Subgroups — #14552371

Order 2187.

1093 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#6900	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#6896	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#6894	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	C₃×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉×3₋¹⁺²	C₃	1	1	yes	maximal, characteristic, complemented
7	#10624566	C₃	1	2	yes	maximal, complemented
8	#10624566	C₃	1	2	yes	maximal, complemented
9	#10624566	C₃	1	2	yes	maximal, complemented
10	#10624566	C₃	1	2	yes	maximal, complemented
11	#10624565	C₃	1	2	yes	maximal, complemented
12	#10624565	C₃	1	2	yes	maximal, complemented
13	#10624565	C₃	1	2	yes	maximal, complemented
14	#10624565	C₃	1	2	yes	maximal, complemented
15	#10624563	C₃	1	2	yes	maximal
16	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
17	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
18	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
19	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
20	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
21	#10624560	C₃	1	1	yes	maximal, characteristic, complemented
22	#10624560	C₃	1	2	yes	maximal, complemented
23	#10624557	C₃	1	2	yes	maximal, complemented
24	#10624557	C₃	1	2	yes	maximal, complemented
25	#10624556	C₃	1	2	yes	maximal, complemented
26	#10624548	C₃	1	1	yes	maximal, characteristic, complemented
27	C₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
28	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
29	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
30	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
31	C₃²×3₋¹⁺²	C₃²	1	2	yes	—
32	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
33	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
34	C₃²×3₋¹⁺²	C₃²	1	1	yes	characteristic
35	C₃²×H(3,𝔽₃)	C₃²	1	1	yes	characteristic
36	C₃³×C₉	C₃²	1	1	yes	characteristic
37	C₃³×C₉	C₃²	1	1	yes	characteristic
38	#6900	—	3	9	no	—
39	#6896	—	3	9	no	—
40	#6894	—	3	9	no	—
41	C₉⋊H(3,𝔽₃)	—	3	9	no	—
42	C₉⋊H(3,𝔽₃)	—	3	9	no	—
43	C₉×3₋¹⁺²	—	3	9	no	—
44	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
45	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
46	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
