₂×C₄	#14523960	1	2	yes	—
185	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
186	C₂×C₄	#14524002	1	1	yes	characteristic
187	C₂×C₄	#14524017	1	2	yes	—
188	C₂×C₄	#14524022	1	2	yes	—
189	C₂×C₄	#14524063	1	4	yes	—
190	C₂×C₄	#14524074	1	4	yes	—
191	C₈	—	536	4	no	—
192	C₂²	#16863256	1	1	yes	characteristic
193	C₂²	C₂×#14523960	1	1	yes	characteristic
194	C₂²	#16863380	1	1	yes	characteristic
195	C₂²	#16863392	1	2	yes	—
196	C₂²	#16863405	1	2	yes	—
197	C₄	—	2	1	no	—
198	C₄	—	2	1	no	—
199	C₄	—	2	2	no	—
200	C₄	—	4	1	no	—
201	C₄	—	4	2	no	—
202	C₄	—	4	4	no	—
203	C₄	—	8	2	no	—
204	C₄	#16863618	1	4	yes	—
205	C₄	#16863703	1	4	yes	—
206	C₂	#22558871	1	1	yes	characteristic
207	C₂	#22558919	1	2	yes	—
208	C₂	#22558935	1	1	yes	characteristic
209	C₂	#22560201	1	1	yes	characteristic
210	C₂	#22560224	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#22560326

C₂

yes

maximal

C₂×#16863145

C₂

yes

maximal

#22558092

C₂

yes

maximal

C₄×C₄⋊Q₈×C₆₇

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₆₇⋊C₈)

