Subgroups — #41007710

Order 26973.

620 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582589	C₃	1	2	yes	maximal, complemented
2	#22582589	C₃	1	2	yes	maximal, complemented
3	#22582589	C₃	1	2	yes	maximal, complemented
4	#22582589	C₃	1	2	yes	maximal, complemented
5	#22582586	C₃	1	1	yes	maximal, characteristic, complemented
6	#22582585	C₃	1	2	yes	maximal, complemented
7	#22582585	C₃	1	2	yes	maximal, complemented
8	#22582585	C₃	1	2	yes	maximal, complemented
9	#22582585	C₃	1	2	yes	maximal, complemented
10	#22582584	C₃	1	2	yes	maximal, complemented
11	#22582583	C₃	1	2	yes	maximal, complemented
12	#22582582	C₃	1	2	yes	maximal, complemented
13	#22582582	C₃	1	2	yes	maximal, complemented
14	#22582581	C₃	1	1	yes	maximal, characteristic, complemented
15	#22582570	C₃	1	2	yes	maximal, complemented
16	#22582570	C₃	1	2	yes	maximal, complemented
17	#22582567	C₃	1	2	yes	maximal, complemented
18	#22582553	C₃	1	1	yes	maximal, characteristic
19	#22582553	C₃	1	1	yes	maximal, characteristic
20	#22582552	C₃	1	1	yes	maximal, characteristic
21	C₉×#11758605	C₃	1	1	yes	maximal, characteristic, complemented
22	#22582543	C₃	1	2	yes	maximal, complemented
23	C₃²⋊C₉×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
24	C₃₇×#6897	C₃	1	1	yes	maximal, characteristic, complemented
25	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
26	C₃×#11758605	C₃²	1	2	yes	—
27	C₃×#11758605	C₃²	1	1	yes	characteristic
28	C₃×#11758605	C₃²	1	1	yes	characteristic
29	C₃×#11758605	C₃²	1	2	yes	—
30	C₃×#11758606	C₃²	1	1	yes	characteristic
31	C₃×#11758606	C₃²	1	2	yes	—
32	C₃×C₉×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
33	C₃×C₉×C₃₇⋊C₃	C₃²	1	2	yes	—
34	#15688506	C₃²	1	2	yes	complemented
35	#15688506	C₃²	1	2	yes	complemented
36	#15688506	C₃²	1	2	yes	complemented
37	#15688506	C₃²	1	2	yes	complemented
38	#15688505	C₃²	1	2	yes	complemented
39	#15688505	C₃²	1	2	yes	complemented
40	#15688505	C₃²	1	2	yes	complemented
41	#15688505	C₃²	1	2	yes	complemented
42	#15688504	C₃²	1	2	yes	complemented
43	#15688504	C₃²	1	2	yes	complemented
44	#15688504	C₃²	1	2	yes	complemented
45	#15688504	C₃²	1	2	yes	complemented
46	#15688504	C₃²	1	2	yes	complemented
47	#15688504	C₃²	1	2	yes	complemented
48	#15688504	C₃²	1	2	yes	complemented
49	#15688504	C₃²	1	2	yes	complemented
50	#15688504	C₃²	1	2	yes	complemented
51	#15688504	C₃²	1	2	yes	complemented
52	#15688504	C₃²	1	2	yes	complemented
53	#15688504	C₃²	1	2	yes	complemented
54	#15688504	C₃²	1	2	yes	complemented
55	#15688504	C₃²	1	2	yes	complemented
56	#15688504	C₃²	1	2	yes	complemented
57	#15688504	C₃²	1	2	yes	complemented
58	#15688504	C₃²	1	2	yes	complemented
59	#15688504	C₃²	1	2	yes	complemented
60	#15688504	C₃²	1	2	yes	complemented
61	#15688504	C₃²	1	2	yes	complemented
62	#15688504	C₃²	1	2	yes	complemented
63	#15688504	C₃²	1	2	yes	complemented
