Group #13142948 — subgroups

Subgroups — C₉×#5068 #13142948

Order 1728.

344 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 117 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	C₃×C₉×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#875	C₂	1	1	yes	maximal, characteristic
3	C₉×#810	C₂	1	2	yes	maximal, complemented
4	C₉×#809	C₂	1	2	yes	maximal
5	C₄×C₉×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#5068	C₃	1	1	yes	maximal, characteristic
7	C₉×#488	—	3	1	no	maximal
8	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
9	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
10	C₃×C₉×C₄⋊C₄	—	2	2	no	—
11	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
12	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
13	C₉×(C₂×D₃)⋊C₄	—	2	2	no	—
14	C₂×C₉×C₃⋊C₈	C₂²	1	2	yes	—
15	C₃²×#125	C₂×C₃	1	1	yes	characteristic
16	C₃×#875	C₂×C₃	1	1	yes	characteristic
17	C₃×#810	C₂×C₃	1	2	yes	—
18	C₃×#809	C₂×C₃	1	2	yes	—
19	C₃×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic
20	C₉×#125	—	2	1	no	—
21	C₉×#125	D₃	1	1	yes	characteristic, complemented
22	C₉×#124	—	3	1	no	—
23	C₉×#103	—	3	2	no	—
24	C₉×#102	—	3	2	no	—
25	C₄×C₈×C₉	—	3	1	no	—
26	C₂²×D₃×C₉	—	2	1	no	—
27	C₂×C₃×C₄×C₉	—	2	2	no	—
28	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
29	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
30	C₂×C₉×Dic₃	—	2	1	no	—
31	C₉×D₁₂	—	2	2	no	—
32	C₉×Dic₆	—	2	2	no	—
33	C₉×C₃⋊C₈	—	2	2	no	—
34	C₃×#488	—	3	1	no	—
35	#5068	C₉	1	1	yes	characteristic, direct product factor
36	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
37	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
38	C₃²×C₄⋊C₄	—	2	2	no	—
39	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
40	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
41	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
42	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	2	yes	—
43	C₂×Q₈×C₉	—	3	1	no	—
44	C₂×D₄×C₉	—	3	1	no	—
45	C₂×C₈×C₉	—	3	2	no	—
46	C₉×C₄⋊C₄	—	2	4	no	—
47	C₉×C₄⋊C₄	—	2	2	no	—
48	C₉×C₄⋊C₄	—	2	2	no	—
49	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
50	C₉×C₂²⋊C₄	—	6	2	no	—
51	C₄²×C₉	—	2	1	no	—
52	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
53	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
54	C₂×D₃×C₉	—	4	1	no	—
55	C₂×D₃×C₉	—	4	2	no	—
56	C₃×C₄×C₉	—	2	2	no	—
57	C₃×C₄×C₉	—	4	2	no	—
58	C₃×C₄×C₉	#41	1	2	yes	—
59	C₉×Dic₃	—	4	1	no	—
60	C₃×#125	—	2	1	no	—
61	C₃×#125	C₂×C₉	1	1	yes	characteristic, complemented
62	C₃×#125	C₃×D₃	1	1	yes	characteristic
63	C₃×#124	—	3	1	no	—
64	#875	C₂×C₉	1	1	yes	characteristic
65	C₃×#103	—	3	2	no	—
66	C₃×#102	—	3	2	no	—
67	C₃×C₄×C₈	—	3	1	no	—
68	#810	C₂×C₉	1	2	yes	complemented
69	#809	C₂×C₉	1	2	yes	—
70	C₄×C₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
71	C₂²×C₃×D₃	—	2	1	no	—
72	C₂×C₃²×C₄	—	2	2	no	—
73	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
74	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
75	C₂×C₃×Dic₃	—	2	1	no	—
76	C₃×D₁₂	—	2	2	no	—
77	C₃×Dic₆	—	2	2	no	—
78	C₂³×C₉	—	6	1	no	—
79	C₃×C₃⋊C₈	—	2	2	no	—
80	Q₈×C₉	—	6	2	no	—
81	D₄×C₉	—	6	2	no	—
82	C₂×C₄×C₉	—	2	4	no	—
83	C₂×C₄×C₉	—	2	2	no	—
84	C₂×C₄×C₉	—	2	2	no	—
85	C₂×C₄×C₉	—	2	1	no	—
86	C₂×C₄×C₉	—	6	1	no	—
87	C₂×C₄×C₉	#67	1	2	yes	—
88	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
89	C₈×C₉	—	6	2	no	—
90	#488	—	3	1	no	Sylow
91	C₂×C₃×C₉	#124	1	1	yes	characteristic
92	C₂×C₃×C₉	#135	1	2	yes	—
93	D₃×C₉	—	8	1	no	—
94	C₂×C₃×Q₈	—	3	1	no	—
95	C₂×C₃×D₄	—	3	1	no	—
96	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
97	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
