Group #30760271 — subgroups

Subgroups — #30760271

Order 17152.

494 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 135 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	#22565238	C₂	1	1	yes	maximal, characteristic
2	#22560970	C₂	1	2	yes	maximal
3	#22558092	C₂	1	1	yes	maximal, characteristic
4	#22558049	C₂	1	2	yes	maximal
5	C₆₇×#1844	C₂	1	1	yes	maximal, characteristic
6	C₂×#14524042	—	2	2	no	—
7	C₂×#14523974	—	2	2	no	—
8	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
9	#16863316	—	2	2	no	—
10	#16863292	—	2	2	no	—
11	C₄×C₄⋊Dic₆₇	C₂²	1	2	yes	—
12	#16863158	—	2	2	no	—
13	C₂×#106×C₆₇	—	2	2	no	—
14	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
15	#384×C₆₇	C₂²	1	1	yes	characteristic
16	#384×C₆₇	C₂²	1	1	yes	characteristic
17	C₂²×Dic₁₃₄	—	2	2	no	—
18	C₂²×C₆₇⋊C₈	—	2	2	no	—
19	#14524042	—	4	4	no	—
20	#14524042	—	4	4	no	—
21	C₂×C₄⋊Dic₆₇	D₄	1	2	yes	—
22	C₂×C₄⋊Dic₆₇	D₄	1	2	yes	—
23	C₂×Dic₆₇⋊C₄	—	2	4	no	—
24	C₂×C₄×Dic₆₇	—	2	2	no	—
25	#14523974	—	4	4	no	—
26	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
27	C₄⋊(C₆₇⋊C₈)	Q₈	1	4	yes	complemented
28	C₆₇⋊#95	—	2	2	no	—
29	C₆₇⋊#95	—	2	2	no	—
30	C₂²×C₈×C₆₇	—	2	1	no	—
31	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
32	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
33	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
34	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
35	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
36	#106×C₆₇	—	4	4	no	—
37	C₄×C₈×C₆₇	—	2	1	no	—
38	C₄×C₈×C₆₇	Q₈	1	2	yes	complemented
39	C₂×Dic₁₃₄	—	4	8	no	—
40	C₂×Dic₁₃₄	—	8	2	no	—
41	C₂²×Dic₆₇	—	2	2	no	—
42	C₂²×Dic₆₇	—	2	2	no	—
43	C₂×C₆₇⋊C₈	—	2	4	no	—
44	C₂×C₆₇⋊C₈	—	4	2	no	—
45	C₂×C₆₇⋊C₈	—	4	2	no	—
46	C₄⋊Dic₆₇	—	2	2	no	—
47	C₄⋊Dic₆₇	—	2	2	no	—
48	C₄⋊Dic₆₇	SD₁₆	1	4	yes	—
49	C₄⋊Dic₆₇	SD₁₆	1	4	yes	—
50	Dic₆₇⋊C₄	—	4	8	no	—
51	C₄×Dic₆₇	—	4	2	no	—
52	C₄×Dic₆₇	—	4	2	no	—
53	C₂²×C₄×C₆₇	—	2	2	no	—
54	C₂²×C₄×C₆₇	—	4	1	no	—
55	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
56	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
57	C₂×C₈×C₆₇	—	2	2	no	—
58	C₂×C₈×C₆₇	—	2	2	no	—
59	C₂×C₈×C₆₇	—	2	2	no	—
60	C₄⋊C₄×C₆₇	—	4	2	no	—
61	C₄⋊C₄×C₆₇	—	4	2	no	—
62	C₄⋊C₄×C₆₇	—	4	2	no	—
63	C₄⋊C₄×C₆₇	—	4	2	no	—
64	C₄⋊C₄×C₆₇	—	4	2	no	—
65	C₄⋊C₄×C₆₇	—	4	2	no	—
66	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
