Group #30771998 — subgroups

Subgroups — #30771998

Order 17152.

438 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 438 conjugacy classes of subgroups — too many to draw. Only its 139 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×C₁₆×D₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863221	C₂	1	2	yes	maximal, complemented
3	#22560235	C₂	1	2	yes	maximal
4	#22558301	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1380	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₆₇	C₂²	1	1	yes	characteristic
7	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×D₆₇	—	2	4	no	—
9	C₂×C₁₆×D₆₇	C₄	1	4	yes	complemented
10	C₂×#14523977	C₂²	1	2	yes	—
11	#16863253	—	2	2	no	—
12	#16863221	—	2	4	no	—
13	#16863158	—	2	2	no	—
14	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×#107×C₆₇	C₂²	1	2	yes	—
16	C₂²×C₄×D₆₇	D₄	1	1	yes	characteristic
17	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
18	C₂×C₈×D₆₇	—	2	2	no	—
19	C₂×C₈×D₆₇	—	2	2	no	—
20	C₂×C₈×D₆₇	C₂×C₄	1	2	yes	—
21	C₂×C₈×D₆₇	Q₈	1	2	yes	—
22	C₂×C₄⋊Dic₆₇	—	2	2	no	—
23	C₂×(C₂×D₆₇)⋊C₄	—	4	2	no	—
24	C₂×C₆₇⋊C₁₆	C₂×C₄	1	2	yes	—
25	C₂×C₆₇⋊C₁₆	D₄	1	4	yes	—
26	C₁₆×D₆₇	—	2	8	no	—
27	#14523977	—	2	2	no	—
28	#14523977	—	2	2	no	—
29	C₆₇⋊#95	—	4	2	no	—
30	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
31	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
32	C₂×C₁₆×C₆₇	—	2	2	no	—
33	C₂×C₁₆×C₆₇	C₂×C₄	1	2	yes	—
34	#107×C₆₇	—	2	2	no	—
35	#107×C₆₇	—	2	2	no	—
36	C₂³×D₆₇	D₈	1	1	yes	characteristic
37	C₂²×Dic₆₇	—	4	2	no	—
38	C₂²×Dic₆₇	D₈	1	1	yes	characteristic
39	C₂×C₄×D₆₇	—	2	2	no	—
40	C₂×C₄×D₆₇	—	2	2	no	—
41	C₂×C₄×D₆₇	C₄⋊C₄	1	2	yes	—
42	C₂×C₄×D₆₇	Q₁₆	1	2	yes	—
43	C₂×C₆₇⋊C₈	—	2	2	no	—
44	C₂×C₆₇⋊C₈	C₄⋊C₄	1	2	yes	—
45	C₈×D₆₇	—	2	2	no	—
46	C₈×D₆₇	—	2	2	no	—
47	C₈×D₆₇	—	2	4	no	—
48	C₄⋊Dic₆₇	—	4	2	no	—
49	C₄⋊Dic₆₇	—	4	2	no	—
50	(C₂×D₆₇)⋊C₄	—	8	4	no	—
51	C₆₇⋊C₁₆	C₂²⋊C₄	1	4	yes	complemented
52	C₂²×C₄×C₆₇	—	4	2	no	—
53	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₆₇	C₂×Q₈	1	1	yes	characteristic
57	C₂×C₈×C₆₇	#41	1	2	yes	—
58	C₄⋊C₄×C₆₇	—	4	2	no	—
59	C₄⋊C₄×C₆₇	—	4	2	no	—
60	C₁₆×C₆₇	—	2	2	no	—
61	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
62	C₂²×D₆₇	—	2	2	no	—
63	C₂²×D₆₇	—	2	2	no	—
