Subgroups — #41007703

Order 26973.

764 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22582565	C₃	1	3	yes	maximal, complemented
2	#22582563	C₃	1	3	yes	maximal, complemented
3	#22582563	C₃	1	3	yes	maximal, complemented
4	#22582561	C₃	1	1	yes	maximal, characteristic, complemented
5	#22582561	C₃	1	3	yes	maximal, complemented
6	#22582560	C₃	1	1	yes	maximal, characteristic, complemented
7	#22582560	C₃	1	3	yes	maximal, complemented
8	#22582559	C₃	1	1	yes	maximal, characteristic, complemented
9	#22582558	C₃	1	1	yes	maximal, characteristic, complemented
10	#22582557	C₃	1	3	yes	maximal, complemented
11	#22582557	C₃	1	3	yes	maximal, complemented
12	#22582556	C₃	1	1	yes	maximal, characteristic, complemented
13	#22582555	C₃	1	3	yes	maximal, complemented
14	#22582555	C₃	1	3	yes	maximal, complemented
15	#22582553	C₃	1	1	yes	maximal, characteristic, complemented
16	#22582552	C₃	1	1	yes	maximal, characteristic, complemented
17	(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
18	H(3,𝔽₃)×#66524	C₃	1	1	yes	maximal, characteristic, complemented
19	#22582539	C₃	1	1	yes	maximal, characteristic, complemented
20	#22582539	C₃	1	1	yes	maximal, characteristic, complemented
21	C₃×#15688502	C₃	1	1	yes	maximal, characteristic, complemented
22	C₃₇×C₉⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic, complemented
23	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
24	C₃×#11758608	C₃²	1	3	yes	complemented
25	C₃×#11758605	C₃²	1	3	yes	—
26	C₃×#11758605	C₃²	1	3	yes	complemented
27	C₃×#11758605	C₃²	1	3	yes	complemented
28	C₃×#11758606	C₃²	1	3	yes	—
29	C₃×#11758606	C₃²	1	3	yes	complemented
30	C₃×#11758606	C₃²	1	3	yes	complemented
31	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
32	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
33	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	3	yes	—
34	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	3	yes	—
35	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	3	yes	—
36	C₃²×#66524	C₃²	1	1	yes	characteristic
37	C₃²×#66524	C₃²	1	1	yes	characteristic
38	C₃²×#66524	C₃²	1	3	yes	complemented
39	C₃×C₉×C₃₇⋊C₃	C₃²	1	3	yes	complemented
40	C₃×C₉×C₃₇⋊C₃	C₃²	1	3	yes	complemented
41	C₃²⋊#66524	C₃²	1	1	yes	characteristic
42	C₃²⋊#66524	C₃²	1	1	yes	characteristic
43	C₃²⋊#66524	C₃²	1	1	yes	characteristic
44	C₃²⋊#66524	C₃²	1	1	yes	characteristic
