Subgroups — #72254713

Order 2592.

599 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊(C₃⋊AGL(1,ℤ/9))	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₈×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊(3₋¹⁺²⋊C₄))	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63648	—	3	1	no	maximal
5	#11720543	C₃	1	1	yes	maximal, characteristic, complemented
6	#63380⋊C₃	—	3	3	no	maximal
7	C₂²×C₃⋊AGL(1,ℤ/9)	—	2	1	no	—
8	C₂×C₃×C₄×3₋¹⁺²	C₂²	1	1	yes	characteristic
9	C₂×C₃⋊(3₋¹⁺²⋊C₄)	—	2	1	no	—
10	C₄⋊(C₃⋊AGL(1,ℤ/9))	—	2	1	no	—
11	C₄⋊(C₃⋊AGL(1,ℤ/9))	C₄	1	2	yes	complemented
12	C₃×C₈×3₋¹⁺²	—	2	1	no	—
13	C₂×C₃×C₄⋊(C₃⋊D₃)	—	3	1	no	—
14	C₂×C₃³×C₈	D₃	1	1	yes	characteristic
15	C₃×C₄⋊(C₃⋊Dic₃)	—	3	1	no	—
16	C₂×C₄⋊(C₃⋊D₉)	C₂×C₃	1	1	yes	characteristic
17	C₂×C₄⋊AGL(1,ℤ/9)	—	3	3	no	—
18	C₂×C₈×3₋¹⁺²	—	2	3	no	—
19	C₂×C₈×3₋¹⁺²	D₃	1	3	yes	complemented
20	C₂×C₃×C₈×C₉	—	2	1	no	—
21	C₂×C₃×C₈×C₉	C₂×C₃	1	1	yes	characteristic, complemented
22	C₄⋊(C₃⋊Dic₉)	C₂×C₃	1	1	yes	characteristic, complemented
23	C₄⋊(3₋¹⁺²⋊C₄)	—	3	3	no	—
24	C₂²×C₃×3₋¹⁺²	D₄	1	1	yes	characteristic
25	C₂×C₃⋊AGL(1,ℤ/9)	—	2	2	no	—
26	C₂×C₃⋊AGL(1,ℤ/9)	—	4	1	no	—
27	C₂×C₃⋊AGL(1,ℤ/9)	—	4	1	no	—
28	C₃×C₄×3₋¹⁺²	C₂×C₄	1	1	yes	characteristic
29	C₃×C₄×3₋¹⁺²	D₄	1	1	yes	characteristic
30	C₃⋊(3₋¹⁺²⋊C₄)	—	4	1	no	—
31	#63648	—	3	1	no	—
32	C₃×#821	—	9	1	no	—
33	C₃×#821	—	9	2	no	—
34	C₃×#821	—	9	1	no	—
35	#63380	—	3	3	no	—
36	C₂²×C₃×C₃⋊D₃	—	6	1	no	—
37	C₂×C₃³×C₄	C₂×D₃	1	1	yes	characteristic
38	C₂×C₃×C₃⋊Dic₃	—	6	1	no	—
39	C₃×C₄⋊(C₃⋊D₃)	—	3	2	no	—
40	C₃×C₄⋊(C₃⋊D₃)	—	6	1	no	—
41	C₂²×C₃⋊D₉	—	2	1	no	—
42	C₂²×AGL(1,ℤ/9)	—	6	3	no	—
43	C₃³×C₈	—	2	1	no	—
44	C₂×C₄×3₋¹⁺²	—	2	3	no	—
45	C₂×C₄×3₋¹⁺²	C₂×D₃	1	3	yes	—
46	C₂×C₃×C₄×C₉	—	2	1	no	—
47	C₂×C₃×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
48	C₂×C₃⋊Dic₉	—	2	1	no	—
49	C₄⋊(C₃⋊D₉)	—	2	1	no	—
50	C₄⋊(C₃⋊D₉)	C₃×C₄	1	2	yes	complemented
51	C₂×3₋¹⁺²⋊C₄	—	6	3	no	—
52	C₄⋊AGL(1,ℤ/9)	—	3	6	no	—
53	C₄⋊AGL(1,ℤ/9)	—	6	3	no	—