64	#15688504	C₃²	1	2	yes	complemented
65	#15688504	C₃²	1	2	yes	complemented
66	C₃²⋊#66524	C₃²	1	2	yes	—
67	C₃²⋊#66524	C₃²	1	2	yes	—
68	C₃²⋊#66524	C₃²	1	2	yes	—
69	C₃²⋊#66524	C₃²	1	2	yes	—
70	#15688502	C₃²	1	1	yes	characteristic
71	#15688502	C₃²	1	2	yes	—
72	#15688502	C₃²	1	1	yes	characteristic
73	#15688502	C₃²	1	2	yes	—
74	#15688502	C₃²	1	2	yes	—
75	#15688502	C₃²	1	2	yes	—
76	#15688502	C₃²	1	1	yes	characteristic
77	#15688502	C₃²	1	1	yes	characteristic
78	#15688502	C₃²	1	1	yes	characteristic
79	#15688502	C₃²	1	2	yes	—
80	#15688502	C₃²	1	1	yes	characteristic
81	#15688502	C₃²	1	2	yes	—
82	#15688502	C₃²	1	1	yes	characteristic
83	#15688502	C₃²	1	1	yes	characteristic
84	#15688502	C₃²	1	2	yes	—
85	#15688502	C₃²	1	2	yes	—
86	C₉×#66524	C₃²	1	2	yes	complemented
87	C₉×#66524	C₃²	1	2	yes	complemented
88	C₉×#66524	C₃²	1	2	yes	complemented
89	C₉×#66524	C₃²	1	2	yes	complemented
90	C₃₇×C₉⋊C₉	C₃²	1	2	yes	complemented
91	C₃₇×C₉⋊C₉	C₃²	1	2	yes	complemented
92	C₃₇×C₉⋊C₉	C₃²	1	2	yes	complemented
93	C₃₇×C₉⋊C₉	C₃²	1	2	yes	complemented
94	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
95	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
96	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
97	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
98	C₉²×C₃₇	C₃²	1	1	yes	characteristic, complemented
99	C₃³×C₃₇	C₃³	1	1	yes	characteristic
100	C₃²×C₃₇⋊C₃	—	3	3	no	—
101	C₃²×C₃₇⋊C₃	—	9	1	no	—
102	C₃²×C₃₇⋊C₃	—	9	1	no	—
103	C₃²×C₃₇⋊C₃	—	9	1	no	—
104	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
105	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
106	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
107	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
108	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
109	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
110	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
111	C₃×C₉×C₃₇	C₃³	1	2	yes	—
112	C₃×C₉×C₃₇	C₃³	1	2	yes	—
113	C₃×C₉×C₃₇	C₃³	1	2	yes	—
114	C₃×C₉×C₃₇	C₃³	1	2	yes	—
115	C₃×#66524	C₃³	1	2	yes	—
116	C₃×#66524	C₃³	1	2	yes	—
117	C₃×#66524	C₃³	1	2	yes	—
118	C₃×#66524	C₃³	1	2	yes	—
119	C₃×#66524	C₃³	1	2	yes	—
120	C₃×#66524	C₃³	1	2	yes	—
121	C₃×#66524	C₃³	1	2	yes	—
122	C₃×#66524	C₃³	1	2	yes	—
123	C₃×#66524	C₃³	1	2	yes	—
124	C₃×#66524	C₃³	1	2	yes	—
125	C₃×#66524	C₃³	1	2	yes	—
126	C₃×#66524	C₃³	1	2	yes	—
127	#11758606	—	9	1	no	—
128	#11758606	—	9	2	no	—
129	#11758605	—	3	6	no	—
130	#11758605	—	3	3	no	—
131	#11758605	—	9	1	no	—
132	#11758605	—	9	2	no	—
133	C₉×C₃₇⋊C₃	—	9	1	no	—
134	C₉×C₃₇⋊C₃	—	9	2	no	—
135	#10624889	—	37	1	no	maximal, Sylow
136	C₃²×C₃₇	—	3	1	no	—
137	C₃²×C₃₇	—	3	1	no	—
138	C₃²×C₃₇	—	3	1	no	—
139	C₃²×C₃₇	—	3	1	no	—
140	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
141	C₃×C₃₇⋊C₃	—	3	1	no	—
142	C₃×C₃₇⋊C₃	—	3	1	no	—
