Subgroups — #41007629

Order 26973.

758 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688531	C₃	1	1	yes	maximal, characteristic
2	#22582605	C₃	1	1	yes	maximal, characteristic, complemented
3	#22582604	C₃	1	1	yes	maximal, characteristic, complemented
4	#22582601	C₃	1	1	yes	maximal, characteristic, complemented
5	#22582598	C₃	1	2	yes	maximal, complemented
6	#22582597	C₃	1	2	yes	maximal, complemented
7	#22582593	C₃	1	2	yes	maximal, complemented
8	#22582584	C₃	1	1	yes	maximal, characteristic, complemented
9	#22582583	C₃	1	1	yes	maximal, characteristic, complemented
10	#22582582	C₃	1	2	yes	maximal, complemented
11	#22582582	C₃	1	2	yes	maximal, complemented
12	#22582580	C₃	1	1	yes	maximal, characteristic, complemented
13	#22582579	C₃	1	2	yes	maximal, complemented
14	#22582570	C₃	1	2	yes	maximal, complemented
15	#22582569	C₃	1	2	yes	maximal, complemented
16	#22582567	C₃	1	1	yes	maximal, characteristic, complemented
17	#22582566	C₃	1	1	yes	maximal, characteristic, complemented
18	#22582557	C₃	1	2	yes	maximal
19	#22582555	C₃	1	1	yes	maximal, characteristic
20	C₉×#11758606	C₃	1	2	yes	maximal, complemented
21	C₉×#11758606	C₃	1	1	yes	maximal, characteristic, complemented
22	C₉×#11758605	C₃	1	2	yes	maximal, complemented
23	C₉×#11758605	C₃	1	1	yes	maximal, characteristic, complemented
24	C₉×#11758608	C₃	1	2	yes	maximal, complemented
25	#22582536	C₃	1	2	yes	maximal, complemented
26	C₉²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
27	C₉×3₋¹⁺²×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
28	#15688531	—	3	9	no	—
29	C₃×#11758608	C₃²	1	2	yes	—
30	C₃×#11758608	C₃²	1	1	yes	characteristic
31	C₃×#11758608	C₃²	1	1	yes	characteristic
32	C₃×#11758605	C₃²	1	1	yes	characteristic
33	C₃×#11758605	C₃²	1	2	yes	—
34	C₃×#11758605	C₃²	1	1	yes	characteristic
35	C₃×#11758605	C₃²	1	1	yes	characteristic
36	C₃×#11758605	C₃²	1	1	yes	characteristic
37	C₃×#11758606	C₃²	1	1	yes	characteristic
38	C₃×#11758606	C₃²	1	2	yes	—
39	C₃×#11758606	C₃²	1	1	yes	characteristic
40	C₃×#11758606	C₃²	1	1	yes	characteristic
41	C₃×#11758606	C₃²	1	1	yes	characteristic
42	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
43	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
44	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
45	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
46	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	—
47	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
48	#15688506	C₃²	1	2	yes	—
49	#15688506	C₃²	1	1	yes	characteristic
50	#15688506	C₃²	1	1	yes	characteristic
51	#15688506	C₃²	1	2	yes	—
52	#15688505	C₃²	1	1	yes	characteristic
53	#15688505	C₃²	1	2	yes	—
54	#15688505	C₃²	1	1	yes	characteristic
55	#15688505	C₃²	1	2	yes	—
56	#15688504	C₃²	1	2	yes	—
57	#15688504	C₃²	1	2	yes	—
58	#15688504	C₃²	1	2	yes	—
