Group #13509182 — subgroups

Subgroups — D₇×#2247 #13509182

Order 1792.

814 conjugacy classes of subgroups; only the 199 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 199 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×D₇×Q₃₂	C₂	1	4	yes	maximal
2	D₇×#494	C₂	1	2	yes	maximal
3	C₇×#2247	C₂	1	1	yes	maximal, characteristic, complemented
4	#11729253	C₂	1	4	yes	maximal, complemented
5	#11729066	C₂	1	2	yes	maximal, complemented
6	#11726820	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×D₇×C₁₆	C₂	1	1	yes	maximal, characteristic
8	C₂×D₇×Q₁₆	—	2	2	no	—
9	C₂×D₇×Q₁₆	C₂²	1	4	yes	—
10	D₇×C₄⋊Q₈	—	2	2	no	—
11	C₂×C₇×Q₃₂	C₂²	1	4	yes	—
12	C₇×#494	C₂²	1	2	yes	—
13	#89953	—	2	2	no	—
14	#89953	C₂²	1	4	yes	—
15	C₂×#6403	C₂²	1	8	yes	—
16	#89864	—	2	2	no	—
17	D₇×Q₃₂	—	2	16	no	—
18	C₂×Dic₅₆	C₂²	1	4	yes	—
19	C₂×D₇×C₁₆	C₂²	1	2	yes	—
20	#89471	C₂²	1	2	yes	—
21	C₄×C₈×D₇	C₂²	1	1	yes	characteristic
22	C₄×C₇×C₁₆	C₂²	1	1	yes	characteristic
23	C₁₆×Dic₇	C₂²	1	2	yes	—
24	C₄×C₇⋊C₁₆	C₂²	1	1	yes	characteristic
25	C₂×#2247	—	7	1	no	maximal, Sylow
26	C₂×Q₈×D₇	—	2	4	no	—
27	C₂×C₇×Q₁₆	—	2	2	no	—
28	C₂×C₇×Q₁₆	C₂³	1	4	yes	—
29	C₇×C₄⋊Q₈	—	2	2	no	—
30	#6507	—	2	4	no	—
31	C₂×#1144	—	2	4	no	—
32	C₂×#1144	—	2	4	no	—
33	D₇×Q₁₆	—	2	16	no	—
34	D₇×Q₁₆	—	4	8	no	—
35	C₂×Dic₂₈	—	2	2	no	—
36	C₂×Dic₂₈	C₂³	1	4	yes	—
37	C₂×C₈×D₇	D₄	1	1	yes	characteristic
38	C₂×C₈×D₇	C₂³	1	1	yes	characteristic
39	D₇×C₄⋊C₄	—	4	4	no	—
40	#6451	—	4	4	no	—
41	C₄²×D₇	D₄	1	1	yes	characteristic
42	#6432	—	2	2	no	—
43	C₇×Q₃₂	—	2	8	no	—
44	C₂×C₇×C₁₆	C₂³	1	2	yes	—
45	C₄×C₇×C₈	C₂³	1	1	yes	characteristic
46	#6403	—	2	16	no	—
47	C₈×Dic₇	D₄	1	1	yes	characteristic
48	C₈×Dic₇	C₂³	1	1	yes	characteristic
49	C₂×C₇⋊C₁₆	C₂³	1	2	yes	—
50	C₄×C₇⋊C₈	D₄	1	1	yes	characteristic
51	Dic₅₆	—	2	8	no	—
52	D₇×C₁₆	D₄	1	8	yes	—
53	C₂²×Q₃₂	—	7	4	no	—
54	C₂×#494	—	7	2	no	—
55	#2247	—	7	4	no	—
56	#2247	—	7	2	no	—
57	#2247	—	7	1	no	—
58	#2247	D₇	1	1	yes	characteristic, direct product factor
59	C₂×C₄×C₁₆	—	7	1	no	—
60	C₂×C₇×Q₈	—	2	4	no	—
61	Q₈×D₇	—	4	8	no	—
62	Q₈×D₇	—	4	8	no	—
63	C₂×C₄×D₇	—	4	4	no	—
64	C₂×C₄×D₇	D₈	1	2	yes	—