47	C₃×C₉⋊C₉	C₃²	1	2	yes	—
48	C₃×C₉⋊C₉	C₃²	1	2	yes	—
49	C₃×C₉⋊C₉	C₃²	1	2	yes	—
50	C₃×C₉⋊C₉	C₃²	1	2	yes	—
51	C₃×C₉⋊C₉	C₃²	1	2	yes	—
52	C₃×C₉⋊C₉	C₃²	1	2	yes	—
53	C₃×C₉⋊C₉	C₃²	1	2	yes	—
54	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
55	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
56	C₃×C₉⋊C₉	C₃²	1	2	yes	—
57	C₃×C₉⋊C₉	C₃²	1	2	yes	—
58	C₃×C₉⋊C₉	C₃²	1	2	yes	—
59	C₃×C₉⋊C₉	C₃²	1	2	yes	—
60	C₃×C₉⋊C₉	C₃²	1	1	yes	characteristic
61	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
62	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
63	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
64	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
65	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
66	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
67	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
68	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
69	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
70	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
71	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
72	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
73	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
74	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
75	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
76	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
77	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
78	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
79	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
80	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
81	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
82	C₃×C₃²⋊C₉	C₃²	1	2	yes	—
83	C₃×C₃²⋊C₉	C₃²	1	1	yes	characteristic
84	C₃×C₉²	C₃²	1	1	yes	characteristic
85	C₃×C₉²	C₃²	1	1	yes	characteristic
86	C₃×C₉²	C₃²	1	1	yes	characteristic
87	C₃×C₉²	C₃²	1	2	yes	—
88	#6855	C₃²	1	2	yes	—
89	#6855	C₃²	1	2	yes	—
90	#6855	C₃²	1	2	yes	—
91	#6855	C₃²	1	2	yes	—
92	#6855	C₃²	1	2	yes	—
93	#6855	C₃²	1	2	yes	—
94	#6855	C₃²	1	2	yes	—
95	#6855	C₃²	1	2	yes	—
96	#6855	C₃²	1	2	yes	—
97	#6855	C₃²	1	2	yes	—
98	#6855	C₃²	1	2	yes	—
99	#6855	C₃²	1	2	yes	—
100	#6855	C₃²	1	2	yes	—
101	#6855	C₃²	1	2	yes	—
102	#6855	C₃²	1	2	yes	—
