Group #36470610 — subgroups

Subgroups — #36470610

Order 22784.

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

normal subgroups only

This group has 374 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	C₂²×#15667951	C₂	1	1	yes	maximal, characteristic
2	C₂×#19151428	C₂	1	1	yes	maximal, characteristic, complemented
3	#26020287	C₂	1	2	yes	maximal
4	#26018345	C₂	1	2	yes	maximal, complemented
5	C₂×#368×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
7	C₂×#15667951	—	2	2	no	—
8	C₂×#15667951	—	2	2	no	—
9	C₂×#15667951	C₄	1	4	yes	—
10	C₂²×#13083549	C₂²	1	1	yes	characteristic
11	C₂×#15667948	C₂²	1	2	yes	—
12	#19151561	—	2	2	no	—
13	#19151428	—	2	2	no	—
14	#19151362	—	2	2	no	—
15	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#108×C₈₉	C₂²	1	2	yes	—
17	#368×C₈₉	—	2	2	no	—
18	C₂²×C₄×D₈₉	D₄	1	1	yes	characteristic
19	C₂×#13083558	—	2	2	no	—
20	C₂²×#10623494	D₄	1	1	yes	characteristic
21	C₂×C₈×D₈₉	—	2	1	no	—
22	C₂×C₈×D₈₉	—	2	1	no	—
23	C₂×C₈×D₈₉	—	2	1	no	—
24	C₂×C₈×D₈₉	—	2	1	no	—
25	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
26	C₂×C₈×D₈₉	Q₈	1	2	yes	—
27	#15667951	—	2	8	no	—
28	C₂×#13083549	—	2	1	no	—
29	C₂×#13083549	—	2	1	no	—
30	C₂×#13083549	C₂×C₄	1	2	yes	—
31	#15667948	—	2	2	no	—
32	#15667948	—	2	2	no	—
33	#15667924	—	4	4	no	—
34	C₂×M₁₆×C₈₉	—	2	2	no	—
35	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
36	C₂×C₁₆×C₈₉	C₂×C₄	1	2	yes	—
37	C₂×C₁₆×C₈₉	D₄	1	2	yes	—
38	C₂×C₁₆×C₈₉	D₄	1	2	yes	—
39	#108×C₈₉	—	2	2	no	—
40	#108×C₈₉	—	2	2	no	—
41	C₂³×D₈₉	Q₁₆	1	1	yes	characteristic
42	C₂²×Dic₈₉	Q₁₆	1	1	yes	characteristic
43	C₂×C₄×D₈₉	—	2	1	no	—
44	C₂×C₄×D₈₉	—	2	1	no	—
45	C₂×C₄×D₈₉	—	2	1	no	—
46	C₂×C₄×D₈₉	—	2	1	no	—
47	C₂×C₄×D₈₉	C₄⋊C₄	1	2	yes	—
48	C₂×C₄×D₈₉	D₈	1	2	yes	—
49	#13083558	—	4	2	no	—
50	#13083558	—	4	2	no	—
51	C₂×#10623494	—	2	1	no	—
52	C₂×#10623494	—	2	1	no	—
53	C₂×#10623494	—	4	2	no	—
54	C₂×#10623494	C₄⋊C₄	1	2	yes	—
55	C₈×D₈₉	—	2	2	no	—
56	C₈×D₈₉	—	2	2	no	—
57	C₈×D₈₉	—	2	2	no	—
58	C₈×D₈₉	—	2	2	no	—
59	#13083549	—	2	2	no	—
60	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
61	M₁₆×C₈₉	—	4	2	no	—
62	M₁₆×C₈₉	—	4	2	no	—
63	C₂×C₈×C₈₉	—	4	2	no	—
64	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
65	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
66	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
67	C₂×C₈×C₈₉	C₂×Q₈	1	1	yes	characteristic
68	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