64	C₂²×D₆₇	#107	1	2	yes	—
65	C₂²×D₆₇	D₁₆	1	2	yes	—
66	C₂²×D₆₇	Q₃₂	1	2	yes	—
67	C₂×C₄×C₆₇	—	8	2	no	—
68	C₂×C₄×C₆₇	—	8	2	no	—
69	C₂×C₄×C₆₇	—	8	2	no	—
70	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₆₇	#121	1	2	yes	—
72	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
73	C₂×C₄×C₆₇	#135	1	2	yes	—
74	C₂×Dic₆₇	—	2	2	no	—
75	C₂×Dic₆₇	—	8	2	no	—
76	C₂×Dic₆₇	—	8	2	no	—
77	C₂×Dic₆₇	—	8	2	no	—
78	C₂×Dic₆₇	#107	1	2	yes	—
79	C₄×D₆₇	—	2	2	no	—
80	C₄×D₆₇	—	2	2	no	—
81	C₄×D₆₇	—	2	4	no	—
82	C₈×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
83	C₈×C₆₇	#117	1	1	yes	characteristic
84	C₈×C₆₇	C₂²⋊Q₈	1	2	yes	—
85	C₆₇⋊C₈	—	2	2	no	—
86	C₂²×C₆₇	C₂×#107	1	1	yes	characteristic
87	C₂²×C₆₇	#466	1	2	yes	—
88	C₂²×C₆₇	C₂×D₁₆	1	1	yes	characteristic
89	C₂²×C₆₇	C₂×Q₃₂	1	1	yes	characteristic
90	C₂²×C₆₇	#508	1	2	yes	—
91	C₂×D₆₇	—	2	2	no	—
92	C₂×D₆₇	—	2	2	no	—
93	C₂×D₆₇	—	2	4	no	—
94	C₂×D₆₇	—	2	4	no	—
95	C₂×D₆₇	#366	1	4	yes	complemented
96	C₄×C₆₇	—	16	2	no	—
97	C₄×C₆₇	#380	1	1	yes	characteristic
98	C₄×C₆₇	#427	1	1	yes	characteristic
99	C₄×C₆₇	#467	1	2	yes	—
100	Dic₆₇	—	2	2	no	—
101	Dic₆₇	—	16	2	no	—
102	#12834	—	67	1	no	maximal, Sylow
103	C₂×C₆₇	#1808	1	1	yes	characteristic
104	C₂×C₆₇	C₂×#366	1	1	yes	characteristic
105	C₂×C₆₇	#2158	1	1	yes	characteristic
106	C₂×C₆₇	#2215	1	2	yes	—
107	C₂×C₆₇	#2216	1	2	yes	—
108	D₆₇	—	2	4	no	—
109	C₂³×C₁₆	—	67	1	no	—
110	C₂×#366	—	67	2	no	—
111	#1808	—	67	2	no	—
112	#1380	—	67	1	no	—
113	#1380	D₆₇	1	1	yes	characteristic, complemented
114	C₆₇	#12834	1	1	yes	characteristic, complemented, Sylow
115	C₂³×C₈	—	67	1	no	—
116	C₂²×C₁₆	—	67	1	no	—
117	C₂²×C₁₆	—	67	4	no	—
118	C₂²×C₁₆	—	134	4	no	—
119	C₂²×C₁₆	C₂×D₆₇	1	1	yes	characteristic
120	C₂×#107	—	67	2	no	—
121	C₂×#107	C₂×D₆₇	1	2	yes	—
122	#380	—	134	2	no	—
123	#366	—	134	4	no	—
124	#340	—	134	2	no	—
125	C₂³×C₄	—	67	1	no	—
126	C₂²×C₈	—	67	1	no	—
127	C₂²×C₈	—	67	2	no	—
128	C₂²×C₈	—	67	2	no	—
129	C₂²×C₈	—	134	2	no	—
130	C₂²×C₈	—	134	2	no	—
131	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
132	C₂×C₄⋊C₄	—	2	2	no	—
133	C₂×C₄⋊C₄	—	134	2	no	—
134	C₂×C₂²⋊C₄	—	268	2	no	—
135	C₂×C₁₆	—	2	2	no	—
136	C₂×C₁₆	—	67	2	no	—
137	C₂×C₁₆	—	67	4	no	—
138	C₂×C₁₆	—	134	8	no	—