103	#6855	C₃²	1	2	yes	—
104	#6855	C₃²	1	2	yes	—
105	#6855	C₃²	1	2	yes	—
106	#6855	C₃²	1	2	yes	—
107	#6855	C₃²	1	2	yes	—
108	#6855	C₃²	1	2	yes	—
109	#6855	C₃²	1	2	yes	—
110	#6855	C₃²	1	2	yes	—
111	#6855	C₃²	1	2	yes	—
112	C₃⁴	C₃³	1	1	yes	characteristic
113	C₃⁴	C₃³	1	1	yes	characteristic
114	C₃⁴	C₃³	1	1	yes	characteristic
115	C₃⁴	C₃³	1	1	yes	characteristic
116	C₃×3₋¹⁺²	—	3	3	no	—
117	C₃×3₋¹⁺²	—	3	3	no	—
118	C₃×3₋¹⁺²	—	3	3	no	—
119	C₃×3₋¹⁺²	—	3	3	no	—
120	C₃×3₋¹⁺²	—	3	3	no	—
121	C₃×3₋¹⁺²	—	3	6	no	—
122	C₃×3₋¹⁺²	—	3	3	no	—
123	C₃×3₋¹⁺²	—	3	3	no	—
124	C₃×3₋¹⁺²	—	3	3	no	—
125	C₃×3₋¹⁺²	—	3	3	no	—
126	C₃×3₋¹⁺²	—	3	3	no	—
127	C₃×3₋¹⁺²	—	3	3	no	—
128	C₃×3₋¹⁺²	—	3	3	no	—
129	C₃×3₋¹⁺²	—	3	3	no	—
130	C₃×3₋¹⁺²	—	3	6	no	—
131	C₃×3₋¹⁺²	—	3	3	no	—
132	C₃×3₋¹⁺²	—	3	3	no	—
133	C₃×3₋¹⁺²	—	3	3	no	—
134	C₃×3₋¹⁺²	—	3	3	no	—
135	C₃×3₋¹⁺²	—	9	2	no	—
136	C₃×3₋¹⁺²	—	9	2	no	—
137	C₃×3₋¹⁺²	—	9	2	no	—
138	C₃×3₋¹⁺²	—	9	2	no	—
139	C₃×3₋¹⁺²	—	9	2	no	—
140	C₃×3₋¹⁺²	3₋¹⁺²	1	9	yes	complemented
141	C₃×H(3,𝔽₃)	—	3	3	no	—
142	C₃×H(3,𝔽₃)	—	3	3	no	—
143	C₃×H(3,𝔽₃)	—	9	2	no	—
144	C₃²×C₉	—	3	3	no	—
145	C₃²×C₉	—	3	3	no	—
146	C₃²×C₉	—	3	3	no	—
147	C₃²×C₉	—	3	3	no	—
148	C₃²×C₉	—	3	3	no	—
149	C₃²×C₉	—	3	3	no	—
150	C₃²×C₉	—	9	2	no	—
151	C₃²×C₉	C₃³	1	2	yes	—
152	C₃²×C₉	C₃³	1	1	yes	characteristic
153	C₃²×C₉	C₃³	1	2	yes	—
154	C₃²×C₉	C₃³	1	2	yes	—
155	C₃²×C₉	C₃³	1	1	yes	characteristic
156	C₃²×C₉	C₃³	1	1	yes	characteristic
157	C₃²×C₉	C₃³	1	1	yes	characteristic
158	C₃²×C₉	C₃³	1	1	yes	characteristic
159	C₃²×C₉	C₃³	1	2	yes	—
160	C₃²×C₉	C₃³	1	2	yes	—
161	C₃²×C₉	C₃³	1	2	yes	—
162	C₃²×C₉	C₃³	1	2	yes	—
163	C₃²×C₉	C₃³	1	2	yes	—
164	C₃²×C₉	C₃³	1	2	yes	—
165	C₃²×C₉	C₃³	1	2	yes	—
166	C₃²×C₉	C₃³	1	1	yes	characteristic
167	C₃²×C₉	C₃³	1	2	yes	—
168	C₃²×C₉	C₃³	1	1	yes	characteristic
169	C₃²×C₉	C₃³	1	2	yes	—
170	C₃²×C₉	C₃³	1	1	yes	characteristic
171	C₃²×C₉	C₃³	1	1	yes	characteristic
172	C₃²×C₉	C₃³	1	2	yes	—
173	C₃²×C₉	C₃³	1	1	yes	characteristic
174	C₉⋊C₉	—	3	6	no	—
175	C₉⋊C₉	—	3	6	no	—
176	C₉⋊C₉	—	3	3	no	—
177	C₉⋊C₉	—	3	6	no	—
178	C₉⋊C₉	—	3	3	no	—
179	C₉⋊C₉	—	3	3	no	—
180	C₉⋊C₉	—	3	6	no	—
181	C₉⋊C₉	—	3	6	no	—
182	C₉⋊C₉	—	3	6	no	—
183	C₉⋊C₉	—	3	6	no	—
184	C₉⋊C₉	—	3	6	no	—
185	C₉⋊C₉	—	3	3	no	—
186	C₉⋊C₉	—	3	6	no	—
187	C₉⋊C₉	—	3	6	no	—
