Group #30774248 — subgroups

Subgroups — #30774248

Order 17152.

402 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 115 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	C₂²×Dic₅₃₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863211	C₂	1	2	yes	maximal
3	#22561805	C₂	1	1	yes	maximal, characteristic
4	#22561122	C₂	1	2	yes	maximal
5	C₂×#368×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₂₆₈	C₂²	1	2	yes	—
7	C₂×Dic₅₃₆	—	2	1	no	—
8	C₂×Dic₅₃₆	—	2	1	no	—
9	C₂×Dic₅₃₆	—	2	2	no	—
10	C₂×Dic₅₃₆	C₄	1	4	yes	complemented
11	C₂×#14523983	C₂²	1	1	yes	characteristic
12	#16863406	—	2	2	no	—
13	C₂×#14523961	—	2	2	no	—
14	#16863351	C₂²	1	1	yes	characteristic
15	#16863211	—	2	4	no	—
16	#16863171	—	2	1	no	—
17	C₁₆×Dic₆₇	—	2	1	no	—
18	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#108×C₆₇	C₂²	1	2	yes	—
20	#368×C₆₇	—	2	2	no	—
21	C₂²×Dic₁₃₄	—	2	2	no	—
22	C₂×Dic₂₆₈	—	2	2	no	—
23	C₂×Dic₂₆₈	—	2	2	no	—
24	C₂×Dic₂₆₈	—	2	2	no	—
25	C₂×Dic₂₆₈	—	2	2	no	—
26	C₂×Dic₂₆₈	—	2	2	no	—
27	C₂×Dic₂₆₈	C₂×C₄	1	4	yes	—
28	C₂×#11761612	D₄	1	1	yes	characteristic
29	#14524002	D₄	1	1	yes	characteristic
30	Dic₅₃₆	—	2	4	no	—
31	Dic₅₃₆	—	2	4	no	—
32	#14523983	—	2	1	no	—
33	#14523983	D₄	1	2	yes	—
34	C₂×C₆₇⋊C₁₆	—	2	1	no	—
35	#14523968	—	4	4	no	—
36	#14523961	—	4	4	no	—
37	#14523953	—	2	1	no	—
38	C₈×Dic₆₇	—	2	1	no	—
39	C₂×M₁₆×C₆₇	—	2	2	no	—
40	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
41	C₂×C₁₆×C₆₇	C₂×C₄	1	2	yes	—
42	C₂×C₁₆×C₆₇	D₄	1	1	yes	characteristic
43	C₂×C₁₆×C₆₇	D₄	1	1	yes	characteristic
44	C₂×C₁₆×C₆₇	D₄	1	2	yes	—
45	#108×C₆₇	—	2	2	no	—
46	#108×C₆₇	—	2	2	no	—
47	C₂×Dic₁₃₄	—	2	4	no	—
48	C₂×Dic₁₃₄	—	4	2	no	—
49	C₂×Dic₁₃₄	—	4	2	no	—
50	C₂×Dic₁₃₄	—	4	2	no	—
51	C₂×Dic₁₃₄	—	4	2	no	—
52	C₂×Dic₁₃₄	—	4	2	no	—
53	C₂²×Dic₆₇	—	4	2	no	—
54	Dic₂₆₈	—	2	4	no	—
55	Dic₂₆₈	—	2	4	no	—
56	Dic₂₆₈	—	4	2	no	—
57	Dic₂₆₈	—	4	2	no	—
58	#11761612	—	2	1	no	—
59	#11761612	D₈	1	2	yes	—
60	C₂×C₆₇⋊C₈	—	2	1	no	—
61	C₄⋊Dic₆₇	D₈	1	2	yes	—
62	C₂²⋊Dic₆₇	—	2	1	no	—
63	C₄×Dic₆₇	—	2	1	no	—
64	C₆₇⋊C₁₆	—	2	2	no	—
65	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
66	M₁₆×C₆₇	—	4	2	no	—
67	M₁₆×C₆₇	—	4	2	no	—
68	C₂×C₈×C₆₇	—	4	2	no	—
69	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
71	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
73	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
74	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