45	C₃²⋊#66524	C₃²	1	3	yes	complemented
46	C₃²⋊#66524	C₃²	1	3	yes	complemented
47	C₃²⋊#66524	C₃²	1	3	yes	complemented
48	C₃²⋊#66524	C₃²	1	3	yes	complemented
49	#15688502	C₃²	1	1	yes	characteristic
50	#15688502	C₃²	1	1	yes	characteristic
51	#15688502	C₃²	1	1	yes	characteristic
52	#15688502	C₃²	1	1	yes	characteristic
53	#15688502	C₃²	1	1	yes	characteristic
54	#15688502	C₃²	1	1	yes	characteristic
55	#15688502	C₃²	1	1	yes	characteristic
56	#15688502	C₃²	1	1	yes	characteristic
57	#15688502	C₃²	1	1	yes	characteristic
58	#15688502	C₃²	1	3	yes	—
59	#15688502	C₃²	1	3	yes	—
60	#15688502	C₃²	1	3	yes	—
61	#15688502	C₃²	1	3	yes	—
62	#15688502	C₃²	1	3	yes	complemented
63	#15688502	C₃²	1	3	yes	complemented
64	#15688502	C₃²	1	3	yes	complemented
65	#15688502	C₃²	1	3	yes	complemented
66	#15688502	C₃²	1	3	yes	complemented
67	#15688502	C₃²	1	3	yes	complemented
68	#15688502	C₃²	1	3	yes	complemented
69	#15688502	C₃²	1	3	yes	complemented
70	#15688502	C₃²	1	3	yes	complemented
71	#15688502	C₃²	1	3	yes	complemented
72	#15688502	C₃²	1	3	yes	complemented
73	#15688502	C₃²	1	3	yes	complemented
74	C₃×3₋¹⁺²×C₃₇	C₃²	1	3	yes	complemented
75	C₃×H(3,𝔽₃)×C₃₇	C₃²	1	1	yes	characteristic
76	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
77	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
78	C₃₇×C₃²⋊C₉	C₃²	1	1	yes	characteristic
79	C₃₇×C₃²⋊C₉	C₃²	1	3	yes	complemented
80	C₃₇×C₃²⋊C₉	C₃²	1	3	yes	complemented
81	C₃³×C₃₇	C₃³	1	3	yes	—
82	C₃³×C₃₇	C₃³	1	1	yes	characteristic
83	C₃²×C₃₇⋊C₃	—	3	3	no	—
84	C₃²×C₃₇⋊C₃	—	9	1	no	—
85	C₃²×C₃₇⋊C₃	—	9	1	no	—
86	C₃²×C₃₇⋊C₃	—	9	1	no	—
87	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
88	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
89	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
90	C₃²×C₃₇⋊C₃	C₃³	1	3	yes	—
91	C₃²×C₃₇⋊C₃	C₃³	1	3	yes	—
92	3₋¹⁺²×C₃₇	—	9	3	no	—
93	H(3,𝔽₃)×C₃₇	—	3	3	no	—
94	C₃×C₉×C₃₇	—	9	1	no	—
95	C₃×C₉×C₃₇	C₃³	1	3	yes	—
96	C₃×C₉×C₃₇	C₃³	1	3	yes	—
97	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
98	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
99	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
100	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
101	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
102	C₃²⋊(C₃₇⋊C₃)	—	9	3	no	—
103	C₃²⋊(C₃₇⋊C₃)	—	9	3	no	—
104	C₃²⋊(C₃₇⋊C₃)	—	9	3	no	—
