Subgroups — #28356116

Order 13851.

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	#17987455	C₃	1	2	yes	maximal, complemented
2	#17987455	C₃	1	2	yes	maximal, complemented
3	#17987455	C₃	1	2	yes	maximal, complemented
4	#17987455	C₃	1	2	yes	maximal, complemented
5	#17987454	C₃	1	1	yes	maximal, characteristic, complemented
6	#17987452	C₃	1	2	yes	maximal, complemented
7	#17987452	C₃	1	2	yes	maximal, complemented
8	#17987452	C₃	1	2	yes	maximal, complemented
9	#17987452	C₃	1	2	yes	maximal, complemented
10	#17987451	C₃	1	2	yes	maximal, complemented
11	#17987450	C₃	1	2	yes	maximal, complemented
12	#17987449	C₃	1	2	yes	maximal, complemented
13	#17987449	C₃	1	2	yes	maximal, complemented
14	#17987448	C₃	1	1	yes	maximal, characteristic, complemented
15	#17987436	C₃	1	2	yes	maximal, complemented
16	#17987436	C₃	1	2	yes	maximal, complemented
17	#17987433	C₃	1	2	yes	maximal, complemented
18	#17987420	C₃	1	1	yes	maximal, characteristic
19	#17987419	C₃	1	1	yes	maximal, characteristic
20	#17987419	C₃	1	1	yes	maximal, characteristic
21	C₉×#10587023	C₃	1	1	yes	maximal, characteristic, complemented
22	#17987409	C₃	1	2	yes	maximal, complemented
23	C₁₉⋊C₃×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
24	C₁₉×#6897	C₃	1	1	yes	maximal, characteristic, complemented
25	C₃³×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
26	C₃×#10587022	C₃²	1	1	yes	characteristic
27	C₃×#10587022	C₃²	1	2	yes	—
28	C₃×#10587023	C₃²	1	2	yes	—
29	C₃×#10587023	C₃²	1	1	yes	characteristic
30	C₃×#10587023	C₃²	1	1	yes	characteristic
31	C₃×#10587023	C₃²	1	2	yes	—
32	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
33	C₃×C₉×C₁₉⋊C₃	C₃²	1	2	yes	—
34	#13095307	C₃²	1	2	yes	complemented
35	#13095307	C₃²	1	2	yes	complemented
36	#13095307	C₃²	1	2	yes	complemented
37	#13095307	C₃²	1	2	yes	complemented
38	#13095306	C₃²	1	2	yes	complemented
39	#13095306	C₃²	1	2	yes	complemented
40	#13095306	C₃²	1	2	yes	complemented
41	#13095306	C₃²	1	2	yes	complemented
42	#13095305	C₃²	1	2	yes	complemented
43	#13095305	C₃²	1	2	yes	complemented
44	#13095305	C₃²	1	2	yes	complemented
45	#13095305	C₃²	1	2	yes	complemented
46	#13095305	C₃²	1	2	yes	complemented
47	#13095305	C₃²	1	2	yes	complemented
48	#13095305	C₃²	1	2	yes	complemented
49	#13095305	C₃²	1	2	yes	complemented
50	#13095305	C₃²	1	2	yes	complemented