98	C₂×C₃×C₈	—	3	2	no	—
99	C₃×C₄⋊C₄	—	2	4	no	—
100	C₃×C₄⋊C₄	—	2	2	no	—
101	C₃×C₄⋊C₄	—	2	2	no	—
102	C₃×C₄⋊C₄	—	2	2	no	—
103	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
104	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
105	C₃×C₂²⋊C₄	—	6	2	no	—
106	C₃×C₄²	—	2	1	no	—
107	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
108	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
109	(C₂×D₃)⋊C₄	—	2	2	no	—
110	C₂×C₃⋊C₈	C₂²×C₉	1	2	yes	—
111	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
112	C₂×C₃×D₃	—	4	1	no	—
113	C₂×C₃×D₃	—	4	2	no	—
114	C₃²×C₄	—	2	2	no	—
115	C₃²×C₄	—	4	2	no	—
116	C₃²×C₄	C₃×#41	1	2	yes	—
117	C₃×Dic₃	—	4	1	no	—
118	C₂²×C₉	—	2	1	no	—
119	C₂²×C₉	—	12	1	no	—
120	C₂²×C₉	—	12	2	no	—
121	C₂²×C₉	C₂×#67	1	1	yes	characteristic
122	C₄×C₉	—	2	2	no	—
123	C₄×C₉	—	2	2	no	—
124	C₄×C₉	—	4	2	no	—
125	C₄×C₉	—	4	4	no	—
126	C₄×C₉	—	4	2	no	—
127	C₄×C₉	—	12	1	no	—
128	C₄×C₉	#239	1	2	yes	—
129	#125	D₃×C₉	1	1	yes	characteristic, complemented
130	#124	—	3	1	no	—
131	#103	—	3	2	no	—
132	#102	—	3	2	no	—
133	C₄×C₈	—	3	1	no	—
134	C₃×C₉	#488	1	1	yes	characteristic, complemented, Sylow
135	C₂³×C₃	—	6	1	no	—
136	C₂²×D₃	—	2	1	no	—
137	C₃×Q₈	—	6	2	no	—
138	C₃×D₄	—	6	2	no	—
139	C₂×C₃×C₄	—	2	4	no	—
140	C₂×C₃×C₄	—	2	2	no	—
141	C₂×C₃×C₄	—	2	2	no	—
142	C₂×C₃×C₄	—	2	2	no	—
143	C₂×C₃×C₄	—	2	1	no	—
144	C₂×C₃×C₄	—	6	1	no	—
145	C₂×C₃×C₄	D₄×C₉	1	2	yes	—
146	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
147	C₂×C₃×C₄	C₃×#67	1	2	yes	—
148	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
149	C₂×Dic₃	—	2	1	no	—
150	D₁₂	—	2	2	no	—
151	Dic₆	—	2	2	no	—
152	C₃×C₈	—	6	2	no	—
153	C₃⋊C₈	—	2	2	no	—
154	C₂×C₃²	C₃×#124	1	1	yes	characteristic
155	C₂×C₃²	C₃×#135	1	2	yes	—
156	C₃×D₃	—	8	1	no	—
157	C₂×C₉	—	2	1	no	—
158	C₂×C₉	—	2	2	no	—
159	C₂×C₉	—	24	1	no	—
160	C₂×C₉	#947	1	1	yes	characteristic
161	C₂×C₉	#950	1	2	yes	—
162	C₂×Q₈	—	3	1	no	—
163	C₂×D₄	—	3	1	no	—
164	C₂×C₈	—	3	2	no	—
165	C₄⋊C₄	—	2	2	no	—
166	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
167	C₂²⋊C₄	—	6	2	no	—
168	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
169	C₂²×C₃	—	2	1	no	—
170	C₂²×C₃	—	12	1	no	—
171	C₂²×C₃	—	12	2	no	—
172	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
173	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
174	C₂×D₃	—	4	1	no	—
175	C₂×D₃	—	4	2	no	—
176	C₃×C₄	—	2	2	no	—
177	C₃×C₄	—	2	2	no	—
178	C₃×C₄	—	2	2	no	—
179	C₃×C₄	—	4	2	no	—
180	C₃×C₄	—	4	4	no	—
181	C₃×C₄	—	4	2	no	—
182	C₃×C₄	—	4	2	no	—
183	C₃×C₄	—	12	1	no	—
184	C₃×C₄	C₉×#41	1	2	yes	—
185	C₃×C₄	C₃×#239	1	2	yes	—
186	Dic₃	—	4	1	no	—
187	C₃²	C₃×#488	1	1	yes	characteristic
188	C₉	—	2	1	no	—
189	C₉	#5068	1	1	yes	characteristic, direct product factor
190	C₂³	—	6	1	no	—
191	Q₈	—	6	2	no	—
192	D₄	—	6	2	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	6	1	no	—
195	C₂×C₄	C₉×#67	1	2	yes	—
196	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
197	C₈	—	6	2	no	—
198	C₂×C₃	—	2	1	no	—
199	C₂×C₃	—	2	2	no	—
200	C₂×C₃	—	24	1	no	—
201	C₂×C₃	C₉×#124	1	1	yes	characteristic
202	C₂×C₃	C₉×#135	1	2	yes	—
203	C₂×C₃	C₃×#947	1	1	yes	characteristic
204	C₂×C₃	C₃×#950	1	2	yes	—
205	D₃	—	8	1	no	—
206	C₂²	—	12	1	no	—
207	C₂²	—	12	2	no	—
208	C₂²	C₂×C₉×#67	1	1	yes	characteristic
209	C₄	—	2	2	no	—
210	C₄	—	4	2	no	—
211	C₄	—	12	1	no	—
212	C₄	C₉×#239	1	2	yes	—
213	C₃	—	2	1	no	—
214	C₃	C₉×#488	1	1	yes	characteristic, complemented
215	C₃	C₃×#5068	1	1	yes	characteristic
216	C₂	—	24	1	no	—
217	C₂	C₉×#947	1	1	yes	characteristic
218	C₂	C₉×#950	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×C₉×#125