139	C₂×C₁₆	C₄×D₆₇	1	2	yes	—
140	#107	—	2	2	no	—
141	#107	—	2	2	no	—
142	#107	—	134	2	no	—
143	#107	—	134	2	no	—
144	#95	—	268	2	no	—
145	C₂⁴	—	67	1	no	—
146	C₂²×C₄	—	4	2	no	—
147	C₂²×C₄	—	268	2	no	—
148	C₂²×C₄	—	67	1	no	—
149	C₂²×C₄	—	67	2	no	—
150	C₂²×C₄	—	67	2	no	—
151	C₂²×C₄	—	134	2	no	—
152	C₂²×C₄	—	134	2	no	—
153	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
154	C₂×C₈	—	67	2	no	—
155	C₂×C₈	—	134	2	no	—
156	C₂×C₈	—	134	2	no	—
157	C₂×C₈	—	134	2	no	—
158	C₂×C₈	—	134	4	no	—
159	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
160	C₂×C₈	D₄×D₆₇	1	2	yes	—
161	C₂×C₈	Q₈×D₆₇	1	1	yes	characteristic
162	C₂×C₈	#11761628	1	2	yes	—
163	C₄⋊C₄	—	4	2	no	—
164	C₄⋊C₄	—	4	2	no	—
165	C₄⋊C₄	—	268	2	no	—
166	C₄⋊C₄	—	268	2	no	—
167	C₂²⋊C₄	—	536	4	no	—
168	C₁₆	—	2	2	no	—
169	C₁₆	—	67	4	no	—
170	C₂³	—	67	2	no	—
171	C₂³	—	67	2	no	—
172	C₂³	—	67	2	no	—
173	C₂³	—	134	2	no	—
174	C₂³	—	134	2	no	—
175	C₂³	D₈×D₆₇	1	1	yes	characteristic
176	C₂×C₄	—	8	2	no	—
177	C₂×C₄	—	8	2	no	—
178	C₂×C₄	—	8	2	no	—
179	C₂×C₄	—	536	2	no	—
180	C₂×C₄	—	536	2	no	—
181	C₂×C₄	—	536	2	no	—
182	C₂×C₄	—	67	2	no	—
183	C₂×C₄	—	134	2	no	—
184	C₂×C₄	—	134	2	no	—
185	C₂×C₄	—	134	4	no	—
186	C₂×C₄	—	134	2	no	—
187	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
188	C₂×C₄	#14524016	1	2	yes	—
189	C₂×C₄	Q₁₆×D₆₇	1	1	yes	characteristic
190	C₂×C₄	#14524064	1	2	yes	—
191	C₈	—	134	2	no	—
192	C₈	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
193	C₈	#14524000	1	1	yes	characteristic
194	C₈	#14524021	1	2	yes	—
195	C₂²	—	67	4	no	—
196	C₂²	—	134	2	no	—
197	C₂²	—	134	2	no	—
198	C₂²	—	134	4	no	—
199	C₂²	—	134	4	no	—
200	C₂²	#107×D₆₇	1	1	yes	characteristic
201	C₂²	#16863631	1	2	yes	—
202	C₂²	D₁₆×D₆₇	1	1	yes	characteristic
203	C₂²	Q₃₂×D₆₇	1	1	yes	characteristic
204	C₂²	#16863827	1	2	yes	—
205	C₄	—	16	2	no	—
206	C₄	—	1072	2	no	—
207	C₄	—	134	2	no	—
208	C₄	#16863255	1	1	yes	characteristic
209	C₄	#16863431	1	1	yes	characteristic
210	C₄	#16863636	1	2	yes	—
211	C₂	—	134	4	no	—
212	C₂	#22560237	1	1	yes	characteristic
213	C₂	#366×D₆₇	1	1	yes	characteristic
214	C₂	#22561992	1	1	yes	characteristic
215	C₂	#22562294	1	2	yes	—
216	C₂	#22562299	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×C₁₆×D₆₇

