Group #30765019 — subgroups

Subgroups — #30765019

Order 17152.

364 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₂×#16863178	C₂	1	2	yes	maximal
2	#22558160	C₂	1	4	yes	maximal, complemented
3	C₆₇×#2905	C₂	1	1	yes	maximal, characteristic
4	C₂×#14523983	—	2	2	no	—
5	#16863178	—	2	2	no	—
6	#16863178	C₂²	1	4	yes	—
7	C₂²×M₁₆×C₆₇	C₄	1	1	yes	characteristic
8	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
9	C₂×#117×C₆₇	C₄	1	1	yes	characteristic
10	#424×C₆₇	—	2	2	no	—
11	#424×C₆₇	—	2	2	no	—
12	#423×C₆₇	C₄	1	2	yes	—
13	#423×C₆₇	C₂²	1	2	yes	—
14	#14523983	—	2	4	no	—
15	#14523983	—	4	2	no	—
16	C₂×C₆₇⋊C₁₆	—	4	2	no	—
17	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
18	C₂×M₁₆×C₆₇	—	2	1	no	—
19	C₂×M₁₆×C₆₇	—	4	2	no	—
20	C₂×M₁₆×C₆₇	—	4	2	no	—
21	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
22	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
23	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
24	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₆₇	—	2	1	no	—
26	C₂²×C₈×C₆₇	D₄	1	2	yes	—
27	#117×C₆₇	—	2	1	no	—
28	#117×C₆₇	—	2	1	no	—
29	#117×C₆₇	C₈	1	2	yes	—
30	#117×C₆₇	C₈	1	2	yes	—
31	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
32	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
33	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
34	C₄⋊C₈×C₆₇	—	2	4	no	—
35	C₄⋊C₈×C₆₇	—	2	4	no	—
36	C₆₇⋊C₁₆	—	4	4	no	—
37	C₂⁴×C₆₇	M₁₆	1	1	yes	characteristic
38	C₂²×C₄×C₆₇	—	2	2	no	—
39	C₂²×C₄×C₆₇	—	2	2	no	—
40	C₂²×C₄×C₆₇	—	2	2	no	—
41	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
42	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
44	C₂²×C₄×C₆₇	C₂×C₈	1	1	yes	characteristic
45	C₂²×C₄×C₆₇	M₁₆	1	1	yes	characteristic
46	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
47	M₁₆×C₆₇	—	4	1	no	—
48	M₁₆×C₆₇	—	4	2	no	—
49	M₁₆×C₆₇	—	4	1	no	—
50	M₁₆×C₆₇	—	4	2	no	—
51	M₁₆×C₆₇	—	4	2	no	—
52	C₂×C₈×C₆₇	—	2	2	no	—
53	C₂×C₈×C₆₇	—	2	2	no	—
54	C₂×C₈×C₆₇	—	2	2	no	—
55	C₂×C₈×C₆₇	—	4	2	no	—
56	C₂×C₈×C₆₇	C₂²⋊C₄	1	2	yes	—
57	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
58	C₄⋊C₄×C₆₇	—	2	2	no	—
59	C₄⋊C₄×C₆₇	—	2	2	no	—
60	C₂²⋊C₄×C₆₇	—	2	2	no	—
61	C₂²⋊C₄×C₆₇	—	2	2	no	—
62	C₄²×C₆₇	—	2	2	no	—
63	C₄²×C₆₇	C₂×C₈	1	4	yes	—
64	C₂³×C₆₇	—	2	2	no	—
65	C₂³×C₆₇	—	8	1	no	—
66	C₂³×C₆₇	C₂²⋊C₈	1	1	yes	characteristic
67	C₂³×C₆₇	C₂²⋊C₈	1	1	yes	characteristic
68	C₂³×C₆₇	C₂×M₁₆	1	1	yes	characteristic
69	C₂×C₄×C₆₇	—	2	2	no	—
70	C₂×C₄×C₆₇	—	2	2	no	—
71	C₂×C₄×C₆₇	—	2	2	no	—
72	C₂×C₄×C₆₇	—	2	1	no	—
73	C₂×C₄×C₆₇	—	2	1	no	—
74	C₂×C₄×C₆₇	—	2	1	no	—
75	C₂×C₄×C₆₇	—	2	1	no	—
76	C₂×C₄×C₆₇	—	2	4	no	—
77	C₂×C₄×C₆₇	—	8	2	no	—
78	C₂×C₄×C₆₇	C₂²⋊C₈	1	1	yes	characteristic
79	C₂×C₄×C₆₇	C₂²⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₆₇	#99	1	2	yes	—
81	C₂×C₄×C₆₇	#101	1	2	yes	—
82	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
84	C₈×C₆₇	—	2	2	no	—
85	C₈×C₆₇	—	2	2	no	—
86	C₈×C₆₇	—	4	2	no	—
87	C₂²×C₆₇	—	2	1	no	—
88	C₂²×C₆₇	—	2	1	no	—
89	C₂²×C₆₇	—	4	1	no	—
90	C₂²×C₆₇	—	4	1	no	—
91	C₂²×C₆₇	—	4	1	no	—
92	C₂²×C₆₇	—	8	2	no	—
93	C₂²×C₆₇	#324	1	2	yes	—
94	C₂²×C₆₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
95	C₄×C₆₇	—	2	1	no	—
96	C₄×C₆₇	—	2	1	no	—
97	C₄×C₆₇	—	4	4	no	—
98	C₄×C₆₇	#324	1	2	yes	—
99	C₄×C₆₇	C₂×#99	1	1	yes	characteristic
100	C₄×C₆₇	C₂×#101	1	1	yes	characteristic
101	#11456	—	67	1	no	maximal, Sylow