51	#13095305	C₃²	1	2	yes	complemented
52	#13095305	C₃²	1	2	yes	complemented
53	#13095305	C₃²	1	2	yes	complemented
54	#13095305	C₃²	1	2	yes	complemented
55	#13095305	C₃²	1	2	yes	complemented
56	#13095305	C₃²	1	2	yes	complemented
57	#13095305	C₃²	1	2	yes	complemented
58	#13095305	C₃²	1	2	yes	complemented
59	#13095305	C₃²	1	2	yes	complemented
60	#13095305	C₃²	1	2	yes	complemented
61	#13095305	C₃²	1	2	yes	complemented
62	#13095305	C₃²	1	2	yes	complemented
63	#13095305	C₃²	1	2	yes	complemented
64	#13095305	C₃²	1	2	yes	complemented
65	#13095305	C₃²	1	2	yes	complemented
66	C₃²⋊#4294	C₃²	1	2	yes	—
67	C₃²⋊#4294	C₃²	1	2	yes	—
68	C₃²⋊#4294	C₃²	1	2	yes	—
69	C₃²⋊#4294	C₃²	1	2	yes	—
70	#13095303	C₃²	1	1	yes	characteristic
71	#13095303	C₃²	1	2	yes	—
72	#13095303	C₃²	1	1	yes	characteristic
73	#13095303	C₃²	1	2	yes	—
74	#13095303	C₃²	1	2	yes	—
75	#13095303	C₃²	1	2	yes	—
76	#13095303	C₃²	1	1	yes	characteristic
77	#13095303	C₃²	1	1	yes	characteristic
78	#13095303	C₃²	1	1	yes	characteristic
79	#13095303	C₃²	1	2	yes	—
80	#13095303	C₃²	1	1	yes	characteristic
81	#13095303	C₃²	1	1	yes	characteristic
82	#13095303	C₃²	1	2	yes	—
83	#13095303	C₃²	1	2	yes	—
84	#13095303	C₃²	1	1	yes	characteristic
85	#13095303	C₃²	1	2	yes	—
86	C₉×#4294	C₃²	1	2	yes	complemented
87	C₉×#4294	C₃²	1	2	yes	complemented
88	C₉×#4294	C₃²	1	2	yes	complemented
89	C₉×#4294	C₃²	1	2	yes	complemented
90	C₁₉×C₉⋊C₉	C₃²	1	2	yes	complemented
91	C₁₉×C₉⋊C₉	C₃²	1	2	yes	complemented
92	C₁₉×C₉⋊C₉	C₃²	1	2	yes	complemented
93	C₁₉×C₉⋊C₉	C₃²	1	2	yes	complemented
94	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
95	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
96	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
97	C₁₉×C₃²⋊C₉	C₃²	1	1	yes	characteristic
98	C₉²×C₁₉	C₃²	1	1	yes	characteristic, complemented
99	#10624889	—	19	1	no	maximal, Sylow
100	C₃³×C₁₉	C₃³	1	1	yes	characteristic
101	C₃²×C₁₉⋊C₃	—	3	3	no	—
102	C₃²×C₁₉⋊C₃	—	9	1	no	—
103	C₃²×C₁₉⋊C₃	—	9	1	no	—
104	C₃²×C₁₉⋊C₃	—	9	1	no	—
105	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
106	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
107	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
108	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
109	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