188	C₉⋊C₉	—	3	6	no	—
189	C₉⋊C₉	—	3	3	no	—
190	C₉⋊C₉	H(3,𝔽₃)	1	9	yes	complemented
191	C₃²⋊C₉	—	3	6	no	—
192	C₃²⋊C₉	—	3	3	no	—
193	C₃²⋊C₉	—	3	6	no	—
194	C₃²⋊C₉	—	3	6	no	—
195	C₃²⋊C₉	—	3	6	no	—
196	C₃²⋊C₉	—	3	6	no	—
197	C₃²⋊C₉	—	3	6	no	—
198	C₃²⋊C₉	—	3	3	no	—
199	C₃²⋊C₉	—	3	3	no	—
200	C₃²⋊C₉	—	3	6	no	—
201	C₃²⋊C₉	—	3	3	no	—
202	C₃²⋊C₉	—	3	3	no	—
203	C₃²⋊C₉	—	3	3	no	—
204	C₃²⋊C₉	—	3	3	no	—
205	C₃²⋊C₉	—	3	6	no	—
206	C₃²⋊C₉	—	3	6	no	—
207	C₃²⋊C₉	—	3	6	no	—
208	C₃²⋊C₉	—	9	2	no	—
209	C₃²⋊C₉	—	9	2	no	—
210	C₃²⋊C₉	—	9	2	no	—
211	C₃²⋊C₉	—	9	2	no	—
212	C₃²⋊C₉	—	9	2	no	—
213	C₃²⋊C₉	3₋¹⁺²	1	9	yes	complemented
214	C₉²	—	3	6	no	—
215	C₉²	—	3	3	no	—
216	C₉²	—	3	3	no	—
217	C₉²	—	3	3	no	—
218	C₃³	—	3	1	no	—
219	C₃³	—	3	1	no	—
220	C₃³	—	3	1	no	—
221	C₃³	—	3	1	no	—
222	C₃³	—	3	2	no	—
223	C₃³	—	3	2	no	—
224	C₃³	—	3	1	no	—
225	C₃³	—	3	1	no	—
226	C₃³	—	3	1	no	—
227	C₃³	—	3	1	no	—
228	C₃³	—	3	2	no	—
229	C₃³	—	3	2	no	—
230	C₃³	—	3	2	no	—
231	C₃³	—	3	2	no	—
232	C₃³	—	3	2	no	—
233	C₃³	—	3	2	no	—
234	C₃³	—	3	1	no	—
235	C₃³	—	3	1	no	—
236	C₃³	—	3	1	no	—
237	C₃³	—	3	1	no	—
238	C₃³	—	3	1	no	—
239	C₃³	—	3	1	no	—
240	C₃³	—	3	2	no	—
241	C₃³	—	3	1	no	—
242	C₃³	—	3	1	no	—
243	C₃³	—	3	1	no	—
244	C₃³	—	3	1	no	—
245	C₃³	—	3	2	no	—
246	C₃³	—	3	2	no	—
247	C₃³	—	3	2	no	—
248	C₃³	—	3	2	no	—
249	C₃³	—	3	2	no	—
250	C₃³	—	3	2	no	—
251	C₃³	—	3	2	no	—
252	C₃³	C₃×3₋¹⁺²	1	3	yes	—
253	C₃³	C₃×3₋¹⁺²	1	3	yes	—
254	C₃³	C₃⁴	1	1	yes	characteristic
255	3₋¹⁺²	—	3	27	no	—
256	3₋¹⁺²	—	9	9	no	—
257	3₋¹⁺²	—	9	9	no	—
258	3₋¹⁺²	—	9	18	no	—
259	3₋¹⁺²	—	9	9	no	—
260	3₋¹⁺²	—	9	9	no	—
261	3₋¹⁺²	—	9	9	no	—
262	H(3,𝔽₃)	—	9	9	no	—
263	C₃×C₉	—	3	1	no	—
264	C₃×C₉	—	3	2	no	—
265	C₃×C₉	—	3	1	no	—
266	C₃×C₉	—	3	1	no	—
267	C₃×C₉	—	3	2	no	—
268	C₃×C₉	—	3	1	no	—
269	C₃×C₉	—	3	2	no	—
270	C₃×C₉	—	3	2	no	—
271	C₃×C₉	—	3	2	no	—
272	C₃×C₉	—	3	2	no	—
273	C₃×C₉	—	3	2	no	—
274	C₃×C₉	—	3	2	no	—
275	C₃×C₉	—	3	2	no	—
276	C₃×C₉	—	3	2	no	—
277	C₃×C₉	—	3	2	no	—
278	C₃×C₉	—	3	2	no	—
279	C₃×C₉	—	3	2	no	—
280	C₃×C₉	—	3	2	no	—
281	C₃×C₉	—	3	2	no	—
282	C₃×C₉	—	3	2	no	—
283	C₃×C₉	—	3	2	no	—
284	C₃×C₉	—	3	2	no	—
285	C₃×C₉	—	3	2	no	—
286	C₃×C₉	—	3	2	no	—
287	C₃×C₉	—	3	1	no	—
288	C₃×C₉	—	3	2	no	—
289	C₃×C₉	—	3	2	no	—
290	C₃×C₉	—	3	1	no	—
291	C₃×C₉	—	3	1	no	—
292	C₃×C₉	—	3	1	no	—
