Subgroups — #41007814

Order 26973.

1082 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688532	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×#15688531	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#15688530	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×3₋¹⁺²×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	#22582565	C₃	1	1	yes	maximal, characteristic, complemented
6	#22582565	C₃	1	1	yes	maximal, characteristic, complemented
7	#22582565	C₃	1	1	yes	maximal, characteristic, complemented
8	#22582564	C₃	1	1	yes	maximal, characteristic, complemented
9	#22582562	C₃	1	1	yes	maximal, characteristic, complemented
10	#22582561	C₃	1	3	yes	maximal, complemented
11	#22582560	C₃	1	3	yes	maximal, complemented
12	#22582557	C₃	1	3	yes	maximal, complemented
13	#22582557	C₃	1	3	yes	maximal, complemented
14	#22582557	C₃	1	3	yes	maximal, complemented
15	#22582557	C₃	1	3	yes	maximal, complemented
16	#22582557	C₃	1	3	yes	maximal, complemented
17	#22582557	C₃	1	3	yes	maximal, complemented
18	#22582551	C₃	1	1	yes	maximal, characteristic, complemented
19	(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
20	#22582539	C₃	1	3	yes	maximal, complemented
21	C₃×#15688502	C₃	1	1	yes	maximal, characteristic, complemented
22	C₃₇×#6893	C₃	1	1	yes	maximal, characteristic, complemented
23	C₃³×C₃₇⋊C₃	C₃²	1	1	yes	characteristic
24	#15688532	—	3	9	no	—
25	#15688531	—	3	9	no	—
26	#15688530	—	3	9	no	—
27	C₃×#11758608	C₃²	1	1	yes	characteristic
28	C₃×#11758608	C₃²	1	1	yes	characteristic
29	C₃×#11758608	C₃²	1	1	yes	characteristic
30	C₃×#11758608	C₃²	1	1	yes	characteristic
31	C₃×#11758608	C₃²	1	3	yes	complemented
32	C₃×#11758608	C₃²	1	3	yes	complemented
33	C₃×#11758605	C₃²	1	3	yes	—
34	C₃×#11758605	C₃²	1	3	yes	complemented
35	C₃×#11758605	C₃²	1	3	yes	complemented
36	C₃×#11758606	C₃²	1	3	yes	—
37	C₃×#11758606	C₃²	1	3	yes	complemented
38	C₃×#11758606	C₃²	1	3	yes	complemented
39	3₋¹⁺²×C₃₇⋊C₃	—	3	9	no	—
40	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	3	yes	—
41	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
42	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	1	yes	characteristic
43	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	3	yes	—
44	C₃×C₃²⋊(C₃₇⋊C₃)	C₃²	1	3	yes	—
45	C₃²×#66524	C₃²	1	1	yes	characteristic