67	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
68	C₄²×C₆₇	#41	1	1	yes	characteristic
69	C₂³×C₆₇	#120	1	1	yes	characteristic
70	C₂×C₄×C₆₇	—	2	1	no	—
71	C₂×C₄×C₆₇	—	2	1	no	—
72	C₂×C₄×C₆₇	—	4	4	no	—
73	C₂×C₄×C₆₇	—	4	2	no	—
74	C₂×C₄×C₆₇	—	8	2	no	—
75	C₂×C₄×C₆₇	—	8	1	no	—
76	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
77	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
78	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
79	C₂×C₄×C₆₇	C₄⋊Q₈	1	2	yes	—
80	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
81	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
82	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
83	C₂×C₄×C₆₇	#137	1	2	yes	—
84	C₂×Dic₆₇	—	2	4	no	—
85	C₂×Dic₆₇	—	2	4	no	—
86	C₂×Dic₆₇	—	4	2	no	—
87	C₂×Dic₆₇	—	4	2	no	—
88	C₂×Dic₆₇	—	4	2	no	—
89	C₂×Dic₆₇	—	4	2	no	—
90	Dic₁₃₄	—	8	8	no	—
91	C₈×C₆₇	—	2	4	no	—
92	C₆₇⋊C₈	—	4	4	no	—
93	C₂²×C₆₇	#395	1	1	yes	characteristic
94	C₂²×C₆₇	#448	1	2	yes	—
95	C₂²×C₆₇	#450	1	2	yes	—
96	C₂²×C₆₇	#453	1	1	yes	characteristic
97	C₂²×C₆₇	#456	1	1	yes	characteristic
98	C₄×C₆₇	—	2	1	no	—
99	C₄×C₆₇	—	2	1	no	—
100	C₄×C₆₇	—	8	2	no	—
101	C₄×C₆₇	—	16	1	no	—
102	C₄×C₆₇	#475	1	2	yes	—
103	C₄×C₆₇	#476	1	2	yes	—
104	C₄×C₆₇	#498	1	2	yes	—
105	C₄×C₆₇	#501	1	2	yes	—
106	Dic₆₇	—	4	4	no	—
107	Dic₆₇	—	4	4	no	—
108	#10574	—	67	1	no	maximal, Sylow
109	C₂×C₆₇	#1623	1	1	yes	characteristic
110	C₂×C₆₇	#1629	1	1	yes	characteristic
111	C₂×C₆₇	#1651	1	2	yes	—
112	C₂×C₆₇	#2058	1	2	yes	—
113	C₂×C₆₇	#2060	1	1	yes	characteristic
114	#2551	—	67	1	no	—
115	#1948	—	67	2	no	—
116	#1844	D₆₇	1	1	yes	characteristic
117	#1296	—	67	1	no	—
118	#1279	—	67	2	no	—
119	C₆₇	#10574	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₄⋊Q₈	—	134	2	no	—
121	C₂×#106	—	2	2	no	—
122	C₂×#106	—	134	2	no	—
123	C₂×C₄⋊C₈	—	67	2	no	—
124	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
125	#395	—	134	2	no	—
126	#389	—	134	2	no	—
127	#384	C₂×D₆₇	1	1	yes	characteristic
128	#384	C₂×D₆₇	1	1	yes	characteristic
129	C₄×C₄⋊C₄	—	67	2	no	—
130	#340	—	134	2	no	—
131	C₂²×Q₈	—	134	2	no	—
132	C₂²×C₈	—	2	1	no	—
133	C₂²×C₈	—	134	2	no	—
134	C₄⋊Q₈	—	268	4	no	—
135	C₄⋊Q₈	—	268	4	no	—
136	C₂×C₄⋊C₄	—	2	2	no	—
137	C₂×C₄⋊C₄	—	2	2	no	—
138	C₂×C₄⋊C₄	—	2	1	no	—
139	C₂×C₄⋊C₄	—	67	2	no	—
140	C₂×C₄⋊C₄	—	67	2	no	—
141	C₂×C₄⋊C₄	—	134	4	no	—
142	C₂×C₄⋊C₄	C₂²⋊D₆₇	1	2	yes	—
143	C₂×C₄²	—	134	2	no	—