110	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
111	C₃×C₉×C₁₉	C₃³	1	1	yes	characteristic
112	C₃×C₉×C₁₉	C₃³	1	2	yes	—
113	C₃×C₉×C₁₉	C₃³	1	2	yes	—
114	C₃×C₉×C₁₉	C₃³	1	2	yes	—
115	C₃×C₉×C₁₉	C₃³	1	2	yes	—
116	C₃×#4294	C₃³	1	2	yes	—
117	C₃×#4294	C₃³	1	2	yes	—
118	C₃×#4294	C₃³	1	2	yes	—
119	C₃×#4294	C₃³	1	2	yes	—
120	C₃×#4294	C₃³	1	2	yes	—
121	C₃×#4294	C₃³	1	2	yes	—
122	C₃×#4294	C₃³	1	2	yes	—
123	C₃×#4294	C₃³	1	2	yes	—
124	C₃×#4294	C₃³	1	2	yes	—
125	C₃×#4294	C₃³	1	2	yes	—
126	C₃×#4294	C₃³	1	2	yes	—
127	C₃×#4294	C₃³	1	2	yes	—
128	#10587023	—	3	6	no	—
129	#10587023	—	3	3	no	—
130	#10587023	—	9	1	no	—
131	#10587023	—	9	2	no	—
132	#10587022	—	9	1	no	—
133	#10587022	—	9	2	no	—
134	C₉×C₁₉⋊C₃	—	9	1	no	—
135	C₉×C₁₉⋊C₃	—	9	2	no	—
136	#6897	—	19	2	no	—
137	#6897	—	19	2	no	—
138	#6897	—	19	2	no	—
139	#6897	—	19	2	no	—
140	#6897	—	19	2	no	—
141	#6897	—	19	2	no	—
142	#6897	—	19	2	no	—
143	#6897	—	19	2	no	—
144	#6897	—	19	1	no	—
145	#6897	C₁₉⋊C₃	1	1	yes	characteristic, complemented
146	#6896	—	19	2	no	—
147	#6896	—	19	2	no	—
148	#6896	—	19	2	no	—
149	#6896	—	19	2	no	—
150	#6896	—	19	1	no	—
151	#6894	—	19	2	no	—
152	#6894	—	19	2	no	—
153	#6894	—	19	2	no	—
154	#6891	—	19	1	no	—
155	#6891	—	19	1	no	—
156	#6891	—	19	1	no	—
157	C₉×3₋¹⁺²	—	19	2	no	—
158	C₉×3₋¹⁺²	—	19	1	no	—
159	C₃×C₃²⋊C₉	—	19	1	no	—
160	C₃²×C₁₉	—	3	1	no	—
161	C₃²×C₁₉	—	3	1	no	—
162	C₃²×C₁₉	—	3	1	no	—
163	C₃²×C₁₉	—	3	1	no	—
164	C₃²×C₁₉	C₃⁴	1	1	yes	characteristic
165	C₃×C₁₉⋊C₃	—	3	1	no	—
166	C₃×C₁₉⋊C₃	—	3	1	no	—
167	C₃×C₁₉⋊C₃	—	3	1	no	—
168	C₃×C₁₉⋊C₃	—	3	1	no	—
169	C₃×C₁₉⋊C₃	—	3	1	no	—
170	C₃×C₁₉⋊C₃	—	3	1	no	—
171	C₃×C₁₉⋊C₃	—	3	1	no	—
172	C₃×C₁₉⋊C₃	—	3	1	no	—
173	C₃×C₁₉⋊C₃	—	3	1	no	—
174	C₃×C₁₉⋊C₃	—	3	1	no	—
175	C₃×C₁₉⋊C₃	—	3	1	no	—
176	C₃×C₁₉⋊C₃	—	9	9	no	—
177	C₃×C₁₉⋊C₃	#737	1	3	yes	—
178	C₉×C₁₉	—	3	1	no	—
179	C₉×C₁₉	—	3	2	no	—
180	C₉×C₁₉	—	3	1	no	—
181	C₉×C₁₉	—	3	2	no	—
182	C₉×C₁₉	—	3	1	no	—
183	C₉×C₁₉	—	3	2	no	—
184	C₉×C₁₉	—	3	1	no	—
185	C₉×C₁₉	—	3	2	no	—
186	#4294	—	3	2	no	—
187	#4294	—	3	2	no	—
188	#4294	—	3	2	no	—
189	#4294	—	3	2	no	—
190	#4294	—	3	2	no	—
191	#4294	—	3	2	no	—
192	#4294	—	3	2	no	—
193	#4294	—	3	2	no	—
194	#4294	—	3	2	no	—
195	#4294	—	3	2	no	—
196	#4294	—	3	2	no	—
197	#4294	—	3	2	no	—
198	C₃⁴	—	19	1	no	—
199	C₃×3₋¹⁺²	—	19	2	no	—
200	C₃×3₋¹⁺²	—	19	1	no	—
201	C₃×3₋¹⁺²	—	19	2	no	—
