Group #13159462 — subgroups

Subgroups — #13159462

Order 1728.

616 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 616 conjugacy classes of subgroups — too many to draw. Only its 172 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×#64110	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃⋊(C₃⋊(C₃⋊C₁₆))	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#812	C₂	1	1	yes	maximal, characteristic, complemented
4	#11722002	C₂	1	2	yes	maximal, complemented
5	C₃⋊D₃×C₃⋊C₁₆	C₂	1	2	yes	maximal, complemented
6	#10592606	—	3	1	no	maximal
7	#10590622	—	3	4	no	maximal
8	C₃×#3828	C₄	1	1	yes	characteristic
9	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
10	C₃×#3748	C₄	1	1	yes	characteristic
11	C₃×#3743	C₄	1	2	yes	—
12	C₃×C₈×C₃⋊D₃	C₂²	1	2	yes	—
13	C₃⋊(C₃⋊(C₃⋊C₁₆))	C₂²	1	1	yes	characteristic
14	C₃⋊(C₃⋊(C₃⋊C₁₆))	C₂²	1	1	yes	characteristic
15	C₃²×C₃⋊C₁₆	C₂²	1	2	yes	—
16	#64110	D₃	1	1	yes	characteristic
17	C₃×#901	—	3	4	no	—
18	C₃²×M₃₂	—	3	1	no	—
19	C₂×C₃⋊(C₃⋊C₁₆)	—	3	1	no	—
20	C₂×C₃⋊(C₃⋊C₁₆)	—	3	4	no	—
21	C₂×C₃⋊(C₃⋊C₁₆)	—	6	4	no	—
22	#63625	—	3	2	no	—
23	C₁₆×C₃⋊D₃	—	3	2	no	—
24	C₃×#812	D₃	1	4	yes	complemented
25	#63543	—	3	8	no	—
26	D₃×C₃⋊C₁₆	—	3	8	no	—
27	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
28	C₃×#638	C₈	1	2	yes	—
29	C₃×C₄⋊(C₃⋊D₃)	C₈	1	1	yes	characteristic
30	C₃×C₄×C₃⋊D₃	C₂×C₄	1	2	yes	—
31	C₃×#634	C₈	1	1	yes	characteristic
32	C₃³×C₈	C₂×C₄	1	1	yes	characteristic
33	C₃³×C₈	C₂³	1	1	yes	characteristic
34	C₃×C₃⋊(C₃⋊C₈)	C₂×C₄	1	2	yes	—
35	#5140	—	9	1	no	—
36	#4907	—	9	4	no	—
37	#3828	Dic₃	1	1	yes	characteristic
38	C₃×#235	—	3	4	no	—
39	C₂×C₃²×C₈	—	2	4	no	—
40	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
41	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
42	#3748	Dic₃	1	1	yes	characteristic
43	#3743	Dic₃	1	2	yes	—
44	C₈×C₃⋊D₃	C₂×D₃	1	2	yes	—
45	C₃×#208	—	3	4	no	—
46	C₃×ΓL(1,𝔽₂₅)	—	3	8	no	—
47	C₃×D₃×C₈	—	3	8	no	—
48	C₃²×C₁₆	—	3	2	no	—
49	C₃⋊(C₃⋊C₁₆)	—	3	1	no	—
50	C₃⋊(C₃⋊C₁₆)	—	3	1	no	—
51	C₃⋊(C₃⋊C₁₆)	—	3	4	no	—
52	C₃⋊(C₃⋊C₁₆)	—	3	4	no	—
53	C₃⋊(C₃⋊C₁₆)	—	6	4	no	—
54	C₃⋊(C₃⋊C₁₆)	—	6	4	no	—
55	C₃×C₃⋊C₁₆	C₂×D₃	1	8	yes	—
56	C₂²×C₃³	C₂×C₈	1	1	yes	characteristic
57	C₂×C₃×C₃⋊D₃	C₂×C₈	1	2	yes	—