C₂

yes

maximal, characteristic, complemented

C₉×#875

C₂

yes

maximal, characteristic

C₉×#810

C₂

yes

maximal, complemented

C₉×#809

C₂

yes

maximal

C₄×C₉×C₃⋊C₈

C₂

yes

maximal, characteristic, complemented

C₃×#5068

C₃

yes

maximal, characteristic

C₉×#488

—

maximal

C₂×C₉×D₁₂

C₂²

yes

characteristic

C₂×C₉×Dic₆

C₂²

yes

characteristic

C₃×C₉×C₄⋊C₄

—

C₃×C₉×C₄⋊C₄

C₂²

yes

—

C₃×C₄²×C₉

C₂²

yes

characteristic

C₉×(C₂×D₃)⋊C₄

—

C₂×C₉×C₃⋊C₈

C₂²

yes

—

C₃²×#125

C₂×C₃

yes

characteristic

C₃×#875

C₂×C₃

yes

characteristic

C₃×#810

C₂×C₃

yes

—

C₃×#809

C₂×C₃

yes

—

C₃×C₄×C₃⋊C₈

C₂×C₃

yes

characteristic

C₉×#125

—

C₉×#125

D₃

yes

characteristic, complemented

C₉×#124

—

C₉×#103

—

C₉×#102

—

C₄×C₈×C₉

—

C₂²×D₃×C₉

—

C₂×C₃×C₄×C₉

—

C₂×C₃×C₄×C₉

D₄

yes

—

C₂×C₃×C₄×C₉

C₂³

yes

characteristic

C₂×C₉×Dic₃

—

C₉×D₁₂

—

C₉×Dic₆

—

C₉×C₃⋊C₈

—

C₃×#488

—

#5068

C₉

yes

characteristic, direct product factor

C₂×C₃×D₁₂

C₂²×C₃

yes

characteristic

C₂×C₃×Dic₆

C₂²×C₃

yes

characteristic

C₃²×C₄⋊C₄

—

C₃²×C₄⋊C₄

C₂²×C₃

yes

—

C₃²×C₄²

C₂²×C₃

yes

characteristic

C₃×(C₂×D₃)⋊C₄

—

C₂×C₃×C₃⋊C₈

C₂²×C₃

yes

—

C₂×Q₈×C₉

—

C₂×D₄×C₉

—

C₂×C₈×C₉

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

—

C₉×C₄⋊C₄

C₂×D₃

yes

—

C₉×C₂²⋊C₄

—

C₄²×C₉

—

C₄²×C₉

C₂×D₃

yes

characteristic

C₂²×C₃×C₉

C₂×D₄

yes

characteristic

C₂×D₃×C₉

—

C₂×D₃×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

—

C₃×C₄×C₉

#41

yes

—

C₉×Dic₃

—

C₃×#125

—

C₃×#125

C₂×C₉

yes

characteristic, complemented

C₃×#125

C₃×D₃

yes

characteristic

C₃×#124

—

#875

C₂×C₉

yes

characteristic

C₃×#103

—

C₃×#102

—

C₃×C₄×C₈

—

#810

C₂×C₉

yes

complemented

#809

C₂×C₉

yes

—

C₄×C₃⋊C₈

C₂×C₉

yes

characteristic, complemented

C₂²×C₃×D₃

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₃×D₄

yes

—

C₂×C₃²×C₄

C₂³×C₃

yes

characteristic

C₂×C₃×Dic₃

—

C₃×D₁₂

—

C₃×Dic₆

—

C₂³×C₉

—

C₃×C₃⋊C₈

—

Q₈×C₉

—

D₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

—

C₂×C₄×C₉

#67

yes

—

C₂×C₄×C₉

C₂²×D₃

yes

characteristic

C₈×C₉

—

—

C₂×C₃×C₉

yes

C₂×C₃×C₉

yes

—

D₃×C₉

—

C₂×C₃×Q₈

—

C₂×C₃×D₄

—

C₂×D₁₂

C₂²×C₉

yes

characteristic

C₂×Dic₆

