Subgroups — C₉×#4785 #13141768

Order 1728.

446 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	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₉×#213	C₂	1	1	yes	maximal, characteristic
3	C₉×#893	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
5	C₉×#821	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#815	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#808	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#4785	C₃	1	1	yes	maximal, characteristic
9	C₉×#442	—	3	1	no	maximal
10	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₉×Dic₃	—	2	1	no	—
12	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃×C₉	—	2	1	no	—
14	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
15	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₉×#217	—	2	1	no	—
17	C₉×#213	C₄	1	4	yes	complemented
18	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
21	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
22	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃×#213	C₂×C₃	1	1	yes	characteristic
24	C₃×#893	C₂×C₃	1	1	yes	characteristic
25	C₃²×#102	C₂×C₃	1	1	yes	characteristic
26	C₃×#821	C₂×C₃	1	1	yes	characteristic
27	C₃×#815	C₂×C₃	1	1	yes	characteristic
28	C₃×#808	C₂×C₃	1	1	yes	characteristic
29	C₂×C₉×D₈	—	3	1	no	—
30	C₄×D₄×C₉	—	3	1	no	—
31	C₄×D₄×C₉	—	3	1	no	—
32	C₉×#106	—	3	1	no	—
33	C₉×#102	—	2	1	no	—
34	C₉×#102	—	3	1	no	—
35	C₉×#102	D₃	1	1	yes	characteristic, complemented
36	C₉×#97	—	3	1	no	—
37	C₂³×C₃×C₉	—	2	1	no	—
38	C₂²×D₃×C₉	—	2	1	no	—
39	C₃×D₄×C₉	—	2	1	no	—
40	C₃×D₄×C₉	C₂×C₄	1	2	yes	complemented
41	C₂×C₃×C₄×C₉	—	2	1	no	—
42	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
43	C₂×C₉×Dic₃	—	2	1	no	—
44	C₂×C₉×Dic₃	—	4	2	no	—
45	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
46	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
47	C₉×D₁₂	—	2	1	no	—
48	C₉×D₁₂	C₂×C₄	1	2	yes	complemented
49	C₄×D₃×C₉	—	4	2	no	—
50	C₃×C₈×C₉	—	2	1	no	—
51	C₉×C₃⋊C₈	C₂×C₄	1	2	yes	complemented
52	C₃×#442	—	3	1	no	—
53	#4785	C₉	1	1	yes	characteristic, direct product factor
54	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
55	C₂²×C₃×Dic₃	—	2	1	no	—
56	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₃×C₄×D₃	—	2	1	no	—
58	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
59	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
60	C₃×#217	—	2	1	no	—
61	C₃×#213	C₃×C₄	1	4	yes	—
62	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
63	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
64	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
66	C₂×D₄×C₉	—	2	1	no	—
67	C₂×D₄×C₉	—	3	1	no	—
68	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
69	C₂²×C₄×C₉	—	6	1	no	—
70	C₂²×C₄×C₉	—	6	1	no	—
71	C₉×D₈	—	3	4	no	—
72	C₂×C₈×C₉	—	2	1	no	—
73	C₂×C₈×C₉	—	3	1	no	—
74	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
75	C₉×C₄⋊C₄	—	2	1	no	—
76	C₉×C₄⋊C₄	—	3	1	no	—
77	C₉×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₉×C₂²⋊C₄	—	6	1	no	—
79	C₉×C₂²⋊C₄	—	6	1	no	—
80	C₄²×C₉	—	3	1	no	—
81	C₂²×C₃×C₉	—	2	2	no	—
82	C₂²×C₃×C₉	—	4	1	no	—
83	C₂²×C₃×C₉	—	4	1	no	—
84	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
85	C₂×D₃×C₉	—	2	2	no	—
86	C₂×D₃×C₉	—	4	1	no	—
87	C₂×D₃×C₉	—	4	1	no	—
88	C₃×C₄×C₉	—	4	1	no	—
89	C₃×C₄×C₉	C₂²×C₄	1	1	yes	characteristic