102	C₂×C₆₇	—	2	1	no	—
103	C₂×C₆₇	—	2	2	no	—
104	C₂×C₆₇	—	4	1	no	—
105	C₂×C₆₇	—	4	1	no	—
106	C₂×C₆₇	C₂×#324	1	1	yes	characteristic
107	#2905	D₆₇	1	1	yes	characteristic
108	C₂×#349	—	67	2	no	—
109	#1327	—	67	4	no	—
110	C₆₇	#11456	1	1	yes	characteristic, complemented, Sylow
111	C₂²×M₁₆	Dic₆₇	1	1	yes	characteristic
112	C₂²×M₁₆	C₂×D₆₇	1	1	yes	characteristic
113	C₂×#117	Dic₆₇	1	1	yes	characteristic
114	C₂×M₃₂	—	134	2	no	—
115	#424	—	2	2	no	—
116	#424	—	2	2	no	—
117	#423	Dic₆₇	1	2	yes	—
118	#423	C₂×D₆₇	1	2	yes	—
119	#349	—	67	4	no	—
120	#349	—	134	2	no	—
121	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
122	C₂×M₁₆	—	2	1	no	—
123	C₂×M₁₆	—	4	2	no	—
124	C₂×M₁₆	—	4	2	no	—
125	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
126	C₂×M₁₆	C₂×Dic₆₇	1	1	yes	characteristic
127	C₂×M₁₆	C₂²⋊D₆₇	1	2	yes	—
128	C₂×M₁₆	C₂²×D₆₇	1	1	yes	characteristic
129	C₂²×C₈	—	2	1	no	—
130	C₂²×C₈	C₂²⋊D₆₇	1	2	yes	—
131	#117	—	2	1	no	—
132	#117	—	2	1	no	—
133	#117	C₆₇⋊C₈	1	2	yes	—
134	#117	C₆₇⋊C₈	1	2	yes	—
135	C₂×C₄⋊C₄	—	2	1	no	—
136	C₂×C₂²⋊C₄	—	2	1	no	—
137	C₂×C₄²	C₂×Dic₆₇	1	2	yes	—
138	M₃₂	—	268	2	no	—
139	M₃₂	—	134	4	no	—
140	C₂×C₁₆	—	268	2	no	—
141	C₄⋊C₈	—	2	4	no	—
142	C₄⋊C₈	—	2	4	no	—
143	C₂⁴	#11761612	1	1	yes	characteristic
144	C₂²×C₄	—	2	2	no	—
145	C₂²×C₄	—	2	2	no	—
146	C₂²×C₄	—	2	2	no	—
147	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
148	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
149	C₂²×C₄	C₂×C₆₇⋊C₈	1	1	yes	characteristic
150	C₂²×C₄	C₂×C₆₇⋊C₈	1	1	yes	characteristic
151	C₂²×C₄	#11761612	1	1	yes	characteristic
152	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
153	M₁₆	—	4	1	no	—
154	M₁₆	—	4	2	no	—
155	M₁₆	—	4	1	no	—
156	M₁₆	—	4	2	no	—
157	M₁₆	—	4	2	no	—
158	C₂×C₈	—	2	2	no	—
159	C₂×C₈	—	2	2	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	4	2	no	—
162	C₂×C₈	C₂²⋊Dic₆₇	1	2	yes	—
163	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
164	C₄⋊C₄	—	2	2	no	—
165	C₄⋊C₄	—	2	2	no	—
166	C₂²⋊C₄	—	2	2	no	—
167	C₂²⋊C₄	—	2	2	no	—
168	C₄²	—	2	2	no	—
169	C₄²	C₂×C₆₇⋊C₈	1	4	yes	—
170	C₁₆	—	268	4	no	—
171	C₂³	—	2	2	no	—
172	C₂³	—	8	1	no	—
173	C₂³	C₂²⋊(C₆₇⋊C₈)	1	1	yes	characteristic
174	C₂³	C₂²⋊(C₆₇⋊C₈)	1	1	yes	characteristic
175	C₂³	C₂×#11761612	1	1	yes	characteristic
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	1	no	—
178	C₂×C₄	—	2	1	no	—
179	C₂×C₄	—	2	1	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	2	no	—
183	C₂×C₄	—	2	4	no	—
184	C₂×C₄	—	8	2	no	—
185	C₂×C₄	C₂²⋊(C₆₇⋊C₈)	1	1	yes	characteristic
186	C₂×C₄	C₂²⋊(C₆₇⋊C₈)	1	1	yes	characteristic
187	C₂×C₄	#14523958	1	2	yes	—
188	C₂×C₄	#14523962	1	2	yes	—
189	C₂×C₄	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
190	C₂×C₄	C₂²×C₆₇⋊C₈	1	1	yes	characteristic
191	C₈	—	2	2	no	—
192	C₈	—	2	2	no	—
193	C₈	—	4	2	no	—
194	C₂²	—	2	1	no	—
195	C₂²	—	2	1	no	—
196	C₂²	—	4	1	no	—
197	C₂²	—	4	1	no	—
198	C₂²	—	4	1	no	—
199	C₂²	—	8	2	no	—
200	C₂²	#16863122	1	2	yes	—
201	C₂²	C₂×C₂²⋊(C₆₇⋊C₈)	1	1	yes	characteristic
202	C₄	—	2	1	no	—
203	C₄	—	2	1	no	—
204	C₄	—	4	4	no	—
205	C₄	#16863122	1	2	yes	—
206	C₄	C₂×#14523958	1	1	yes	characteristic
207	C₄	C₂×#14523962	1	1	yes	characteristic
208	C₂	—	2	1	no	—
209	C₂	—	2	2	no	—
210	C₂	—	4	1	no	—
211	C₂	—	4	1	no	—
212	C₂	C₂×#16863122	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#16863178