46	C₃²×#66524	C₃²	1	1	yes	characteristic
47	C₃²×#66524	C₃²	1	3	yes	complemented
48	C₃×C₉×C₃₇⋊C₃	C₃²	1	3	yes	—
49	C₃×C₉×C₃₇⋊C₃	C₃²	1	3	yes	complemented
50	C₃×C₉×C₃₇⋊C₃	C₃²	1	3	yes	complemented
51	C₃²⋊#66524	C₃²	1	3	yes	complemented
52	C₃²⋊#66524	C₃²	1	3	yes	complemented
53	C₃²⋊#66524	C₃²	1	3	yes	complemented
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	1	yes	characteristic
59	#15688502	C₃²	1	1	yes	characteristic
60	#15688502	C₃²	1	1	yes	characteristic
61	#15688502	C₃²	1	1	yes	characteristic
62	#15688502	C₃²	1	1	yes	characteristic
63	#15688502	C₃²	1	3	yes	—
64	#15688502	C₃²	1	3	yes	—
65	#15688502	C₃²	1	3	yes	—
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	#15688502	C₃²	1	3	yes	complemented
75	#15688502	C₃²	1	3	yes	complemented
76	#15688502	C₃²	1	3	yes	complemented
77	#15688502	C₃²	1	3	yes	complemented
78	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
79	C₃×3₋¹⁺²×C₃₇	C₃²	1	1	yes	characteristic
80	C₃×H(3,𝔽₃)×C₃₇	C₃²	1	1	yes	characteristic
81	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
82	C₃₇×C₃²⋊C₉	C₃²	1	3	yes	complemented
83	C₃₇×C₃²⋊C₉	C₃²	1	3	yes	complemented
84	C₃₇×C₃²⋊C₉	C₃²	1	3	yes	complemented
85	C₃³×C₃₇	C₃³	1	3	yes	—
86	C₃³×C₃₇	C₃³	1	1	yes	characteristic
87	C₃²×C₃₇⋊C₃	—	3	3	no	—
88	C₃²×C₃₇⋊C₃	—	3	3	no	—
89	C₃²×C₃₇⋊C₃	—	9	1	no	—
90	C₃²×C₃₇⋊C₃	—	9	1	no	—
91	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
92	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
93	C₃²×C₃₇⋊C₃	C₃³	1	3	yes	—
94	C₃²×C₃₇⋊C₃	C₃³	1	3	yes	—
95	C₃²×C₃₇⋊C₃	C₃³	1	1	yes	characteristic
96	3₋¹⁺²×C₃₇	—	3	3	no	—
97	3₋¹⁺²×C₃₇	—	3	3	no	—
98	H(3,𝔽₃)×C₃₇	—	3	3	no	—
99	C₃×C₉×C₃₇	—	3	3	no	—
100	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
101	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
102	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
103	C₃×C₉×C₃₇	C₃³	1	3	yes	—
104	C₃×C₉×C₃₇	C₃³	1	3	yes	—
105	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
106	C₃²⋊(C₃₇⋊C₃)	—	3	3	no	—
107	C₃²⋊(C₃₇⋊C₃)	—	3	9	no	—
108	C₃²⋊(C₃₇⋊C₃)	—	9	3	no	—
109	C₃²⋊(C₃₇⋊C₃)	—	9	3	no	—
110	#11758608	—	3	3	no	—
111	#11758608	—	3	3	no	—
112	#11758608	—	3	3	no	—
113	#11758608	—	3	9	no	—
114	#11758608	—	3	9	no	—
115	#11758608	H(3,𝔽₃)	1	9	yes	complemented
116	C₃×#66524	—	3	3	no	—
117	C₃×#66524	—	3	3	no	—
118	C₃×#66524	—	3	9	no	—