293	C₃×C₉	—	3	1	no	—
294	C₃×C₉	—	3	2	no	—
295	C₃×C₉	—	3	2	no	—
296	C₃×C₉	—	3	1	no	—
297	C₃×C₉	—	3	2	no	—
298	C₃×C₉	—	3	2	no	—
299	C₃×C₉	—	3	1	no	—
300	C₃×C₉	—	3	1	no	—
301	C₃×C₉	—	3	1	no	—
302	C₃×C₉	—	3	1	no	—
303	C₃×C₉	—	3	2	no	—
304	C₃×C₉	—	3	2	no	—
305	C₃×C₉	—	3	2	no	—
306	C₃×C₉	—	3	2	no	—
307	C₃×C₉	—	3	2	no	—
308	C₃×C₉	—	3	2	no	—
309	C₃×C₉	—	3	2	no	—
310	C₃×C₉	—	3	2	no	—
311	C₃×C₉	—	3	2	no	—
312	C₃×C₉	—	3	2	no	—
313	C₃×C₉	—	3	2	no	—
314	C₃×C₉	—	3	2	no	—
315	C₃×C₉	—	3	2	no	—
316	C₃×C₉	—	3	2	no	—
317	C₃×C₉	—	3	2	no	—
318	C₃×C₉	—	3	2	no	—
319	C₃×C₉	—	3	2	no	—
320	C₃×C₉	—	3	2	no	—
321	C₃×C₉	—	3	2	no	—
322	C₃×C₉	—	3	2	no	—
323	C₃×C₉	—	3	2	no	—
324	C₃×C₉	—	3	2	no	—
325	C₃×C₉	—	3	2	no	—
326	C₃×C₉	—	3	2	no	—
327	C₃×C₉	—	3	2	no	—
328	C₃×C₉	—	3	2	no	—
329	C₃×C₉	—	3	2	no	—
330	C₃×C₉	—	3	2	no	—
331	C₃×C₉	—	3	2	no	—
332	C₃×C₉	—	3	2	no	—
333	C₃×C₉	—	3	2	no	—
334	C₃×C₉	—	3	2	no	—
335	C₃×C₉	—	9	9	no	—
336	C₃×C₉	—	9	9	no	—
337	C₃×C₉	C₃×H(3,𝔽₃)	1	6	yes	—
338	C₃×C₉	C₃×H(3,𝔽₃)	1	3	yes	—
339	C₃×C₉	C₃×H(3,𝔽₃)	1	3	yes	—
340	C₃×C₉	C₃×3₋¹⁺²	1	6	yes	—
341	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
342	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
343	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
344	C₃×C₉	C₃×3₋¹⁺²	1	3	yes	—
345	C₃×C₉	#737	1	6	yes	—
346	C₃×C₉	#737	1	3	yes	—
347	C₃×C₉	#737	1	3	yes	—
348	C₃²	—	3	3	no	—
349	C₃²	—	3	3	no	—
350	C₃²	—	3	3	no	—
351	C₃²	—	3	3	no	—
352	C₃²	—	3	3	no	—
353	C₃²	—	3	6	no	—
354	C₃²	—	3	3	no	—
355	C₃²	—	9	1	no	—
356	C₃²	—	9	1	no	—
357	C₃²	—	9	2	no	—
358	C₃²	—	9	2	no	—
359	C₃²	—	9	1	no	—
360	C₃²	—	9	2	no	—
361	C₃²	—	9	2	no	—
362	C₃²	—	9	2	no	—
363	C₃²	—	9	1	no	—
364	C₃²	—	9	2	no	—
365	C₃²	—	9	2	no	—
366	C₃²	—	9	1	no	—
367	C₃²	—	9	1	no	—
368	C₃²	—	9	1	no	—
369	C₃²	—	9	1	no	—
370	C₃²	—	9	2	no	—
371	C₃²	—	9	2	no	—
372	C₃²	—	9	1	no	—
373	C₃²	—	9	1	no	—
374	C₃²	—	9	2	no	—
375	C₃²	—	9	2	no	—
376	C₃²	—	9	1	no	—
377	C₃²	—	9	1	no	—
378	C₃²	—	9	2	no	—
379	C₃²	—	9	1	no	—
380	C₃²	—	9	2	no	—
381	C₃²	—	9	1	no	—
382	C₃²	—	9	2	no	—
383	C₃²	—	9	2	no	—
384	C₃²	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
385	C₃²	C₃²×3₋¹⁺²	1	1	yes	characteristic
386	C₃²	C₃²×3₋¹⁺²	1	1	yes	characteristic
387	C₃²	C₃×#737	1	1	yes	characteristic