C₂

yes

maximal, characteristic

C₂×#16863221

C₂

yes

maximal, complemented

#22560235

C₂

yes

maximal

#22558301

C₂

yes

maximal, characteristic, complemented

C₆₇×#1380

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₆₇

C₂²

yes

characteristic

C₂²×C₆₇⋊C₁₆

C₂²

yes

characteristic

C₂×C₁₆×D₆₇

—

C₂×C₁₆×D₆₇

C₄

yes

complemented

C₂×#14523977

C₂²

yes

—

#16863253

—

#16863221

—

#16863158

—

C₂²×C₁₆×C₆₇

C₂²

yes

characteristic

C₂×#107×C₆₇

C₂²

yes

—

C₂²×C₄×D₆₇

D₄

yes

characteristic

C₂²×C₆₇⋊C₈

D₄

yes

characteristic

C₂×C₈×D₆₇

—

C₂×C₈×D₆₇

—

C₂×C₈×D₆₇

C₂×C₄

yes

—

C₂×C₈×D₆₇

Q₈

yes

—

C₂×C₄⋊Dic₆₇

—

C₂×(C₂×D₆₇)⋊C₄

—

C₂×C₆₇⋊C₁₆

C₂×C₄

yes

—

C₂×C₆₇⋊C₁₆

D₄

yes

—

C₁₆×D₆₇

—

#14523977

—

#14523977

—

C₆₇⋊#95

—

C₂²×C₈×C₆₇

C₂³

yes

characteristic

C₂×C₄⋊C₄×C₆₇

—

C₂×C₁₆×C₆₇

—

C₂×C₁₆×C₆₇

C₂×C₄

yes

—

#107×C₆₇

—

#107×C₆₇

—

C₂³×D₆₇

D₈

yes

characteristic

C₂²×Dic₆₇

—

C₂²×Dic₆₇

D₈

yes

characteristic

C₂×C₄×D₆₇

—

C₂×C₄×D₆₇

—

C₂×C₄×D₆₇

C₄⋊C₄

yes

—

C₂×C₄×D₆₇

Q₁₆

yes

—

C₂×C₆₇⋊C₈

—

C₂×C₆₇⋊C₈

C₄⋊C₄

yes

—

C₈×D₆₇

—

C₈×D₆₇

—

C₈×D₆₇

—

C₄⋊Dic₆₇

—

C₄⋊Dic₆₇

—

(C₂×D₆₇)⋊C₄

—

C₆₇⋊C₁₆

C₂²⋊C₄

yes

complemented

C₂²×C₄×C₆₇

—

C₂²×C₄×C₆₇

C₂×D₄

yes

characteristic

C₂×C₈×C₆₇

C₂²×C₄

yes

characteristic

C₂×C₈×C₆₇

C₂×D₄

yes

—

C₂×C₈×C₆₇

C₂×Q₈

yes

characteristic

C₂×C₈×C₆₇

#41

yes

—

C₄⋊C₄×C₆₇

—

C₄⋊C₄×C₆₇

—

C₁₆×C₆₇

—

C₂³×C₆₇

C₂×D₈

yes

characteristic

C₂²×D₆₇

—

C₂²×D₆₇

—

C₂²×D₆₇

#107

yes

—

C₂²×D₆₇

D₁₆

yes

—

C₂²×D₆₇

Q₃₂

yes

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

—

C₂×C₄×C₆₇

C₂×C₄⋊C₄

yes

characteristic

C₂×C₄×C₆₇

#121

yes

—

C₂×C₄×C₆₇

C₂×Q₁₆

yes

characteristic

C₂×C₄×C₆₇

#135

yes

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

—

C₂×Dic₆₇

#107

yes

—

C₄×D₆₇

—

C₄×D₆₇

—

C₄×D₆₇

—

C₈×C₆₇

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₆₇

#117

yes

characteristic

C₈×C₆₇

C₂²⋊Q₈

yes

—

C₆₇⋊C₈

—

C₂²×C₆₇

C₂×#107

yes

characteristic

C₂²×C₆₇

#466

yes

—

C₂²×C₆₇

C₂×D₁₆

yes

characteristic

C₂²×C₆₇

C₂×Q₃₂

yes

characteristic

C₂²×C₆₇

#508

yes

—

C₂×D₆₇

—

C₂×D₆₇

—

C₂×D₆₇

—