119	C₃×#66524	C₃³	1	1	yes	characteristic
120	C₃×#66524	C₃³	1	1	yes	characteristic
121	C₃×#66524	C₃³	1	1	yes	characteristic
122	C₃×#66524	C₃³	1	3	yes	—
123	C₃×#66524	C₃³	1	1	yes	characteristic
124	C₃×#66524	C₃³	1	3	yes	—
125	C₃×#66524	C₃³	1	1	yes	characteristic
126	C₃×#66524	C₃³	1	1	yes	characteristic
127	C₃×#66524	C₃³	1	3	yes	—
128	C₃×#66524	C₃³	1	3	yes	—
129	#11758606	—	3	9	no	—
130	#11758606	—	3	9	no	—
131	#11758606	—	3	9	no	—
132	#11758605	—	3	9	no	—
133	#11758605	—	3	9	no	—
134	#11758605	—	3	9	no	—
135	C₉×C₃₇⋊C₃	—	3	9	no	—
136	C₉×C₃₇⋊C₃	—	3	9	no	—
137	C₉×C₃₇⋊C₃	—	3	9	no	—
138	#10624896	—	37	1	no	maximal, Sylow
139	C₃²×C₃₇	—	3	1	no	—
140	C₃²×C₃₇	—	3	1	no	—
141	C₃²×C₃₇	—	3	1	no	—
142	C₃²×C₃₇	—	3	3	no	—
143	C₃²×C₃₇	—	3	3	no	—
144	C₃²×C₃₇	—	3	3	no	—
145	C₃²×C₃₇	—	3	3	no	—
146	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	3	yes	—
147	C₃²×C₃₇	C₃⁴	1	1	yes	characteristic
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	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	3	no	—
156	C₃×C₃₇⋊C₃	—	3	3	no	—
157	C₃×C₃₇⋊C₃	—	3	1	no	—
158	C₃×C₃₇⋊C₃	—	3	1	no	—
159	C₃×C₃₇⋊C₃	—	3	1	no	—
160	C₃×C₃₇⋊C₃	—	3	1	no	—
161	C₃×C₃₇⋊C₃	—	3	3	no	—
162	C₃×C₃₇⋊C₃	—	3	3	no	—
163	C₃×C₃₇⋊C₃	—	3	3	no	—
164	C₃×C₃₇⋊C₃	—	3	3	no	—
165	C₃×C₃₇⋊C₃	—	3	1	no	—
166	C₃×C₃₇⋊C₃	—	3	1	no	—
167	C₃×C₃₇⋊C₃	—	9	9	no	—
168	C₃×C₃₇⋊C₃	#737	1	3	yes	complemented
169	C₉×C₃₇	—	3	1	no	—
170	C₉×C₃₇	—	3	3	no	—
171	C₉×C₃₇	—	3	3	no	—
172	C₉×C₃₇	—	3	1	no	—
173	C₉×C₃₇	—	3	1	no	—
174	#66524	—	3	1	no	—
175	#66524	—	3	3	no	—
176	#66524	—	3	3	no	—
177	#66524	—	3	1	no	—
178	#66524	—	3	1	no	—
179	#66524	—	3	1	no	—
180	#66524	—	3	1	no	—
181	#66524	—	3	1	no	—
182	#66524	—	3	3	no	—
183	#66524	C₃×H(3,𝔽₃)	1	9	yes	—
184	C₃×#737	—	37	1	no	—
185	C₃×#737	—	37	1	no	—
186	C₃×#737	—	37	1	no	—
187	C₃²×3₋¹⁺²	—	37	1	no	—
188	#6893	—	37	1	no	—
189	#6893	—	37	1	no	—
190	#6893	—	37	1	no	—
191	#6893	—	37	1	no	—
192	#6893	—	37	1	no	—
193	#6893	C₃₇⋊C₃	1	1	yes	characteristic, complemented
194	C₉⋊H(3,𝔽₃)	—	37	3	no	—
195	C₉⋊H(3,𝔽₃)	—	37	3	no	—
196	C₉⋊H(3,𝔽₃)	—	37	3	no	—
197	C₉⋊H(3,𝔽₃)	—	37	3	no	—
198	C₉⋊H(3,𝔽₃)	—	37	3	no	—
199	C₉⋊H(3,𝔽₃)	—	37	3	no	—
200	C₉⋊H(3,𝔽₃)	—	37	3	no	—
201	C₉⋊H(3,𝔽₃)	—	37	3	no	—
202	#6891	—	37	1	no	—
203	C₃²⋊H(3,𝔽₃)	—	37	1	no	—
204	C₉×H(3,𝔽₃)	—	37	3	no	—
205	C₃×C₃²⋊C₉	—	37	1	no	—