65	C₂×C₄×D₇	C₂×D₄	1	1	yes	characteristic
66	C₂×Dic₁₄	—	2	4	no	—
67	C₂×Dic₁₄	—	4	4	no	—
68	C₇×Q₁₆	—	2	8	no	—
69	C₇×Q₁₆	—	4	4	no	—
70	C₂×C₇×C₈	C₂×D₄	1	1	yes	characteristic
71	C₂×C₇×C₈	C₂⁴	1	1	yes	characteristic
72	C₇×C₄⋊C₄	—	4	4	no	—
73	C₄²×C₇	C₂×D₄	1	1	yes	characteristic
74	#1144	—	4	8	no	—
75	#1144	—	4	8	no	—
76	C₄⋊Dic₇	—	4	4	no	—
77	Dic₇⋊C₄	—	4	8	no	—
78	C₄×Dic₇	D₈	1	2	yes	—
79	C₄×Dic₇	C₂×D₄	1	1	yes	characteristic
80	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
81	C₂×C₇⋊C₈	C₂×D₄	1	1	yes	characteristic
82	Dic₂₈	—	2	8	no	—
83	Dic₂₈	—	4	4	no	—
84	C₈×D₇	D₈	1	4	yes	—
85	C₈×D₇	C₂×D₄	1	4	yes	—
86	C₇×C₁₆	C₂×D₄	1	4	yes	—
87	C₇⋊C₁₆	C₂×D₄	1	4	yes	—
88	C₂²×Q₁₆	—	7	4	no	—
89	C₂²×Q₁₆	—	14	2	no	—
90	C₂×C₄⋊Q₈	—	14	2	no	—
91	C₂×Q₃₂	—	7	8	no	—
92	C₂×Q₃₂	—	7	4	no	—
93	C₂×Q₃₂	—	14	16	no	—
94	C₂×Q₃₂	C₂×D₇	1	4	yes	—
95	C₂²×C₁₆	—	7	2	no	—
96	#494	—	7	4	no	—
97	#494	—	7	2	no	—
98	#494	—	14	2	no	—
99	#494	—	14	2	no	—
100	#494	C₂×D₇	1	2	yes	—
101	C₂×C₄×C₈	—	7	1	no	—
102	C₄×C₁₆	—	7	2	no	—
103	C₄×C₁₆	—	7	1	no	—
104	C₄×C₁₆	C₂×D₇	1	1	yes	characteristic
105	C₂²×D₇	C₂×D₈	1	1	yes	characteristic
106	C₇×Q₈	—	4	4	no	—
107	C₇×Q₈	—	4	4	no	—
108	C₂×C₄×C₇	—	4	4	no	—
109	C₂×C₄×C₇	C₂×D₈	1	2	yes	—
110	C₂×C₄×C₇	C₂²×D₄	1	1	yes	characteristic
111	C₂×Dic₇	—	4	4	no	—
112	C₂×Dic₇	C₂×D₈	1	1	yes	characteristic
113	C₂×Dic₇	C₂×D₈	1	2	yes	—
114	C₄×D₇	—	8	8	no	—
115	C₄×D₇	Q₃₂	1	8	yes	complemented
116	C₄×D₇	#127	1	2	yes	—
117	C₄×D₇	C₂×D₈	1	2	yes	—
118	Dic₁₄	—	4	4	no	—
119	Dic₁₄	—	4	4	no	—
120	Dic₁₄	—	8	8	no	—
121	C₇×C₈	C₂×D₈	1	2	yes	—
122	C₇×C₈	C₂²×D₄	1	2	yes	—
123	C₇⋊C₈	#127	1	2	yes	—
124	C₇⋊C₈	C₂×D₈	1	2	yes	—
125	C₂²×Q₈	—	14	4	no	—
126	C₂×Q₁₆	—	2	2	no	—
127	C₂×Q₁₆	—	7	4	no	—
128	C₂×Q₁₆	—	14	16	no	—
129	C₂×Q₁₆	—	14	4	no	—
130	C₂×Q₁₆	—	14	4	no	—
131	C₂×Q₁₆	—	14	2	no	—
132	C₂×Q₁₆	—	28	8	no	—
133	C₂×Q₁₆	C₂²×D₇	1	4	yes	—
134	C₂²×C₈	—	7	1	no	—
135	C₂²×C₈	—	7	1	no	—
136	C₄⋊Q₈	—	2	2	no	—
137	C₄⋊Q₈	—	14	4	no	—
138	C₄⋊Q₈	—	14	2	no	—
139	C₄⋊Q₈	—	28	4	no	—
140	C₂×C₄⋊C₄	—	28	4	no	—
141	C₂×C₄²	—	7	1	no	—
142	Q₃₂	—	2	8	no	—
143	Q₃₂	—	14	16	no	—
144	Q₃₂	—	14	8	no	—
145	C₂×C₁₆	—	7	2	no	—
146	C₂×C₁₆	—	7	8	no	—