143	C₃×C₃₇⋊C₃	—	3	1	no	—
144	C₃×C₃₇⋊C₃	—	3	1	no	—
145	C₃×C₃₇⋊C₃	—	3	1	no	—
146	C₃×C₃₇⋊C₃	—	3	1	no	—
147	C₃×C₃₇⋊C₃	—	3	1	no	—
148	C₃×C₃₇⋊C₃	—	3	1	no	—
149	C₃×C₃₇⋊C₃	—	3	1	no	—
150	C₃×C₃₇⋊C₃	—	3	1	no	—
151	C₃×C₃₇⋊C₃	—	3	1	no	—
152	C₃×C₃₇⋊C₃	—	9	9	no	—
153	C₃×C₃₇⋊C₃	#737	1	3	yes	—
154	C₉×C₃₇	—	3	1	no	—
155	C₉×C₃₇	—	3	2	no	—
156	C₉×C₃₇	—	3	1	no	—
157	C₉×C₃₇	—	3	2	no	—
158	C₉×C₃₇	—	3	1	no	—
159	C₉×C₃₇	—	3	2	no	—
160	C₉×C₃₇	—	3	1	no	—
161	C₉×C₃₇	—	3	2	no	—
162	#66524	—	3	2	no	—
163	#66524	—	3	2	no	—
164	#66524	—	3	2	no	—
165	#66524	—	3	2	no	—
166	#66524	—	3	2	no	—
167	#66524	—	3	2	no	—
168	#66524	—	3	2	no	—
169	#66524	—	3	2	no	—
170	#66524	—	3	2	no	—
171	#66524	—	3	2	no	—
172	#66524	—	3	2	no	—
173	#66524	—	3	2	no	—
174	#6897	—	37	2	no	—
175	#6897	—	37	2	no	—
176	#6897	—	37	2	no	—
177	#6897	—	37	2	no	—
178	#6897	—	37	2	no	—
179	#6897	—	37	2	no	—
180	#6897	—	37	2	no	—
181	#6897	—	37	2	no	—
182	#6897	—	37	1	no	—
183	#6897	C₃₇⋊C₃	1	1	yes	characteristic, complemented
184	#6896	—	37	2	no	—
185	#6896	—	37	2	no	—
186	#6896	—	37	2	no	—
187	#6896	—	37	2	no	—
188	#6896	—	37	1	no	—
189	#6894	—	37	2	no	—
190	#6894	—	37	2	no	—
191	#6894	—	37	2	no	—
192	#6891	—	37	1	no	—
193	#6891	—	37	1	no	—
194	#6891	—	37	1	no	—
195	C₉×3₋¹⁺²	—	37	2	no	—
196	C₉×3₋¹⁺²	—	37	1	no	—
197	C₃×C₃²⋊C₉	—	37	1	no	—
198	C₃×C₃₇	—	9	1	no	—
199	C₃×C₃₇	C₃×#737	1	1	yes	characteristic
200	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
201	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
202	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
203	C₃₇⋊C₃	—	3	3	no	—
204	C₃₇⋊C₃	—	9	1	no	—
205	C₃₇⋊C₃	—	9	1	no	—
206	C₃⁴	—	37	1	no	—
207	C₃×3₋¹⁺²	—	37	2	no	—
208	C₃×3₋¹⁺²	—	37	1	no	—
209	C₃×3₋¹⁺²	—	37	2	no	—
210	C₃×3₋¹⁺²	—	37	1	no	—
211	C₃×3₋¹⁺²	—	37	2	no	—
212	C₃×3₋¹⁺²	—	37	1	no	—
213	C₃²×C₉	—	37	1	no	—
214	C₃²×C₉	—	37	2	no	—
215	C₉⋊C₉	—	37	2	no	—
216	C₉⋊C₉	—	37	2	no	—
217	C₉⋊C₉	—	37	2	no	—
218	C₉⋊C₉	—	37	2	no	—
219	C₉⋊C₉	—	37	2	no	—
220	C₉⋊C₉	—	37	2	no	—
221	C₉⋊C₉	—	37	2	no	—
222	C₉⋊C₉	—	37	2	no	—
223	C₉⋊C₉	—	37	2	no	—
224	C₉⋊C₉	—	37	2	no	—
225	C₉⋊C₉	—	37	2	no	—
226	C₉⋊C₉	—	37	2	no	—
227	C₉⋊C₉	—	37	2	no	—
228	C₉⋊C₉	—	37	2	no	—
229	C₉⋊C₉	—	37	2	no	—
230	C₉⋊C₉	—	37	2	no	—
231	C₉⋊C₉	—	37	2	no	—
232	C₉⋊C₉	—	37	2	no	—
233	C₉⋊C₉	—	37	2	no	—
234	C₉⋊C₉	—	37	2	no	—
235	C₉⋊C₉	—	37	2	no	—
236	C₉⋊C₉	—	37	2	no	—
237	C₉⋊C₉	—	37	2	no	—
238	C₉⋊C₉	—	37	2	no	—
239	C₉⋊C₉	—	37	2	no	—
240	C₉⋊C₉	—	37	2	no	—
241	C₉⋊C₉	—	37	2	no	—
242	C₉⋊C₉	—	37	2	no	—
243	C₉⋊C₉	—	37	2	no	—
244	C₉⋊C₉	—	37	2	no	—
245	C₉⋊C₉	—	37	2	no	—
246	C₉⋊C₉	—	37	2	no	—
247	C₉⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
248	C₉⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
249	C₉⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
250	C₉⋊C₉	C₃×C₃₇⋊C₃	1	2	yes	complemented
251	C₃²⋊C₉	—	37	2	no	—
252	C₃²⋊C₉	—	37	2	no	—
