Group #30749708 — subgroups

Subgroups — #30749708

Order 17152.

386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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	#22561146	C₂	1	1	yes	maximal, characteristic
2	C₄×#14523962	C₂	1	1	yes	maximal, characteristic
3	#22558962	C₂	1	2	yes	maximal
4	#22558045	C₂	1	2	yes	maximal
5	C₆₇×#2983	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
7	C₂×#14523962	C₄	1	2	yes	—
8	C₄×#11761612	C₂²	1	2	yes	—
9	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
10	#16863165	C₄	1	1	yes	characteristic
11	#16863165	C₄	1	1	yes	characteristic
12	#16863151	—	2	2	no	—
13	#16863148	—	2	2	no	—
14	#16863146	—	2	2	no	—
15	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
16	#446×C₆₇	—	2	2	no	—
17	#446×C₆₇	—	2	2	no	—
18	#432×C₆₇	—	2	2	no	—
19	#431×C₆₇	C₂²	1	2	yes	—
20	C₂×#11761612	C₂×C₄	1	2	yes	—
21	C₂×#11761612	C₂×C₄	1	2	yes	—
22	C₂²×C₆₇⋊C₈	—	2	1	no	—
23	C₂²×C₆₇⋊C₈	—	2	1	no	—
24	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
25	#14523962	—	2	4	no	—
26	#14523954	—	2	2	no	—
27	C₄×C₆₇⋊C₈	—	2	2	no	—
28	C₄×C₆₇⋊C₈	—	2	2	no	—
29	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
30	C₄×Q₈×C₆₇	—	2	2	no	—
31	C₄×Q₈×C₆₇	—	2	2	no	—
32	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₆₇	Q₈	1	2	yes	—
34	C₂×C₄²×C₆₇	D₄	1	2	yes	—
35	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
36	C₄⋊C₈×C₆₇	—	2	2	no	—
37	C₄⋊C₈×C₆₇	—	2	2	no	—
38	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
39	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
40	C₂²⋊C₈×C₆₇	—	2	2	no	—
41	#97×C₆₇	—	2	4	no	—
42	C₄×C₈×C₆₇	—	2	2	no	—
43	#11761612	—	2	2	no	—
44	#11761612	—	2	2	no	—
45	#11761612	—	2	2	no	—
46	#11761612	M₁₆	1	4	yes	—
47	C₂×C₆₇⋊C₈	—	2	2	no	—
48	C₂×C₆₇⋊C₈	—	2	2	no	—
49	C₂×C₆₇⋊C₈	—	2	2	no	—
50	C₂×C₆₇⋊C₈	—	4	1	no	—
51	C₂×C₆₇⋊C₈	—	4	1	no	—
52	C₂×C₆₇⋊C₈	—	4	2	no	—
53	C₂×C₆₇⋊C₈	—	4	1	no	—
54	C₂×Q₈×C₆₇	—	2	2	no	—
55	C₂×Q₈×C₆₇	—	2	2	no	—
56	C₂×Q₈×C₆₇	—	2	1	no	—
57	C₂×Q₈×C₆₇	—	2	1	no	—
58	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
59	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
60	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
61	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
62	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
63	C₂×C₈×C₆₇	—	2	2	no	—
64	C₂×C₈×C₆₇	—	2	2	no	—