58	C₃³×C₄	C₂×C₈	1	1	yes	characteristic
59	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
60	C₃×C₃⋊Dic₃	C₂×C₈	1	2	yes	—
61	C₃×#131	—	9	1	no	—
62	#901	—	3	4	no	—
63	C₃×M₃₂	—	3	4	no	—
64	#812	—	9	2	no	—
65	#812	C₃⋊D₃	1	1	yes	characteristic, complemented
66	C₂×C₃⋊C₁₆	—	9	4	no	—
67	C₂×C₃⋊C₁₆	—	9	1	no	—
68	C₂×C₃⋊C₁₆	—	9	2	no	—
69	C₂×C₃⋊C₁₆	—	18	4	no	—
70	#798	—	9	8	no	—
71	D₃×C₁₆	—	9	8	no	—
72	C₂×C₃²×C₄	—	2	4	no	—
73	C₂×C₃²×C₄	C₄×D₃	1	4	yes	—
74	C₂×C₃²×C₄	C₂×Dic₃	1	1	yes	characteristic
75	#638	C₃⋊C₈	1	2	yes	—
76	C₄⋊(C₃⋊D₃)	C₃⋊C₈	1	1	yes	characteristic
77	C₄×C₃⋊D₃	C₂×Dic₃	1	2	yes	—
78	#634	C₃⋊C₈	1	1	yes	characteristic
79	C₃×#67	—	3	8	no	—
80	C₃×D₁₂	—	3	4	no	—
81	C₃×C₄×D₃	—	3	8	no	—
82	C₃×Dic₆	—	3	4	no	—
83	C₃²×C₈	—	2	4	no	—
84	C₃²×C₈	—	2	4	no	—
85	C₃²×C₈	C₄×D₃	1	4	yes	—
86	C₃²×C₈	C₂×Dic₃	1	1	yes	characteristic
87	C₃²×C₈	C₂²×D₃	1	4	yes	—
88	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
89	C₃⋊(C₃⋊C₈)	C₂×Dic₃	1	2	yes	—
90	C₃×C₃⋊C₈	—	3	8	no	—
91	#504	—	27	1	no	Sylow
92	C₂×C₃³	—	2	1	no	—
93	C₂×C₃³	C₂²×C₈	1	1	yes	characteristic
94	C₃×C₃⋊D₃	—	2	2	no	—
95	C₃×#41	—	9	1	no	—
96	#235	—	3	4	no	—
97	C₃×M₁₆	—	9	1	no	—
98	C₃×M₁₆	—	9	2	no	—
99	C₂×C₃×C₈	—	2	4	no	—
100	C₂×C₃×C₈	—	9	2	no	—
101	C₂×C₃×C₈	D₃²	1	4	yes	—
102	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
103	#208	—	3	4	no	—
104	ΓL(1,𝔽₂₅)	—	3	8	no	—
105	D₃×C₈	—	3	8	no	—
106	C₃×C₁₆	—	3	8	no	—
107	C₃⋊C₁₆	—	9	4	no	—
108	C₃⋊C₁₆	—	9	4	no	—
109	C₃⋊C₁₆	—	9	1	no	—
110	C₃⋊C₁₆	—	9	1	no	—
111	C₃⋊C₁₆	—	18	4	no	—
112	C₃⋊C₁₆	—	18	4	no	—
113	C₃⋊C₁₆	C₂×C₃⋊D₃	1	2	yes	—
114	C₂²×C₃²	—	2	4	no	—
115	C₂²×C₃²	D₃×C₈	1	4	yes	—
116	C₂²×C₃²	C₂×C₃⋊C₈	1	1	yes	characteristic
117	C₂×C₃⋊D₃	C₂×C₃⋊C₈	1	2	yes	—
118	C₂×C₃×D₃	—	3	8	no	—
119	C₃²×C₄	—	2	4	no	—
120	C₃²×C₄	—	2	4	no	—
121	C₃²×C₄	D₃×C₈	1	4	yes	—
122	C₃²×C₄	C₂×C₃⋊C₈	1	1	yes	characteristic
123	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
124	C₃²×C₄	C₂²×Dic₃	1	1	yes	characteristic
125	C₃⋊Dic₃	C₂×C₃⋊C₈	1	2	yes	—
126	C₃×Dic₃	—	3	8	no	—
127	#131	—	9	1	no	—
128	M₃₂	—	3	1	no	—
129	M₃₂	—	27	2	no	—
130	C₂×C₁₆	—	27	2	no	—
131	C₂×C₁₆	—	27	1	no	—
132	C₃³	#504	1	1	yes	characteristic, complemented, Sylow
133	C₃×Q₈	—	9	1	no	—
134	C₃×D₄	—	9	2	no	—
135	C₃×D₄	—	9	1	no	—