147	C₂×C₁₆	C₂²×D₇	1	2	yes	—
148	C₄×C₈	—	7	1	no	—
149	C₄×C₈	—	7	1	no	—
150	C₄×C₈	—	7	1	no	—
151	C₄×C₈	C₂²×D₇	1	1	yes	characteristic
152	C₂²×C₇	C₂²×D₈	1	1	yes	characteristic
153	C₂×D₇	#493	1	2	yes	—
154	C₂×D₇	C₂×Q₃₂	1	4	yes	—
155	C₄×C₇	—	8	4	no	—
156	C₄×C₇	C₂×Q₃₂	1	4	yes	complemented
157	C₄×C₇	C₂×#127	1	1	yes	characteristic
158	C₄×C₇	C₂²×D₈	1	1	yes	characteristic
159	Dic₇	—	8	4	no	—
160	Dic₇	#493	1	2	yes	—
161	Dic₇	C₂×Q₃₂	1	4	yes	complemented
162	C₂×Q₈	—	2	4	no	—
163	C₂×Q₈	—	14	4	no	—
164	C₂×Q₈	—	28	4	no	—
165	C₂×Q₈	—	28	8	no	—
166	C₂×Q₈	—	28	8	no	—
167	C₂²×C₄	—	7	2	no	—
168	C₂²×C₄	—	7	1	no	—
169	C₂²×C₄	—	28	4	no	—
170	Q₁₆	—	2	8	no	—
171	Q₁₆	—	4	4	no	—
172	Q₁₆	—	14	8	no	—
173	Q₁₆	—	28	8	no	—
174	Q₁₆	—	28	8	no	—
175	Q₁₆	—	28	4	no	—
176	C₂×C₈	—	7	1	no	—
177	C₂×C₈	—	7	1	no	—
178	C₂×C₈	—	7	4	no	—
179	C₂×C₈	—	7	4	no	—
180	C₂×C₈	D₄×D₇	1	1	yes	characteristic
181	C₂×C₈	C₂³×D₇	1	1	yes	characteristic
182	C₄⋊C₄	—	4	4	no	—
183	C₄⋊C₄	—	28	8	no	—
184	C₄⋊C₄	—	28	4	no	—
185	C₄²	—	7	2	no	—
186	C₄²	—	7	1	no	—
187	C₄²	D₄×D₇	1	1	yes	characteristic
188	C₁₆	—	7	4	no	—
189	C₁₆	D₄×D₇	1	4	yes	—
190	C₂×C₇	C₂×#493	1	1	yes	characteristic
191	C₂×C₇	C₂²×Q₃₂	1	2	yes	—
192	D₇	#2247	1	4	yes	direct product factor
193	C₂³	—	7	1	no	—
194	Q₈	—	4	4	no	—
195	Q₈	—	4	4	no	—
196	Q₈	—	28	4	no	—
197	Q₈	—	28	4	no	—
198	Q₈	—	56	8	no	—
199	C₂×C₄	—	4	4	no	—
200	C₂×C₄	—	7	2	no	—
201	C₂×C₄	—	7	1	no	—
202	C₂×C₄	—	7	2	no	—
203	C₂×C₄	—	7	2	no	—
204	C₂×C₄	—	7	8	no	—
205	C₂×C₄	—	28	4	no	—
206	C₂×C₄	—	56	8	no	—
207	C₂×C₄	D₇×D₈	1	2	yes	—
208	C₂×C₄	C₂×D₄×D₇	1	1	yes	characteristic
209	C₈	—	7	2	no	—
210	C₈	—	7	2	no	—
211	C₈	D₇×D₈	1	2	yes	—
212	C₈	C₂×D₄×D₇	1	2	yes	—
213	C₇	C₂×#2247	1	1	yes	characteristic, complemented, Sylow
214	C₂²	—	7	4	no	—
215	C₂²	—	7	2	no	—
216	C₂²	C₂×D₇×D₈	1	1	yes	characteristic
217	C₄	—	7	4	no	—
218	C₄	—	7	2	no	—
219	C₄	—	8	4	no	—
220	C₄	—	56	4	no	—
221	C₄	D₇×Q₃₂	1	4	yes	complemented
222	C₄	D₇×#127	1	1	yes	characteristic
223	C₄	C₂×D₇×D₈	1	1	yes	characteristic
224	C₂	—	7	4	no	—
225	C₂	D₇×#493	1	1	yes	characteristic
226	C₂	C₂×D₇×Q₃₂	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₇×Q₃₂