65	C₄⋊C₄×C₆₇	—	2	2	no	—
66	C₄⋊C₄×C₆₇	—	2	4	no	—
67	C₄²×C₆₇	—	2	2	no	—
68	C₄²×C₆₇	—	2	2	no	—
69	C₄²×C₆₇	C₂×D₄	1	2	yes	—
70	C₄²×C₆₇	#41	1	2	yes	—
71	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
72	Q₈×C₆₇	—	4	2	no	—
73	Q₈×C₆₇	—	4	2	no	—
74	C₂×C₄×C₆₇	—	2	1	no	—
75	C₂×C₄×C₆₇	—	2	1	no	—
76	C₂×C₄×C₆₇	—	2	2	no	—
77	C₂×C₄×C₆₇	—	2	2	no	—
78	C₂×C₄×C₆₇	—	2	2	no	—
79	C₂×C₄×C₆₇	—	2	2	no	—
80	C₂×C₄×C₆₇	—	4	1	no	—
81	C₂×C₄×C₆₇	—	4	2	no	—
82	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
83	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
84	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
85	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
86	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
87	C₂×C₄×C₆₇	#131	1	1	yes	characteristic
88	C₂×C₄×C₆₇	#131	1	1	yes	characteristic
89	C₈×C₆₇	—	4	2	no	—
90	C₈×C₆₇	—	4	2	no	—
91	C₆₇⋊C₈	—	2	4	no	—
92	C₆₇⋊C₈	—	4	2	no	—
93	C₆₇⋊C₈	—	4	2	no	—
94	C₆₇⋊C₈	—	8	1	no	—
95	C₂²×C₆₇	—	2	1	no	—
96	C₂²×C₆₇	—	2	1	no	—
97	C₂²×C₆₇	#385	1	1	yes	characteristic
98	C₂²×C₆₇	#423	1	1	yes	characteristic
99	C₂²×C₆₇	#424	1	1	yes	characteristic
100	C₄×C₆₇	—	2	1	no	—
101	C₄×C₆₇	—	2	2	no	—
102	C₄×C₆₇	—	4	2	no	—
103	C₄×C₆₇	—	4	2	no	—
104	C₄×C₆₇	#435	1	2	yes	—
105	C₄×C₆₇	#436	1	2	yes	—
106	C₄×C₆₇	#454	1	1	yes	characteristic
107	C₄×C₆₇	#456	1	1	yes	characteristic
108	#8838	—	67	1	no	maximal, Sylow
109	C₂×C₆₇	—	2	1	no	—
110	C₂×C₆₇	—	2	1	no	—
111	C₂×C₆₇	#1851	1	1	yes	characteristic
112	C₂×C₆₇	#1857	1	1	yes	characteristic
113	C₂×C₆₇	#1858	1	1	yes	characteristic
114	#2983	D₆₇	1	1	yes	characteristic
115	#1984	—	67	1	no	—
116	C₄×#101	—	67	1	no	—
117	#1565	—	67	2	no	—
118	#1278	—	67	2	no	—
119	C₆₇	#8838	1	1	yes	characteristic, complemented, Sylow
120	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
121	#446	—	2	2	no	—
122	#446	—	2	2	no	—
123	#432	—	2	2	no	—
124	#431	C₂×D₆₇	1	2	yes	—
125	C₂×C₄⋊C₈	—	67	1	no	—
126	C₂×#101	—	67	2	no	—
127	C₄×M₁₆	—	67	2	no	—
128	C₂×C₄×C₈	—	67	1	no	—
129	#343	—	67	1	no	—
130	#343	—	67	1	no	—
131	#336	—	134	2	no	—
132	#335	—	134	2	no	—
133	#334	—	134	2	no	—
134	C₂²×Q₈	C₄×D₆₇	1	1	yes	characteristic
135	C₂×M₁₆	—	67	2	no	—
136	C₂×M₁₆	—	67	2	no	—
137	C₂²×C₈	—	134	1	no	—
138	C₂²×C₈	—	134	1	no	—
139	C₄×Q₈	—	2	2	no	—
140	C₄×Q₈	—	2	2	no	—
141	C₂×C₄⋊C₄	Dic₁₃₄	1	2	yes	—