136	C₂×C₃×C₄	—	2	4	no	—
137	C₂×C₃×C₄	—	9	2	no	—
138	C₂×C₃×C₄	D₃×Dic₃	1	4	yes	—
139	C₂×C₃×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
140	#67	—	3	8	no	—
141	D₁₂	—	3	4	no	—
142	C₄×D₃	—	3	8	no	—
143	Dic₆	—	3	4	no	—
144	C₃×C₈	—	2	4	no	—
145	C₃×C₈	—	2	4	no	—
146	C₃×C₈	—	9	2	no	—
147	C₃×C₈	D₃×Dic₃	1	4	yes	—
148	C₃×C₈	C₄×C₃⋊D₃	1	1	yes	characteristic
149	C₃×C₈	C₂×D₃²	1	4	yes	—
150	C₃×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
151	C₃⋊C₈	—	3	8	no	—
152	C₂×C₃²	—	2	8	no	—
153	C₂×C₃²	—	2	1	no	—
154	C₂×C₃²	—	2	4	no	—
155	C₂×C₃²	—	2	4	no	—
156	C₂×C₃²	C₂×D₃×C₈	1	4	yes	—
157	C₂×C₃²	C₂²×C₃⋊C₈	1	1	yes	characteristic
158	C₃⋊D₃	—	2	2	no	—
159	C₃×D₃	—	6	8	no	—
160	#41	—	9	1	no	—
161	M₁₆	—	9	1	no	—
162	M₁₆	—	9	2	no	—
163	C₂×C₈	—	9	2	no	—
164	C₂×C₈	D₃×C₃⋊D₃	1	1	yes	characteristic
165	C₁₆	—	3	2	no	—
166	C₁₆	—	27	1	no	—
167	C₁₆	—	27	1	no	—
168	C₂²×C₃	—	2	4	no	—
169	C₂²×C₃	—	9	2	no	—
170	C₂²×C₃	D₃×C₃⋊C₈	1	4	yes	—
171	C₂²×C₃	C₈×C₃⋊D₃	1	1	yes	characteristic
172	C₂×D₃	—	3	8	no	—
173	C₃×C₄	—	2	4	no	—
174	C₃×C₄	—	2	4	no	—
175	C₃×C₄	—	9	2	no	—
176	C₃×C₄	D₃×C₃⋊C₈	1	4	yes	—
177	C₃×C₄	C₈×C₃⋊D₃	1	1	yes	characteristic
178	C₃×C₄	C₂×D₃×Dic₃	1	4	yes	—
179	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
180	Dic₃	—	3	8	no	—
181	C₃²	—	2	4	no	—
182	C₃²	#4907	1	4	yes	complemented
183	C₃²	#5140	1	1	yes	characteristic, complemented
184	Q₈	—	9	1	no	—
185	D₄	—	9	2	no	—
186	D₄	—	9	1	no	—
187	C₂×C₄	—	9	2	no	—
188	C₂×C₄	Dic₃×C₃⋊D₃	1	1	yes	characteristic
189	C₈	—	9	2	no	—
190	C₈	Dic₃×C₃⋊D₃	1	1	yes	characteristic
191	C₈	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
192	C₂×C₃	—	2	8	no	—
193	C₂×C₃	—	2	1	no	—
194	C₂×C₃	—	2	4	no	—
195	C₂×C₃	—	2	4	no	—
196	C₂×C₃	—	18	2	no	—
197	C₂×C₃	C₂×D₃×C₃⋊C₈	1	4	yes	—
198	C₂×C₃	C₂×C₈×C₃⋊D₃	1	1	yes	characteristic
199	D₃	—	6	8	no	—
200	C₂²	—	9	2	no	—
201	C₂²	C₃⋊D₃×C₃⋊C₈	1	1	yes	characteristic
202	C₄	—	9	2	no	—
203	C₄	C₃⋊D₃×C₃⋊C₈	1	1	yes	characteristic
204	C₄	C₂×Dic₃×C₃⋊D₃	1	1	yes	characteristic
205	C₃	—	2	4	no	—
206	C₃	#10590622	1	4	yes	complemented
207	C₃	#10592606	1	1	yes	characteristic, complemented
208	C₂	—	2	1	no	—
209	C₂	—	18	2	no	—
210	C₂	C₂×C₃⋊D₃×C₃⋊C₈	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₃×#64110