59	#15688504	C₃²	1	2	yes	—
60	#15688504	C₃²	1	2	yes	—
61	#15688504	C₃²	1	2	yes	—
62	#15688504	C₃²	1	2	yes	—
63	#15688504	C₃²	1	2	yes	—
64	#15688504	C₃²	1	2	yes	—
65	#15688504	C₃²	1	2	yes	—
66	#15688504	C₃²	1	2	yes	—
67	#15688504	C₃²	1	2	yes	—
68	#15688504	C₃²	1	2	yes	—
69	#15688504	C₃²	1	2	yes	—
70	#15688504	C₃²	1	2	yes	—
71	#15688504	C₃²	1	2	yes	—
72	#15688504	C₃²	1	2	yes	—
73	#15688504	C₃²	1	2	yes	—
74	#15688504	C₃²	1	2	yes	—
75	#15688504	C₃²	1	2	yes	—
76	#15688504	C₃²	1	2	yes	—
77	#15688504	C₃²	1	2	yes	—
78	#15688504	C₃²	1	2	yes	—
79	#15688504	C₃²	1	2	yes	—
80	C₃²⋊#66524	C₃²	1	2	yes	—
81	C₃²⋊#66524	C₃²	1	2	yes	—
82	#15688502	C₃²	1	2	yes	—
83	#15688502	C₃²	1	2	yes	—
84	#15688502	C₃²	1	2	yes	—
85	#15688502	C₃²	1	2	yes	—
86	#15688502	C₃²	1	2	yes	—
87	#15688502	C₃²	1	2	yes	—
88	#15688502	C₃²	1	2	yes	—
89	#15688502	C₃²	1	2	yes	—
90	#15688502	C₃²	1	2	yes	—
91	C₉×#66524	C₃²	1	2	yes	—
92	C₉×#66524	C₃²	1	2	yes	—
93	C₉×#66524	C₃²	1	2	yes	—
94	C₉×#66524	C₃²	1	2	yes	—
95	C₉×#66524	C₃²	1	1	yes	characteristic
96	C₉×#66524	C₃²	1	2	yes	—
97	C₉×#66524	C₃²	1	1	yes	characteristic
98	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
99	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
100	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
101	C₃₇×C₉⋊C₉	C₃²	1	1	yes	characteristic
102	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
103	C₃₇×C₉⋊C₉	C₃²	1	2	yes	—
104	C₃₇×C₃²⋊C₉	C₃²	1	2	yes	—
105	C₉²×C₃₇	C₃²	1	2	yes	—
106	C₉²×C₃₇	C₃²	1	1	yes	characteristic
107	C₃³×C₃₇	C₃³	1	1	yes	characteristic
108	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
109	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
110	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
111	3₋¹⁺²×C₃₇	—	3	3	no	—
112	C₃×C₉×C₃₇	—	3	3	no	—
113	C₃×C₉×C₃₇	C₃³	1	2	yes	—
114	C₃×C₉×C₃₇	C₃³	1	2	yes	—
115	C₃×C₉×C₃₇	C₃³	1	2	yes	—
116	C₃×C₉×C₃₇	C₃³	1	2	yes	—
117	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
118	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
119	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
120	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
121	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
122	#11758608	—	3	3	no	—
123	#11758608	—	3	3	no	—
124	#11758608	—	3	6	no	—
125	C₃×#66524	C₃³	1	2	yes	—
126	C₃×#66524	C₃³	1	2	yes	—
127	C₃×#66524	C₃³	1	2	yes	—
128	C₃×#66524	C₃³	1	2	yes	—
129	C₃×#66524	C₃³	1	2	yes	—
130	C₃×#66524	C₃³	1	2	yes	—
131	C₃×#66524	C₃³	1	2	yes	—
132	C₃×#66524	C₃³	1	2	yes	—
133	C₃×#66524	C₃³	1	1	yes	characteristic
134	C₃×#66524	C₃³	1	1	yes	characteristic
135	C₃×#66524	C₃³	1	1	yes	characteristic
136	C₃×#66524	C₃³	1	1	yes	characteristic
137	C₃×#66524	C₃³	1	1	yes	characteristic
138	C₃×#66524	C₃³	1	1	yes	characteristic
139	C₃×#66524	C₃³	1	2	yes	—
140	#11758606	—	3	3	no	—
141	#11758606	—	3	3	no	—
