Group #13141446 — subgroups

Subgroups — #10592381⋊C₃ #13141446

Order 1728.

387 conjugacy classes of subgroups; only the 132 normal subgroups are shown.

normal subgroups only

This group has 387 conjugacy classes of subgroups — too many to draw. Only its 132 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	#64078⋊C₃	C₂	1	2	yes	maximal
2	C₄×C₈×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
3	#63645⋊C₃	C₂	1	4	yes	maximal
4	#10592381	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃×#4682	—	3	1	no	maximal
6	C₂×#634⋊C₃	—	2	2	no	—
7	C₂×C₈×H(3,𝔽₃)	C₂²	1	2	yes	—
8	C₄²×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
9	C₄⋊((C₃⋊Dic₃)⋊C₃)	—	2	2	no	—
10	C₄⋊((C₃⋊Dic₃)⋊C₃)	C₂²	1	4	yes	—
11	#64078	C₂×C₃	1	2	yes	—
12	C₃×#869	—	3	2	no	—
13	C₃²×C₄×C₈	—	2	1	no	—
14	C₃²×C₄×C₈	D₃	1	1	yes	characteristic
15	C₃²×C₄×C₈	C₂×C₃	1	1	yes	characteristic
16	#63645	C₂×C₃	1	4	yes	—
17	C₃×#818	—	3	4	no	—
18	C₂×C₄×H(3,𝔽₃)	D₄	1	1	yes	characteristic
19	C₂×C₄×H(3,𝔽₃)	D₄	1	1	yes	characteristic
20	C₂×C₄×H(3,𝔽₃)	C₂³	1	1	yes	characteristic
21	C₂×(C₃⋊Dic₃)⋊C₃	—	2	4	no	—
22	#634⋊C₃	—	4	4	no	—
23	C₈×H(3,𝔽₃)	Q₈	1	4	yes	complemented
24	C₃×#500	—	9	1	no	—
25	#4682	—	3	1	no	—
26	#4682	—	9	1	no	—
27	C₂×#634	—	2	2	no	—
28	C₂×C₃×Dic₆	—	6	2	no	—
29	C₂×C₃²×C₈	—	2	2	no	—
30	C₂×C₃²×C₈	C₂×D₃	1	2	yes	—
31	C₂×C₃²×C₈	C₂²×C₃	1	2	yes	—
32	C₃²×C₄²	—	2	1	no	—
33	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
34	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
35	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
36	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	4	yes	—
37	C₃×C₄⋊Dic₃	—	3	4	no	—
38	C₃×C₄⋊Dic₃	—	6	2	no	—
39	C₂²×H(3,𝔽₃)	C₂×D₄	1	1	yes	characteristic
40	C₄×H(3,𝔽₃)	D₈	1	2	yes	—
41	C₄×H(3,𝔽₃)	Q₁₆	1	2	yes	—
42	C₄×H(3,𝔽₃)	C₂×Q₈	1	2	yes	—
43	(C₃⋊Dic₃)⋊C₃	—	4	4	no	—
44	C₃×C₄⋊Q₈	—	9	2	no	—
45	#869	—	3	2	no	—
46	#869	—	9	2	no	—
47	C₃×#107	—	9	4	no	—
48	C₃×C₄×C₈	—	3	1	no	—
49	C₃×C₄×C₈	—	3	1	no	—
50	C₃×C₄×C₈	—	6	1	no	—
51	C₃×C₄×C₈	C₃×D₃	1	1	yes	characteristic
52	#818	—	3	4	no	—
53	#818	—	9	4	no	—
54	C₂×C₃²×C₄	—	2	1	no	—
55	C₂×C₃²×C₄	—	2	1	no	—
56	C₂×C₃²×C₄	—	2	1	no	—
57	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
58	C₂×C₃²×C₄	D₁₂	1	1	yes	characteristic
59	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
60	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
61	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
62	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
63	C₂×C₃⋊Dic₃	—	2	4	no	—
64	#634	—	4	4	no	—
65	C₂×C₃×Dic₃	—	6	4	no	—
66	C₃×Dic₆	—	12	4	no	—
67	C₃²×C₈	—	2	4	no	—
68	C₃²×C₈	Dic₆	1	4	yes	complemented
69	C₃²×C₈	C₃×Q₈	1	4	yes	complemented
70	#500	—	9	1	no	Sylow
71	C₂×H(3,𝔽₃)	C₄⋊Q₈	1	1	yes	characteristic
72	C₂×H(3,𝔽₃)	C₂×D₈	1	1	yes	characteristic
73	C₂×H(3,𝔽₃)	C₂×Q₁₆	1	1	yes	characteristic
74	C₂×C₃×Q₈	—	18	2	no	—
75	C₂×Dic₆	—	6	2	no	—
76	C₂×Dic₆	—	18	2	no	—
77	C₂×C₃×C₈	—	3	2	no	—
78	C₂×C₃×C₈	—	3	2	no	—
79	C₂×C₃×C₈	—	6	2	no	—
80	C₂×C₃×C₈	C₂×C₃×D₃	1	2	yes	—
81	C₃×C₄⋊C₄	—	9	4	no	—
82	C₃×C₄⋊C₄	—	18	2	no	—
83	C₃×C₄²	—	3	1	no	—
84	C₃×C₄²	—	3	1	no	—
85	C₃×C₄²	—	6	1	no	—
86	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
87	C₄⋊Dic₃	—	3	4	no	—
88	C₄⋊Dic₃	—	6	2	no	—
89	C₄⋊Dic₃	—	9	4	no	—
90	C₄⋊Dic₃	—	18	2	no	—
91	C₂²×C₃²	—	2	1	no	—