C₂

yes

maximal

#22558160

C₂

yes

maximal, complemented

C₆₇×#2905

C₂

yes

maximal, characteristic

C₂×#14523983

—

#16863178

—

#16863178

C₂²

yes

—

C₂²×M₁₆×C₆₇

C₄

yes

characteristic

C₂²×M₁₆×C₆₇

C₂²

yes

characteristic

C₂×#117×C₆₇

C₄

yes

characteristic

#424×C₆₇

—

#424×C₆₇

—

#423×C₆₇

C₄

yes

—

#423×C₆₇

C₂²

yes

—

#14523983

—

#14523983

—

C₂×C₆₇⋊C₁₆

—

C₂³×C₄×C₆₇

C₂×C₄

yes

characteristic

C₂×M₁₆×C₆₇

—

C₂×M₁₆×C₆₇

—

C₂×M₁₆×C₆₇

—

C₂×M₁₆×C₆₇

C₂×C₄

yes

—

C₂×M₁₆×C₆₇

C₂×C₄

yes

characteristic

C₂×M₁₆×C₆₇

D₄

yes

—

C₂×M₁₆×C₆₇

C₂³

yes

characteristic

C₂²×C₈×C₆₇

—

C₂²×C₈×C₆₇

D₄

yes

—

#117×C₆₇

—

#117×C₆₇

—

#117×C₆₇

C₈

yes

—

#117×C₆₇

C₈

yes

—

C₂×C₄⋊C₄×C₆₇

—

C₂×C₂²⋊C₄×C₆₇

—

C₂×C₄²×C₆₇

C₂×C₄

yes

—

C₄⋊C₈×C₆₇

—

C₄⋊C₈×C₆₇

—

C₆₇⋊C₁₆

—

C₂⁴×C₆₇

M₁₆

yes

characteristic

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₆₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₆₇