202	C₃×3₋¹⁺²	—	19	1	no	—
203	C₃×3₋¹⁺²	—	19	2	no	—
204	C₃×3₋¹⁺²	—	19	1	no	—
205	C₃²×C₉	—	19	1	no	—
206	C₃²×C₉	—	19	2	no	—
207	C₉⋊C₉	—	19	2	no	—
208	C₉⋊C₉	—	19	2	no	—
209	C₉⋊C₉	—	19	2	no	—
210	C₉⋊C₉	—	19	2	no	—
211	C₉⋊C₉	—	19	2	no	—
212	C₉⋊C₉	—	19	2	no	—
213	C₉⋊C₉	—	19	2	no	—
214	C₉⋊C₉	—	19	2	no	—
215	C₉⋊C₉	—	19	2	no	—
216	C₉⋊C₉	—	19	2	no	—
217	C₉⋊C₉	—	19	2	no	—
218	C₉⋊C₉	—	19	2	no	—
219	C₉⋊C₉	—	19	2	no	—
220	C₉⋊C₉	—	19	2	no	—
221	C₉⋊C₉	—	19	2	no	—
222	C₉⋊C₉	—	19	2	no	—
223	C₉⋊C₉	—	19	2	no	—
224	C₉⋊C₉	—	19	2	no	—
225	C₉⋊C₉	—	19	2	no	—
226	C₉⋊C₉	—	19	2	no	—
227	C₉⋊C₉	—	19	2	no	—
228	C₉⋊C₉	—	19	2	no	—
229	C₉⋊C₉	—	19	2	no	—
230	C₉⋊C₉	—	19	2	no	—
231	C₉⋊C₉	—	19	2	no	—
232	C₉⋊C₉	—	19	2	no	—
233	C₉⋊C₉	—	19	2	no	—
234	C₉⋊C₉	—	19	2	no	—
235	C₉⋊C₉	—	19	2	no	—
236	C₉⋊C₉	—	19	2	no	—
237	C₉⋊C₉	—	19	2	no	—
238	C₉⋊C₉	—	19	2	no	—
239	C₉⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
240	C₉⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
241	C₉⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
242	C₉⋊C₉	C₃×C₁₉⋊C₃	1	2	yes	complemented
243	C₃²⋊C₉	—	19	2	no	—
244	C₃²⋊C₉	—	19	2	no	—
245	C₃²⋊C₉	—	19	2	no	—
246	C₃²⋊C₉	—	19	2	no	—
247	C₃²⋊C₉	—	19	2	no	—
248	C₃²⋊C₉	—	19	1	no	—
249	C₃²⋊C₉	—	19	2	no	—
250	C₃²⋊C₉	—	19	1	no	—
251	C₃²⋊C₉	—	19	2	no	—
252	C₃²⋊C₉	—	19	2	no	—
253	C₃²⋊C₉	—	19	1	no	—
254	C₃²⋊C₉	—	19	1	no	—
255	C₃²⋊C₉	—	19	2	no	—
256	C₃²⋊C₉	—	19	1	no	—
257	C₃²⋊C₉	—	19	2	no	—
258	C₃²⋊C₉	—	19	2	no	—
259	C₃²⋊C₉	—	19	2	no	—
260	C₃²⋊C₉	—	19	1	no	—
261	C₃²⋊C₉	—	19	1	no	—
262	C₃²⋊C₉	—	19	1	no	—
263	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
264	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
265	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
266	C₃²⋊C₉	C₃×C₁₉⋊C₃	1	1	yes	characteristic
267	C₉²	—	19	2	no	—
268	C₉²	—	19	2	no	—
269	C₉²	—	19	2	no	—
270	C₉²	—	19	2	no	—
271	C₉²	C₃×C₁₉⋊C₃	1	1	yes	characteristic, complemented
272	C₃×C₁₉	—	9	1	no	—
273	C₃×C₁₉	C₃×#737	1	1	yes	characteristic
274	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
275	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
276	C₃×C₁₉	3₋¹⁺⁴	1	1	yes	characteristic
277	C₁₉⋊C₃	—	3	3	no	—
278	C₁₉⋊C₃	—	9	1	no	—
279	C₁₉⋊C₃	—	9	1	no	—
280	C₃³	—	19	1	no	—
281	C₃³	—	19	1	no	—
282	C₃³	—	19	1	no	—
283	C₃³	—	57	3	no	—
284	C₃³	—	171	1	no	—
285	C₃³	—	171	1	no	—
286	C₃³	—	171	1	no	—