C₂²

yes

—

#16863151

—

#16863151

—

#16863145

—

C₂×C₄⋊Q₈×C₆₇

C₂²

yes

characteristic

C₂×C₄×Q₈×C₆₇

C₄

yes

—

#391×C₆₇

C₄

yes

—

#389×C₆₇

—

#384×C₆₇

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₆₇

—

C₄³×C₆₇

C₂²

yes

characteristic

C₂²×C₆₇⋊C₈

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

—

C₂²×Q₈×C₆₇

C₂×C₄

yes

—

C₄⋊Q₈×C₆₇

—

C₄⋊Q₈×C₆₇

D₄

yes

—

C₄⋊Q₈×C₆₇

Q₈

yes

—

C₄×Q₈×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

C₂×C₄

yes

—

C₂×C₄²×C₆₇

—

C₂×C₄²×C₆₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₆₇

C₂×C₄

yes

characteristic

C₂×C₄²×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

#95×C₆₇

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

C₄⋊C₄

yes

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂²⋊C₄

yes

—

C₂²×C₄×C₆₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

C₂×D₄

yes

characteristic

C₄²×C₆₇

C₂×Q₈

yes

characteristic

C₄²×C₆₇

#41

yes

—

C₂³×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₆₇

—

Q₈×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

#100

yes

—

C₂×C₄×C₆₇

C₂×C₄⋊C₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

—

C₂×C₄×C₆₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₆₇

#135

yes

—

C₂×C₄×C₆₇

#137

yes

—

C₆₇⋊C₈

—

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

—

C₂²×C₆₇

#419

yes

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

#464

yes

—

C₄×C₆₇

#479

yes

—

100

#8594

—

maximal, Sylow

101

C₂×C₆₇

#1543

yes

characteristic

102

C₂×C₆₇

#1554

yes

—

103

C₂×C₆₇

#1558

yes

characteristic

104

C₂×C₆₇

#1800

yes

characteristic

105

C₂×C₆₇

#1805

yes

—

106

C₄×C₄⋊Q₈

D₆₇

yes

characteristic

107

#1831

—

108

C₂×#333

—

109

#1296

—

110

C₆₇

#8594

yes

characteristic, complemented, Sylow

111

C₂×C₄⋊Q₈

C₂×D₆₇

yes

characteristic

112

C₂×C₄×Q₈

Dic₆₇

yes

—

113

C₂×C₄⋊C₈

—

114

#391

Dic₆₇

yes

—

115

#389

—

116

#384

C₂×D₆₇

yes

characteristic

117

C₄×C₄⋊C₄

—

118

C₄³

C₂×D₆₇

yes

characteristic

119

#336

—

134

—

120

#336

—

134

—

121

#333

—

134

—

122

C₂²×Q₈

C₂×Dic₆₇

yes

—

123

C₂²×C₈

—

134

—

124

C₄⋊Q₈

—

125

C₄⋊Q₈

Dic₁₃₄

yes

—

126

C₄⋊Q₈

D₂₆₈

yes

—

127

C₄×Q₈

—

128

C₂×C₄⋊C₄

—

129

C₂×C₄⋊C₄

—

130

C₂×C₄⋊C₄

—

131

C₂×C₄⋊C₄

C₂×Dic₆₇

yes

—

132

C₂×C₄²

—

133

C₂×C₄²

C₂×Dic₆₇

yes

characteristic

134

C₂×C₄²

C₂×Dic₆₇

yes

characteristic

135

C₂×C₄²

C₂²⋊D₆₇

yes

—

136

C₂×C₄²

C₂²⋊D₆₇

yes

—

137

C₂×C₄²

C₂²×D₆₇

yes

characteristic

138

C₄⋊C₈

—

134

—

139

C₄⋊C₈

—

134

—

140

#95

—

141

C₂×Q₈

—

142

C₂×Q₈

—

143

C₂×Q₈

—

144

C₂×Q₈

C₄⋊Dic₆₇

yes

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²⋊Dic₆₇

yes

—

148

C₂²×C₄

C₂²⋊Dic₆₇

yes

characteristic

149

C₂²×C₄

C₂²⋊Dic₆₇

yes

characteristic

150

C₂²×C₄

C₂²×Dic₆₇

yes

characteristic

151

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

—

152

C₂×C₈

—

268

—

153

C₂×C₈

—

268

—

154

C₂×C₈

—

268

—

155

C₄⋊C₄

—

156

C₄⋊C₄

—

157

C₄⋊C₄

—

158

C₄⋊C₄

—

159

C₄⋊C₄

—

160

C₄²

—

161

C₄²

—

162

C₄²

—

163

C₄²

—

164

C₄²

—

165

C₄²

C₂×D₂₆₈

yes

characteristic

166

C₄²

C₂×Dic₁₃₄

yes

characteristic

167

C₄²

#11761628

yes

—

168

C₂³

C₂×C₂²⋊Dic₆₇

yes

characteristic

169

Q₈

—

170

Q₈

—

171

C₂×C₄

—

172

C₂×C₄

—

173

C₂×C₄

—

174

C₂×C₄

—

175

C₂×C₄

—

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

180

C₂×C₄

—

181

C₂×C₄

—

182

C₂×C₄

—

183

C₂×C₄

—

184

C₂×C₄

#14523960

yes

—

185

C₂×C₄

C₂×C₄⋊Dic₆₇

yes

characteristic

186

C₂×C₄

#14524002

yes

characteristic

187

C₂×C₄

#14524017

yes

—

188

C₂×C₄

#14524022

yes

—

189

C₂×C₄

#14524063

yes

—

190

C₂×C₄

#14524074

yes

—

191

C₈

—

536

—

192

C₂²

#16863256

yes

characteristic

193

C₂²

C₂×#14523960

yes

characteristic

194

C₂²

#16863380

yes

characteristic

195

C₂²

#16863392

yes

—

196

C₂²

#16863405

yes

—

197

C₄

—

198

C₄

—

199

C₄

—

200

C₄

—

201

C₄

—

202

C₄

—

203

C₄

—

204

C₄

#16863618

yes

—

205

C₄

#16863703

yes

—

206

C₂

#22558871

yes

characteristic

207

C₂

#22558919

yes

—

208

C₂

#22558935

yes

characteristic

209

C₂

#22560201

yes

characteristic

210

C₂

#22560224

yes

—

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₆₇
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₄×C₄⋊Q₈×C₆₇	C₂
socle, prime radical	C₂³×C₆₇	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₄×C₄⋊Q₈	D₆₇
hypocenter	C₆₇	#8594
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₆₇

commutator

C₂²×C₄×C₆₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₄×C₄⋊Q₈×C₆₇

C₂

socle, prime radical

C₂³×C₆₇

C₂×C₂²⋊C₄

cosocle

C₂×C₄²×C₆₇

C₂³

hypercenter

C₄×C₄⋊Q₈

D₆₇

hypocenter

C₆₇

#8594

LCS

G ▷ C₂²×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

N	H ≅ G/N	type
110. C₆₇	#8594	semidirect

H ≅ G/N

type

110. C₆₇

#8594

semidirect

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

subgroup	index
#22560326	2
C₂×#16863145	2
#22558092	2
C₄×C₄⋊Q₈×C₆₇	2
#8594	67

subgroup

index

C₄×C₄⋊Q₈×C₆₇

Subgroups — #30748662

Conjugacy classes of subgroups

Complements

Maximal subgroups