92	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
93	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
94	C₃²×C₄	—	2	2	no	—
95	C₃²×C₄	—	2	2	no	—
96	C₃²×C₄	—	2	2	no	—
97	C₃²×C₄	D₂₄	1	2	yes	—
98	C₃²×C₄	Dic₁₂	1	2	yes	—
99	C₃²×C₄	C₃×D₈	1	2	yes	—
100	C₃²×C₄	C₃×Q₁₆	1	2	yes	—
101	C₃²×C₄	C₂×Dic₆	1	2	yes	—
102	C₃²×C₄	C₂×C₃×Q₈	1	2	yes	—
103	C₃⋊Dic₃	—	4	4	no	—
104	C₃×Dic₃	—	12	4	no	—
105	C₄⋊Q₈	—	9	2	no	—
106	#107	—	9	4	no	—
107	C₄×C₈	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
108	H(3,𝔽₃)	#500	1	1	yes	characteristic, complemented, Sylow
109	C₃×Q₈	—	36	4	no	—
110	C₂×C₃×C₄	—	3	1	no	—
111	C₂×C₃×C₄	—	3	1	no	—
112	C₂×C₃×C₄	—	3	1	no	—
113	C₂×C₃×C₄	—	3	1	no	—
114	C₂×C₃×C₄	—	3	1	no	—
115	C₂×C₃×C₄	—	3	1	no	—
116	C₂×C₃×C₄	—	6	1	no	—
117	C₂×C₃×C₄	—	6	1	no	—
118	C₂×C₃×C₄	—	6	1	no	—
119	C₂×C₃×C₄	—	18	4	no	—
120	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
121	C₂×C₃×C₄	C₃×D₁₂	1	1	yes	characteristic
122	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
123	C₂×Dic₃	—	6	4	no	—
124	C₂×Dic₃	—	18	4	no	—
125	Dic₆	—	12	4	no	—
126	Dic₆	—	36	4	no	—
127	C₃×C₈	—	3	4	no	—
128	C₃×C₈	—	3	4	no	—
129	C₃×C₈	—	6	4	no	—
130	C₃×C₈	C₃×Dic₆	1	4	yes	—
131	C₂×C₃²	—	2	1	no	—
132	C₂×C₃²	—	2	1	no	—
133	C₂×C₃²	—	2	1	no	—
134	C₂×C₃²	#869	1	1	yes	characteristic
135	C₂×C₃²	C₂×D₂₄	1	1	yes	characteristic
136	C₂×C₃²	C₂×Dic₁₂	1	1	yes	characteristic
137	C₂×C₃²	C₃×C₄⋊Q₈	1	1	yes	characteristic
138	C₂×C₃²	C₂×C₃×D₈	1	1	yes	characteristic
139	C₂×C₃²	C₂×C₃×Q₁₆	1	1	yes	characteristic
140	C₂×Q₈	—	18	2	no	—
141	C₂×C₈	C₂×(C₃⋊D₃)⋊C₃	1	2	yes	—
142	C₄⋊C₄	—	9	4	no	—
143	C₄⋊C₄	—	18	2	no	—
144	C₄²	C₂×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
145	C₂²×C₃	—	3	1	no	—
146	C₂²×C₃	—	3	1	no	—
147	C₂²×C₃	—	6	1	no	—
148	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
149	C₃×C₄	—	3	2	no	—
150	C₃×C₄	—	3	2	no	—
151	C₃×C₄	—	3	2	no	—
152	C₃×C₄	—	3	2	no	—
153	C₃×C₄	—	3	2	no	—
154	C₃×C₄	—	3	2	no	—
155	C₃×C₄	—	6	2	no	—
156	C₃×C₄	—	6	2	no	—
157	C₃×C₄	—	6	2	no	—
158	C₃×C₄	—	36	4	no	—
159	C₃×C₄	C₃×D₂₄	1	2	yes	—
160	C₃×C₄	C₃×Dic₁₂	1	2	yes	—
161	C₃×C₄	C₂×C₃×Dic₆	1	2	yes	—
162	Dic₃	—	12	4	no	—
163	Dic₃	—	36	4	no	—
164	C₃²	—	2	1	no	—
165	C₃²	#4682	1	1	yes	characteristic, complemented
166	C₃²	C₃×#500	1	1	yes	characteristic, complemented
167	Q₈	—	36	4	no	—
168	C₂×C₄	—	18	4	no	—
169	C₂×C₄	C₄⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
170	C₂×C₄	C₄⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
171	C₂×C₄	C₂²×(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
172	C₈	#634⋊C₃	1	4	yes	complemented
173	C₂×C₃	—	3	1	no	—
174	C₂×C₃	—	3	1	no	—
175	C₂×C₃	—	3	1	no	—
176	C₂×C₃	—	3	1	no	—
177	C₂×C₃	—	3	1	no	—
178	C₂×C₃	—	3	1	no	—
179	C₂×C₃	—	6	1	no	—
180	C₂×C₃	—	6	1	no	—
181	C₂×C₃	—	6	1	no	—
182	C₂×C₃	C₃×#869	1	1	yes	characteristic
183	C₂×C₃	C₂×C₃×D₂₄	1	1	yes	characteristic
184	C₂×C₃	C₂×C₃×Dic₁₂	1	1	yes	characteristic
185	C₂²	C₂×C₄⋊((C₃⋊D₃)⋊C₃)	1	1	yes	characteristic
186	C₄	—	36	4	no	—
187	C₄	#3746⋊C₃	1	2	yes	—
188	C₄	#3745⋊C₃	1	2	yes	—
189	C₄	C₂×#634⋊C₃	1	2	yes	—
190	C₃	—	3	1	no	—
191	C₃	—	3	1	no	—
192	C₃	—	6	1	no	—
193	C₃	C₃×#4682	1	1	yes	characteristic
194	C₂	#64078⋊C₃	1	1	yes	characteristic
195	C₂	C₂×#3746⋊C₃	1	1	yes	characteristic
196	C₂	C₂×#3745⋊C₃	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#64078⋊C₃