287	C₃³	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
288	3₋¹⁺²	—	57	6	no	—
289	3₋¹⁺²	—	57	3	no	—
290	3₋¹⁺²	—	171	2	no	—
291	3₋¹⁺²	—	171	1	no	—
292	3₋¹⁺²	—	171	2	no	—
293	3₋¹⁺²	—	171	1	no	—
294	C₃×C₉	—	19	2	no	—
295	C₃×C₉	—	19	2	no	—
296	C₃×C₉	—	19	2	no	—
297	C₃×C₉	—	19	2	no	—
298	C₃×C₉	—	19	2	no	—
299	C₃×C₉	—	19	2	no	—
300	C₃×C₉	—	19	2	no	—
301	C₃×C₉	—	19	2	no	—
302	C₃×C₉	—	19	2	no	—
303	C₃×C₉	—	19	2	no	—
304	C₃×C₉	—	19	2	no	—
305	C₃×C₉	—	19	2	no	—
306	C₃×C₉	—	171	1	no	—
307	C₃×C₉	—	171	2	no	—
308	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
309	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
310	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
311	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
312	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
313	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
314	C₃×C₉	C₃²×C₁₉⋊C₃	1	1	yes	characteristic
315	C₃×C₉	C₃²×C₁₉⋊C₃	1	2	yes	—
316	C₁₉	#10624889	1	1	yes	characteristic, complemented, Sylow
317	C₃²	—	3	1	no	—
318	C₃²	—	3	1	no	—
319	C₃²	—	3	1	no	—
320	C₃²	—	3	1	no	—
321	C₃²	—	19	3	no	—
322	C₃²	—	57	1	no	—
323	C₃²	—	57	1	no	—
324	C₃²	—	57	1	no	—
325	C₃²	—	57	1	no	—
326	C₃²	—	57	1	no	—
327	C₃²	—	57	1	no	—
328	C₃²	—	57	1	no	—
329	C₃²	—	57	1	no	—
330	C₃²	—	57	1	no	—
331	C₃²	—	57	1	no	—
332	C₃²	—	57	1	no	—
333	C₃²	—	171	9	no	—
334	C₃²	C₃³×C₁₉⋊C₃	1	1	yes	characteristic
335	C₉	—	3	2	no	—
336	C₉	—	3	1	no	—
337	C₉	—	3	1	no	—
338	C₉	—	3	2	no	—
339	C₉	—	3	2	no	—
340	C₉	—	3	1	no	—
341	C₉	—	3	2	no	—
342	C₉	—	3	1	no	—
343	C₉	—	57	2	no	—
344	C₉	—	57	2	no	—
345	C₉	—	57	2	no	—
346	C₉	—	57	2	no	—
347	C₉	—	57	2	no	—
348	C₉	—	57	2	no	—
349	C₉	—	57	2	no	—
350	C₉	—	57	2	no	—
351	C₉	—	57	2	no	—
352	C₉	—	57	2	no	—
353	C₉	—	57	2	no	—
354	C₉	—	57	2	no	—
355	C₃	—	9	1	no	—
356	C₃	—	57	3	no	—
357	C₃	—	171	1	no	—
358	C₃	—	171	1	no	—
359	C₃	C₁₉⋊C₃×#737	1	1	yes	characteristic
360	C₃	#17987544	1	1	yes	characteristic
361	C₃	#17987544	1	1	yes	characteristic
362	C₃	#17987545	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃³×C₁₉⋊C₃
commutator, socle, cosocle	C₃²×C₁₉	C₃⁴
Fitting	C₁₉×#6897	C₃
prime radical	C₃³×C₁₉⋊C₃	C₃²
hypercenter	#6897	C₁₉⋊C₃
hypocenter	C₁₉	#10624889
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ #6897

Complements

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