C₂×C₈

yes

characteristic

C₂²×C₄×C₆₇

M₁₆

yes

characteristic

C₂²×C₄×C₆₇

C₂²×C₄

yes

characteristic

M₁₆×C₆₇

—

M₁₆×C₆₇

—

M₁₆×C₆₇

—

M₁₆×C₆₇

—

M₁₆×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²⋊C₄

yes

—

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₂²⋊C₄×C₆₇

—

C₄²×C₆₇

—

C₄²×C₆₇

C₂×C₈

yes

—

C₂³×C₆₇

—

C₂³×C₆₇

—

C₂³×C₆₇

C₂²⋊C₈

yes

characteristic

C₂³×C₆₇

C₂²⋊C₈

yes

characteristic

C₂³×C₆₇

C₂×M₁₆

yes

characteristic

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

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₆₇

C₂²⋊C₈

yes

characteristic

C₂×C₄×C₆₇

#99

yes

—

C₂×C₄×C₆₇

#101

yes

—

C₂×C₄×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₆₇

C₂²×C₈

yes

characteristic

C₈×C₆₇

—

C₈×C₆₇

—

C₈×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

—

C₂²×C₆₇

#324

yes

—

C₂²×C₆₇

C₂×C₂²⋊C₈

yes

characteristic

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

—

C₄×C₆₇

#324

yes

—

C₄×C₆₇

C₂×#99

yes

characteristic

100

C₄×C₆₇

yes

101

—

102

C₂×C₆₇

—

103

C₂×C₆₇

—

104

C₂×C₆₇

—

105

C₂×C₆₇

—

106

C₂×C₆₇

C₂×#324

yes

characteristic

107

#2905

D₆₇

yes

characteristic

108

C₂×#349

—

109

#1327

—

110

C₆₇

#11456

yes

characteristic, complemented, Sylow

111

C₂²×M₁₆

Dic₆₇

yes

characteristic

112

C₂²×M₁₆

C₂×D₆₇

yes

characteristic

113

C₂×#117

Dic₆₇

yes

characteristic

114

C₂×M₃₂

—

134

—

115

#424

—

116

#424

—

117

#423

Dic₆₇

yes

—

118

#423

C₂×D₆₇

yes

—

119

#349

—

120

#349

—

134

—

121

C₂³×C₄

C₂×Dic₆₇

yes

characteristic

122

C₂×M₁₆

—

123

C₂×M₁₆

—

124

C₂×M₁₆

—

125

C₂×M₁₆

C₂×Dic₆₇

yes

—

126

C₂×M₁₆

C₂×Dic₆₇

yes

characteristic

127

C₂×M₁₆

C₂²⋊D₆₇

yes

—

128

C₂×M₁₆

C₂²×D₆₇

yes

characteristic

129

C₂²×C₈

—

130

C₂²×C₈

C₂²⋊D₆₇

yes

—

131

#117

—

132

#117

—

133

#117

C₆₇⋊C₈

yes

—

134

#117

C₆₇⋊C₈

yes

—

135

C₂×C₄⋊C₄

—

136

C₂×C₂²⋊C₄

—

137

C₂×C₄²

C₂×Dic₆₇

yes

—

138

M₃₂

—

268

—

139

M₃₂

—

134

—

140

C₂×C₁₆

—

268

—

141

C₄⋊C₈

—

142

C₄⋊C₈

—

143

C₂⁴

#11761612

yes

characteristic

144

C₂²×C₄

—

145

C₂²×C₄

—

146

C₂²×C₄

—

147

C₂²×C₄

C₂²⋊Dic₆₇

yes

characteristic

148

C₂²×C₄

C₂²⋊Dic₆₇

yes

characteristic

149

C₂²×C₄

C₂×C₆₇⋊C₈

yes

characteristic

150

C₂²×C₄