C₂

yes

maximal

C₄×C₈×H(3,𝔽₃)

C₂

yes

maximal, characteristic

#63645⋊C₃

C₂

yes

maximal

#10592381

C₃

yes

maximal, characteristic, complemented

C₃×#4682

—

maximal

C₂×#634⋊C₃

—

C₂×C₈×H(3,𝔽₃)

C₂²

yes

—

C₄²×H(3,𝔽₃)

C₂²

yes

characteristic

C₄⋊((C₃⋊Dic₃)⋊C₃)

—

C₄⋊((C₃⋊Dic₃)⋊C₃)

C₂²

yes

—

#64078

C₂×C₃

yes

—

C₃×#869

—

C₃²×C₄×C₈

—

C₃²×C₄×C₈

D₃

yes

characteristic

C₃²×C₄×C₈

C₂×C₃

yes

characteristic

#63645

C₂×C₃

yes

—

C₃×#818

—

C₂×C₄×H(3,𝔽₃)

D₄

yes

characteristic

C₂×C₄×H(3,𝔽₃)

D₄

yes

characteristic

C₂×C₄×H(3,𝔽₃)

C₂³

yes

characteristic

C₂×(C₃⋊Dic₃)⋊C₃

—

#634⋊C₃

—

C₈×H(3,𝔽₃)

Q₈

yes

—

—

—

—

C₂×C₃×Dic₆

—

C₂×C₃²×C₈

—

C₂×C₃²×C₈

C₂×D₃

yes

—

C₂×C₃²×C₈

C₂²×C₃

yes

—

C₃²×C₄²

—

C₃²×C₄²

C₂×D₃

yes

characteristic

C₃²×C₄²

C₂²×C₃

yes

characteristic

C₄⋊(C₃⋊Dic₃)

—

C₄⋊(C₃⋊Dic₃)

C₂²×C₃

yes

—

C₃×C₄⋊Dic₃

—

C₃×C₄⋊Dic₃

—

C₂²×H(3,𝔽₃)

C₂×D₄

yes

characteristic

C₄×H(3,𝔽₃)

D₈

yes

—

C₄×H(3,𝔽₃)