144	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
145	#106	—	4	4	no	—
146	#106	—	268	4	no	—
147	C₄⋊C₈	—	67	4	no	—
148	C₄⋊C₈	—	134	2	no	—
149	C₄×C₈	—	2	1	no	—
150	C₄×C₈	Dic₁₃₄	1	2	yes	complemented
151	#95	—	134	2	no	—
152	#95	—	134	2	no	—
153	C₂×Q₈	—	268	8	no	—
154	C₂×Q₈	—	536	2	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	4	1	no	—
157	C₂²×C₄	—	134	2	no	—
158	C₂²×C₄	—	134	2	no	—
159	C₂²×C₄	D₄×D₆₇	1	2	yes	—
160	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
161	C₂×C₈	—	2	2	no	—
162	C₂×C₈	—	2	2	no	—
163	C₂×C₈	—	2	2	no	—
164	C₂×C₈	—	268	2	no	—
165	C₂×C₈	—	268	2	no	—
166	C₂×C₈	—	134	4	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	4	2	no	—
169	C₄⋊C₄	—	4	2	no	—
170	C₄⋊C₄	—	4	2	no	—
171	C₄⋊C₄	—	4	2	no	—
172	C₄⋊C₄	—	4	2	no	—
173	C₄⋊C₄	—	268	8	no	—
174	C₄⋊C₄	—	67	4	no	—
175	C₄⋊C₄	—	67	4	no	—
176	C₄⋊C₄	—	134	2	no	—
177	C₄⋊C₄	—	134	2	no	—
178	C₄²	—	268	2	no	—
179	C₄²	—	268	2	no	—
180	C₄²	Q₈×D₆₇	1	2	yes	—
181	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
182	C₄²	#11761628	1	1	yes	characteristic
183	C₂³	#14524011	1	1	yes	characteristic
184	Q₈	—	536	8	no	—
185	C₂×C₄	—	2	1	no	—
186	C₂×C₄	—	2	1	no	—
187	C₂×C₄	—	4	4	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	8	2	no	—
190	C₂×C₄	—	8	1	no	—
191	C₂×C₄	—	268	2	no	—
192	C₂×C₄	—	268	2	no	—
193	C₂×C₄	—	268	2	no	—
194	C₂×C₄	—	268	2	no	—
195	C₂×C₄	—	134	4	no	—
196	C₂×C₄	—	134	4	no	—
197	C₂×C₄	#14524021	1	2	yes	—
198	C₂×C₄	#14524022	1	1	yes	characteristic
199	C₂×C₄	#14524041	1	1	yes	characteristic
200	C₂×C₄	#14524042	1	2	yes	—
201	C₂×C₄	SD₁₆×D₆₇	1	2	yes	—
202	C₂×C₄	SD₁₆×D₆₇	1	2	yes	—
203	C₂×C₄	#14524070	1	2	yes	—
204	C₂×C₄	#14524072	1	2	yes	—
205	C₈	—	2	4	no	—
206	C₈	—	268	4	no	—
207	C₂²	#16863316	1	1	yes	characteristic
208	C₂²	#16863533	1	2	yes	—
209	C₂²	#16863545	1	2	yes	—
210	C₂²	#16863563	1	1	yes	characteristic
211	C₂²	#16863578	1	1	yes	characteristic
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	8	2	no	—
215	C₄	—	268	4	no	—
216	C₄	—	268	4	no	—
217	C₄	—	16	1	no	—
218	C₄	#16863680	1	2	yes	—
219	C₄	#16863685	1	2	yes	—
220	C₄	#16863793	1	2	yes	—
221	C₄	#16863803	1	2	yes	—
222	C₂	#22559285	1	1	yes	characteristic
223	C₂	#22559323	1	1	yes	characteristic
224	C₂	#22559469	1	2	yes	—
225	C₂	#22561540	1	2	yes	—
226	C₂	#22561554	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22565238