54	C₈×3₋¹⁺²	—	2	6	no	—
55	C₈×3₋¹⁺²	—	2	3	no	—
56	C₃×C₈×C₉	—	2	2	no	—
57	C₃×C₈×C₉	—	2	1	no	—
58	C₂×C₃×3₋¹⁺²	C₂²⋊C₄	1	1	yes	characteristic
59	C₂×C₃×3₋¹⁺²	D₈	1	1	yes	characteristic
60	C₂×C₃×3₋¹⁺²	SD₁₆	1	1	yes	characteristic
61	C₃⋊AGL(1,ℤ/9)	—	4	2	no	—
62	C₂×C₄⋊(C₃⋊D₃)	—	3	1	no	—
63	C₂×C₃×D₁₂	—	9	1	no	—
64	C₂×C₃×D₁₂	—	9	2	no	—
65	C₂×C₃×D₁₂	—	9	1	no	—
66	C₂×C₃²×C₈	—	2	1	no	—
67	C₂×C₃²×C₈	—	3	1	no	—
68	C₂×C₃²×C₈	—	6	2	no	—
69	C₂×C₃²×C₈	C₃×D₃	1	1	yes	characteristic
70	C₂×C₃²×C₈	C₃⋊D₃	1	1	yes	characteristic
71	C₄⋊(C₃⋊Dic₃)	—	3	1	no	—
72	C₃×C₄⋊Dic₃	—	9	1	no	—
73	C₃×C₄⋊Dic₃	—	9	2	no	—
74	C₃×C₄⋊Dic₃	—	9	1	no	—
75	C₂×D₃₆	—	3	3	no	—
76	C₂×C₈×C₉	—	2	3	no	—
77	C₂×C₈×C₉	C₃×D₃	1	3	yes	complemented
78	C₄⋊Dic₉	—	3	3	no	—
79	C₂²×C₃³	D₁₂	1	1	yes	characteristic
80	C₂×C₃×C₃⋊D₃	—	6	2	no	—
81	C₂×C₃×C₃⋊D₃	—	12	1	no	—
82	C₂×C₃×C₃⋊D₃	—	12	1	no	—
83	C₃³×C₄	C₄×D₃	1	1	yes	characteristic
84	C₃³×C₄	#67	1	1	yes	characteristic
85	C₃×C₃⋊Dic₃	—	12	1	no	—
86	C₂²×3₋¹⁺²	—	2	3	no	—
87	C₂²×3₋¹⁺²	D₁₂	1	3	yes	—
88	C₂²×C₃×C₉	—	2	1	no	—
89	C₂²×C₃×C₉	C₃×D₄	1	1	yes	characteristic
90	C₂×C₃⋊D₉	—	2	2	no	—
91	C₂×C₃⋊D₉	—	4	1	no	—
92	C₂×C₃⋊D₉	—	4	1	no	—
93	C₂×AGL(1,ℤ/9)	—	6	6	no	—
94	C₂×AGL(1,ℤ/9)	—	12	3	no	—
95	C₂×AGL(1,ℤ/9)	—	12	3	no	—
96	C₄×3₋¹⁺²	—	2	3	no	—
97	C₄×3₋¹⁺²	—	2	3	no	—
98	C₄×3₋¹⁺²	C₄×D₃	1	3	yes	—
99	C₄×3₋¹⁺²	#67	1	3	yes	—
100	C₃×C₄×C₉	—	2	1	no	—
101	C₃×C₄×C₉	—	2	1	no	—
102	C₃×C₄×C₉	C₂×C₃×C₄	1	1	yes	characteristic
103	C₃×C₄×C₉	C₃×D₄	1	1	yes	characteristic
104	C₃⋊Dic₉	—	4	1	no	—
105	3₋¹⁺²⋊C₄	—	12	3	no	—
106	C₃×#102	—	27	1	no	—
107	#821	—	9	1	no	—
108	#821	—	9	2	no	—
109	#821	—	9	1	no	—
110	C₃×3₋¹⁺²	#102	1	1	yes	characteristic, complemented, Sylow
111	C₂²×C₃⋊D₃	—	6	1	no	—
112	C₂²×C₃×D₃	—	18	1	no	—
113	C₂²×C₃×D₃	—	18	2	no	—
114	C₂²×C₃×D₃	—	18	1	no	—
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	3	1	no	—
117	C₂×C₃²×C₄	—	6	2	no	—
118	C₂×C₃²×C₄	C₂×C₃×D₃	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
120	C₂×C₃⋊Dic₃	—	6	1	no	—
121	C₄⋊(C₃⋊D₃)	—	3	2	no	—