Q₁₆

yes

—

C₄×H(3,𝔽₃)

C₂×Q₈

yes

—

(C₃⋊Dic₃)⋊C₃

—

C₃×C₄⋊Q₈

—

#869

—

#869

—

C₃×#107

—

C₃×C₄×C₈

—

C₃×C₄×C₈

—

C₃×C₄×C₈

—

C₃×C₄×C₈

C₃×D₃

yes

characteristic

#818

—

#818

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

—

C₂×C₃²×C₄

D₁₂

yes

characteristic

C₂×C₃²×C₄

D₁₂

yes

characteristic

C₂×C₃²×C₄

C₃×D₄

yes

characteristic

C₂×C₃²×C₄

C₃×D₄

yes

characteristic

C₂×C₃²×C₄

C₂²×D₃

yes

characteristic

C₂×C₃²×C₄

C₂³×C₃

yes

characteristic

C₂×C₃⋊Dic₃

—

#634

—

C₂×C₃×Dic₃

—

C₃×Dic₆

—

C₃²×C₈

—

C₃²×C₈

Dic₆

yes

complemented

C₃²×C₈

C₃×Q₈

yes

complemented

#500

—

Sylow

C₂×H(3,𝔽₃)

C₄⋊Q₈

yes

characteristic

C₂×H(3,𝔽₃)

C₂×D₈

yes

characteristic

C₂×H(3,𝔽₃)

C₂×Q₁₆

yes

characteristic

C₂×C₃×Q₈

—

C₂×Dic₆

—

C₂×Dic₆

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

—

C₂×C₃×C₈

C₂×C₃×D₃

yes

—

C₃×C₄⋊C₄

—

C₃×C₄⋊C₄

—

C₃×C₄²

—

C₃×C₄²

—

C₃×C₄²

—

C₃×C₄²

C₂×C₃×D₃

yes

characteristic

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₄⋊Dic₃

—

C₂²×C₃²

—

C₂²×C₃²

C₂×D₁₂

yes

characteristic

C₂²×C₃²

C₂×C₃×D₄

yes

characteristic

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

—

C₃²×C₄

D₂₄

yes

—

C₃²×C₄

Dic₁₂

yes

—

C₃²×C₄

C₃×D₈

yes

—

100

C₃²×C₄

C₃×Q₁₆

yes

—

101

C₃²×C₄

C₂×Dic₆

yes

—

102

C₃²×C₄

C₂×C₃×Q₈

yes

—

103

C₃⋊Dic₃

—

104

C₃×Dic₃

—

105

C₄⋊Q₈

—

106

#107

—

107

C₄×C₈

(C₃⋊D₃)⋊C₃

yes

characteristic

108

H(3,𝔽₃)