C₂×D₆₇

—

C₂×D₆₇

#366

yes

complemented

C₄×C₆₇

—

C₄×C₆₇

yes

C₄×C₆₇

yes

C₄×C₆₇

yes

—

100

Dic₆₇

—

101

Dic₆₇

—

102

#12834

—

maximal, Sylow

103

C₂×C₆₇

#1808

yes

characteristic

104

C₂×C₆₇

C₂×#366

yes

characteristic

105

C₂×C₆₇

#2158

yes

characteristic

106

C₂×C₆₇

#2215

yes

—

107

C₂×C₆₇

#2216

yes

—

108

D₆₇

—

109

C₂³×C₁₆

—

110

C₂×#366

—

111

#1808

—

112

#1380

—

113

#1380

D₆₇

yes

characteristic, complemented

114

C₆₇

#12834

yes

characteristic, complemented, Sylow

115

C₂³×C₈

—

116

C₂²×C₁₆

—

117

C₂²×C₁₆

—

118

C₂²×C₁₆

—

134

—

119

C₂²×C₁₆

C₂×D₆₇

yes

characteristic

120

C₂×#107

—

121

C₂×#107

C₂×D₆₇

yes

—

122

#380

—

134

—

123

#366

—

134

—

124

#340

—

134

—

125

C₂³×C₄

—

126

C₂²×C₈

—

127

C₂²×C₈

—

128

C₂²×C₈

—

129

C₂²×C₈

—

134

—

130

C₂²×C₈

—

134

—

131

C₂²×C₈

C₂²×D₆₇

yes

characteristic

132

C₂×C₄⋊C₄

—

133

C₂×C₄⋊C₄

—

134

—

134

C₂×C₂²⋊C₄

—

268

—

135

C₂×C₁₆

—

136

C₂×C₁₆

—

137

C₂×C₁₆

—

138

C₂×C₁₆

—

134

—

139

C₂×C₁₆

C₄×D₆₇

yes

—

140

#107

—

141

#107

—

142

#107

—

134

—

143

#107

—

134

—

144

#95

—

268

—

145

C₂⁴

—

146

C₂²×C₄

—

147

C₂²×C₄

—

268

—

148

C₂²×C₄

—

149

C₂²×C₄

—

150

C₂²×C₄

—

151

C₂²×C₄

—

134

—

152

C₂²×C₄

—

134

—

153

C₂²×C₄

D₄×D₆₇

yes

characteristic

154

C₂×C₈

—

155

C₂×C₈

—

134

—

156

C₂×C₈

—

134

—

157

C₂×C₈

—

134

—

158

C₂×C₈

—

134

—

159

C₂×C₈

C₂×C₄×D₆₇

yes

characteristic

160

C₂×C₈

D₄×D₆₇

yes

—

161

C₂×C₈

Q₈×D₆₇

yes

characteristic

162

C₂×C₈

#11761628

yes

—

163

C₄⋊C₄

—

164

C₄⋊C₄

—

165

C₄⋊C₄

—

268

—

166

C₄⋊C₄

—

268

—

167

C₂²⋊C₄

—

536

—

168

C₁₆

—

169

C₁₆

—

170

C₂³

—

171

C₂³

—

172

C₂³

—

173

C₂³

—

134

—

174

C₂³

—

134

—

175

C₂³

D₈×D₆₇

yes

characteristic

176

C₂×C₄

—

177

C₂×C₄

—

178

C₂×C₄

—

179

C₂×C₄

—

536

—

180

C₂×C₄

—

536

—

181

C₂×C₄

—

536

—

182

C₂×C₄

—

183

C₂×C₄

—

134

—

184

C₂×C₄

—

134

—

185

C₂×C₄

—

134

—

186

C₂×C₄

—

134

—

187

C₂×C₄

C₄⋊C₄×D₆₇

yes

characteristic

188

C₂×C₄

#14524016

yes

—

189

C₂×C₄