105	#11758608	—	9	3	no	—
106	C₃×#66524	—	9	1	no	—
107	C₃×#66524	—	9	1	no	—
108	C₃×#66524	—	9	3	no	—
109	C₃×#66524	C₃³	1	1	yes	characteristic
110	C₃×#66524	C₃³	1	1	yes	characteristic
111	C₃×#66524	C₃³	1	1	yes	characteristic
112	C₃×#66524	C₃³	1	1	yes	characteristic
113	C₃×#66524	C₃³	1	1	yes	characteristic
114	C₃×#66524	C₃³	1	1	yes	characteristic
115	C₃×#66524	C₃³	1	3	yes	—
116	C₃×#66524	C₃³	1	3	yes	—
117	C₃×#66524	C₃³	1	3	yes	—
118	C₃×#66524	C₃³	1	3	yes	—
119	#11758606	—	9	3	no	—
120	#11758606	—	9	3	no	—
121	#11758606	—	9	3	no	—
122	#11758605	—	9	3	no	—
123	#11758605	—	9	3	no	—
124	#11758605	—	9	3	no	—
125	C₉×C₃₇⋊C₃	—	9	3	no	—
126	C₉×C₃₇⋊C₃	—	9	3	no	—
127	#10624888	—	37	1	no	maximal, Sylow
128	C₃²×C₃₇	—	3	1	no	—
129	C₃²×C₃₇	—	3	1	no	—
130	C₃²×C₃₇	—	3	1	no	—
131	C₃²×C₃₇	—	3	3	no	—
132	C₃²×C₃₇	—	3	3	no	—
133	C₃²×C₃₇	—	3	3	no	—
134	C₃²×C₃₇	—	3	3	no	—
135	C₃²×C₃₇	#737	1	3	yes	—
136	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
137	C₃×C₃₇⋊C₃	—	3	3	no	—
138	C₃×C₃₇⋊C₃	—	3	3	no	—
139	C₃×C₃₇⋊C₃	—	3	1	no	—
140	C₃×C₃₇⋊C₃	—	3	1	no	—
141	C₃×C₃₇⋊C₃	—	3	1	no	—
142	C₃×C₃₇⋊C₃	—	3	3	no	—
143	C₃×C₃₇⋊C₃	—	3	3	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	3	no	—
150	C₃×C₃₇⋊C₃	—	3	3	no	—
151	C₃×C₃₇⋊C₃	—	3	3	no	—
152	C₃×C₃₇⋊C₃	—	3	3	no	—
153	C₃×C₃₇⋊C₃	—	3	1	no	—
154	C₃×C₃₇⋊C₃	—	3	1	no	—
155	C₃×C₃₇⋊C₃	—	3	1	no	—
156	C₃×C₃₇⋊C₃	—	3	1	no	—
157	C₃×C₃₇⋊C₃	—	9	9	no	—
158	C₉×C₃₇	—	3	3	no	—
159	C₉×C₃₇	—	3	3	no	—
160	C₉×C₃₇	—	3	1	no	—
161	C₉×C₃₇	—	3	1	no	—
162	C₉×C₃₇	—	3	1	no	—
163	#66524	—	3	1	no	—
164	#66524	—	3	1	no	—
165	#66524	—	3	3	no	—
166	#66524	—	3	3	no	—
167	#66524	—	3	3	no	—
168	#66524	—	3	1	no	—
169	#66524	—	3	3	no	—
170	#66524	—	3	1	no	—
171	#66524	—	3	1	no	—
172	#66524	—	3	1	no	—
173	#6893	—	37	3	no	—
174	#6893	—	37	3	no	—
175	#6893	—	37	3	no	—
176	C₉⋊H(3,𝔽₃)	—	37	3	no	—
177	C₉⋊H(3,𝔽₃)	—	37	3	no	—
178	C₉⋊H(3,𝔽₃)	—	37	1	no	—
179	C₉⋊H(3,𝔽₃)	—	37	1	no	—
180	C₉⋊H(3,𝔽₃)	—	37	1	no	—
181	C₉⋊H(3,𝔽₃)	—	37	1	no	—
182	C₉⋊H(3,𝔽₃)	—	37	1	no	—
183	C₉⋊H(3,𝔽₃)	—	37	3	no	—
184	C₉⋊H(3,𝔽₃)	—	37	3	no	—
185	C₉⋊H(3,𝔽₃)	—	37	3	no	—
186	C₉⋊H(3,𝔽₃)	—	37	3	no	—
187	C₉⋊H(3,𝔽₃)	C₃₇⋊C₃	1	1	yes	characteristic, complemented
188	#6891	—	37	1	no	—
189	#6891	—	37	1	no	—
190	C₃²⋊H(3,𝔽₃)	—	37	1	no	—
191	C₉×H(3,𝔽₃)	—	37	1	no	—
192	C₉×H(3,𝔽₃)	—	37	1	no	—
193	C₉×H(3,𝔽₃)	—	37	1	no	—
194	C₃×C₃²⋊C₉	—	37	1	no	—
195	C₃×C₃₇	—	3	3	no	—