C₂

yes

maximal, characteristic

#22560970

C₂

yes

maximal

#22558092

C₂

yes

maximal, characteristic

#22558049

C₂

yes

maximal

C₆₇×#1844

C₂

yes

maximal, characteristic

C₂×#14524042

—

C₂×#14523974

—

C₂×C₄⋊(C₆₇⋊C₈)

C₂²

yes

—

#16863316

—

#16863292

—

C₄×C₄⋊Dic₆₇

C₂²

yes

—

#16863158

—

C₂×#106×C₆₇

—

C₂×C₄×C₈×C₆₇

C₂²

yes

characteristic

#384×C₆₇

C₂²

yes

characteristic

#384×C₆₇

C₂²

yes

characteristic

C₂²×Dic₁₃₄

—

C₂²×C₆₇⋊C₈

—

#14524042

—

#14524042

—

C₂×C₄⋊Dic₆₇

D₄

yes

—

C₂×C₄⋊Dic₆₇

D₄

yes

—

C₂×Dic₆₇⋊C₄

—

C₂×C₄×Dic₆₇

—

#14523974

—

C₄⋊(C₆₇⋊C₈)

—

C₄⋊(C₆₇⋊C₈)

Q₈

yes

complemented

C₆₇⋊#95

—

C₆₇⋊#95

—

C₂²×C₈×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₄⋊C₄×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

#106×C₆₇

—

C₄×C₈×C₆₇

—

C₄×C₈×C₆₇

Q₈

yes

complemented

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂²×Dic₆₇

—

C₂²×Dic₆₇

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

SD₁₆

yes

—

C₄⋊Dic₆₇

SD₁₆

yes

—

Dic₆₇⋊C₄

—

C₄×Dic₆₇

—

C₄×Dic₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄²×C₆₇

C₂×Q₈

yes

—

C₄²×C₆₇

C₂×Q₈

yes

C₄²×C₆₇

yes

C₂³×C₆₇

yes

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₆₇

C₂²⋊Q₈

yes

characteristic

C₂×C₄×C₆₇

C₄⋊Q₈

yes

characteristic

C₂×C₄×C₆₇

C₄⋊Q₈

yes

—

C₂×C₄×C₆₇

C₂×SD₁₆

yes

—

C₂×C₄×C₆₇

C₂×SD₁₆

yes

—

C₂×C₄×C₆₇

AGL(1,ℤ/8)