142	C₂×C₄⋊C₄	C₄×D₆₇	1	1	yes	characteristic
143	C₂×C₄²	C₂²⋊D₆₇	1	2	yes	—
144	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
145	C₄⋊C₈	—	2	2	no	—
146	C₄⋊C₈	—	2	2	no	—
147	C₄⋊C₈	—	134	2	no	—
148	C₄⋊C₈	C₂²⋊D₆₇	1	2	yes	—
149	C₄⋊C₈	C₂²⋊D₆₇	1	2	yes	—
150	#101	—	134	4	no	—
151	C₂²⋊C₈	—	2	2	no	—
152	#97	—	2	4	no	—
153	#97	—	134	2	no	—
154	C₄×C₈	—	2	2	no	—
155	C₄×C₈	—	134	2	no	—
156	C₄×C₈	—	134	2	no	—
157	C₂×Q₈	—	2	2	no	—
158	C₂×Q₈	—	2	2	no	—
159	C₂×Q₈	—	2	1	no	—
160	C₂×Q₈	—	2	1	no	—
161	C₂²×C₄	Dic₆₇⋊C₄	1	2	yes	—
162	C₂²×C₄	Dic₆₇⋊C₄	1	2	yes	—
163	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
164	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
165	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
166	M₁₆	—	67	4	no	—
167	M₁₆	—	134	2	no	—
168	M₁₆	—	134	2	no	—
169	M₁₆	—	134	2	no	—
170	C₂×C₈	—	2	2	no	—
171	C₂×C₈	—	2	2	no	—
172	C₂×C₈	—	268	1	no	—
173	C₂×C₈	—	268	1	no	—
174	C₂×C₈	—	268	2	no	—
175	C₂×C₈	—	268	1	no	—
176	C₂×C₈	—	134	2	no	—
177	C₂×C₈	—	134	2	no	—
178	C₂×C₈	—	134	2	no	—
179	C₄⋊C₄	—	2	2	no	—
180	C₄⋊C₄	—	2	4	no	—
181	C₄²	—	2	2	no	—
182	C₄²	—	2	2	no	—
183	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
184	C₄²	#11761628	1	2	yes	—
185	C₂³	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
186	Q₈	—	4	2	no	—
187	Q₈	—	4	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	4	1	no	—
195	C₂×C₄	—	4	2	no	—
196	C₂×C₄	C₄×C₂²⋊D₆₇	1	2	yes	—
197	C₂×C₄	#14524012	1	1	yes	characteristic
198	C₂×C₄	#14524022	1	2	yes	—
199	C₂×C₄	#14524026	1	1	yes	characteristic
200	C₂×C₄	M₁₆×D₆₇	1	2	yes	—
201	C₂×C₄	#14524051	1	1	yes	characteristic
202	C₂×C₄	#14524051	1	1	yes	characteristic
203	C₈	—	4	2	no	—
204	C₈	—	4	2	no	—
205	C₈	—	268	2	no	—
206	C₈	—	268	2	no	—
207	C₈	—	536	1	no	—
208	C₈	—	134	4	no	—
209	C₂²	—	2	1	no	—
210	C₂²	—	2	1	no	—
211	C₂²	#16863269	1	1	yes	characteristic
212	C₂²	#16863419	1	1	yes	characteristic
213	C₂²	#16863424	1	1	yes	characteristic
214	C₄	—	2	1	no	—
215	C₄	—	2	2	no	—
216	C₄	—	4	2	no	—
217	C₄	—	4	2	no	—
218	C₄	#16863465	1	2	yes	—
219	C₄	#16863472	1	2	yes	—
220	C₄	#16863569	1	1	yes	characteristic
221	C₄	#16863579	1	1	yes	characteristic
222	C₂	—	2	1	no	—
223	C₂	—	2	1	no	—
224	C₂	#22560392	1	1	yes	characteristic
225	C₂	#22560424	1	1	yes	characteristic
226	C₂	#22560429	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22561146