196	C₃×C₃₇	—	9	3	no	—
197	C₃×C₃₇	C₃×#737	1	1	yes	characteristic
198	C₃×C₃₇	H(5,𝔽₃)	1	1	yes	characteristic
199	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
200	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
201	C₃₇⋊C₃	—	9	3	no	—
202	C₃₇⋊C₃	—	9	3	no	—
203	C₃₇⋊C₃	—	9	1	no	—
204	C₃₇⋊C₃	—	9	1	no	—
205	C₃₇⋊C₃	—	9	1	no	—
206	C₃⁴	—	37	1	no	—
207	C₃×3₋¹⁺²	—	37	3	no	—
208	C₃×3₋¹⁺²	—	37	3	no	—
209	C₃×3₋¹⁺²	—	37	3	no	—
210	C₃×3₋¹⁺²	—	37	3	no	—
211	C₃×3₋¹⁺²	—	37	3	no	—
212	C₃×3₋¹⁺²	—	37	3	no	—
213	C₃×3₋¹⁺²	—	37	3	no	—
214	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	3	yes	complemented
215	C₃×H(3,𝔽₃)	—	37	3	no	—
216	C₃×H(3,𝔽₃)	—	37	3	no	—
217	C₃×H(3,𝔽₃)	—	37	3	no	—
218	C₃×H(3,𝔽₃)	—	37	1	no	—
219	C₃×H(3,𝔽₃)	—	37	1	no	—
220	C₃×H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	1	yes	characteristic
221	C₃²×C₉	—	37	1	no	—
222	C₃²×C₉	—	37	1	no	—
223	C₃²×C₉	—	37	3	no	—
224	C₃²×C₉	—	37	3	no	—
225	C₃²×C₉	—	37	3	no	—
226	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
227	C₃²⋊C₉	—	37	1	no	—
228	C₃²⋊C₉	—	37	1	no	—
229	C₃²⋊C₉	—	37	1	no	—
230	C₃²⋊C₉	—	37	1	no	—
231	C₃²⋊C₉	—	37	3	no	—
232	C₃²⋊C₉	—	37	3	no	—
233	C₃²⋊C₉	—	37	3	no	—
234	C₃²⋊C₉	—	37	3	no	—
235	C₃²⋊C₉	—	37	1	no	—
236	C₃²⋊C₉	—	37	1	no	—
237	C₃²⋊C₉	—	37	1	no	—
238	C₃²⋊C₉	—	37	1	no	—
239	C₃²⋊C₉	—	37	1	no	—
240	C₃²⋊C₉	—	37	1	no	—
241	C₃²⋊C₉	—	37	1	no	—
242	C₃²⋊C₉	—	37	1	no	—
243	C₃²⋊C₉	—	37	1	no	—
244	C₃²⋊C₉	—	37	3	no	—
245	C₃²⋊C₉	—	37	3	no	—
246	C₃²⋊C₉	—	37	3	no	—
247	C₃²⋊C₉	—	37	3	no	—
248	C₃²⋊C₉	—	37	3	no	—
249	C₃²⋊C₉	—	37	3	no	—
250	C₃²⋊C₉	—	37	3	no	—
251	C₃²⋊C₉	—	37	3	no	—
252	C₃²⋊C₉	—	37	3	no	—
253	C₃²⋊C₉	—	37	3	no	—
254	C₃²⋊C₉	—	37	3	no	—
255	C₃²⋊C₉	—	37	3	no	—
256	C₃²⋊C₉	—	37	3	no	—
257	C₃²⋊C₉	—	37	3	no	—
258	C₃²⋊C₉	—	37	3	no	—
259	C₃²⋊C₉	—	37	3	no	—
260	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
261	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
262	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	3	yes	complemented
263	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	3	yes	complemented
264	C₃₇	#10624888	1	1	yes	characteristic, complemented, Sylow
265	C₃³	—	37	1	no	—
266	C₃³	—	37	3	no	—
267	C₃³	—	37	3	no	—
268	C₃³	—	37	1	no	—
269	C₃³	—	37	1	no	—
270	C₃³	—	333	1	no	—
271	C₃³	—	333	1	no	—
272	C₃³	—	333	1	no	—
273	C₃³	—	111	3	no	—
274	C₃³	C₃²×C₃₇⋊C₃	1	3	yes	—