206	C₃×C₃₇	—	3	3	no	—
207	C₃×C₃₇	—	9	3	no	—
208	C₃×C₃₇	C₃²×H(3,𝔽₃)	1	1	yes	characteristic
209	C₃×C₃₇	C₃×#737	1	1	yes	characteristic
210	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
211	C₃×C₃₇	3₋¹⁺⁴	1	1	yes	characteristic
212	C₃₇⋊C₃	—	3	3	no	—
213	C₃₇⋊C₃	—	9	3	no	—
214	C₃₇⋊C₃	—	9	3	no	—
215	C₃₇⋊C₃	—	9	1	no	—
216	C₃₇⋊C₃	—	9	1	no	—
217	C₃⁴	—	37	1	no	—
218	#737	—	111	9	no	—
219	#737	—	111	9	no	—
220	#737	—	111	9	no	—
221	C₃×3₋¹⁺²	—	37	1	no	—
222	C₃×3₋¹⁺²	—	37	1	no	—
223	C₃×3₋¹⁺²	—	37	1	no	—
224	C₃×3₋¹⁺²	—	37	1	no	—
225	C₃×3₋¹⁺²	—	37	3	no	—
226	C₃×3₋¹⁺²	—	37	3	no	—
227	C₃×3₋¹⁺²	—	37	3	no	—
228	C₃×3₋¹⁺²	—	37	3	no	—
229	C₃×3₋¹⁺²	—	37	3	no	—
230	C₃×3₋¹⁺²	—	37	3	no	—
231	C₃×3₋¹⁺²	—	37	3	no	—
232	C₃×3₋¹⁺²	—	37	3	no	—
233	C₃×3₋¹⁺²	—	111	9	no	—
234	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
235	C₃×3₋¹⁺²	C₃×C₃₇⋊C₃	1	1	yes	characteristic
236	C₃×H(3,𝔽₃)	—	37	3	no	—
237	C₃×H(3,𝔽₃)	—	37	3	no	—
238	C₃×H(3,𝔽₃)	—	37	1	no	—
239	C₃×H(3,𝔽₃)	—	37	1	no	—
240	C₃×H(3,𝔽₃)	—	37	3	no	—
241	C₃×H(3,𝔽₃)	C₃×C₃₇⋊C₃	1	1	yes	characteristic
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	C₃×C₃₇⋊C₃	1	1	yes	characteristic
249	C₃²⋊C₉	—	37	3	no	—
250	C₃²⋊C₉	—	37	3	no	—
251	C₃²⋊C₉	—	37	3	no	—
252	C₃²⋊C₉	—	37	1	no	—
253	C₃²⋊C₉	—	37	1	no	—
254	C₃²⋊C₉	—	37	1	no	—
255	C₃²⋊C₉	—	37	1	no	—
256	C₃²⋊C₉	—	37	1	no	—
257	C₃²⋊C₉	—	37	1	no	—
258	C₃²⋊C₉	—	37	1	no	—
259	C₃²⋊C₉	—	37	1	no	—
260	C₃²⋊C₉	—	37	1	no	—
261	C₃²⋊C₉	—	37	3	no	—
262	C₃²⋊C₉	—	37	3	no	—
263	C₃²⋊C₉	—	37	3	no	—
264	C₃²⋊C₉	—	37	3	no	—
265	C₃²⋊C₉	—	37	3	no	—
266	C₃²⋊C₉	—	37	3	no	—
267	C₃²⋊C₉	—	37	3	no	—
268	C₃²⋊C₉	—	37	3	no	—
269	C₃²⋊C₉	—	37	3	no	—
270	C₃²⋊C₉	—	37	3	no	—
271	C₃²⋊C₉	—	37	3	no	—
272	C₃²⋊C₉	—	37	3	no	—
273	C₃²⋊C₉	—	37	3	no	—
274	C₃²⋊C₉	—	37	3	no	—
275	C₃²⋊C₉	—	37	3	no	—
276	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	3	yes	complemented
277	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	3	yes	complemented
278	C₃²⋊C₉	C₃×C₃₇⋊C₃	1	3	yes	complemented
279	C₃₇	#10624896	1	1	yes	characteristic, complemented, Sylow
280	C₃³	—	37	1	no	—
281	C₃³	—	37	3	no	—
282	C₃³	—	37	3	no	—
283	C₃³	—	37	1	no	—
284	C₃³	—	37	1	no	—
285	C₃³	—	333	1	no	—
286	C₃³	—	333	1	no	—
287	C₃³	—	111	3	no	—
288	C₃³	—	111	3	no	—
289	C₃³	C₃²×C₃₇⋊C₃	1	3	yes	—
290	C₃³	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