C₂

yes

maximal, characteristic

C₂×C₃⋊(C₃⋊(C₃⋊C₁₆))

C₂

yes

maximal, characteristic, complemented

C₃²×#812

C₂

yes

maximal, characteristic, complemented

#11722002

C₂

yes

maximal, complemented

C₃⋊D₃×C₃⋊C₁₆

C₂

yes

maximal, complemented

—

—

C₄

yes

characteristic

C₂×C₃³×C₈

C₂²

yes

characteristic

C₃×#3748

C₄

yes

characteristic

C₃×#3743

C₄

yes

—

C₃×C₈×C₃⋊D₃

C₂²

yes

—

C₃⋊(C₃⋊(C₃⋊C₁₆))

C₂²

yes

characteristic

C₃⋊(C₃⋊(C₃⋊C₁₆))

C₂²

yes

characteristic

C₃²×C₃⋊C₁₆

C₂²

yes

—

#64110

D₃

yes

characteristic

C₃×#901

—

C₃²×M₃₂

—

C₂×C₃⋊(C₃⋊C₁₆)

—

C₂×C₃⋊(C₃⋊C₁₆)

—

C₂×C₃⋊(C₃⋊C₁₆)

—

#63625

—

C₁₆×C₃⋊D₃

—

C₃×#812

D₃

yes

complemented

#63543

—

D₃×C₃⋊C₁₆

—

C₂×C₃³×C₄

C₂×C₄

yes

characteristic

C₃×#638

C₈

yes

—

C₃×C₄⋊(C₃⋊D₃)

C₈

yes

characteristic

C₃×C₄×C₃⋊D₃

C₂×C₄

yes

—

C₃×#634

C₈

yes

characteristic

C₃³×C₈

C₂×C₄

yes

characteristic

C₃³×C₈

C₂³

yes

characteristic

C₃×C₃⋊(C₃⋊C₈)

C₂×C₄

yes

—

#5140

—

#4907

—

#3828

Dic₃

yes

characteristic

C₃×#235

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

C₂×D₃

yes

—

C₂×C₃²×C₈

C₂×D₃

yes

characteristic

#3748

Dic₃

yes

characteristic

#3743

Dic₃

yes

—

C₈×C₃⋊D₃

C₂×D₃

yes

—

C₃×#208

—

C₃×ΓL(1,𝔽₂₅)

—

C₃×D₃×C₈

—

C₃²×C₁₆

—

C₃⋊(C₃⋊C₁₆)

—

C₃⋊(C₃⋊C₁₆)

—

C₃⋊(C₃⋊C₁₆)

—

C₃⋊(C₃⋊C₁₆)

—

C₃⋊(C₃⋊C₁₆)

—

C₃⋊(C₃⋊C₁₆)

—

C₃×C₃⋊C₁₆

C₂×D₃

yes

—

C₂²×C₃³

C₂×C₈

yes

characteristic

C₂×C₃×C₃⋊D₃

C₂×C₈

yes

—

C₃³×C₄

C₂×C₈

yes

characteristic

C₃³×C₄

C₂²×C₄

yes

characteristic

C₃×C₃⋊Dic₃

C₂×C₈

yes

—

C₃×#131

—

#901

—

C₃×M₃₂

—

#812

—

#812

C₃⋊D₃

yes

characteristic, complemented

C₂×C₃⋊C₁₆

—

C₂×C₃⋊C₁₆

—

C₂×C₃⋊C₁₆

—

C₂×C₃⋊C₁₆

—

#798

—

D₃×C₁₆

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

C₄×D₃

yes

—

C₂×C₃²×C₄

C₂×Dic₃

yes

characteristic

#638

C₃⋊C₈

yes

—

C₄⋊(C₃⋊D₃)

C₃⋊C₈

yes

characteristic

C₄×C₃⋊D₃

C₂×Dic₃

yes

—

#634

C₃⋊C₈

yes

characteristic

C₃×#67

—

C₃×D₁₂

—

C₃×C₄×D₃

—

C₃×Dic₆

—

C₃²×C₈

—

C₃²×C₈

—

C₃²×C₈

C₄×D₃

yes

—

C₃²×C₈

C₂×Dic₃

yes

characteristic

C₃²×C₈

C₂²×D₃

yes

—

C₃²×C₈

C₂²×D₃

yes

characteristic

C₃⋊(C₃⋊C₈)