275	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
276	3₋¹⁺²	—	9	3	no	—
277	3₋¹⁺²	—	333	3	no	—
278	3₋¹⁺²	—	333	3	no	—
279	3₋¹⁺²	—	333	3	no	—
280	3₋¹⁺²	—	333	3	no	—
281	3₋¹⁺²	—	333	3	no	—
282	3₋¹⁺²	—	333	3	no	—
283	3₋¹⁺²	—	333	3	no	—
284	H(3,𝔽₃)	—	3	3	no	—
285	H(3,𝔽₃)	—	333	3	no	—
286	H(3,𝔽₃)	—	333	3	no	—
287	H(3,𝔽₃)	—	333	3	no	—
288	H(3,𝔽₃)	—	111	3	no	—
289	H(3,𝔽₃)	—	111	3	no	—
290	C₃×C₉	—	9	1	no	—
291	C₃×C₉	—	37	1	no	—
292	C₃×C₉	—	37	1	no	—
293	C₃×C₉	—	37	1	no	—
294	C₃×C₉	—	37	1	no	—
295	C₃×C₉	—	37	1	no	—
296	C₃×C₉	—	37	1	no	—
297	C₃×C₉	—	37	3	no	—
298	C₃×C₉	—	37	3	no	—
299	C₃×C₉	—	37	3	no	—
300	C₃×C₉	—	37	3	no	—
301	C₃×C₉	—	333	3	no	—
302	C₃×C₉	—	333	3	no	—
303	C₃×C₉	—	333	1	no	—
304	C₃×C₉	—	333	3	no	—
305	C₃×C₉	—	333	1	no	—
306	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
307	C₃×C₉	C₃²×C₃₇⋊C₃	1	3	yes	—
308	C₃×C₉	C₃²×C₃₇⋊C₃	1	3	yes	—
309	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
310	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
311	C₃²	—	3	1	no	—
312	C₃²	—	3	1	no	—
313	C₃²	—	3	1	no	—
314	C₃²	—	3	3	no	—
315	C₃²	—	3	3	no	—
316	C₃²	—	3	3	no	—
317	C₃²	—	3	3	no	—
318	C₃²	—	333	9	no	—
319	C₃²	—	111	3	no	—
320	C₃²	—	111	3	no	—
321	C₃²	—	111	1	no	—
322	C₃²	—	111	1	no	—
323	C₃²	—	111	1	no	—
324	C₃²	—	111	3	no	—
325	C₃²	—	111	3	no	—
326	C₃²	—	111	1	no	—
327	C₃²	—	111	1	no	—
328	C₃²	—	111	1	no	—
329	C₃²	—	111	1	no	—
330	C₃²	—	111	3	no	—
331	C₃²	—	111	3	no	—
332	C₃²	—	111	1	no	—
333	C₃²	—	111	1	no	—
334	C₃²	—	111	1	no	—
335	C₃²	—	111	3	no	—
336	C₃²	—	111	3	no	—
337	C₃²	—	111	1	no	—
338	C₃²	—	111	1	no	—
339	C₃²	#15688532	1	3	yes	—
340	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
341	C₉	—	3	1	no	—
342	C₉	—	3	1	no	—
343	C₉	—	3	1	no	—
344	C₉	—	3	3	no	—
345	C₉	—	3	3	no	—
346	C₉	—	111	1	no	—
347	C₉	—	111	1	no	—
348	C₉	—	111	1	no	—
349	C₉	—	111	3	no	—
350	C₉	—	111	3	no	—
351	C₉	—	111	1	no	—
352	C₉	—	111	3	no	—
353	C₉	—	111	1	no	—
354	C₉	—	111	3	no	—
355	C₉	—	111	1	no	—
356	C₃	—	3	3	no	—
357	C₃	—	9	3	no	—
358	C₃	—	333	1	no	—
359	C₃	—	333	1	no	—
360	C₃	—	333	1	no	—
361	C₃	—	333	3	no	—
362	C₃	—	333	3	no	—
363	C₃	C₃×#15688532	1	1	yes	characteristic
364	C₃	C₃₇⋊H(5,𝔽₃)	1	1	yes	characteristic
365	C₃	#22582677	1	1	yes	characteristic
366	C₃	#22582678	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₃₇⋊C₃
commutator, socle, cosocle	C₃²×C₃₇	C₃⁴