N	H ≅ G/N	type
1. #17987455	C₃	semidirect
2. #17987455	C₃	semidirect
3. #17987455	C₃	semidirect
4. #17987455	C₃	semidirect
5. #17987454	C₃	semidirect
6. #17987452	C₃	semidirect
7. #17987452	C₃	semidirect
8. #17987452	C₃	semidirect
9. #17987452	C₃	semidirect
10. #17987451	C₃	semidirect
11. #17987450	C₃	semidirect
12. #17987449	C₃	semidirect
13. #17987449	C₃	semidirect
14. #17987448	C₃	semidirect
15. #17987436	C₃	semidirect
16. #17987436	C₃	semidirect
17. #17987433	C₃	semidirect
21. C₉×#10587023	C₃	semidirect
22. #17987409	C₃	semidirect
24. C₁₉×#6897	C₃	semidirect
34. #13095307	C₃²	semidirect
35. #13095307	C₃²	semidirect
36. #13095307	C₃²	semidirect
37. #13095307	C₃²	semidirect
38. #13095306	C₃²	semidirect
39. #13095306	C₃²	semidirect
40. #13095306	C₃²	semidirect
41. #13095306	C₃²	semidirect
42. #13095305	C₃²	semidirect
43. #13095305	C₃²	semidirect
44. #13095305	C₃²	semidirect
45. #13095305	C₃²	semidirect
46. #13095305	C₃²	semidirect
47. #13095305	C₃²	semidirect
48. #13095305	C₃²	semidirect
49. #13095305	C₃²	semidirect
50. #13095305	C₃²	semidirect
51. #13095305	C₃²	semidirect
52. #13095305	C₃²	semidirect
53. #13095305	C₃²	semidirect
54. #13095305	C₃²	semidirect
55. #13095305	C₃²	semidirect
56. #13095305	C₃²	semidirect
57. #13095305	C₃²	semidirect
58. #13095305	C₃²	semidirect
59. #13095305	C₃²	semidirect
60. #13095305	C₃²	semidirect
61. #13095305	C₃²	semidirect
62. #13095305	C₃²	semidirect
63. #13095305	C₃²	semidirect
64. #13095305	C₃²	semidirect
65. #13095305	C₃²	semidirect
86. C₉×#4294	C₃²	semidirect
87. C₉×#4294	C₃²	semidirect
88. C₉×#4294	C₃²	semidirect
89. C₉×#4294	C₃²	semidirect
90. C₁₉×C₉⋊C₉	C₃²	semidirect
91. C₁₉×C₉⋊C₉	C₃²	semidirect
92. C₁₉×C₉⋊C₉	C₃²	semidirect
93. C₁₉×C₉⋊C₉	C₃²	semidirect
98. C₉²×C₁₉	C₃²	semidirect
145. #6897	C₁₉⋊C₃	semidirect
239. C₉⋊C₉	C₃×C₁₉⋊C₃	semidirect
240. C₉⋊C₉	C₃×C₁₉⋊C₃	semidirect
241. C₉⋊C₉	C₃×C₁₉⋊C₃	semidirect
242. C₉⋊C₉	C₃×C₁₉⋊C₃	semidirect
271. C₉²	C₃×C₁₉⋊C₃	semidirect
316. C₁₉	#10624889	semidirect

Maximal subgroups

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

subgroup	index
#17987455	3
#17987454	3
#17987452	3
#17987451	3
#17987450	3
#17987449	3
#17987448	3
#17987436	3
#17987433	3
#17987420	3
#17987419	3
C₉×#10587023	3
#17987409	3
C₁₉⋊C₃×C₃²⋊C₉	3
C₁₉×#6897	3
#10624889	19