C₂

yes

maximal

D₇×#494

C₂

yes

maximal

C₇×#2247

C₂

yes

maximal, characteristic, complemented

#11729253

C₂

yes

maximal, complemented

#11729066

C₂

yes

maximal, complemented

#11726820

C₂

yes

maximal, characteristic, complemented

C₄×D₇×C₁₆

C₂

yes

maximal, characteristic

C₂×D₇×Q₁₆

—

C₂×D₇×Q₁₆

C₂²

yes

—

D₇×C₄⋊Q₈

—

C₂×C₇×Q₃₂

C₂²

yes

—

C₇×#494

C₂²

yes

—

#89953

—

#89953

C₂²

yes

—

C₂×#6403

C₂²

yes

—

#89864

—

D₇×Q₃₂

—

C₂×Dic₅₆

C₂²

yes

—

C₂×D₇×C₁₆

C₂²

yes

—

#89471

C₂²

yes

—

C₄×C₈×D₇

C₂²

yes

characteristic

C₄×C₇×C₁₆

C₂²

yes

characteristic

C₁₆×Dic₇

C₂²

yes

—

C₄×C₇⋊C₁₆

C₂²

yes

characteristic

C₂×#2247

—

maximal, Sylow

C₂×Q₈×D₇

—

C₂×C₇×Q₁₆

—

C₂×C₇×Q₁₆

C₂³

yes

—

C₇×C₄⋊Q₈

—

#6507

—

C₂×#1144

—

C₂×#1144

—

D₇×Q₁₆

—

D₇×Q₁₆

—

C₂×Dic₂₈

—

C₂×Dic₂₈

C₂³

yes

—

C₂×C₈×D₇

D₄

yes

characteristic

C₂×C₈×D₇

C₂³

yes

characteristic

D₇×C₄⋊C₄

—

#6451

—

C₄²×D₇

D₄

yes

characteristic

#6432

—

C₇×Q₃₂

—

C₂×C₇×C₁₆

C₂³

yes

—

C₄×C₇×C₈

C₂³

yes

characteristic

#6403

—

C₈×Dic₇

D₄

yes

characteristic

C₈×Dic₇

C₂³

yes

characteristic

C₂×C₇⋊C₁₆

C₂³

yes

—

C₄×C₇⋊C₈

D₄

yes

characteristic

Dic₅₆

—

D₇×C₁₆

D₄

yes

—

C₂²×Q₃₂

—

—

—

—

—

D₇

yes

characteristic, direct product factor

C₂×C₄×C₁₆

—

C₂×C₇×Q₈

—

Q₈×D₇

—

Q₈×D₇

—

C₂×C₄×D₇

—

C₂×C₄×D₇

D₈

yes

—

C₂×C₄×D₇

C₂×D₄

yes

characteristic

C₂×Dic₁₄

—

C₂×Dic₁₄

—

C₇×Q₁₆

—

C₇×Q₁₆

—

C₂×C₇×C₈

C₂×D₄

yes

characteristic

C₂×C₇×C₈

C₂⁴

yes

characteristic

C₇×C₄⋊C₄

—

C₄²×C₇

C₂×D₄

yes

characteristic

#1144

—

#1144

—

C₄⋊Dic₇

—

Dic₇⋊C₄

—

C₄×Dic₇

D₈

yes

—

C₄×Dic₇

C₂×D₄

yes

characteristic

C₂×C₇⋊C₈

C₂×D₄

yes

characteristic

C₂×C₇⋊C₈

C₂×D₄

yes

characteristic

Dic₂₈

—

Dic₂₈

—

C₈×D₇

D₈

yes

—

C₈×D₇

C₂×D₄

yes

—

C₇×C₁₆

C₂×D₄

yes

—

C₇⋊C₁₆

C₂×D₄

yes

—

C₂²×Q₁₆

—

C₂²×Q₁₆

—

C₂×C₄⋊Q₈

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×Q₃₂

—

C₂×Q₃₂

C₂×D₇

yes

—

C₂²×C₁₆

—

—

—

—

—

100

#494

C₂×D₇

yes

—

101

C₂×C₄×C₈

—

102

C₄×C₁₆

—

103

C₄×C₁₆

—

104

C₄×C₁₆