C₂²×C₉

yes

characteristic

C₂×C₃×C₈

—

C₃×C₄⋊C₄

—

100

C₃×C₄⋊C₄

—

101

C₃×C₄⋊C₄

—

102

C₃×C₄⋊C₄

—

103

C₃×C₄⋊C₄

C₂²×C₉

yes

—

104

C₃×C₄⋊C₄

C₂×C₃×D₃

yes

—

105

C₃×C₂²⋊C₄

—

106

C₃×C₄²

—

107

C₃×C₄²

C₂²×C₉

yes

characteristic

108

C₃×C₄²

C₂×C₃×D₃

yes

characteristic

109

(C₂×D₃)⋊C₄

—

110

C₂×C₃⋊C₈

C₂²×C₉

yes

—

111

C₂²×C₃²

C₂×C₃×D₄

yes

characteristic

112

C₂×C₃×D₃

—

113

C₂×C₃×D₃

—

114

C₃²×C₄

—

115

C₃²×C₄

—

116

C₃²×C₄

C₃×#41

yes

—

117

C₃×Dic₃

—

118

C₂²×C₉

—

119

C₂²×C₉

—

120

C₂²×C₉

—

121

C₂²×C₉

C₂×#67

yes

characteristic

122

C₄×C₉

—

123

C₄×C₉

—

124

C₄×C₉

—

125

C₄×C₉

—

126

C₄×C₉

—

127

C₄×C₉

—

128

C₄×C₉

#239

yes

—

129

#125

D₃×C₉

yes

characteristic, complemented

130

#124

—

131

#103

—

132

#102

—

133

C₄×C₈

—

134

C₃×C₉

#488

yes

characteristic, complemented, Sylow

135

C₂³×C₃

—

136

C₂²×D₃

—

137

C₃×Q₈

—

138

C₃×D₄

—

139

C₂×C₃×C₄

—

140

C₂×C₃×C₄

—

141

C₂×C₃×C₄

—

142

C₂×C₃×C₄

—

143

C₂×C₃×C₄

—

144

C₂×C₃×C₄

—

145

C₂×C₃×C₄

D₄×C₉

yes

—

146

C₂×C₃×C₄

C₂³×C₉

yes

characteristic

147

C₂×C₃×C₄

C₃×#67

yes

—

148

C₂×C₃×C₄

C₂²×C₃×D₃

yes

characteristic

149

C₂×Dic₃

—

150

D₁₂

—

151

Dic₆

—

152

C₃×C₈

—

153

C₃⋊C₈

—

154

C₂×C₃²

C₃×#124

yes

characteristic

155

C₂×C₃²

C₃×#135

yes

—

156

C₃×D₃

—

157

C₂×C₉

—

158

C₂×C₉

—

159

C₂×C₉

—

160

C₂×C₉

#947

yes

characteristic

161

C₂×C₉

#950

yes

—

162

C₂×Q₈

—

163

C₂×D₄

—

164

C₂×C₈

—

165

C₄⋊C₄

—

166

C₄⋊C₄

C₂×D₃×C₉

yes

—

167

C₂²⋊C₄

—

168

C₄²

C₂×D₃×C₉

yes

characteristic

169

C₂²×C₃

—

170

C₂²×C₃

—

171

C₂²×C₃

—

172

C₂²×C₃

C₂×D₄×C₉

yes

characteristic

173

C₂²×C₃

C₂×C₃×#67

yes

characteristic

174

C₂×D₃

—

175

C₂×D₃

—

176

C₃×C₄

—

177

C₃×C₄

—

178

C₃×C₄

—

179

C₃×C₄

—

180

C₃×C₄

—

181

C₃×C₄

—

182

C₃×C₄

—

183

C₃×C₄

—

184

C₃×C₄

C₉×#41

yes

—

185

C₃×C₄

C₃×#239

yes

—

186

Dic₃

—

187

C₃²

C₃×#488

yes

characteristic

188

C₉

—

189

C₉

#5068

yes

characteristic, direct product factor

190

C₂³

—

191

Q₈

—

192

D₄

—

193

C₂×C₄

—

194

C₂×C₄

—

195

C₂×C₄

C₉×#67

yes

—

196

C₂×C₄

C₂²×D₃×C₉

yes

characteristic