C₂

yes

maximal, characteristic

C₄×#14523962

C₂

yes

maximal, characteristic

#22558962

C₂

yes

maximal

#22558045

C₂

yes

maximal

C₆₇×#2983

C₂

yes

maximal, characteristic

C₂×C₄⋊(C₆₇⋊C₈)

C₂²

yes

characteristic

C₂×#14523962

C₄

yes

—

C₄×#11761612

C₂²

yes

—

C₂×C₄×C₆₇⋊C₈

C₂²

yes

characteristic

#16863165

C₄

yes

characteristic

#16863165

C₄

yes

—

—

—

C₂×C₄×Q₈×C₆₇

C₂²

yes

characteristic

#446×C₆₇

—

#446×C₆₇

—

#432×C₆₇

—

#431×C₆₇

C₂²

yes

—

C₂×#11761612

C₂×C₄

yes

—

C₂×#11761612

C₂×C₄

yes

—

C₂²×C₆₇⋊C₈

—

C₂²×C₆₇⋊C₈

—

C₄⋊(C₆₇⋊C₈)

—

#14523962

—

#14523954

—

C₄×C₆₇⋊C₈

—

C₄×C₆₇⋊C₈

—

C₂²×Q₈×C₆₇

C₂×C₄

yes

characteristic

C₄×Q₈×C₆₇

—

C₄×Q₈×C₆₇

—

C₂×C₄⋊C₄×C₆₇

C₂×C₄

yes

characteristic

C₂×C₄⋊C₄×C₆₇

Q₈

yes

—

C₂×C₄²×C₆₇

D₄

yes

—

C₂×C₄²×C₆₇

C₂³

yes

characteristic

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

D₄

yes

—

C₄⋊C₈×C₆₇

D₄

yes

—

C₂²⋊C₈×C₆₇

—

#97×C₆₇

—

C₄×C₈×C₆₇

—

—

—

—

M₁₆

yes

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂×Q₈×C₆₇

—

C₂²×C₄×C₆₇

C₄⋊C₄

yes

—

C₂²×C₄×C₆₇

C₄⋊C₄

yes

—

C₂²×C₄×C₆₇

C₂²×C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

C₂×D₄

yes

—

C₄²×C₆₇

#41

yes

—

C₂³×C₆₇

C₂×C₄⋊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

C₄×D₄

yes

—

C₂×C₄×C₆₇

#120

yes

characteristic

C₂×C₄×C₆₇

C₂²⋊Q₈

yes

—

C₂×C₄×C₆₇

#123

yes

characteristic

C₂×C₄×C₆₇

C₂×M₁₆

yes

—

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₈×C₆₇

—

C₈×C₆₇

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

yes

C₂²×C₆₇

yes

C₂²×C₆₇

yes

100

C₄×C₆₇

—

101

C₄×C₆₇

—

102

C₄×C₆₇

—

103

C₄×C₆₇

—

104

C₄×C₆₇

#435

yes

—

105

C₄×C₆₇

#436

yes

—

106

C₄×C₆₇

#454

yes

characteristic

107

C₄×C₆₇

yes

108

—

109

C₂×C₆₇

—

110

C₂×C₆₇

—

111

C₂×C₆₇

#1851

yes

characteristic

112

C₂×C₆₇

#1857

yes

characteristic

113

C₂×C₆₇

#1858

yes

characteristic

114

#2983

D₆₇

yes

characteristic

115

#1984

—

116

C₄×#101

—

117

#1565

—

118

#1278

—

119

C₆₇

#8838

yes

characteristic, complemented, Sylow

120

C₂×C₄×Q₈

C₂×D₆₇

yes

characteristic

121

#446

—

122

#446

—

123

#432

—

124

#431

C₂×D₆₇

yes

—

125

C₂×C₄⋊C₈

—

126

C₂×#101

—

127

C₄×M₁₆

—

128

C₂×C₄×C₈

—

129

#343

—

130

#343

—

131

#336

—

134

—

132

#335

—

134

—

133

#334

—

134

—

134

C₂²×Q₈

C₄×D₆₇

yes

characteristic

135

C₂×M₁₆

—

136

C₂×M₁₆

—

137

C₂²×C₈

—

134

—

138

C₂²×C₈

—

134

—

139

C₄×Q₈

—

140

C₄×Q₈

—

141

C₂×C₄⋊C₄

Dic₁₃₄

yes

—

142

C₂×C₄⋊C₄

C₄×D₆₇

yes

characteristic

143

C₂×C₄²

C₂²⋊D₆₇

yes

—

144

C₂×C₄²

C₂²×D₆₇

yes

characteristic

145

C₄⋊C₈

—

146

C₄⋊C₈

—

147

C₄⋊C₈

—

134

—

148

C₄⋊C₈

C₂²⋊D₆₇

yes

—

149

C₄⋊C₈

C₂²⋊D₆₇

yes

—

150