C₂×D₇

yes

characteristic

105

C₂²×D₇

C₂×D₈

yes

characteristic

106

C₇×Q₈

—

107

C₇×Q₈

—

108

C₂×C₄×C₇

—

109

C₂×C₄×C₇

C₂×D₈

yes

—

110

C₂×C₄×C₇

C₂²×D₄

yes

characteristic

111

C₂×Dic₇

—

112

C₂×Dic₇

C₂×D₈

yes

characteristic

113

C₂×Dic₇

C₂×D₈

yes

—

114

C₄×D₇

—

115

C₄×D₇

Q₃₂

yes

complemented

116

C₄×D₇

#127

yes

—

117

C₄×D₇

C₂×D₈

yes

—

118

Dic₁₄

—

119

Dic₁₄

—

120

Dic₁₄

—

121

C₇×C₈

C₂×D₈

yes

—

122

C₇×C₈

C₂²×D₄

yes

—

123

C₇⋊C₈

#127

yes

—

124

C₇⋊C₈

C₂×D₈

yes

—

125

C₂²×Q₈

—

126

C₂×Q₁₆

—

127

C₂×Q₁₆

—

128

C₂×Q₁₆

—

129

C₂×Q₁₆

—

130

C₂×Q₁₆

—

131

C₂×Q₁₆

—

132

C₂×Q₁₆

—

133

C₂×Q₁₆

C₂²×D₇

yes

—

134

C₂²×C₈

—

135

C₂²×C₈

—

136

C₄⋊Q₈

—

137

C₄⋊Q₈

—

138

C₄⋊Q₈

—

139

C₄⋊Q₈

—

140

C₂×C₄⋊C₄

—

141

C₂×C₄²

—

142

Q₃₂

—

143

Q₃₂

—

144

Q₃₂

—

145

C₂×C₁₆

—

146

C₂×C₁₆

—

147

C₂×C₁₆

C₂²×D₇

yes

—

148

C₄×C₈

—

149

C₄×C₈

—

150

C₄×C₈

—

151

C₄×C₈

C₂²×D₇

yes

characteristic

152

C₂²×C₇

C₂²×D₈

yes

characteristic

153

C₂×D₇

#493

yes

—

154

C₂×D₇

C₂×Q₃₂

yes

—

155

C₄×C₇

—

156

C₄×C₇

C₂×Q₃₂

yes

complemented

157

C₄×C₇

C₂×#127

yes

characteristic

158

C₄×C₇

C₂²×D₈

yes

characteristic

159

Dic₇

—

160

Dic₇

#493

yes

—

161

Dic₇

C₂×Q₃₂

yes

complemented

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×Q₈

—

166

C₂×Q₈

—

167

C₂²×C₄

—

168

C₂²×C₄

—

169

C₂²×C₄

—

170

Q₁₆

—

171

Q₁₆

—

172

Q₁₆

—

173

Q₁₆

—

174

Q₁₆

—

175

Q₁₆

—

176

C₂×C₈

—

177

C₂×C₈

—

178

C₂×C₈

—

179

C₂×C₈

—

180

C₂×C₈

D₄×D₇

yes

characteristic

181

C₂×C₈

C₂³×D₇

yes

characteristic

182

C₄⋊C₄

—

183

C₄⋊C₄

—

184

C₄⋊C₄

—

185

C₄²

—

186

C₄²

—

187

C₄²

D₄×D₇

yes

characteristic

188

C₁₆

—

189

C₁₆

D₄×D₇

yes

—

190

C₂×C₇

C₂×#493

yes

characteristic

191

C₂×C₇

C₂²×Q₃₂

yes

—

192

D₇

#2247

yes

direct product factor

193

C₂³

—

194

Q₈

—

195

Q₈

—

196

Q₈

—

197

Q₈

—

198

Q₈

—

199

C₂×C₄

—

200

C₂×C₄

—

201

C₂×C₄

—

202

C₂×C₄

—

203

C₂×C₄

—

204

C₂×C₄

—

205

C₂×C₄

—

206

C₂×C₄