69	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
70	C₁₆×C₈₉	C₂²⋊C₄	1	4	yes	—
71	C₂³×C₈₉	C₂×Q₁₆	1	1	yes	characteristic
72	C₂²×D₈₉	—	2	1	no	—
73	C₂²×D₈₉	—	2	1	no	—
74	C₂²×D₈₉	—	4	2	no	—
75	C₂²×D₈₉	#107	1	2	yes	—
76	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
78	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
79	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
80	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
81	C₂×C₄×C₈₉	#135	1	1	yes	characteristic
82	C₂×Dic₈₉	—	2	1	no	—
83	C₂×Dic₈₉	—	2	1	no	—
84	C₂×Dic₈₉	#107	1	2	yes	—
85	C₄×D₈₉	—	2	2	no	—
86	C₄×D₈₉	—	2	2	no	—
87	C₄×D₈₉	—	2	2	no	—
88	C₄×D₈₉	—	2	2	no	—
89	C₈×C₈₉	—	8	2	no	—
90	C₈×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
91	C₈×C₈₉	#117	1	1	yes	characteristic
92	C₈×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
93	C₈×C₈₉	C₂²⋊Q₈	1	1	yes	characteristic
94	#10623494	—	2	2	no	—
95	#10623494	—	8	2	no	—
96	C₂²×C₈₉	—	2	2	no	—
97	C₂²×C₈₉	C₂×#107	1	1	yes	characteristic
98	C₂²×C₈₉	#467	1	1	yes	characteristic
99	C₂²×C₈₉	#467	1	1	yes	characteristic
100	C₂×D₈₉	—	2	2	no	—
101	C₂×D₈₉	—	2	4	no	—
102	C₂×D₈₉	—	4	2	no	—
103	C₂×D₈₉	—	4	2	no	—
104	C₄×C₈₉	#380	1	1	yes	characteristic
105	C₄×C₈₉	#427	1	1	yes	characteristic
106	C₄×C₈₉	#466	1	1	yes	characteristic
107	C₄×C₈₉	#466	1	1	yes	characteristic
108	Dic₈₉	—	2	2	no	—
109	#12838	—	89	1	no	maximal, Sylow
110	C₂×C₈₉	—	2	1	no	—
111	C₂×C₈₉	—	2	1	no	—
112	C₂×C₈₉	#1808	1	1	yes	characteristic
113	C₂×C₈₉	#2161	1	2	yes	—
114	D₈₉	—	4	2	no	—
115	C₂²×M₃₂	—	89	1	no	—
116	C₂×#368	—	89	1	no	—
117	C₂×#368	D₈₉	1	1	yes	characteristic, complemented
118	#1810	—	89	2	no	—
119	#1381	—	89	2	no	—
120	C₈₉	#12838	1	1	yes	characteristic, complemented, Sylow
121	C₂³×C₈	—	89	1	no	—
122	C₂×M₃₂	—	89	4	no	—
123	C₂×M₃₂	—	178	2	no	—
124	C₂×M₃₂	—	178	2	no	—
125	C₂²×C₁₆	—	89	1	no	—
126	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
127	C₂×#108	—	89	2	no	—
128	C₂×#108	C₂×D₈₉	1	2	yes	—
129	#407	—	178	2	no	—
130	#368	—	2	2	no	—
131	#368	—	178	2	no	—
132	#341	—	178	2	no	—
133	C₂³×C₄	—	89	1	no	—
134	C₂×M₁₆	—	2	2	no	—
135	C₂×M₁₆	—	178	2	no	—
136	C₂²×C₈	—	89	1	no	—
137	C₂²×C₈	—	89	2	no	—
138	C₂²×C₈	—	89	2	no	—
139	C₂²×C₈	—	178	1	no	—
140	C₂²×C₈	—	178	1	no	—
141	C₂²×C₈	—	178	1	no	—
142	C₂²×C₈	—	178	1	no	—
143	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
144	M₃₂	—	178	8	no	—
145	C₂×C₁₆	—	89	2	no	—
146	C₂×C₁₆	—	178	1	no	—
147	C₂×C₁₆	—	178	1	no	—
148	C₂×C₁₆	C₄×D₈₉	1	2	yes	—