Q₁₆×D₆₇

yes

characteristic

190

C₂×C₄

#14524064

yes

—

191

C₈

—

134

—

192

C₈

C₂²⋊C₄×D₆₇

yes

characteristic

193

C₈

#14524000

yes

characteristic

194

C₈

#14524021

yes

—

195

C₂²

—

196

C₂²

—

134

—

197

C₂²

—

134

—

198

C₂²

—

134

—

199

C₂²

—

134

—

200

C₂²

#107×D₆₇

yes

characteristic

201

C₂²

#16863631

yes

—

202

C₂²

D₁₆×D₆₇

yes

characteristic

203

C₂²

Q₃₂×D₆₇

yes

characteristic

204

C₂²

#16863827

yes

—

205

C₄

—

206

C₄

—

1072

—

207

C₄

—

134

—

208

C₄

#16863255

yes

characteristic

209

C₄

#16863431

yes

characteristic

210

C₄

#16863636

yes

—

211

C₂

—

134

—

212

C₂

#22560237

yes

characteristic

213

C₂

#366×D₆₇

yes

characteristic

214

C₂

#22561992

yes

characteristic

215

C₂

#22562294

yes

—

216

C₂

#22562299

yes

—

	subgroup	G/H
center	C₂³	D₈×D₆₇
commutator	C₂×C₈×C₆₇	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₆₇
Fitting	C₆₇×#1380	C₂
socle	C₂³×C₆₇	C₂×D₈
prime radical	C₂³×D₆₇	D₈
cosocle	C₂²×C₈×C₆₇	C₂³
hypercenter	#1380	D₆₇
hypocenter	C₆₇	#12834
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

subgroup

G/H

center

C₂³

D₈×D₆₇

commutator

C₂×C₈×C₆₇

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₆₇

Fitting

C₆₇×#1380

C₂

socle

C₂³×C₆₇

C₂×D₈

prime radical

C₂³×D₆₇

D₈

cosocle

C₂²×C₈×C₆₇

C₂³

D₆₇

C₆₇

G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #1380

N	H ≅ G/N	type
2. C₂×#16863221	C₂	semidirect
4. #22558301	C₂	semidirect
5. C₆₇×#1380	C₂	semidirect
9. C₂×C₁₆×D₆₇	C₄	semidirect
51. C₆₇⋊C₁₆	C₂²⋊C₄	semidirect
95. C₂×D₆₇	#366	semidirect
113. #1380	D₆₇	semidirect
114. C₆₇	#12834	semidirect

H ≅ G/N

type

2. C₂×#16863221

C₂

semidirect

4. #22558301

C₂

semidirect

5. C₆₇×#1380

C₂

semidirect

9. C₂×C₁₆×D₆₇

C₄

semidirect

51. C₆₇⋊C₁₆

C₂²⋊C₄

semidirect

95. C₂×D₆₇

#366

semidirect

113. #1380

D₆₇

semidirect

114. C₆₇

#12834

semidirect

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

subgroup	index
C₂²×C₁₆×D₆₇	2
C₂×#16863221	2
#22560235	2
#22558301	2
C₆₇×#1380	2
#12834	67

subgroup

index

C₂²×C₁₆×D₆₇

C₆₇×#1380

Subgroups — #30771998

Conjugacy classes of subgroups

Complements

Maximal subgroups