—

207

C₂×C₄

D₇×D₈

yes

—

208

C₂×C₄

C₂×D₄×D₇

yes

characteristic

209

C₈

—

210

C₈

—

211

C₈

D₇×D₈

yes

—

212

C₈

C₂×D₄×D₇

yes

—

213

C₇

C₂×#2247

yes

characteristic, complemented, Sylow

214

C₂²

—

215

C₂²

—

216

C₂²

C₂×D₇×D₈

yes

characteristic

217

C₄

—

218

C₄

—

219

C₄

—

220

C₄

—

221

C₄

D₇×Q₃₂

yes

complemented

222

C₄

D₇×#127

yes

characteristic

223

C₄

C₂×D₇×D₈

yes

characteristic

224

C₂

—

225

C₂

D₇×#493

yes

characteristic

226

C₂

C₂×D₇×Q₃₂

yes

—

	subgroup	G/H
center	C₂²	C₂×D₇×D₈
commutator, cosocle	C₂×C₇×C₈	C₂⁴
Frattini	C₂×C₈	C₂³×D₇
Fitting	C₇×#2247	C₂
socle	C₂²×C₇	C₂²×D₈
prime radical	C₂²×D₇	C₂×D₈
hypercenter	#2247	D₇
hypocenter	C₇	C₂×#2247
LCS	G ▷ C₂×C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2247

subgroup

G/H

center

C₂²

C₂×D₇×D₈

commutator, cosocle

C₂×C₇×C₈

C₂⁴

Frattini

C₂×C₈

C₂³×D₇

Fitting

C₇×#2247

C₂

socle

C₂²×C₇

C₂²×D₈

prime radical

C₂²×D₇

C₂×D₈

D₇

C₇

G ▷ C₂×C₇×C₈ ▷ C₄×C₇ ▷ C₂×C₇ ▷ C₇

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2247

N	H ≅ G/N	type
3. C₇×#2247	C₂	semidirect
4. #11729253	C₂	semidirect
5. #11729066	C₂	semidirect
6. #11726820	C₂	semidirect
58. #2247	D₇	direct (N × H)
115. C₄×D₇	Q₃₂	semidirect
156. C₄×C₇	C₂×Q₃₂	semidirect
161. Dic₇	C₂×Q₃₂	semidirect
192. D₇	#2247	direct (N × H)
213. C₇	C₂×#2247	semidirect
221. C₄	D₇×Q₃₂	semidirect

H ≅ G/N

type

3. C₇×#2247

C₂

semidirect

4. #11729253

C₂

semidirect

5. #11729066

C₂

semidirect

6. #11726820

C₂

semidirect

58. #2247

D₇

direct (N × H)

115. C₄×D₇

Q₃₂

semidirect

156. C₄×C₇

C₂×Q₃₂

semidirect

161. Dic₇

C₂×Q₃₂

semidirect

192. D₇

#2247

direct (N × H)

213. C₇

C₂×#2247

semidirect

221. C₄

D₇×Q₃₂

semidirect

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

subgroup	index
C₂×D₇×Q₃₂	2
D₇×#494	2
C₇×#2247	2
#11729253	2
#11729066	2
#11726820	2
C₄×D₇×C₁₆	2
C₂×#2247	7

subgroup

index

C₂×D₇×Q₃₂

C₄×D₇×C₁₆

Subgroups — D₇×#2247 #13509182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D7×#2247 #13509182

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₇×#2247 #13509182