149	C₂×C₁₆	D₃₅₆	1	2	yes	—
150	C₂×C₁₆	C₂²⋊D₈₉	1	2	yes	—
151	#108	—	2	2	no	—
152	#108	—	2	2	no	—
153	#108	—	178	2	no	—
154	#108	—	178	2	no	—
155	C₂²⋊C₈	—	356	4	no	—
156	C₂⁴	—	89	1	no	—
157	C₂²×C₄	—	89	1	no	—
158	C₂²×C₄	—	89	2	no	—
159	C₂²×C₄	—	89	2	no	—
160	C₂²×C₄	—	178	1	no	—
161	C₂²×C₄	—	178	1	no	—
162	C₂²×C₄	—	178	1	no	—
163	C₂²×C₄	—	178	1	no	—
164	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
165	M₁₆	—	4	2	no	—
166	M₁₆	—	4	2	no	—
167	M₁₆	—	356	2	no	—
168	M₁₆	—	356	2	no	—
169	C₂×C₈	—	4	2	no	—
170	C₂×C₈	—	89	2	no	—
171	C₂×C₈	—	356	2	no	—
172	C₂×C₈	—	178	1	no	—
173	C₂×C₈	—	178	1	no	—
174	C₂×C₈	—	178	2	no	—
175	C₂×C₈	—	178	2	no	—
176	C₂×C₈	—	178	2	no	—
177	C₂×C₈	—	178	2	no	—
178	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
179	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
180	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
181	C₂×C₈	Q₈×D₈₉	1	1	yes	characteristic
182	C₂×C₈	#13083573	1	1	yes	characteristic
183	C₂×C₈	#13083575	1	1	yes	characteristic
184	C₁₆	—	178	2	no	—
185	C₁₆	#13083551	1	4	yes	—
186	C₂³	—	89	2	no	—
187	C₂³	—	356	2	no	—
188	C₂³	—	178	1	no	—
189	C₂³	—	178	1	no	—
190	C₂³	Q₁₆×D₈₉	1	1	yes	characteristic
191	C₂×C₄	—	89	2	no	—
192	C₂×C₄	—	178	1	no	—
193	C₂×C₄	—	178	1	no	—
194	C₂×C₄	—	178	2	no	—
195	C₂×C₄	—	178	2	no	—
196	C₂×C₄	—	178	2	no	—
197	C₂×C₄	—	178	2	no	—
198	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
199	C₂×C₄	#15667983	1	1	yes	characteristic
200	C₂×C₄	#15667987	1	1	yes	characteristic
201	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
202	C₂×C₄	#15668031	1	1	yes	characteristic
203	C₂×C₄	#15668035	1	1	yes	characteristic
204	C₈	—	8	2	no	—
205	C₈	—	178	2	no	—
206	C₈	—	712	2	no	—
207	C₈	C₂×#13083551	1	1	yes	characteristic
208	C₈	#15667970	1	1	yes	characteristic
209	C₈	#15667988	1	1	yes	characteristic
210	C₈	#15667992	1	1	yes	characteristic
211	C₂²	—	2	2	no	—
212	C₂²	—	356	2	no	—
213	C₂²	—	356	2	no	—
214	C₂²	—	178	4	no	—
215	C₂²	—	178	2	no	—
216	C₂²	#107×D₈₉	1	1	yes	characteristic
217	C₂²	#19151836	1	1	yes	characteristic
218	C₂²	#19151840	1	1	yes	characteristic
219	C₄	—	178	2	no	—
220	C₄	#19151455	1	1	yes	characteristic
221	C₄	#19151635	1	1	yes	characteristic
222	C₄	#19151831	1	1	yes	characteristic
223	C₄	#19151835	1	1	yes	characteristic
224	C₂	—	2	1	no	—
225	C₂	—	2	1	no	—
226	C₂	—	356	2	no	—
227	C₂	#26020278	1	1	yes	characteristic
228	C₂	#26022045	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#15667951