75	C₁₆×C₆₇	C₂²⋊C₄	1	2	yes	—
76	C₁₆×C₆₇	C₂²⋊C₄	1	2	yes	—
77	C₂³×C₆₇	#135	1	1	yes	characteristic
78	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
79	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
80	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
81	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
82	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
83	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
84	C₂×Dic₆₇	—	2	2	no	—
85	C₂×Dic₆₇	—	4	4	no	—
86	C₂×Dic₆₇	—	8	2	no	—
87	C₂×Dic₆₇	—	8	2	no	—
88	Dic₁₃₄	—	4	4	no	—
89	Dic₁₃₄	—	4	4	no	—
90	Dic₁₃₄	—	8	2	no	—
91	Dic₁₃₄	—	8	2	no	—
92	C₈×C₆₇	—	8	2	no	—
93	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
94	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
95	C₈×C₆₇	#121	1	1	yes	characteristic
96	C₈×C₆₇	#124	1	1	yes	characteristic
97	C₆₇⋊C₈	—	2	2	no	—
98	C₂²×C₆₇	—	2	2	no	—
99	C₂²×C₆₇	C₄×D₈	1	1	yes	characteristic
100	C₂²×C₆₇	#466	1	1	yes	characteristic
101	C₂²×C₆₇	#495	1	1	yes	characteristic
102	C₄×C₆₇	#390	1	1	yes	characteristic
103	C₄×C₆₇	C₄×D₈	1	1	yes	characteristic
104	C₄×C₆₇	#466	1	1	yes	characteristic
105	C₄×C₆₇	#493	1	1	yes	characteristic
106	Dic₆₇	—	4	2	no	—
107	Dic₆₇	—	8	4	no	—
108	#13244	—	67	1	no	maximal, Sylow
109	C₂×C₆₇	—	2	1	no	—
110	C₂×C₆₇	—	2	1	no	—
111	C₂×C₆₇	#1970	1	1	yes	characteristic
112	C₂×C₆₇	#2222	1	2	yes	—
113	C₂²×Q₃₂	—	67	1	no	—
114	C₂×#368	D₆₇	1	1	yes	characteristic
115	C₂×#362	—	67	2	no	—
116	#2108	—	67	1	no	—
117	#1979	—	67	2	no	—
118	C₆₇	#13244	1	1	yes	characteristic, complemented, Sylow
119	C₂²×Q₁₆	—	67	2	no	—
120	C₂×Q₃₂	—	67	4	no	—
121	C₂×Q₃₂	—	134	1	no	—
122	C₂×Q₃₂	—	134	1	no	—
123	C₂×Q₃₂	—	134	2	no	—
124	C₂×M₃₂	—	67	1	no	—
125	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
126	C₂×#108	C₂×D₆₇	1	2	yes	—
127	#419	—	134	2	no	—
128	C₂×#101	—	134	2	no	—
129	#405	—	67	1	no	—
130	#368	—	2	2	no	—
131	#362	—	134	4	no	—
132	#346	—	134	1	no	—
133	C₄×C₁₆	—	134	1	no	—
134	C₂²×Q₈	—	134	2	no	—
135	C₂×Q₁₆	—	67	4	no	—
136	C₂×Q₁₆	—	134	2	no	—
137	C₂×Q₁₆	—	134	2	no	—
138	C₂×Q₁₆	—	134	2	no	—
139	C₂×Q₁₆	—	134	2	no	—
140	C₂×Q₁₆	—	134	2	no	—
141	C₂×M₁₆	—	2	2	no	—
142	C₂×M₁₆	—	67	1	no	—
143	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
144	#117	—	67	1	no	—
145	Q₃₂	—	134	4	no	—
146	Q₃₂	—	134	4	no	—
147	M₃₂	—	67	2	no	—
148	M₃₂	—	134	1	no	—
149	C₂×C₁₆	—	134	1	no	—
150	C₂×C₁₆	C₄×D₆₇	1	2	yes	—