122	C₄⋊(C₃⋊D₃)	—	6	1	no	—
123	C₂×C₃×Dic₃	—	18	1	no	—
124	C₂×C₃×Dic₃	—	18	2	no	—
125	C₂×C₃×Dic₃	—	18	1	no	—
126	C₃×D₁₂	—	9	2	no	—
127	C₃×D₁₂	—	9	4	no	—
128	C₃×D₁₂	—	9	2	no	—
129	C₃×D₁₂	—	18	1	no	—
130	C₃×D₁₂	—	18	2	no	—
131	C₃×D₁₂	—	18	1	no	—
132	C₂²×D₉	—	6	3	no	—
133	C₃²×C₈	—	2	1	no	—
134	C₃²×C₈	—	2	2	no	—
135	C₃²×C₈	—	2	1	no	—
136	C₃²×C₈	—	6	1	no	—
137	C₃²×C₈	—	6	2	no	—
138	C₂×C₄×C₉	—	2	3	no	—
139	C₂×C₄×C₉	C₂×C₃×D₃	1	3	yes	—
140	C₂×Dic₉	—	6	3	no	—
141	D₃₆	—	3	6	no	—
142	D₃₆	—	6	3	no	—
143	C₈×C₉	—	2	6	no	—
144	C₈×C₉	—	2	3	no	—
145	C₂×C₃³	#204	1	1	yes	characteristic
146	C₂×C₃³	D₂₄	1	1	yes	characteristic
147	C₂×C₃³	(C₂×D₃)⋊C₄	1	1	yes	characteristic
148	C₃×C₃⋊D₃	—	12	2	no	—
149	C₂×3₋¹⁺²	—	2	3	no	—
150	C₂×3₋¹⁺²	—	2	3	no	—
151	C₂×3₋¹⁺²	—	2	3	no	—
152	C₂×3₋¹⁺²	#204	1	3	yes	—
153	C₂×3₋¹⁺²	D₂₄	1	3	yes	—
154	C₂×3₋¹⁺²	(C₂×D₃)⋊C₄	1	3	yes	—
155	C₂×C₃×C₉	—	2	1	no	—
156	C₂×C₃×C₉	—	2	1	no	—
157	C₂×C₃×C₉	—	2	1	no	—
158	C₂×C₃×C₉	C₃×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₃×C₉	C₃×D₈	1	1	yes	characteristic
160	C₂×C₃×C₉	C₃×SD₁₆	1	1	yes	characteristic
161	C₃⋊D₉	—	4	2	no	—
162	AGL(1,ℤ/9)	—	12	6	no	—
163	C₂×C₃×D₄	—	27	1	no	—
164	C₂×D₁₂	—	9	1	no	—
165	C₂×D₁₂	—	9	2	no	—
166	C₂×D₁₂	—	9	1	no	—
167	C₂×C₃×C₈	—	6	1	no	—
168	C₂×C₃×C₈	—	6	1	no	—
169	C₂×C₃×C₈	AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
170	C₂×C₃×C₈	AGL(1,ℤ/9)	1	2	yes	complemented
171	C₂×C₃×C₈	C₃×C₃⋊D₃	1	1	yes	characteristic
172	C₃×C₄⋊C₄	—	27	1	no	—
173	C₄⋊Dic₃	—	9	1	no	—
174	C₄⋊Dic₃	—	9	2	no	—
175	C₄⋊Dic₃	—	9	1	no	—
176	C₂²×C₃²	—	2	1	no	—
177	C₂²×C₃²	—	3	1	no	—
178	C₂²×C₃²	—	6	2	no	—
179	C₂²×C₃²	C₃×D₁₂	1	1	yes	characteristic
180	C₂²×C₃²	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
181	C₂×C₃⋊D₃	—	6	2	no	—
182	C₂×C₃⋊D₃	—	12	1	no	—
183	C₂×C₃⋊D₃	—	12	1	no	—
184	C₂×C₃×D₃	—	18	2	no	—
185	C₂×C₃×D₃	—	18	4	no	—
186	C₂×C₃×D₃	—	18	2	no	—
187	C₂×C₃×D₃	—	36	1	no	—
188	C₂×C₃×D₃	—	36	1	no	—
189	C₂×C₃×D₃	—	36	2	no	—
190	C₂×C₃×D₃	—	36	2	no	—