197

C₈

—

198

C₂×C₃

—

199

C₂×C₃

—

200

C₂×C₃

—

201

C₂×C₃

C₉×#124

yes

characteristic

202

C₂×C₃

C₉×#135

yes

—

203

C₂×C₃

C₃×#947

yes

characteristic

204

C₂×C₃

C₃×#950

yes

—

205

D₃

—

206

C₂²

—

207

C₂²

—

208

C₂²

C₂×C₉×#67

yes

characteristic

209

C₄

—

210

C₄

—

211

C₄

—

212

C₄

C₉×#239

yes

—

213

C₃

—

214

C₃

C₉×#488

yes

characteristic, complemented

215

C₃

C₃×#5068

yes

characteristic

216

C₂

—

217

C₂

C₉×#947

yes

characteristic

218

C₂

C₉×#950

yes

—

	subgroup	G/H
center	C₂²×C₉	C₂×#67
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#125	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×D₁₂	C₂²×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#125	D₃
hypocenter	C₃	C₉×#488
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ C₉×#125

subgroup

G/H

center

C₂²×C₉

C₂×#67

commutator

C₂×C₃×C₄

C₂³×C₉

Frattini

C₂×C₃×C₄

C₂²×C₃×D₃

Fitting

C₃×C₉×#125

C₂

socle

C₂²×C₃²

C₂×C₃×D₄

prime radical

C₂×C₃×D₁₂

C₂²×C₃

cosocle

C₂×C₃²×C₄

C₂³×C₃

D₃

C₃

G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃

UCS

C₁ ◁ C₂²×C₉ ◁ C₄²×C₉ ◁ C₉×#125

N	H ≅ G/N	type
1. C₃×C₉×#125	C₂	semidirect
3. C₉×#810	C₂	semidirect
5. C₄×C₉×C₃⋊C₈	C₂	semidirect
21. C₉×#125	D₃	semidirect
35. #5068	C₉	direct (N × H)
61. C₃×#125	C₂×C₉	semidirect
68. #810	C₂×C₉	semidirect
70. C₄×C₃⋊C₈	C₂×C₉	semidirect
129. #125	D₃×C₉	semidirect
134. C₃×C₉	#488	semidirect
189. C₉	#5068	direct (N × H)
214. C₃	C₉×#488	semidirect

H ≅ G/N

type

1. C₃×C₉×#125

C₂

semidirect

3. C₉×#810

C₂

semidirect

5. C₄×C₉×C₃⋊C₈

C₂

semidirect

21. C₉×#125

D₃

semidirect

35. #5068

C₉

direct (N × H)

61. C₃×#125

C₂×C₉

semidirect

68. #810

C₂×C₉

semidirect

70. C₄×C₃⋊C₈

C₂×C₉

semidirect

129. #125

D₃×C₉

semidirect

134. C₃×C₉

#488

semidirect

189. C₉

#5068

direct (N × H)

214. C₃

C₉×#488

semidirect

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

subgroup	index
C₃×C₉×#125	2
C₉×#875	2
C₉×#810	2
C₉×#809	2
C₄×C₉×C₃⋊C₈	2
C₃×#5068	3
C₉×#488	3

subgroup

index

C₃×C₉×#125

C₄×C₉×C₃⋊C₈

Subgroups — C₉×#5068 #13142948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C9×#5068 #13142948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5068 #13142948