151	C₂×C₁₆	D₂₆₈	1	1	yes	characteristic
152	C₂×C₁₆	D₂₆₈	1	1	yes	characteristic
153	C₂×C₁₆	C₂²⋊D₆₇	1	2	yes	—
154	#108	—	2	2	no	—
155	#108	—	2	2	no	—
156	#103	—	268	4	no	—
157	#101	—	268	4	no	—
158	#97	—	134	1	no	—
159	C₄×C₈	—	134	1	no	—
160	C₂×Q₈	—	268	2	no	—
161	C₂×Q₈	—	268	2	no	—
162	C₂×Q₈	—	268	2	no	—
163	C₂×Q₈	—	268	2	no	—
164	C₂×Q₈	—	268	2	no	—
165	C₂×Q₈	—	134	4	no	—
166	C₂²×C₄	—	268	2	no	—
167	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
168	Q₁₆	—	268	2	no	—
169	Q₁₆	—	268	2	no	—
170	Q₁₆	—	134	4	no	—
171	Q₁₆	—	134	4	no	—
172	M₁₆	—	4	2	no	—
173	M₁₆	—	4	2	no	—
174	M₁₆	—	67	2	no	—
175	M₁₆	—	134	1	no	—
176	C₂×C₈	—	4	2	no	—
177	C₂×C₈	—	134	1	no	—
178	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
179	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
180	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
181	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
182	C₂×C₈	#11761629	1	1	yes	characteristic
183	C₂×C₈	#11761629	1	1	yes	characteristic
184	C₄⋊C₄	—	67	2	no	—
185	C₂²⋊C₄	—	134	1	no	—
186	C₄²	—	134	1	no	—
187	C₁₆	—	134	2	no	—
188	C₁₆	(C₂×D₆₇)⋊C₄	1	2	yes	—
189	C₁₆	(C₂×D₆₇)⋊C₄	1	2	yes	—
190	C₂³	#14524066	1	1	yes	characteristic
191	Q₈	—	268	4	no	—
192	Q₈	—	268	4	no	—
193	Q₈	—	536	2	no	—
194	Q₈	—	536	2	no	—
195	C₂×C₄	—	268	4	no	—
196	C₂×C₄	—	536	2	no	—
197	C₂×C₄	—	536	2	no	—
198	C₂×C₄	—	134	2	no	—
199	C₂×C₄	#14524005	1	1	yes	characteristic
200	C₂×C₄	#14524018	1	1	yes	characteristic
201	C₂×C₄	#14524039	1	1	yes	characteristic
202	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
203	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
204	C₂×C₄	#14524066	1	1	yes	characteristic
205	C₈	—	8	2	no	—
206	C₈	—	134	2	no	—
207	C₈	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
208	C₈	#14524005	1	1	yes	characteristic
209	C₈	#14524018	1	1	yes	characteristic
210	C₈	#14524032	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	#16863478	1	1	yes	characteristic
213	C₂²	#16863633	1	1	yes	characteristic
214	C₂²	#16863781	1	1	yes	characteristic
215	C₄	—	268	2	no	—
216	C₄	—	536	4	no	—
217	C₄	#16863297	1	1	yes	characteristic
218	C₄	#16863478	1	1	yes	characteristic
219	C₄	#16863633	1	1	yes	characteristic
220	C₄	#16863771	1	1	yes	characteristic
221	C₂	—	2	1	no	—
222	C₂	—	2	1	no	—
223	C₂	#22561073	1	1	yes	characteristic
224	C₂	#22562335	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₅₃₆