191	C₂×C₃×D₃	—	36	1	no	—
192	C₂×C₃×D₃	—	36	1	no	—
193	C₃²×C₄	—	2	1	no	—
194	C₃²×C₄	—	2	1	no	—
195	C₃²×C₄	—	3	1	no	—
196	C₃²×C₄	—	3	1	no	—
197	C₃²×C₄	—	6	2	no	—
198	C₃²×C₄	—	6	2	no	—
199	C₃²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
200	C₃²×C₄	C₃×#67	1	1	yes	characteristic
201	C₃²×C₄	C₄×C₃⋊D₃	1	1	yes	characteristic
202	C₃²×C₄	#638	1	1	yes	characteristic
203	C₃⋊Dic₃	—	12	1	no	—
204	C₃×Dic₃	—	36	1	no	—
205	C₃×Dic₃	—	36	2	no	—
206	C₃×Dic₃	—	36	1	no	—
207	C₂²×C₉	—	2	3	no	—
208	C₂²×C₉	C₃×D₁₂	1	3	yes	—
209	C₂×D₉	—	6	6	no	—
210	C₂×D₉	—	12	3	no	—
211	C₂×D₉	—	12	3	no	—
212	C₄×C₉	—	2	3	no	—
213	C₄×C₉	—	2	3	no	—
214	C₄×C₉	C₃×C₄×D₃	1	3	yes	—
215	C₄×C₉	C₃×#67	1	3	yes	—
216	Dic₉	—	12	3	no	—
217	#102	—	27	1	no	Sylow
218	C₃³	#821	1	1	yes	characteristic
219	3₋¹⁺²	—	2	3	no	—
220	3₋¹⁺²	#821	1	3	yes	complemented
221	C₃×C₉	—	2	1	no	—
222	C₃×C₉	C₃×#102	1	1	yes	characteristic, complemented
223	C₂³×C₃	—	54	1	no	—
224	C₂²×D₃	—	18	1	no	—
225	C₂²×D₃	—	18	2	no	—
226	C₂²×D₃	—	18	1	no	—
227	C₃×D₄	—	27	2	no	—
228	C₃×D₄	—	54	1	no	—
229	C₂×C₃×C₄	—	6	1	no	—
230	C₂×C₃×C₄	—	6	1	no	—
231	C₂×C₃×C₄	—	54	1	no	—
232	C₂×C₃×C₄	C₂×AGL(1,ℤ/9)	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×AGL(1,ℤ/9)	1	2	yes	—
234	C₂×C₃×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
235	C₂×Dic₃	—	18	1	no	—
236	C₂×Dic₃	—	18	2	no	—
237	C₂×Dic₃	—	18	1	no	—
238	D₁₂	—	9	2	no	—
239	D₁₂	—	9	4	no	—
240	D₁₂	—	9	2	no	—
241	D₁₂	—	18	1	no	—
242	D₁₂	—	18	2	no	—
243	D₁₂	—	18	1	no	—
244	C₃×C₈	—	2	1	no	—
245	C₃×C₈	—	2	2	no	—
246	C₃×C₈	—	2	1	no	—
247	C₃×C₈	—	6	2	no	—
248	C₃×C₈	—	6	1	no	—
249	C₂×C₃²	—	2	1	no	—
250	C₂×C₃²	—	2	1	no	—
251	C₂×C₃²	—	2	1	no	—
252	C₂×C₃²	—	3	1	no	—
253	C₂×C₃²	—	3	1	no	—
254	C₂×C₃²	—	3	1	no	—
255	C₂×C₃²	—	6	2	no	—
256	C₂×C₃²	—	6	2	no	—
257	C₂×C₃²	—	6	2	no	—
258	C₂×C₃²	C₃×#204	1	1	yes	characteristic
259	C₂×C₃²	C₃×D₂₄	1	1	yes	characteristic
260	C₂×C₃²	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
261	C₂×C₃²	#3744	1	1	yes	characteristic