#101

—

134

—

151

C₂²⋊C₈

—

152

#97

—

153

#97

—

134

—

154

C₄×C₈

—

155

C₄×C₈

—

134

—

156

C₄×C₈

—

134

—

157

C₂×Q₈

—

158

C₂×Q₈

—

159

C₂×Q₈

—

160

C₂×Q₈

—

161

C₂²×C₄

Dic₆₇⋊C₄

yes

—

162

C₂²×C₄

Dic₆₇⋊C₄

yes

—

163

C₂²×C₄

C₂×C₄×D₆₇

yes

characteristic

164

C₂²×C₄

C₂×C₂²⋊D₆₇

yes

characteristic

165

C₂²×C₄

C₂×Dic₁₃₄

yes

characteristic

166

M₁₆

—

167

M₁₆

—

134

—

168

M₁₆

—

134

—

169

M₁₆

—

134

—

170

C₂×C₈

—

171

C₂×C₈

—

172

C₂×C₈

—

268

—

173

C₂×C₈

—

268

—

174

C₂×C₈

—

268

—

175

C₂×C₈

—

268

—

176

C₂×C₈

—

134

—

177

C₂×C₈

—

134

—

178

C₂×C₈

—

134

—

179

C₄⋊C₄

—

180

C₄⋊C₄

—

181

C₄²

—

182

C₄²

—

183

C₄²

C₂×C₂²⋊D₆₇

yes

—

184

C₄²

#11761628

yes

—

185

C₂³

C₂×Dic₆₇⋊C₄

yes

characteristic

186

Q₈

—

187

Q₈

—

188

C₂×C₄

—

189

C₂×C₄

—

190

C₂×C₄

—

191

C₂×C₄

—

192

C₂×C₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

—

196

C₂×C₄

C₄×C₂²⋊D₆₇

yes

—

197

C₂×C₄

#14524012

yes

characteristic

198

C₂×C₄

#14524022

yes

—

199

C₂×C₄

#14524026

yes

characteristic

200

C₂×C₄

M₁₆×D₆₇

yes

—

201

C₂×C₄

#14524051

yes

characteristic

202

C₂×C₄

#14524051

yes

characteristic

203

C₈

—

204

C₈

—

205

C₈

—

268

—

206

C₈

—

268

—

207

C₈

—

536

—

208

C₈

—

134

—

209

C₂²

—

210

C₂²

—

211

C₂²

#16863269

yes

characteristic

212

C₂²

#16863419

yes

characteristic

213

C₂²

#16863424

yes

characteristic

214

C₄

—

215

C₄

—

216

C₄

—

217

C₄

—

218

C₄

#16863465

yes

—

219

C₄

#16863472

yes

—

220

C₄

#16863569

yes

characteristic

221

C₄

#16863579

yes

characteristic

222

C₂

—

223

C₂

—

224

C₂

#22560392

yes

characteristic

225

C₂

#22560424

yes

characteristic

226

C₂

#22560429

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#14524012
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#2983	C₂
socle	C₂²×C₆₇	#385
prime radical	C₂³×C₆₇	C₂×C₄⋊C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#2983	D₆₇
hypocenter	C₆₇	#8838
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2983

subgroup

G/H

center

C₂×C₄

#14524012

commutator

C₂²×C₄×C₆₇

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₆₇

Fitting

C₆₇×#2983

C₂

socle

C₂²×C₆₇

#385

prime radical

C₂³×C₆₇

C₂×C₄⋊C₄

cosocle

C₂×C₄²×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂²×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #2983

N	H ≅ G/N	type
119. C₆₇	#8838	semidirect

H ≅ G/N

type

119. C₆₇

#8838

semidirect

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

subgroup	index
#22561146	2
C₄×#14523962	2
#22558962	2
#22558045	2
C₆₇×#2983	2
#8838	67

subgroup

index

C₆₇×#2983

Subgroups — #30749708

Conjugacy classes of subgroups

Complements

Maximal subgroups