C₂

yes

maximal, characteristic

C₂×#16863211

C₂

yes

maximal

#22561805

C₂

yes

maximal, characteristic

#22561122

C₂

yes

maximal

C₂×#368×C₆₇

C₂

yes

maximal, characteristic

C₂²×Dic₂₆₈

C₂²

yes

—

C₂×Dic₅₃₆

—

C₂×Dic₅₃₆

—

C₂×Dic₅₃₆

—

C₂×Dic₅₃₆

C₄

yes

complemented

C₂×#14523983

C₂²

yes

—

—

C₂²

yes

characteristic

#16863211

—

#16863171

—

C₁₆×Dic₆₇

—

C₂²×C₁₆×C₆₇

C₂²

yes

characteristic

C₂×#108×C₆₇

C₂²

yes

—

#368×C₆₇

—

C₂²×Dic₁₃₄

—

C₂×Dic₂₆₈

—

C₂×Dic₂₆₈

—

C₂×Dic₂₆₈

—

C₂×Dic₂₆₈

—

C₂×Dic₂₆₈

—

C₂×Dic₂₆₈

C₂×C₄

yes

—

C₂×#11761612

D₄

yes

characteristic

#14524002

D₄

yes

characteristic

Dic₅₃₆

—

Dic₅₃₆

—

#14523983

—

#14523983

D₄

yes

—

C₂×C₆₇⋊C₁₆

—

#14523968

—

#14523961

—

#14523953

—

C₈×Dic₆₇

—

C₂×M₁₆×C₆₇

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

C₂×C₁₆×C₆₇

C₂×C₄

yes

—

C₂×C₁₆×C₆₇

D₄

yes

characteristic

C₂×C₁₆×C₆₇

D₄

yes

characteristic

C₂×C₁₆×C₆₇

D₄

yes

—

#108×C₆₇

—

#108×C₆₇

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂×Dic₁₃₄

—

C₂²×Dic₆₇

—

Dic₂₆₈

—

Dic₂₆₈

—

Dic₂₆₈

—

Dic₂₆₈

—

#11761612

—

#11761612

D₈

yes

—

C₂×C₆₇⋊C₈

—

C₄⋊Dic₆₇

D₈

yes

—

C₂²⋊Dic₆₇

—

C₄×Dic₆₇

—

C₆₇⋊C₁₆

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

M₁₆×C₆₇

—

M₁₆×C₆₇

—

C₂×C₈×C₆₇

—

C₂×C₈×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

C₂×C₈×C₆₇

yes

C₂×C₈×C₆₇

yes

C₁₆×C₆₇

C₂²⋊C₄

yes

—

C₁₆×C₆₇

C₂²⋊C₄

yes

—

C₂³×C₆₇

#135

yes

characteristic

C₂×C₄×C₆₇

C₄×D₄

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

yes

C₂×C₄×C₆₇

C₂×D₈

yes

characteristic

C₂×C₄×C₆₇

C₂×D₈

yes

characteristic

C₂×C₄×C₆₇

#135

yes

characteristic

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

Dic₁₃₄

—

Dic₁₃₄

—

Dic₁₃₄

—

Dic₁₃₄

—

C₈×C₆₇

—

C₈×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₆₇

C₄×D₄

yes

C₈×C₆₇

yes

C₈×C₆₇

yes

C₆₇⋊C₈

—

C₂²×C₆₇

—

C₂²×C₆₇

C₄×D₈

yes

characteristic

100

C₂²×C₆₇

#466

yes

characteristic

101

C₂²×C₆₇

#495

yes

characteristic

102

C₄×C₆₇

#390

yes

characteristic

103

C₄×C₆₇

C₄×D₈

yes

characteristic

104

C₄×C₆₇

#466

yes

characteristic

105

C₄×C₆₇

#493

yes

characteristic

106

Dic₆₇

—

107

Dic₆₇

—

108

#13244

—

maximal, Sylow

109

C₂×C₆₇

—

110

C₂×C₆₇

—

111

C₂×C₆₇

#1970

yes

characteristic

112

C₂×C₆₇

#2222

yes

—

113

C₂²×Q₃₂

—

114

C₂×#368

D₆₇

yes

characteristic

115

C₂×#362

—

116

#2108

—

117

#1979

—

118

C₆₇

#13244

yes

characteristic, complemented, Sylow

119

C₂²×Q₁₆

—

120

C₂×Q₃₂

—

121

C₂×Q₃₂

—

134

—

122

C₂×Q₃₂

—

134

—

123

C₂×Q₃₂

—

134

—

124

C₂×M₃₂

—

125

C₂²×C₁₆

C₂×D₆₇

yes

characteristic

126

C₂×#108

C₂×D₆₇

yes

—

127

#419

—

134

—

128

C₂×#101

—

134

—

129

#405

—

130

#368

—

131

#362

—

134

—

132

#346

—

134

—

133

C₄×C₁₆

—

134

—

134

C₂²×Q₈

—

134

—

135

C₂×Q₁₆

—

136

C₂×Q₁₆

—

134

—

137

C₂×Q₁₆

—

134

—

138

C₂×Q₁₆

—

134

—

139

C₂×Q₁₆

—

134

—

140

C₂×Q₁₆

—

134

—

141

C₂×M₁₆

—

142

C₂×M₁₆

—

143

C₂²×C₈

C₂²×D₆₇

yes

characteristic

144

#117

—

145

Q₃₂

—

134

—

146

Q₃₂

—

134