388	C₃²	C₃×#737	1	1	yes	characteristic
389	C₃²	C₃×#737	1	2	yes	—
390	C₃²	3₋¹⁺⁴	1	2	yes	—
391	C₃²	3₋¹⁺⁴	1	2	yes	—
392	C₃²	3₋¹⁺⁴	1	2	yes	—
393	C₉	—	3	6	no	—
394	C₉	—	3	3	no	—
395	C₉	—	3	3	no	—
396	C₉	—	3	3	no	—
397	C₉	—	3	3	no	—
398	C₉	—	3	6	no	—
399	C₉	—	3	6	no	—
400	C₉	—	9	2	no	—
401	C₉	—	9	2	no	—
402	C₉	—	9	2	no	—
403	C₉	—	9	1	no	—
404	C₉	—	9	1	no	—
405	C₉	—	9	1	no	—
406	C₉	—	9	1	no	—
407	C₉	—	9	1	no	—
408	C₉	—	9	2	no	—
409	C₉	—	9	2	no	—
410	C₉	—	9	2	no	—
411	C₉	—	9	2	no	—
412	C₉	—	9	2	no	—
413	C₉	—	9	2	no	—
414	C₉	—	9	2	no	—
415	C₉	C₉⋊H(3,𝔽₃)	1	9	yes	complemented
416	C₃	—	9	3	no	—
417	C₃	—	9	3	no	—
418	C₃	—	27	1	no	—
419	C₃	—	27	1	no	—
420	C₃	C₃×C₉⋊H(3,𝔽₃)	1	1	yes	characteristic
421	C₃	#10624879	1	1	yes	characteristic
422	C₃	#10624892	1	2	yes	—
423	C₃	H(3,𝔽₃)×3₋¹⁺²	1	1	yes	characteristic
424	C₃	#10624896	1	2	yes	—
425	C₃	3₋¹⁺²²	1	1	yes	characteristic
426	C₃	#10624901	1	2	yes	—
427	C₃	#10624901	1	1	yes	characteristic
428	C₃	#10624908	1	2	yes	—

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₃³	C₃⁴
prime radical	C₃²×H(3,𝔽₃)	C₃²
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³ ◁ G
LECS	G ▷ C₃³ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₃×#6900	C₃	semidirect
2. C₃×#6896	C₃	semidirect
3. C₃×#6894	C₃	semidirect
6. C₃×C₉×3₋¹⁺²	C₃	semidirect
7. #10624566	C₃	semidirect
8. #10624566	C₃	semidirect
9. #10624566	C₃	semidirect
10. #10624566	C₃	semidirect
11. #10624565	C₃	semidirect
12. #10624565	C₃	semidirect
13. #10624565	C₃	semidirect
14. #10624565	C₃	semidirect
16. #10624560	C₃	semidirect
17. #10624560	C₃	semidirect
18. #10624560	C₃	semidirect
19. #10624560	C₃	semidirect
20. #10624560	C₃	semidirect
21. #10624560	C₃	semidirect
22. #10624560	C₃	semidirect
23. #10624557	C₃	semidirect
24. #10624557	C₃	semidirect
25. #10624556	C₃	semidirect
26. #10624548	C₃	semidirect
27. C₉×C₃²⋊C₉	C₃	semidirect
140. C₃×3₋¹⁺²	3₋¹⁺²	semidirect
190. C₉⋊C₉	H(3,𝔽₃)	semidirect
213. C₃²⋊C₉	3₋¹⁺²	semidirect
415. C₉	C₉⋊H(3,𝔽₃)	semidirect

Maximal subgroups

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

subgroup	index
C₃×#6900	3
C₃×#6896	3
C₃×#6894	3
C₃×C₉⋊H(3,𝔽₃)	3
C₃×C₉×3₋¹⁺²	3
#10624566	3
#10624565	3
#10624563	3
#10624560	3
#10624557	3
#10624556	3
#10624548	3
C₉×C₃²⋊C₉	3