291	3₋¹⁺²	—	3	3	no	—
292	3₋¹⁺²	—	3	3	no	—
293	3₋¹⁺²	—	37	9	no	—
294	3₋¹⁺²	—	111	9	no	—
295	3₋¹⁺²	—	111	9	no	—
296	3₋¹⁺²	—	111	9	no	—
297	3₋¹⁺²	—	111	9	no	—
298	3₋¹⁺²	—	111	9	no	—
299	3₋¹⁺²	—	111	9	no	—
300	3₋¹⁺²	—	111	9	no	—
301	3₋¹⁺²	—	111	9	no	—
302	3₋¹⁺²	—	111	3	no	—
303	3₋¹⁺²	—	111	3	no	—
304	3₋¹⁺²	—	111	3	no	—
305	H(3,𝔽₃)	—	3	3	no	—
306	H(3,𝔽₃)	—	333	3	no	—
307	H(3,𝔽₃)	—	333	3	no	—
308	H(3,𝔽₃)	—	111	9	no	—
309	H(3,𝔽₃)	—	111	3	no	—
310	H(3,𝔽₃)	—	111	3	no	—
311	C₃×C₉	—	3	3	no	—
312	C₃×C₉	—	37	3	no	—
313	C₃×C₉	—	37	1	no	—
314	C₃×C₉	—	37	1	no	—
315	C₃×C₉	—	37	1	no	—
316	C₃×C₉	—	37	1	no	—
317	C₃×C₉	—	37	3	no	—
318	C₃×C₉	—	37	3	no	—
319	C₃×C₉	—	37	1	no	—
320	C₃×C₉	—	37	1	no	—
321	C₃×C₉	—	37	3	no	—
322	C₃×C₉	—	111	9	no	—
323	C₃×C₉	—	111	9	no	—
324	C₃×C₉	—	111	9	no	—
325	C₃×C₉	—	111	9	no	—
326	C₃×C₉	—	111	3	no	—
327	C₃×C₉	—	111	3	no	—
328	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
329	C₃×C₉	C₃²×C₃₇⋊C₃	1	3	yes	—
330	C₃×C₉	C₃²×C₃₇⋊C₃	1	3	yes	—
331	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
332	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
333	C₃²	—	3	1	no	—
334	C₃²	—	3	1	no	—
335	C₃²	—	3	1	no	—
336	C₃²	—	3	3	no	—
337	C₃²	—	3	3	no	—
338	C₃²	—	3	3	no	—
339	C₃²	—	3	3	no	—
340	C₃²	—	37	3	no	—
341	C₃²	—	333	9	no	—
342	C₃²	—	111	3	no	—
343	C₃²	—	111	3	no	—
344	C₃²	—	111	1	no	—
345	C₃²	—	111	1	no	—
346	C₃²	—	111	3	no	—
347	C₃²	—	111	3	no	—
348	C₃²	—	111	1	no	—
349	C₃²	—	111	1	no	—
350	C₃²	—	111	1	no	—
351	C₃²	—	111	3	no	—
352	C₃²	—	111	3	no	—
353	C₃²	—	111	1	no	—
354	C₃²	—	111	1	no	—
355	C₃²	—	111	3	no	—
356	C₃²	—	111	3	no	—
357	C₃²	—	111	1	no	—
358	C₃²	—	111	1	no	—
359	C₃²	—	111	1	no	—
360	C₃²	—	111	1	no	—
361	C₃²	H(3,𝔽₃)×C₃₇⋊C₃	1	3	yes	—
362	C₃²	C₃³×C₃₇⋊C₃	1	1	yes	characteristic
363	C₉	—	3	1	no	—
364	C₉	—	3	1	no	—
365	C₉	—	3	1	no	—
366	C₉	—	3	3	no	—
367	C₉	—	3	3	no	—
368	C₉	—	37	9	no	—
369	C₉	—	111	1	no	—
370	C₉	—	111	1	no	—
371	C₉	—	111	3	no	—
372	C₉	—	111	3	no	—
373	C₉	—	111	3	no	—
374	C₉	—	111	1	no	—
375	C₉	—	111	1	no	—
376	C₉	—	111	1	no	—
377	C₉	—	111	1	no	—
378	C₃	—	3	3	no	—
379	C₃	—	9	3	no	—
380	C₃	—	333	1	no	—
381	C₃	—	333	1	no	—
382	C₃	—	333	3	no	—
383	C₃	—	333	3	no	—
384	C₃	—	111	3	no	—
385	C₃	C₃×H(3,𝔽₃)×C₃₇⋊C₃	1	1	yes	characteristic
386	C₃	#737×C₃₇⋊C₃	1	1	yes	characteristic