253	C₃²⋊C₉	—	37	2	no	—
254	C₃²⋊C₉	—	37	2	no	—
255	C₃²⋊C₉	—	37	2	no	—
256	C₃²⋊C₉	—	37	1	no	—
257	C₃²⋊C₉	—	37	2	no	—
258	C₃²⋊C₉	—	37	1	no	—
259	C₃²⋊C₉	—	37	2	no	—
260	C₃²⋊C₉	—	37	2	no	—
261	C₃²⋊C₉	—	37	1	no	—
262	C₃²⋊C₉	—	37	1	no	—
263	C₃²⋊C₉	—	37	2	no	—
264	C₃²⋊C₉	—	37	1	no	—
265	C₃²⋊C₉	—	37	2	no	—
266	C₃²⋊C₉	—	37	2	no	—
267	C₃²⋊C₉	—	37	2	no	—
268	C₃²⋊C₉	—	37	1	no	—
269	C₃²⋊C₉	—	37	1	no	—
270	C₃²⋊C₉	—	37	1	no	—
271	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
272	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
273	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
274	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
275	C₉²	—	37	2	no	—
276	C₉²	—	37	2	no	—
277	C₉²	—	37	2	no	—
278	C₉²	—	37	2	no	—
279	C₉²	C₃×C₃₇⋊C₃	1	1	yes	characteristic, complemented
280	C₃₇	#10624889	1	1	yes	characteristic, complemented, Sylow
281	C₃³	—	37	1	no	—
282	C₃³	—	37	1	no	—
283	C₃³	—	37	1	no	—
284	C₃³	—	333	1	no	—
285	C₃³	—	333	1	no	—
286	C₃³	—	333	1	no	—
287	C₃³	—	111	3	no	—
288	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
289	3₋¹⁺²	—	333	2	no	—
290	3₋¹⁺²	—	333	1	no	—
291	3₋¹⁺²	—	333	2	no	—
292	3₋¹⁺²	—	333	1	no	—
293	3₋¹⁺²	—	111	6	no	—
294	3₋¹⁺²	—	111	3	no	—
295	C₃×C₉	—	37	2	no	—
296	C₃×C₉	—	37	2	no	—
297	C₃×C₉	—	37	2	no	—
298	C₃×C₉	—	37	2	no	—
299	C₃×C₉	—	37	2	no	—
300	C₃×C₉	—	37	2	no	—
301	C₃×C₉	—	37	2	no	—
302	C₃×C₉	—	37	2	no	—
303	C₃×C₉	—	37	2	no	—
304	C₃×C₉	—	37	2	no	—
305	C₃×C₉	—	37	2	no	—
306	C₃×C₉	—	37	2	no	—
307	C₃×C₉	—	333	1	no	—
308	C₃×C₉	—	333	2	no	—
309	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
310	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
311	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
312	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
313	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
314	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
315	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
316	C₃×C₉	C₃²×C₃₇⋊C₃	1	2	yes	—
317	C₃²	—	3	1	no	—
318	C₃²	—	3	1	no	—
319	C₃²	—	3	1	no	—
320	C₃²	—	3	1	no	—
321	C₃²	—	37	3	no	—
322	C₃²	—	333	9	no	—
323	C₃²	—	111	1	no	—
324	C₃²	—	111	1	no	—
325	C₃²	—	111	1	no	—
326	C₃²	—	111	1	no	—
327	C₃²	—	111	1	no	—
328	C₃²	—	111	1	no	—
329	C₃²	—	111	1	no	—
330	C₃²	—	111	1	no	—
331	C₃²	—	111	1	no	—
332	C₃²	—	111	1	no	—
333	C₃²	—	111	1	no	—
334	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
335	C₉	—	3	2	no	—
336	C₉	—	3	1	no	—
337	C₉	—	3	2	no	—
338	C₉	—	3	1	no	—
339	C₉	—	3	1	no	—
340	C₉	—	3	2	no	—
341	C₉	—	3	2	no	—
342	C₉	—	3	1	no	—
343	C₉	—	111	2	no	—
344	C₉	—	111	2	no	—
345	C₉	—	111	2	no	—
346	C₉	—	111	2	no	—
347	C₉	—	111	2	no	—
348	C₉	—	111	2	no	—
349	C₉	—	111	2	no	—
350	C₉	—	111	2	no	—
351	C₉	—	111	2	no	—
352	C₉	—	111	2	no	—
353	C₉	—	111	2	no	—
354	C₉	—	111	2	no	—
355	C₃	—	9	1	no	—
356	C₃	—	333	1	no	—