#500

yes

characteristic, complemented, Sylow

109

C₃×Q₈

—

110

C₂×C₃×C₄

—

111

C₂×C₃×C₄

—

112

C₂×C₃×C₄

—

113

C₂×C₃×C₄

—

114

C₂×C₃×C₄

—

115

C₂×C₃×C₄

—

116

C₂×C₃×C₄

—

117

C₂×C₃×C₄

—

118

C₂×C₃×C₄

—

119

C₂×C₃×C₄

—

120

C₂×C₃×C₄

C₃×D₁₂

yes

characteristic

121

C₂×C₃×C₄

C₃×D₁₂

yes

characteristic

122

C₂×C₃×C₄

C₂²×C₃×D₃

yes

characteristic

123

C₂×Dic₃

—

124

C₂×Dic₃

—

125

Dic₆

—

126

Dic₆

—

127

C₃×C₈

—

128

C₃×C₈

—

129

C₃×C₈

—

130

C₃×C₈

C₃×Dic₆

yes

—

131

C₂×C₃²

—

132

C₂×C₃²

—

133

C₂×C₃²

—

134

C₂×C₃²

#869

yes

characteristic

135

C₂×C₃²

C₂×D₂₄

yes

characteristic

136

C₂×C₃²

C₂×Dic₁₂

yes

characteristic

137

C₂×C₃²

C₃×C₄⋊Q₈

yes

characteristic

138

C₂×C₃²

C₂×C₃×D₈

yes

characteristic

139

C₂×C₃²

C₂×C₃×Q₁₆

yes

characteristic

140

C₂×Q₈

—

141

C₂×C₈

C₂×(C₃⋊D₃)⋊C₃

yes

—

142

C₄⋊C₄

—

143

C₄⋊C₄

—

144

C₄²

C₂×(C₃⋊D₃)⋊C₃

yes

characteristic

145

C₂²×C₃

—

146

C₂²×C₃

—

147

C₂²×C₃

—

148

C₂²×C₃

C₂×C₃×D₁₂

yes

characteristic

149

C₃×C₄

—

150

C₃×C₄

—

151

C₃×C₄

—

152

C₃×C₄

—

153

C₃×C₄

—

154

C₃×C₄

—

155

C₃×C₄

—

156

C₃×C₄

—

157

C₃×C₄

—

158

C₃×C₄

—

159

C₃×C₄

C₃×D₂₄

yes

—

160

C₃×C₄

C₃×Dic₁₂

yes

—

161

C₃×C₄

C₂×C₃×Dic₆

yes

—

162

Dic₃

—

163

Dic₃

—

164

C₃²

—

165

C₃²

#4682

yes

characteristic, complemented

166

C₃²

C₃×#500

yes

characteristic, complemented

167

Q₈

—

168

C₂×C₄

—

169

C₂×C₄

C₄⋊((C₃⋊D₃)⋊C₃)

yes

characteristic

170

C₂×C₄

C₄⋊((C₃⋊D₃)⋊C₃)

yes

characteristic

171

C₂×C₄

C₂²×(C₃⋊D₃)⋊C₃

yes

characteristic

172

C₈

#634⋊C₃

yes

complemented

173

C₂×C₃

—

174

C₂×C₃

—

175

C₂×C₃

—

176

C₂×C₃

—

177

C₂×C₃

—

178

C₂×C₃

—

179

C₂×C₃

—

180

C₂×C₃

—

181

C₂×C₃

—

182

C₂×C₃

C₃×#869

yes

characteristic

183

C₂×C₃

C₂×C₃×D₂₄

yes

characteristic

184

C₂×C₃

C₂×C₃×Dic₁₂

yes

characteristic

185

C₂²

C₂×C₄⋊((C₃⋊D₃)⋊C₃)

yes

characteristic

186

C₄

—

187

C₄

#3746⋊C₃

yes

—

188

C₄

#3745⋊C₃

yes

—

189

C₄

C₂×#634⋊C₃

yes

—

190

C₃

—

191

C₃

—

192

C₃

—

193

C₃

C₃×#4682

yes

characteristic

194

C₂

#64078⋊C₃

yes

characteristic

195

C₂

C₂×#3746⋊C₃

yes

characteristic

196

C₂

C₂×#3745⋊C₃

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊((C₃⋊D₃)⋊C₃)
commutator, cosocle	C₂×C₃²×C₄	C₂³×C₃
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₄×C₈×H(3,𝔽₃)	C₂
socle	C₂²×C₃	C₂×C₃×D₁₂
prime radical	C₂²×H(3,𝔽₃)	C₂×D₄
hypercenter	C₄×C₈	(C₃⋊D₃)⋊C₃
hypocenter	C₃²	C₃×#500
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊((C₃⋊D₃)⋊C₃)

commutator, cosocle

C₂×C₃²×C₄

C₂³×C₃

Frattini

C₂×C₃×C₄

C₂²×C₃×D₃

Fitting

C₄×C₈×H(3,𝔽₃)

C₂

socle

C₂²×C₃

C₂×C₃×D₁₂

prime radical

C₂²×H(3,𝔽₃)

C₂×D₄

hypercenter

C₄×C₈

(C₃⋊D₃)⋊C₃

hypocenter

C₃²

C₃×#500

LCS

G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²

UCS

C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈

N	H ≅ G/N	type
4. #10592381	C₃	semidirect
23. C₈×H(3,𝔽₃)	Q₈	semidirect
68. C₃²×C₈	Dic₆	semidirect
69. C₃²×C₈	C₃×Q₈	semidirect
108. H(3,𝔽₃)	#500	semidirect
165. C₃²	#4682	semidirect
166. C₃²	C₃×#500	semidirect
172. C₈	#634⋊C₃	semidirect

H ≅ G/N

type

4. #10592381

C₃

semidirect

23. C₈×H(3,𝔽₃)

Q₈

semidirect

68. C₃²×C₈

Dic₆

semidirect

69. C₃²×C₈

C₃×Q₈

semidirect

108. H(3,𝔽₃)

#500

semidirect

165. C₃²

#4682

semidirect

166. C₃²

C₃×#500

semidirect

172. C₈

#634⋊C₃

semidirect

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

subgroup	index
#64078⋊C₃	2
C₄×C₈×H(3,𝔽₃)	2
#63645⋊C₃	2
#10592381	3
C₃×#4682	3

subgroup

index

C₄×C₈×H(3,𝔽₃)

Subgroups — #10592381⋊C₃ #13141446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10592381⋊C3 #13141446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #10592381⋊C₃ #13141446