C₂×Dic₃

yes

—

C₃×C₃⋊C₈

—

#504

—

Sylow

C₂×C₃³

—

C₂×C₃³

C₂²×C₈

yes

characteristic

C₃×C₃⋊D₃

—

C₃×#41

—

#235

—

C₃×M₁₆

—

C₃×M₁₆

—

C₂×C₃×C₈

—

100

C₂×C₃×C₈

—

101

C₂×C₃×C₈

D₃²

yes

—

102

C₂×C₃×C₈

C₂×C₃⋊D₃

yes

characteristic

103

#208

—

104

ΓL(1,𝔽₂₅)

—

105

D₃×C₈

—

106

C₃×C₁₆

—

107

C₃⋊C₁₆

—

108

C₃⋊C₁₆

—

109

C₃⋊C₁₆

—

110

C₃⋊C₁₆

—

111

C₃⋊C₁₆

—

112

C₃⋊C₁₆

—

113

C₃⋊C₁₆

C₂×C₃⋊D₃

yes

—

114

C₂²×C₃²

—

115

C₂²×C₃²

D₃×C₈

yes

—

116

C₂²×C₃²

C₂×C₃⋊C₈

yes

characteristic

117

C₂×C₃⋊D₃

C₂×C₃⋊C₈

yes

—

118

C₂×C₃×D₃

—

119

C₃²×C₄

—

120

C₃²×C₄

—

121

C₃²×C₄

D₃×C₈

yes

—

122

C₃²×C₄

C₂×C₃⋊C₈

yes

characteristic

123

C₃²×C₄

C₂×C₄×D₃

yes

—

124

C₃²×C₄

C₂²×Dic₃

yes

characteristic

125

C₃⋊Dic₃

C₂×C₃⋊C₈

yes

—

126

C₃×Dic₃

—

127

#131

—

128

M₃₂

—

129

M₃₂

—

130

C₂×C₁₆

—

131

C₂×C₁₆

—

132

C₃³

#504

yes

characteristic, complemented, Sylow

133

C₃×Q₈

—

134

C₃×D₄

—

135

C₃×D₄

—

136

C₂×C₃×C₄

—

137

C₂×C₃×C₄

—

138

C₂×C₃×C₄

D₃×Dic₃

yes

—

139

C₂×C₃×C₄

C₄×C₃⋊D₃

yes

characteristic

140

#67

—

141

D₁₂

—

142

C₄×D₃

—

143

Dic₆

—

144

C₃×C₈

—

145

C₃×C₈

—

146

C₃×C₈

—

147

C₃×C₈

D₃×Dic₃

yes

—

148

C₃×C₈

C₄×C₃⋊D₃

yes

characteristic

149

C₃×C₈

C₂×D₃²

yes

—

150

C₃×C₈

C₂²×C₃⋊D₃

yes

characteristic

151

C₃⋊C₈

—

152

C₂×C₃²

—

153

C₂×C₃²

—

154

C₂×C₃²

—

155

C₂×C₃²

—

156

C₂×C₃²

C₂×D₃×C₈

yes

—

157

C₂×C₃²

C₂²×C₃⋊C₈

yes

characteristic

158

C₃⋊D₃

—

159

C₃×D₃

—

160

#41

—

161

M₁₆

—

162

M₁₆

—

163

C₂×C₈

—

164

C₂×C₈

D₃×C₃⋊D₃

yes

characteristic

165

C₁₆

—

166

C₁₆

—

167

C₁₆

—

168

C₂²×C₃

—

169

C₂²×C₃

—

170

C₂²×C₃

D₃×C₃⋊C₈

yes

—

171

C₂²×C₃

C₈×C₃⋊D₃

yes

characteristic

172

C₂×D₃

—

173

C₃×C₄

—

174

C₃×C₄

—

175

C₃×C₄

—

176

C₃×C₄

D₃×C₃⋊C₈

yes

—

177

C₃×C₄

C₈×C₃⋊D₃

yes

characteristic

178

C₃×C₄

C₂×D₃×Dic₃

yes

—

179

C₃×C₄

C₂×C₄×C₃⋊D₃

yes

characteristic

180

Dic₃

—

181

C₃²

—

182

C₃²

#4907

yes

complemented

183

C₃²

#5140

yes

characteristic, complemented

184

Q₈

—

185

D₄

—

186

D₄

—

187

C₂×C₄

—

188