C₂

yes

maximal, characteristic

C₂×#19151428

C₂

yes

maximal, characteristic, complemented

#26020287

C₂

yes

maximal

#26018345

C₂

yes

maximal, complemented

C₂×#368×C₈₉

C₂

yes

maximal, characteristic, complemented

C₂²×C₈×D₈₉

C₂²

yes

—

—

C₄

yes

—

C₂²×#13083549

C₂²

yes

characteristic

C₂×#15667948

C₂²

yes

—

#19151561

—

#19151428

—

#19151362

—

C₂²×C₁₆×C₈₉

C₂²

yes

characteristic

C₂×#108×C₈₉

C₂²

yes

—

#368×C₈₉

—

C₂²×C₄×D₈₉

D₄

yes

characteristic

C₂×#13083558

—

C₂²×#10623494

D₄

yes

characteristic

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

—

C₂×C₈×D₈₉

C₂×C₄

yes

—

C₂×C₈×D₈₉

Q₈

yes

—

—

—

—

C₂×C₄

yes

—

#15667948

—

#15667948

—

#15667924

—

C₂×M₁₆×C₈₉

—

C₂²×C₈×C₈₉

C₂³

yes

characteristic

C₂×C₁₆×C₈₉

C₂×C₄

yes

—

C₂×C₁₆×C₈₉

D₄

yes

—

C₂×C₁₆×C₈₉

D₄

yes

—

#108×C₈₉

—

#108×C₈₉

—

C₂³×D₈₉

Q₁₆

yes

characteristic

C₂²×Dic₈₉

Q₁₆

yes

characteristic

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

—

C₂×C₄×D₈₉

C₄⋊C₄

yes

—

C₂×C₄×D₈₉

D₈

yes

—

—

—

—

—

—

C₄⋊C₄

yes

—

C₈×D₈₉

—

C₈×D₈₉

—

C₈×D₈₉

—

C₈×D₈₉

—

#13083549

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

M₁₆×C₈₉

—

M₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

C₂²×C₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×D₄

yes

characteristic

C₂×C₈×C₈₉

C₂×Q₈

yes

C₂×C₈×C₈₉

yes

C₂×C₈×C₈₉

yes

C₁₆×C₈₉

C₂²⋊C₄

yes

—

C₂³×C₈₉

C₂×Q₁₆

yes

characteristic

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

—

C₂²×D₈₉

#107

yes

—

C₂×C₄×C₈₉

C₂×C₄⋊C₄

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

C₂×D₈

yes

C₂×C₄×C₈₉

yes

C₂×C₄×C₈₉

yes

C₂×Dic₈₉

—

C₂×Dic₈₉

—

C₂×Dic₈₉

#107

yes

—

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₄×D₈₉

—

C₈×C₈₉

—

C₈×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₈×C₈₉

#117

yes

characteristic

C₈×C₈₉

C₂²⋊Q₈

yes

characteristic

C₈×C₈₉

C₂²⋊Q₈

yes

characteristic

#10623494

—

#10623494

—

C₂²×C₈₉

—

C₂²×C₈₉

yes

C₂²×C₈₉

yes

C₂²×C₈₉

yes

100

C₂×D₈₉

—

101

C₂×D₈₉

—

102

C₂×D₈₉

—

103

C₂×D₈₉

—

104

C₄×C₈₉

#380

yes

characteristic

105

C₄×C₈₉

#427

yes

characteristic

106

C₄×C₈₉

#466

yes

characteristic

107

C₄×C₈₉

#466

yes

characteristic

108

Dic₈₉

—

109

#12838

—

maximal, Sylow

110

C₂×C₈₉

—

111

C₂×C₈₉

—

112

C₂×C₈₉

#1808

yes

characteristic

113

C₂×C₈₉

#2161

yes

—

114

D₈₉

—

115

C₂²×M₃₂

—

116

C₂×#368

—

117

C₂×#368

D₈₉

yes

characteristic, complemented

118

#1810

—

119

#1381

—

120

C₈₉

#12838

yes

characteristic, complemented, Sylow

121

C₂³×C₈

—

122

C₂×M₃₂

—

123

C₂×M₃₂

—

178

—

124

C₂×M₃₂

—

178

—

125

C₂²×C₁₆

—

126

C₂²×C₁₆

C₂×D₈₉

yes

characteristic

127

C₂×#108

—

128

C₂×#108

C₂×D₈₉

yes

—

129

#407

—

178

—

130

#368

—

131

#368

—

178

—

132

#341

—

178

—

133

C₂³×C₄

—

134

C₂×M₁₆

—

135

C₂×M₁₆

—

178

—

136

C₂²×C₈

—

137

C₂²×C₈

—

138

C₂²×C₈

—

139

C₂²×C₈

—

178

—

140

C₂²×C₈

—

178

—

141

C₂²×C₈

—

178

—

142

C₂²×C₈

—

178

—

143

C₂²×C₈

C₂²×D₈₉

yes

characteristic

144

M₃₂

—

178

—

145

C₂×C₁₆

—

146

C₂×C₁₆

—

178

—

147

C₂×C₁₆

—

178

—

148

C₂×C₁₆

C₄×D₈₉

yes

—

149

C₂×C₁₆

D₃₅₆

yes

—

150

C₂×C₁₆

C₂²⋊D₈₉

yes

—

151

#108

—

152

#108