142	#11758606	—	3	3	no	—
143	#11758606	—	3	3	no	—
144	#11758606	—	3	6	no	—
145	#11758605	—	3	3	no	—
146	#11758605	—	3	3	no	—
147	#11758605	—	3	3	no	—
148	#11758605	—	3	3	no	—
149	#11758605	—	3	6	no	—
150	C₉×C₃₇⋊C₃	—	3	3	no	—
151	C₉×C₃₇⋊C₃	—	3	3	no	—
152	C₉×C₃₇⋊C₃	—	3	3	no	—
153	C₉×C₃₇⋊C₃	—	3	6	no	—
154	C₉×C₃₇⋊C₃	3₋¹⁺²	1	9	yes	complemented
155	#10624879	—	37	1	no	maximal, Sylow
156	C₃²×C₃₇	—	3	1	no	—
157	C₃²×C₃₇	—	3	2	no	—
158	C₃²×C₃₇	—	3	1	no	—
159	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
160	C₃×C₃₇⋊C₃	—	3	2	no	—
161	C₃×C₃₇⋊C₃	—	3	1	no	—
162	C₃×C₃₇⋊C₃	—	3	1	no	—
163	C₃×C₃₇⋊C₃	—	3	1	no	—
164	C₃×C₃₇⋊C₃	—	3	2	no	—
165	C₃×C₃₇⋊C₃	—	3	1	no	—
166	C₃×C₃₇⋊C₃	—	3	2	no	—
167	C₃×C₃₇⋊C₃	—	3	1	no	—
168	C₃×C₃₇⋊C₃	C₃×3₋¹⁺²	1	3	yes	—
169	C₉×C₃₇	—	3	1	no	—
170	C₉×C₃₇	—	3	1	no	—
171	C₉×C₃₇	—	3	2	no	—
172	C₉×C₃₇	—	3	2	no	—
173	C₉×C₃₇	—	3	2	no	—
174	C₉×C₃₇	—	3	2	no	—
175	C₉×C₃₇	C₃×3₋¹⁺²	1	3	yes	—
176	C₉×C₃₇	#737	1	3	yes	complemented
177	#66524	—	3	1	no	—
178	#66524	—	3	1	no	—
179	#66524	—	3	1	no	—
180	#66524	—	3	1	no	—
181	#66524	—	3	2	no	—
182	#66524	—	3	2	no	—
183	#66524	—	3	2	no	—
184	#66524	—	3	2	no	—
185	#66524	—	3	2	no	—
186	#66524	—	3	2	no	—
187	#66524	—	3	2	no	—
188	#66524	—	3	2	no	—
189	#66524	C₃×3₋¹⁺²	1	3	yes	—
190	#66524	C₃×3₋¹⁺²	1	3	yes	—
191	#66524	#737	1	6	yes	complemented
192	C₃×#737	—	37	1	no	—
193	#6900	—	37	1	no	—
194	#6900	—	37	1	no	—
195	#6900	—	37	1	no	—
196	#6899	—	37	2	no	—
197	#6899	—	37	2	no	—
198	#6899	—	37	2	no	—
199	#6896	—	37	1	no	—
200	#6896	—	37	2	no	—
201	#6896	—	37	2	no	—
202	#6896	—	37	1	no	—
203	#6896	—	37	1	no	—
204	#6896	—	37	2	no	—
205	#6894	—	37	1	no	—
206	#6894	—	37	1	no	—
207	#6894	—	37	2	no	—
208	#6894	—	37	2	no	—
209	C₉⋊H(3,𝔽₃)	—	37	1	no	—
210	C₉⋊H(3,𝔽₃)	—	37	2	no	—
211	C₉×3₋¹⁺²	—	37	2	no	—
212	C₉×3₋¹⁺²	—	37	2	no	—
213	C₉×3₋¹⁺²	—	37	1	no	—
214	C₉×3₋¹⁺²	—	37	2	no	—
215	C₉×3₋¹⁺²	—	37	1	no	—
216	C₉×3₋¹⁺²	C₃₇⋊C₃	1	1	yes	characteristic, complemented
217	#6887	—	37	2	no	—
218	C₃×C₉²	—	37	1	no	—
219	C₃×C₃₇	—	9	1	no	—
220	C₃×C₃₇	C₃²×3₋¹⁺²	1	1	yes	characteristic
221	C₃×C₃₇	C₃×#737	1	2	yes	—
222	C₃×C₃₇	C₃×#737	1	1	yes	characteristic
223	C₃₇⋊C₃	—	3	3	no	—
224	C₃₇⋊C₃	—	9	1	no	—
225	C₃₇⋊C₃	—	9	1	no	—
226	#737	—	111	9	no	—
227	C₃×3₋¹⁺²	—	37	1	no	—
228	C₃×3₋¹⁺²	—	37	1	no	—
229	C₃×3₋¹⁺²	—	37	2	no	—
230	C₃×3₋¹⁺²	—	37	1	no	—
231	C₃×3₋¹⁺²	—	37	1	no	—
232	C₃×3₋¹⁺²	—	37	1	no	—
233	C₃×3₋¹⁺²	—	37	1	no	—
234	C₃×3₋¹⁺²	—	37	1	no	—
235	C₃×3₋¹⁺²	—	37	1	no	—
236	C₃×3₋¹⁺²	—	37	2	no	—
237	C₃×3₋¹⁺²	—	37	1	no	—
238	C₃×3₋¹⁺²	—	37	2	no	—
239	C₃×3₋¹⁺²	—	37	1	no	—
240	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
241	C₃×H(3,𝔽₃)	—	37	1	no	—
242	C₃²×C₉	—	37	1	no	—
243	C₃²×C₉	—	37	2	no	—
244	C₃²×C₉	—	37	1	no	—
245	C₃²×C₉	—	37	1	no	—
246	C₃²×C₉	—	37	1	no	—
247	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