262	C₂×C₃²	#3745	1	1	yes	characteristic
263	C₂×C₃²	#3752	1	1	yes	characteristic
264	C₃⋊D₃	—	12	2	no	—
265	C₃×D₃	—	36	2	no	—
266	C₃×D₃	—	36	4	no	—
267	C₃×D₃	—	36	2	no	—
268	C₂×C₉	—	2	3	no	—
269	C₂×C₉	—	2	3	no	—
270	C₂×C₉	—	2	3	no	—
271	C₂×C₉	C₃×#204	1	3	yes	—
272	C₂×C₉	C₃×D₂₄	1	3	yes	—
273	C₂×C₉	C₃×(C₂×D₃)⋊C₄	1	3	yes	—
274	D₉	—	12	6	no	—
275	C₂×D₄	—	27	1	no	—
276	C₂×C₈	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic, complemented
277	C₄⋊C₄	—	27	1	no	—
278	C₂²×C₃	—	6	1	no	—
279	C₂²×C₃	—	6	1	no	—
280	C₂²×C₃	—	54	2	no	—
281	C₂²×C₃	—	108	1	no	—
282	C₂²×C₃	—	108	1	no	—
283	C₂²×C₃	C₄⋊AGL(1,ℤ/9)	1	1	yes	characteristic
284	C₂²×C₃	C₄⋊AGL(1,ℤ/9)	1	2	yes	—
285	C₂²×C₃	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
286	C₂×D₃	—	18	2	no	—
287	C₂×D₃	—	18	2	no	—
288	C₂×D₃	—	18	4	no	—
289	C₂×D₃	—	36	1	no	—
290	C₂×D₃	—	36	1	no	—
291	C₂×D₃	—	36	1	no	—
292	C₂×D₃	—	36	2	no	—
293	C₂×D₃	—	36	1	no	—
294	C₂×D₃	—	36	2	no	—
295	C₃×C₄	—	6	1	no	—
296	C₃×C₄	—	6	1	no	—
297	C₃×C₄	—	6	1	no	—
298	C₃×C₄	—	6	1	no	—
299	C₃×C₄	—	108	1	no	—
300	C₃×C₄	C₄×AGL(1,ℤ/9)	1	1	yes	characteristic
301	C₃×C₄	C₄×AGL(1,ℤ/9)	1	2	yes	—
302	C₃×C₄	#611⋊C₃	1	1	yes	characteristic
303	C₃×C₄	#611⋊C₃	1	2	yes	—
304	C₃×C₄	C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
305	C₃×C₄	C₃×#638	1	1	yes	characteristic
306	Dic₃	—	36	1	no	—
307	Dic₃	—	36	1	no	—
308	Dic₃	—	36	2	no	—
309	C₃²	—	2	1	no	—
310	C₃²	—	3	1	no	—
311	C₃²	—	6	2	no	—
312	C₃²	C₃×#821	1	1	yes	characteristic
313	C₃²	#63648	1	1	yes	characteristic
314	C₉	—	2	3	no	—
315	C₉	C₃×#821	1	3	yes	complemented
316	C₂³	—	54	1	no	—
317	D₄	—	27	2	no	—
318	D₄	—	54	1	no	—
319	C₂×C₄	—	54	1	no	—
320	C₂×C₄	C₂×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
321	C₈	—	2	1	no	—
322	C₂×C₃	—	6	1	no	—
323	C₂×C₃	—	6	1	no	—
324	C₂×C₃	—	6	1	no	—
325	C₂×C₃	—	6	1	no	—
326	C₂×C₃	—	6	1	no	—
327	C₂×C₃	—	6	1	no	—
328	C₂×C₃	—	108	2	no	—
329	C₂×C₃	#3664⋊C₃	1	1	yes	characteristic
330	C₂×C₃	#3664⋊C₃	1	2	yes	—