—

153

#108

—

178

—

154

#108

—

178

—

155

C₂²⋊C₈

—

356

—

156

C₂⁴

—

157

C₂²×C₄

—

158

C₂²×C₄

—

159

C₂²×C₄

—

160

C₂²×C₄

—

178

—

161

C₂²×C₄

—

178

—

162

C₂²×C₄

—

178

—

163

C₂²×C₄

—

178

—

164

C₂²×C₄

D₄×D₈₉

yes

characteristic

165

M₁₆

—

166

M₁₆

—

167

M₁₆

—

356

—

168

M₁₆

—

356

—

169

C₂×C₈

—

170

C₂×C₈

—

171

C₂×C₈

—

356

—

172

C₂×C₈

—

178

—

173

C₂×C₈

—

178

—

174

C₂×C₈

—

178

—

175

C₂×C₈

—

178

—

176

C₂×C₈

—

178

—

177

C₂×C₈

—

178

—

178

C₂×C₈

C₂×C₄×D₈₉

yes

characteristic

179

C₂×C₈

C₂×C₂²⋊D₈₉

yes

characteristic

180

C₂×C₈

C₂×D₃₅₆

yes

characteristic

181

C₂×C₈

Q₈×D₈₉

yes

characteristic

182

C₂×C₈

#13083573

yes

characteristic

183

C₂×C₈

#13083575

yes

characteristic

184

C₁₆

—

178

—

185

C₁₆

#13083551

yes

—

186

C₂³

—

187

C₂³

—

356

—

188

C₂³

—

178

—

189

C₂³

—

178

—

190

C₂³

Q₁₆×D₈₉

yes

characteristic

191

C₂×C₄

—

192

C₂×C₄

—

178

—

193

C₂×C₄

—

178

—

194

C₂×C₄

—

178

—

195

C₂×C₄

—

178

—

196

C₂×C₄

—

178

—

197

C₂×C₄

—

178

—

198

C₂×C₄

C₄⋊C₄×D₈₉

yes

characteristic

199

C₂×C₄

#15667983

yes

characteristic

200

C₂×C₄

#15667987

yes

characteristic

201

C₂×C₄

D₈×D₈₉

yes

characteristic

202

C₂×C₄

#15668031

yes

characteristic

203

C₂×C₄

#15668035

yes

characteristic

204

C₈

—

205

C₈

—

178

—

206

C₈

—

712

—

207

C₈

C₂×#13083551

yes

characteristic

208

C₈

#15667970

yes

characteristic

209

C₈

#15667988

yes

characteristic

210

C₈

#15667992

yes

characteristic

211

C₂²

—

212

C₂²

—

356

—

213

C₂²

—

356

—

214

C₂²

—

178

—

215

C₂²

—

178

—

216

C₂²

#107×D₈₉

yes

characteristic

217

C₂²

#19151836

yes

characteristic

218

C₂²

#19151840

yes

characteristic

219

C₄

—

178

—

220

C₄

#19151455

yes

characteristic

221

C₄

#19151635

yes

characteristic

222

C₄

#19151831

yes

characteristic

223

C₄

#19151835

yes

characteristic

224

C₂

—

225

C₂

—

226

C₂

—

356

—

227

C₂

#26020278

yes

characteristic

228

C₂

#26022045

yes

—

	subgroup	G/H
center	C₂×C₄	D₈×D₈₉
commutator	C₂×C₈×C₈₉	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₈₉
Fitting	C₂×#368×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#107
prime radical	C₂³×D₈₉	Q₁₆
cosocle	C₂²×C₈×C₈₉	C₂³
hypercenter	C₂×#368	D₈₉
hypocenter	C₈₉	#12838
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

subgroup

G/H

center

C₂×C₄

D₈×D₈₉

commutator

C₂×C₈×C₈₉

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₈₉

Fitting

C₂×#368×C₈₉

C₂

socle

C₂²×C₈₉

C₂×#107

prime radical

C₂³×D₈₉

Q₁₆

cosocle

C₂²×C₈×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#368

N	H ≅ G/N	type
2. C₂×#19151428	C₂	semidirect
4. #26018345	C₂	semidirect
5. C₂×#368×C₈₉	C₂	semidirect
117. C₂×#368	D₈₉	semidirect
120. C₈₉	#12838	semidirect

H ≅ G/N

type

2. C₂×#19151428

C₂

semidirect

4. #26018345

C₂

semidirect

5. C₂×#368×C₈₉

C₂

semidirect

117. C₂×#368

D₈₉

semidirect

120. C₈₉

#12838

semidirect

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

subgroup	index
C₂²×#15667951	2
C₂×#19151428	2
#26020287	2
#26018345	2
C₂×#368×C₈₉	2
#12838	89

subgroup

index

C₂×#368×C₈₉

Subgroups — #36470610

Conjugacy classes of subgroups

Complements

Maximal subgroups