248	C₉⋊C₉	—	37	2	no	—
249	C₉⋊C₉	—	37	2	no	—
250	C₉⋊C₉	—	37	2	no	—
251	C₉⋊C₉	—	37	2	no	—
252	C₉⋊C₉	—	37	2	no	—
253	C₉⋊C₉	—	37	2	no	—
254	C₉⋊C₉	—	37	2	no	—
255	C₉⋊C₉	—	37	2	no	—
256	C₉⋊C₉	—	37	2	no	—
257	C₉⋊C₉	—	37	2	no	—
258	C₉⋊C₉	—	37	2	no	—
259	C₉⋊C₉	—	37	2	no	—
260	C₉⋊C₉	—	37	2	no	—
261	C₉⋊C₉	—	37	2	no	—
262	C₉⋊C₉	—	37	2	no	—
263	C₉⋊C₉	—	37	2	no	—
264	C₉⋊C₉	—	37	2	no	—
265	C₉⋊C₉	—	37	2	no	—
266	C₉⋊C₉	—	37	2	no	—
267	C₉⋊C₉	—	37	2	no	—
268	C₉⋊C₉	—	37	2	no	—
269	C₉⋊C₉	—	37	2	no	—
270	C₉⋊C₉	—	37	2	no	—
271	C₉⋊C₉	—	37	2	no	—
272	C₉⋊C₉	—	37	2	no	—
273	C₉⋊C₉	—	37	2	no	—
274	C₉⋊C₉	—	37	1	no	—
275	C₉⋊C₉	—	37	1	no	—
276	C₉⋊C₉	—	37	2	no	—
277	C₉⋊C₉	—	37	2	no	—
278	C₉⋊C₉	—	37	1	no	—
279	C₉⋊C₉	—	37	1	no	—
280	C₉⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	—
281	C₉⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	—
282	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
283	C₉⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
284	C₃²⋊C₉	—	37	2	no	—
285	C₃²⋊C₉	—	37	2	no	—
286	C₃²⋊C₉	—	37	2	no	—
287	C₃²⋊C₉	—	37	2	no	—
288	C₃²⋊C₉	—	37	2	no	—
289	C₃²⋊C₉	—	37	2	no	—
290	C₃²⋊C₉	—	37	2	no	—
291	C₃²⋊C₉	—	37	2	no	—
292	C₃²⋊C₉	—	37	2	no	—
293	C₃²⋊C₉	—	37	2	no	—
294	C₃²⋊C₉	—	37	2	no	—
295	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	—
296	C₉²	—	37	2	no	—
297	C₉²	—	37	1	no	—
298	C₉²	—	37	2	no	—
299	C₉²	—	37	1	no	—
300	C₉²	—	37	2	no	—
301	C₉²	—	37	2	no	—
302	C₉²	—	37	2	no	—
303	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
304	C₉²	C₃×C₃₇⋊C₃	1	2	yes	—
305	C₃₇	#10624879	1	1	yes	characteristic, complemented, Sylow
306	C₃³	—	37	1	no	—
307	C₃³	—	37	1	no	—
308	C₃³	—	37	1	no	—
309	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
310	3₋¹⁺²	—	3	3	no	—
311	3₋¹⁺²	—	111	6	no	—
312	3₋¹⁺²	—	111	3	no	—
313	3₋¹⁺²	—	111	3	no	—
314	3₋¹⁺²	—	111	6	no	—
315	3₋¹⁺²	—	111	3	no	—
316	3₋¹⁺²	—	111	3	no	—
317	3₋¹⁺²	—	111	3	no	—
318	3₋¹⁺²	—	111	3	no	—
319	3₋¹⁺²	—	111	6	no	—
320	3₋¹⁺²	—	111	3	no	—
321	3₋¹⁺²	—	111	3	no	—
322	3₋¹⁺²	—	111	3	no	—
323	3₋¹⁺²	—	111	3	no	—
324	H(3,𝔽₃)	—	111	3	no	—
325	C₃×C₉	—	3	3	no	—
326	C₃×C₉	—	37	1	no	—
327	C₃×C₉	—	37	1	no	—
328	C₃×C₉	—	37	2	no	—
329	C₃×C₉	—	37	9	no	—
330	C₃×C₉	—	37	2	no	—
331	C₃×C₉	—	37	2	no	—
332	C₃×C₉	—	37	2	no	—
333	C₃×C₉	—	37	2	no	—
334	C₃×C₉	—	37	2	no	—
335	C₃×C₉	—	37	2	no	—
336	C₃×C₉	—	37	2	no	—
337	C₃×C₉	—	37	2	no	—
338	C₃×C₉	—	37	1	no	—
339	C₃×C₉	—	37	1	no	—
340	C₃×C₉	—	37	1	no	—
341	C₃×C₉	—	37	1	no	—
342	C₃×C₉	—	111	6	no	—
343	C₃×C₉	—	111	3	no	—
344	C₃×C₉	—	111	3	no	—
345	C₃×C₉	—	111	3	no	—
346	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
347	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
348	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
349	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