Fitting	C₃₇×C₉⋊H(3,𝔽₃)	C₃
prime radical	(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	C₃
hypercenter	C₉⋊H(3,𝔽₃)	C₃₇⋊C₃
hypocenter	C₃₇	#10624888
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ C₉⋊H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. #22582565	C₃	semidirect
2. #22582563	C₃	semidirect
3. #22582563	C₃	semidirect
4. #22582561	C₃	semidirect
5. #22582561	C₃	semidirect
6. #22582560	C₃	semidirect
7. #22582560	C₃	semidirect
8. #22582559	C₃	semidirect
9. #22582558	C₃	semidirect
10. #22582557	C₃	semidirect
11. #22582557	C₃	semidirect
12. #22582556	C₃	semidirect
13. #22582555	C₃	semidirect
14. #22582555	C₃	semidirect
15. #22582553	C₃	semidirect
16. #22582552	C₃	semidirect
18. H(3,𝔽₃)×#66524	C₃	semidirect
19. #22582539	C₃	semidirect
20. #22582539	C₃	semidirect
21. C₃×#15688502	C₃	semidirect
22. C₃₇×C₉⋊H(3,𝔽₃)	C₃	semidirect
24. C₃×#11758608	C₃²	semidirect
26. C₃×#11758605	C₃²	semidirect
27. C₃×#11758605	C₃²	semidirect
29. C₃×#11758606	C₃²	semidirect
30. C₃×#11758606	C₃²	semidirect
38. C₃²×#66524	C₃²	semidirect
39. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
40. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
45. C₃²⋊#66524	C₃²	semidirect
46. C₃²⋊#66524	C₃²	semidirect
47. C₃²⋊#66524	C₃²	semidirect
48. C₃²⋊#66524	C₃²	semidirect
62. #15688502	C₃²	semidirect
63. #15688502	C₃²	semidirect
64. #15688502	C₃²	semidirect
65. #15688502	C₃²	semidirect
66. #15688502	C₃²	semidirect
67. #15688502	C₃²	semidirect
68. #15688502	C₃²	semidirect
69. #15688502	C₃²	semidirect
70. #15688502	C₃²	semidirect
71. #15688502	C₃²	semidirect
72. #15688502	C₃²	semidirect
73. #15688502	C₃²	semidirect
74. C₃×3₋¹⁺²×C₃₇	C₃²	semidirect
79. C₃₇×C₃²⋊C₉	C₃²	semidirect
80. C₃₇×C₃²⋊C₉	C₃²	semidirect
187. C₉⋊H(3,𝔽₃)	C₃₇⋊C₃	semidirect
214. C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	semidirect
262. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
263. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
264. C₃₇	#10624888	semidirect

Maximal subgroups

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

subgroup	index
#22582565	3
#22582563	3
#22582561	3
#22582560	3
#22582559	3
#22582558	3
#22582557	3
#22582556	3
#22582555	3
#22582553	3
#22582552	3
(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	3
H(3,𝔽₃)×#66524	3
#22582539	3
C₃×#15688502	3
C₃₇×C₉⋊H(3,𝔽₃)	3
#10624888	37