357	C₃	—	333	1	no	—
358	C₃	—	111	3	no	—
359	C₃	#737×C₃₇⋊C₃	1	1	yes	characteristic
360	C₃	#22582677	1	1	yes	characteristic
361	C₃	#22582678	1	1	yes	characteristic
362	C₃	#22582678	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₃₇⋊C₃
commutator, socle, cosocle	C₃²×C₃₇	C₃⁴
Fitting	C₃₇×#6897	C₃
prime radical	C₃³×C₃₇⋊C₃	C₃²
hypercenter	#6897	C₃₇⋊C₃
hypocenter	C₃₇	#10624889
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ #6897

Complements

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

N	H ≅ G/N	type
1. #22582589	C₃	semidirect
2. #22582589	C₃	semidirect
3. #22582589	C₃	semidirect
4. #22582589	C₃	semidirect
5. #22582586	C₃	semidirect
6. #22582585	C₃	semidirect
7. #22582585	C₃	semidirect
8. #22582585	C₃	semidirect
9. #22582585	C₃	semidirect
10. #22582584	C₃	semidirect
11. #22582583	C₃	semidirect
12. #22582582	C₃	semidirect
13. #22582582	C₃	semidirect
14. #22582581	C₃	semidirect
15. #22582570	C₃	semidirect
16. #22582570	C₃	semidirect
17. #22582567	C₃	semidirect
21. C₉×#11758605	C₃	semidirect
22. #22582543	C₃	semidirect
24. C₃₇×#6897	C₃	semidirect
34. #15688506	C₃²	semidirect
35. #15688506	C₃²	semidirect
36. #15688506	C₃²	semidirect
37. #15688506	C₃²	semidirect
38. #15688505	C₃²	semidirect
39. #15688505	C₃²	semidirect
40. #15688505	C₃²	semidirect
41. #15688505	C₃²	semidirect
42. #15688504	C₃²	semidirect
43. #15688504	C₃²	semidirect
44. #15688504	C₃²	semidirect
45. #15688504	C₃²	semidirect
46. #15688504	C₃²	semidirect
47. #15688504	C₃²	semidirect
48. #15688504	C₃²	semidirect
49. #15688504	C₃²	semidirect
50. #15688504	C₃²	semidirect
51. #15688504	C₃²	semidirect
52. #15688504	C₃²	semidirect
53. #15688504	C₃²	semidirect
54. #15688504	C₃²	semidirect
55. #15688504	C₃²	semidirect
56. #15688504	C₃²	semidirect
57. #15688504	C₃²	semidirect
58. #15688504	C₃²	semidirect
59. #15688504	C₃²	semidirect
60. #15688504	C₃²	semidirect
61. #15688504	C₃²	semidirect
62. #15688504	C₃²	semidirect
63. #15688504	C₃²	semidirect
64. #15688504	C₃²	semidirect
65. #15688504	C₃²	semidirect
86. C₉×#66524	C₃²	semidirect
87. C₉×#66524	C₃²	semidirect
88. C₉×#66524	C₃²	semidirect
89. C₉×#66524	C₃²	semidirect
90. C₃₇×C₉⋊C₉	C₃²	semidirect
91. C₃₇×C₉⋊C₉	C₃²	semidirect
92. C₃₇×C₉⋊C₉	C₃²	semidirect
93. C₃₇×C₉⋊C₉	C₃²	semidirect
98. C₉²×C₃₇	C₃²	semidirect
183. #6897	C₃₇⋊C₃	semidirect
247. C₉⋊C₉	C₃×C₃₇⋊C₃	semidirect
248. C₉⋊C₉	C₃×C₃₇⋊C₃	semidirect
249. C₉⋊C₉	C₃×C₃₇⋊C₃	semidirect
250. C₉⋊C₉	C₃×C₃₇⋊C₃	semidirect
279. C₉²	C₃×C₃₇⋊C₃	semidirect
280. C₃₇	#10624889	semidirect

Maximal subgroups

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

subgroup	index
#22582589	3
#22582586	3
#22582585	3
#22582584	3
#22582583	3
#22582582	3
#22582581	3
#22582570	3
#22582567	3
#22582553	3
#22582552	3
C₉×#11758605	3
#22582543	3
C₃²⋊C₉×C₃₇⋊C₃	3
C₃₇×#6897	3
#10624889	37