350	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
351	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
352	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
353	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
354	C₃²	—	3	1	no	—
355	C₃²	—	3	2	no	—
356	C₃²	—	3	1	no	—
357	C₃²	—	37	3	no	—
358	C₃²	—	111	1	no	—
359	C₃²	—	111	1	no	—
360	C₃²	—	111	2	no	—
361	C₃²	—	111	2	no	—
362	C₃²	—	111	1	no	—
363	C₃²	—	111	1	no	—
364	C₃²	—	111	2	no	—
365	C₃²	—	111	1	no	—
366	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
367	C₉	—	3	1	no	—
368	C₉	—	3	1	no	—
369	C₉	—	3	2	no	—
370	C₉	—	3	2	no	—
371	C₉	—	3	2	no	—
372	C₉	—	3	2	no	—
373	C₉	—	37	3	no	—
374	C₉	—	37	3	no	—
375	C₉	—	37	6	no	—
376	C₉	—	111	1	no	—
377	C₉	—	111	1	no	—
378	C₉	—	111	1	no	—
379	C₉	—	111	1	no	—
380	C₉	—	111	2	no	—
381	C₉	—	111	2	no	—
382	C₉	—	111	2	no	—
383	C₉	—	111	2	no	—
384	C₉	—	111	2	no	—
385	C₉	—	111	2	no	—
386	C₉	—	111	2	no	—
387	C₉	—	111	2	no	—
388	C₉	3₋¹⁺²×C₃₇⋊C₃	1	3	yes	—
389	C₉	#15688531	1	3	yes	complemented
390	C₃	—	9	1	no	—
391	C₃	—	333	1	no	—
392	C₃	—	333	1	no	—
393	C₃	—	111	3	no	—
394	C₃	C₃×3₋¹⁺²×C₃₇⋊C₃	1	1	yes	characteristic
395	C₃	#737×C₃₇⋊C₃	1	2	yes	—
396	C₃	C₃×#15688531	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃²×C₃₇⋊C₃
commutator, socle, cosocle	C₃²×C₃₇	C₃⁴
Frattini	C₃²	C₃³×C₃₇⋊C₃
Fitting	C₉×3₋¹⁺²×C₃₇	C₃
prime radical	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²
hypercenter	C₉×3₋¹⁺²	C₃₇⋊C₃
hypocenter	C₃₇	#10624879
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₉ ◁ C₉×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
2. #22582605	C₃	semidirect
3. #22582604	C₃	semidirect
4. #22582601	C₃	semidirect
5. #22582598	C₃	semidirect
6. #22582597	C₃	semidirect
7. #22582593	C₃	semidirect
8. #22582584	C₃	semidirect
9. #22582583	C₃	semidirect
10. #22582582	C₃	semidirect
11. #22582582	C₃	semidirect
12. #22582580	C₃	semidirect
13. #22582579	C₃	semidirect
14. #22582570	C₃	semidirect
15. #22582569	C₃	semidirect
16. #22582567	C₃	semidirect
17. #22582566	C₃	semidirect
20. C₉×#11758606	C₃	semidirect
21. C₉×#11758606	C₃	semidirect
22. C₉×#11758605	C₃	semidirect
23. C₉×#11758605	C₃	semidirect
24. C₉×#11758608	C₃	semidirect
25. #22582536	C₃	semidirect
26. C₉²×C₃₇⋊C₃	C₃	semidirect
27. C₉×3₋¹⁺²×C₃₇	C₃	semidirect
154. C₉×C₃₇⋊C₃	3₋¹⁺²	semidirect
176. C₉×C₃₇	#737	semidirect
191. #66524	#737	semidirect
216. C₉×3₋¹⁺²	C₃₇⋊C₃	semidirect
305. C₃₇	#10624879	semidirect
389. C₉	#15688531	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688531	3
#22582605	3
#22582604	3
#22582601	3
#22582598	3
#22582597	3
#22582593	3
#22582584	3
#22582583	3
#22582582	3
#22582580	3
#22582579	3
#22582570	3
#22582569	3
#22582567	3
#22582566	3
#22582557	3
#22582555	3
C₉×#11758606	3
C₉×#11758605	3
C₉×#11758608	3
#22582536	3
C₉²×C₃₇⋊C₃	3
C₉×3₋¹⁺²×C₃₇	3
#10624879	37