yes

—

C₂×C₄×C₆₇

#137

yes

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

Dic₁₃₄

—

C₈×C₆₇

—

C₆₇⋊C₈

—

C₂²×C₆₇

#395

yes

characteristic

C₂²×C₆₇

#448

yes

—

C₂²×C₆₇

#450

yes

—

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₄×C₆₇

—

C₄×C₆₇

—

100

C₄×C₆₇

—

101

C₄×C₆₇

—

102

C₄×C₆₇

#475

yes

—

103

C₄×C₆₇

#476

yes

—

104

C₄×C₆₇

#498

yes

—

105

C₄×C₆₇

#501

yes

—

106

Dic₆₇

—

107

Dic₆₇

—

108

#10574

—

maximal, Sylow

109

C₂×C₆₇

#1623

yes

characteristic

110

C₂×C₆₇

#1629

yes

characteristic

111

C₂×C₆₇

#1651

yes

—

112

C₂×C₆₇

#2058

yes

—

113

C₂×C₆₇

#2060

yes

characteristic

114

#2551

—

115

#1948

—

116

#1844

D₆₇

yes

characteristic

117

#1296

—

118

#1279

—

119

C₆₇

#10574

yes

characteristic, complemented, Sylow

120

C₂×C₄⋊Q₈

—

134

—

121

C₂×#106

—

122

C₂×#106

—

134

—

123

C₂×C₄⋊C₈

—

124

C₂×C₄×C₈

C₂×D₆₇

yes

characteristic

125

#395

—

134

—

126

#389

—

134

—

127

#384

C₂×D₆₇

yes

characteristic

128

#384

C₂×D₆₇

yes

characteristic

129

C₄×C₄⋊C₄

—

130

#340

—

134

—

131

C₂²×Q₈

—

134

—

132

C₂²×C₈

—

133

C₂²×C₈

—

134

—

134

C₄⋊Q₈

—

268

—

135

C₄⋊Q₈

—

268

—

136

C₂×C₄⋊C₄

—

137

C₂×C₄⋊C₄

—

138

C₂×C₄⋊C₄

—

139

C₂×C₄⋊C₄

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄⋊C₄

—

134

—

142

C₂×C₄⋊C₄

C₂²⋊D₆₇

yes

—

143

C₂×C₄²

—

134

—

144

C₂×C₄²

C₂²×D₆₇

yes

characteristic

145

#106

—

146

#106

—

268

—

147

C₄⋊C₈

—

148

C₄⋊C₈

—

134

—

149

C₄×C₈

—

150

C₄×C₈

Dic₁₃₄

yes

complemented

151

#95

—

134

—

152

#95

—

134

—

153

C₂×Q₈

—

268

—

154

C₂×Q₈

—

536

—

155

C₂²×C₄

—

156

C₂²×C₄

—

157

C₂²×C₄

—

134

—

158

C₂²×C₄

—

134

—

159

C₂²×C₄

D₄×D₆₇

yes

—

160

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

161

C₂×C₈

—

162

C₂×C₈

—

163

C₂×C₈

—

164

C₂×C₈

—

268

—

165

C₂×C₈

—

268

—

166

C₂×C₈

—

134

—

167

C₄⋊C₄

—

168

C₄⋊C₄

—

169

C₄⋊C₄

—

170

C₄⋊C₄

—

171

C₄⋊C₄

—

172

C₄⋊C₄

—

173

C₄⋊C₄

—

268

—

174

C₄⋊C₄

—

175

C₄⋊C₄

—

176

C₄⋊C₄

—

134

—

177

C₄⋊C₄

—

134

—

178

C₄²

—

268

—

179

C₄²

—

268

—

180

C₄²

Q₈×D₆₇

yes

—

181

C₄²

C₂×Dic₁₃₄

yes

characteristic

182

C₄²

#11761628

yes

characteristic

183

C₂³

#14524011

yes

characteristic

184

Q₈

—

536

—

185

C₂×C₄

—

186

C₂×C₄

—

187

C₂×C₄

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

268

—

192

C₂×C₄

—

268

—

193

C₂×C₄

—

268

—

194

C₂×C₄

—

268

—

195

C₂×C₄

—

134

—

196

C₂×C₄

—

134

—

197

C₂×C₄

#14524021

yes

—

198

C₂×C₄

#14524022

yes

characteristic

199

C₂×C₄

#14524041

yes

characteristic

200

C₂×C₄

#14524042

yes

—

201

C₂×C₄

SD₁₆×D₆₇

yes

—

202

C₂×C₄

SD₁₆×D₆₇

yes

—

203

C₂×C₄

#14524070

yes

—

204

C₂×C₄

#14524072

yes

—

205

C₈

—

206

C₈

—

268

—

207

C₂²

#16863316

yes

characteristic

208

C₂²

#16863533

yes

—

209

C₂²

#16863545

yes

—

210

C₂²

#16863563

yes

characteristic

211

C₂²

#16863578

yes

characteristic

212

C₄

—

213

C₄

—

214

C₄

—

215

C₄

—

268

—

216

C₄

—

268

—

217

C₄

—

218

C₄

#16863680

yes

—

219

C₄

#16863685

yes

—

220

C₄

#16863793

yes

—

221

C₄

#16863803

yes

—

222

C₂

#22559285

yes

characteristic

223

C₂

#22559323

yes

characteristic

224

C₂

#22559469

yes

—

225

C₂

#22561540

yes

—

226

C₂

#22561554

yes

characteristic

	subgroup	G/H
center	C₂³	#14524011
commutator, cosocle	C₂×C₄²×C₆₇	C₂³
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#1844	C₂
socle, prime radical	C₂³×C₆₇	#120
hypercenter	#1844	D₆₇
hypocenter	C₆₇	#10574
LCS	G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

subgroup

G/H

center

C₂³

#14524011

commutator, cosocle

C₂×C₄²×C₆₇

C₂³

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₆₇×#1844

C₂

C₂³×C₆₇

D₆₇

C₆₇

G ▷ C₂×C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

N	H ≅ G/N	type
27. C₄⋊(C₆₇⋊C₈)	Q₈	semidirect
38. C₄×C₈×C₆₇	Q₈	semidirect
119. C₆₇	#10574	semidirect
150. C₄×C₈	Dic₁₃₄	semidirect

H ≅ G/N

type

27. C₄⋊(C₆₇⋊C₈)

Q₈

semidirect

38. C₄×C₈×C₆₇

Q₈

semidirect

119. C₆₇

#10574

semidirect

150. C₄×C₈

Dic₁₃₄

semidirect

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

subgroup	index
#22565238	2
#22560970	2
#22558092	2
#22558049	2
C₆₇×#1844	2
#10574	67

subgroup

index

C₆₇×#1844

Subgroups — #30760271

Conjugacy classes of subgroups

Complements

Maximal subgroups