387	C₃	#22582677	1	1	yes	characteristic
388	C₃	#22582678	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₃₇⋊C₃
commutator, socle, cosocle	C₃²×C₃₇	C₃⁴
Fitting	C₃₇×#6893	C₃
prime radical	(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	C₃
hypercenter	#6893	C₃₇⋊C₃
hypocenter	C₃₇	#10624896
LCS	G ▷ C₃²×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃² ◁ #6893

Complements

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

N	H ≅ G/N	type
1. C₃×#15688532	C₃	semidirect
2. C₃×#15688531	C₃	semidirect
3. C₃×#15688530	C₃	semidirect
4. C₃×3₋¹⁺²×C₃₇⋊C₃	C₃	semidirect
5. #22582565	C₃	semidirect
6. #22582565	C₃	semidirect
7. #22582565	C₃	semidirect
8. #22582564	C₃	semidirect
9. #22582562	C₃	semidirect
10. #22582561	C₃	semidirect
11. #22582560	C₃	semidirect
12. #22582557	C₃	semidirect
13. #22582557	C₃	semidirect
14. #22582557	C₃	semidirect
15. #22582557	C₃	semidirect
16. #22582557	C₃	semidirect
17. #22582557	C₃	semidirect
18. #22582551	C₃	semidirect
20. #22582539	C₃	semidirect
21. C₃×#15688502	C₃	semidirect
22. C₃₇×#6893	C₃	semidirect
31. C₃×#11758608	C₃²	semidirect
32. C₃×#11758608	C₃²	semidirect
34. C₃×#11758605	C₃²	semidirect
35. C₃×#11758605	C₃²	semidirect
37. C₃×#11758606	C₃²	semidirect
38. C₃×#11758606	C₃²	semidirect
47. C₃²×#66524	C₃²	semidirect
49. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
50. C₃×C₉×C₃₇⋊C₃	C₃²	semidirect
51. C₃²⋊#66524	C₃²	semidirect
52. C₃²⋊#66524	C₃²	semidirect
53. C₃²⋊#66524	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. #15688502	C₃²	semidirect
75. #15688502	C₃²	semidirect
76. #15688502	C₃²	semidirect
77. #15688502	C₃²	semidirect
82. C₃₇×C₃²⋊C₉	C₃²	semidirect
83. C₃₇×C₃²⋊C₉	C₃²	semidirect
84. C₃₇×C₃²⋊C₉	C₃²	semidirect
115. #11758608	H(3,𝔽₃)	semidirect
168. C₃×C₃₇⋊C₃	#737	semidirect
193. #6893	C₃₇⋊C₃	semidirect
276. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
277. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
278. C₃²⋊C₉	C₃×C₃₇⋊C₃	semidirect
279. C₃₇	#10624896	semidirect

Maximal subgroups

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

subgroup	index
C₃×#15688532	3
C₃×#15688531	3
C₃×#15688530	3
C₃×3₋¹⁺²×C₃₇⋊C₃	3
#22582565	3
#22582564	3
#22582562	3
#22582561	3
#22582560	3
#22582557	3
#22582551	3
(C₃×C₃₇⋊C₃)⋊H(3,𝔽₃)	3
#22582539	3
C₃×#15688502	3
C₃₇×#6893	3
#10624896	37