C₂×C₄

Dic₃×C₃⋊D₃

yes

characteristic

189

C₈

—

190

C₈

Dic₃×C₃⋊D₃

yes

characteristic

191

C₈

C₂×D₃×C₃⋊D₃

yes

characteristic

192

C₂×C₃

—

193

C₂×C₃

—

194

C₂×C₃

—

195

C₂×C₃

—

196

C₂×C₃

—

197

C₂×C₃

C₂×D₃×C₃⋊C₈

yes

—

198

C₂×C₃

C₂×C₈×C₃⋊D₃

yes

characteristic

199

D₃

—

200

C₂²

—

201

C₂²

C₃⋊D₃×C₃⋊C₈

yes

characteristic

202

C₄

—

203

C₄

C₃⋊D₃×C₃⋊C₈

yes

characteristic

204

C₄

C₂×Dic₃×C₃⋊D₃

yes

characteristic

205

C₃

—

206

C₃

#10590622

yes

complemented

207

C₃

#10592606

yes

characteristic, complemented

208

C₂

—

209

C₂

—

210

C₂

C₂×C₃⋊D₃×C₃⋊C₈

yes

characteristic

	subgroup	G/H
center, Frattini	C₈	C₂×D₃×C₃⋊D₃
commutator, socle	C₂×C₃³	C₂²×C₈
Fitting	C₂×C₃³×C₈	C₂²
prime radical	C₃×#3828	C₄
cosocle	C₃³×C₈	C₂³
hypercenter	C₂×C₈	D₃×C₃⋊D₃
hypocenter	C₃³	#504
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₈ ◁ C₂×C₈

subgroup

G/H

center, Frattini

C₈

C₂×D₃×C₃⋊D₃

commutator, socle

C₂×C₃³

C₂²×C₈

Fitting

C₂×C₃³×C₈

C₂²

prime radical

C₃×#3828

C₄

cosocle

C₃³×C₈

C₂³

hypercenter

C₂×C₈

D₃×C₃⋊D₃

C₃³

G ▷ C₂×C₃³ ▷ C₃³

C₁ ◁ C₈ ◁ C₂×C₈

N	H ≅ G/N	type
2. C₂×C₃⋊(C₃⋊(C₃⋊C₁₆))	C₂	semidirect
3. C₃²×#812	C₂	semidirect
4. #11722002	C₂	semidirect
5. C₃⋊D₃×C₃⋊C₁₆	C₂	semidirect
24. C₃×#812	D₃	semidirect
65. #812	C₃⋊D₃	semidirect
132. C₃³	#504	semidirect
182. C₃²	#4907	semidirect
183. C₃²	#5140	semidirect
206. C₃	#10590622	semidirect
207. C₃	#10592606	semidirect

H ≅ G/N

type

2. C₂×C₃⋊(C₃⋊(C₃⋊C₁₆))

C₂

semidirect

3. C₃²×#812

C₂

semidirect

4. #11722002

C₂

semidirect

5. C₃⋊D₃×C₃⋊C₁₆

C₂

semidirect

24. C₃×#812

D₃

semidirect

65. #812

C₃⋊D₃

semidirect

132. C₃³

#504

semidirect

182. C₃²

#4907

semidirect

183. C₃²

#5140

semidirect

206. C₃

#10590622

semidirect

207. C₃

#10592606

semidirect

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

subgroup	index
C₃×#64110	2
C₂×C₃⋊(C₃⋊(C₃⋊C₁₆))	2
C₃²×#812	2
#11722002	2
C₃⋊D₃×C₃⋊C₁₆	2
#10592606	3
#10590622	3

subgroup

index

C₃×#64110

C₂×C₃⋊(C₃⋊(C₃⋊C₁₆))

C₃²×#812

#11722002

C₃⋊D₃×C₃⋊C₁₆

#10592606

#10590622

Subgroups — #13159462

Conjugacy classes of subgroups

Complements

Maximal subgroups