—

147

M₃₂

—

148

M₃₂

—

134

—

149

C₂×C₁₆

—

134

—

150

C₂×C₁₆

C₄×D₆₇

yes

—

151

C₂×C₁₆

D₂₆₈

yes

characteristic

152

C₂×C₁₆

D₂₆₈

yes

characteristic

153

C₂×C₁₆

C₂²⋊D₆₇

yes

—

154

#108

—

155

#108

—

156

#103

—

268

—

157

#101

—

268

—

158

#97

—

134

—

159

C₄×C₈

—

134

—

160

C₂×Q₈

—

268

—

161

C₂×Q₈

—

268

—

162

C₂×Q₈

—

268

—

163

C₂×Q₈

—

268

—

164

C₂×Q₈

—

268

—

165

C₂×Q₈

—

134

—

166

C₂²×C₄

—

268

—

167

C₂²×C₄

D₄×D₆₇

yes

characteristic

168

Q₁₆

—

268

—

169

Q₁₆

—

268

—

170

Q₁₆

—

134

—

171

Q₁₆

—

134

—

172

M₁₆

—

173

M₁₆

—

174

M₁₆

—

175

M₁₆

—

134

—

176

C₂×C₈

—

177

C₂×C₈

—

134

—

178

C₂×C₈

C₂×C₄×D₆₇

yes

characteristic

179

C₂×C₈

D₄×D₆₇

yes

characteristic

180

C₂×C₈

C₂×C₂²⋊D₆₇

yes

characteristic

181

C₂×C₈

C₂×D₂₆₈

yes

characteristic

182

C₂×C₈

#11761629

yes

characteristic

183

C₂×C₈

#11761629

yes

characteristic

184

C₄⋊C₄

—

185

C₂²⋊C₄

—

134

—

186

C₄²

—

134

—

187

C₁₆

—

134

—

188

C₁₆

(C₂×D₆₇)⋊C₄

yes

—

189

C₁₆

(C₂×D₆₇)⋊C₄

yes

—

190

C₂³

#14524066

yes

characteristic

191

Q₈

—

268

—

192

Q₈

—

268

—

193

Q₈

—

536

—

194

Q₈

—

536

—

195

C₂×C₄

—

268

—

196

C₂×C₄

—

536

—

197

C₂×C₄

—

536

—

198

C₂×C₄

—

134

—

199

C₂×C₄

#14524005

yes

characteristic

200

C₂×C₄

#14524018

yes

characteristic

201

C₂×C₄

#14524039

yes

characteristic

202

C₂×C₄

D₈×D₆₇

yes

characteristic

203

C₂×C₄

D₈×D₆₇

yes

characteristic

204

C₂×C₄

#14524066

yes

characteristic

205

C₈

—

206

C₈

—

134

—

207

C₈

C₂×(C₂×D₆₇)⋊C₄

yes

characteristic

208

C₈

#14524005

yes

characteristic

209

C₈

#14524018

yes

characteristic

210

C₈

#14524032

yes

characteristic

211

C₂²

—

212

C₂²

#16863478

yes

characteristic

213

C₂²

#16863633

yes

characteristic

214

C₂²

#16863781

yes

characteristic

215

C₄

—

268

—

216

C₄

—

536

—

217

C₄

#16863297

yes

characteristic

218

C₄

#16863478

yes

characteristic

219

C₄

#16863633

yes

characteristic

220

C₄

#16863771

yes

characteristic

221

C₂

—

222

C₂

—

223

C₂

#22561073

yes

characteristic

224

C₂

#22562335

yes

—

	subgroup	G/H
center	C₂²	#16863633
commutator	C₂×C₈×C₆₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₂×#368×C₆₇	C₂
socle	C₂²×C₆₇	#466
prime radical	C₂³×C₆₇	#135
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	C₂×#368	D₆₇
hypocenter	C₆₇	#13244
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

subgroup

G/H

center

C₂²

#16863633

commutator

C₂×C₈×C₆₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₂×#368×C₆₇

C₂

C₂²×C₆₇

C₂³×C₆₇

C₂²×C₈×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

N	H ≅ G/N	type
10. C₂×Dic₅₃₆	C₄	semidirect
118. C₆₇	#13244	semidirect

H ≅ G/N

type

10. C₂×Dic₅₃₆

C₄

semidirect

118. C₆₇

#13244

semidirect

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

subgroup	index
C₂²×Dic₅₃₆	2
C₂×#16863211	2
#22561805	2
#22561122	2
C₂×#368×C₆₇	2
#13244	67

subgroup

index

C₂²×Dic₅₃₆

C₂×#368×C₆₇

Subgroups — #30774248

Conjugacy classes of subgroups

Complements

Maximal subgroups