C₂×C₆₇⋊C₈

yes

characteristic

151

C₂²×C₄

#11761612

yes

characteristic

152

C₂²×C₄

C₂²×Dic₆₇

yes

characteristic

153

M₁₆

—

154

M₁₆

—

155

M₁₆

—

156

M₁₆

—

157

M₁₆

—

158

C₂×C₈

—

159

C₂×C₈

—

160

C₂×C₈

—

161

C₂×C₈

—

162

C₂×C₈

C₂²⋊Dic₆₇

yes

—

163

C₂×C₈

C₂×C₂²⋊D₆₇

yes

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

166

C₂²⋊C₄

—

167

C₂²⋊C₄

—

168

C₄²

—

169

C₄²

C₂×C₆₇⋊C₈

yes

—

170

C₁₆

—

268

—

171

C₂³

—

172

C₂³

—

173

C₂³

C₂²⋊(C₆₇⋊C₈)

yes

characteristic

174

C₂³

C₂²⋊(C₆₇⋊C₈)

yes

characteristic

175

C₂³

C₂×#11761612

yes

characteristic

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

—

185

C₂×C₄

C₂²⋊(C₆₇⋊C₈)

yes

characteristic

186

C₂×C₄

C₂²⋊(C₆₇⋊C₈)

yes

characteristic

187

C₂×C₄

#14523958

yes

—

188

C₂×C₄

#14523962

yes

—

189

C₂×C₄

C₂×C₂²⋊Dic₆₇

yes

characteristic

190

C₂×C₄

C₂²×C₆₇⋊C₈

yes

characteristic

191

C₈

—

192

C₈

—

193

C₈

—

194

C₂²

—

195

C₂²

—

196

C₂²

—

197

C₂²

—

198

C₂²

—

199

C₂²

—

200

C₂²

#16863122

yes

—

201

C₂²

C₂×C₂²⋊(C₆₇⋊C₈)

yes

characteristic

202

C₄

—

203

C₄

—

204

C₄

—

205

C₄

#16863122

yes

—

206

C₄

C₂×#14523958

yes

characteristic

207

C₄

C₂×#14523962

yes

characteristic

208

C₂

—

209

C₂

—

210

C₂

—

211

C₂

—

212

C₂

C₂×#16863122

yes

characteristic

	subgroup	G/H
center	C₄	C₂×#14523958
commutator	C₂×C₄×C₆₇	C₂²×C₈
Frattini	C₂×M₁₆	C₂²×D₆₇
Fitting	C₆₇×#2905	C₂
socle	C₂×C₆₇	C₂×#324
prime radical	C₂⁴×C₆₇	M₁₆
cosocle	C₂×M₁₆×C₆₇	C₂³
hypercenter	#2905	D₆₇
hypocenter	C₆₇	#11456
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ #2905

subgroup

G/H

center

C₄

C₂×#14523958

commutator

C₂×C₄×C₆₇

C₂²×C₈

Frattini

C₂×M₁₆

C₂²×D₆₇

Fitting

C₆₇×#2905

C₂

socle

C₂×C₆₇

C₂×#324

prime radical

C₂⁴×C₆₇

M₁₆

cosocle

C₂×M₁₆×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×M₁₆ ◁ #2905

N	H ≅ G/N	type
2. #22558160	C₂	semidirect
110. C₆₇	#11456	semidirect

H ≅ G/N

type

2. #22558160

C₂

semidirect

110. C₆₇

#11456

semidirect

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

subgroup	index
C₂×#16863178	2
#22558160	2
C₆₇×#2905	2
#11456	67

subgroup

index

C₂×#16863178

#22558160

C₆₇×#2905

#11456

Subgroups — #30765019

Conjugacy classes of subgroups

Complements

Maximal subgroups