331	C₂×C₃	D₇₂⋊C₃	1	1	yes	characteristic
332	C₂×C₃	D₇₂⋊C₃	1	2	yes	—
333	C₂×C₃	(C₂×AGL(1,ℤ/9))⋊C₄	1	1	yes	characteristic
334	C₂×C₃	(C₂×AGL(1,ℤ/9))⋊C₄	1	2	yes	—
335	C₂×C₃	C₃×#3744	1	1	yes	characteristic
336	C₂×C₃	C₃×#3745	1	1	yes	characteristic
337	C₂×C₃	C₃×#3752	1	1	yes	characteristic
338	D₃	—	36	2	no	—
339	D₃	—	36	2	no	—
340	D₃	—	36	4	no	—
341	C₂²	—	54	2	no	—
342	C₂²	—	108	1	no	—
343	C₂²	—	108	1	no	—
344	C₂²	C₄⋊(C₃⋊AGL(1,ℤ/9))	1	1	yes	characteristic
345	C₄	—	108	1	no	—
346	C₄	C₄×C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
347	C₄	#10619980	1	1	yes	characteristic
348	C₃	—	6	1	no	—
349	C₃	—	6	1	no	—
350	C₃	#63380⋊C₃	1	1	yes	characteristic, complemented
351	C₃	#63380⋊C₃	1	2	yes	complemented
352	C₃	C₃×#63648	1	1	yes	characteristic
353	C₂	—	108	2	no	—
354	C₂	#13047908	1	1	yes	characteristic
355	C₂	#13047909	1	1	yes	characteristic
356	C₂	#13047949	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊(C₃⋊AGL(1,ℤ/9))
commutator	C₃×C₄×C₉	C₂×C₃×C₄
Frattini	C₂×C₃×C₄	C₂×C₃×C₃⋊D₃
Fitting	C₂×C₃×C₈×3₋¹⁺²	C₂
socle	C₂²×C₃²	C₃×D₁₂
prime radical	C₂×C₄⋊(C₃⋊AGL(1,ℤ/9))	C₂
cosocle	C₂×C₃×C₄×C₉	C₂²×C₃
hypercenter	C₂×C₈	C₃⋊AGL(1,ℤ/9)
hypocenter	C₃×C₉	C₃×#102
LCS	G ▷ C₃×C₄×C₉ ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₃×C₈×3₋¹⁺²	C₂	semidirect
3. C₄⋊(C₃⋊(3₋¹⁺²⋊C₄))	C₂	semidirect
5. #11720543	C₃	semidirect
11. C₄⋊(C₃⋊AGL(1,ℤ/9))	C₄	semidirect
19. C₂×C₈×3₋¹⁺²	D₃	semidirect
21. C₂×C₃×C₈×C₉	C₂×C₃	semidirect
22. C₄⋊(C₃⋊Dic₉)	C₂×C₃	semidirect
50. C₄⋊(C₃⋊D₉)	C₃×C₄	semidirect
77. C₂×C₈×C₉	C₃×D₃	semidirect
110. C₃×3₋¹⁺²	#102	semidirect
169. C₂×C₃×C₈	AGL(1,ℤ/9)	semidirect
170. C₂×C₃×C₈	AGL(1,ℤ/9)	semidirect
220. 3₋¹⁺²	#821	semidirect
222. C₃×C₉	C₃×#102	semidirect
276. C₂×C₈	C₃⋊AGL(1,ℤ/9)	semidirect
315. C₉	C₃×#821	semidirect
350. C₃	#63380⋊C₃	semidirect
351. C₃	#63380⋊C₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊(C₃⋊AGL(1,ℤ/9))	2
C₂×C₃×C₈×3₋¹⁺²	2
C₄⋊(C₃⋊(3₋¹⁺²⋊C₄))	2
C₃×#63648	3
#11720543	3
#63380⋊C₃	3