90	C₃×C₄×C₉	#41	1	1	yes	characteristic
91	C₉×Dic₃	—	2	1	no	—
92	C₉×Dic₃	—	2	1	no	—
93	C₉×Dic₃	—	4	1	no	—
94	C₂×C₃×D₈	—	3	1	no	—
95	C₃×C₄×D₄	—	3	1	no	—
96	C₃×C₄×D₄	—	3	1	no	—
97	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
98	C₂×#213	C₂×C₉	1	1	yes	characteristic
99	#893	C₂×C₉	1	1	yes	characteristic, complemented
100	C₃×#106	—	3	1	no	—
101	C₃×#102	—	2	1	no	—
102	C₃×#102	—	3	1	no	—
103	C₃×#102	C₂×C₉	1	1	yes	characteristic, complemented
104	C₃×#102	C₃×D₃	1	1	yes	characteristic
105	C₃×#97	—	3	1	no	—
106	#821	C₂×C₉	1	1	yes	characteristic, complemented
107	#815	C₂×C₉	1	1	yes	characteristic, complemented
108	#808	C₂×C₉	1	1	yes	characteristic, complemented
109	C₂³×C₃²	—	2	1	no	—
110	C₂²×C₃×D₃	—	2	1	no	—
111	C₃²×D₄	—	2	1	no	—
112	C₃²×D₄	C₂×C₃×C₄	1	2	yes	—
113	C₂×C₃²×C₄	—	2	1	no	—
114	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
115	C₂×C₃×Dic₃	—	2	1	no	—
116	C₂×C₃×Dic₃	—	4	2	no	—
117	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
118	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
119	C₃×D₁₂	—	2	1	no	—
120	C₃×D₁₂	C₂×C₃×C₄	1	2	yes	—
121	C₃×C₄×D₃	—	4	2	no	—
122	C₂³×C₉	—	2	1	no	—
123	C₂³×C₉	—	4	1	no	—
124	C₂³×C₉	—	6	1	no	—
125	C₃²×C₈	—	2	1	no	—
126	C₃×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
127	D₄×C₉	—	2	1	no	—
128	D₄×C₉	—	2	2	no	—
129	D₄×C₉	—	3	2	no	—
130	D₄×C₉	—	4	1	no	—
131	D₄×C₉	—	6	1	no	—
132	D₄×C₉	C₄×D₃	1	2	yes	complemented
133	C₂×C₄×C₉	—	2	1	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	3	1	no	—
136	C₂×C₄×C₉	—	3	1	no	—
137	C₂×C₄×C₉	—	4	1	no	—
138	C₂×C₄×C₉	—	6	1	no	—
139	C₂×C₄×C₉	—	12	2	no	—
140	C₂×C₄×C₉	—	12	2	no	—
141	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
142	C₈×C₉	—	2	1	no	—
143	C₈×C₉	—	3	2	no	—
144	C₈×C₉	—	4	1	no	—
145	#442	—	3	1	no	Sylow
146	C₂×C₃×C₉	—	4	2	no	—
147	C₂×C₃×C₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
150	D₃×C₉	—	4	2	no	—
151	C₂×C₃×D₄	—	2	1	no	—
152	C₂×C₃×D₄	—	3	1	no	—
153	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
154	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
155	C₂²×C₃×C₄	—	6	1	no	—
156	C₂²×C₃×C₄	—	6	1	no	—
157	C₂²×Dic₃	—	2	1	no	—
158	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
159	C₂×C₄×D₃	—	2	1	no	—
160	C₃×D₈	—	3	4	no	—
161	C₂×C₃×C₈	—	2	1	no	—
162	C₂×C₃×C₈	—	3	1	no	—
163	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
164	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
165	C₃×C₄⋊C₄	—	2	1	no	—
166	C₃×C₄⋊C₄	—	3	1	no	—
167	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
168	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
169	C₃×C₂²⋊C₄	—	6	1	no	—
170	C₃×C₂²⋊C₄	—	6	1	no	—
171	C₃×C₄²	—	3	1	no	—
172	#217	—	2	1	no	—
173	#213	C₄×C₉	1	4	yes	complemented
174	(C₂×D₃)⋊C₄	—	2	1	no	—
175	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
176	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
177	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
178	C₂²×C₃²	—	2	2	no	—
179	C₂²×C₃²	—	4	1	no	—
180	C₂²×C₃²	—	4	1	no	—
181	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
182	C₂×C₃×D₃	—	2	2	no	—
183	C₂×C₃×D₃	—	4	1	no	—
184	C₂×C₃×D₃	—	4	1	no	—
185	C₃²×C₄	—	4	1	no	—
186	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
187	C₃²×C₄	C₃×#41	1	1	yes	characteristic
188	C₃×Dic₃	—	2	1	no	—
189	C₃×Dic₃	—	2	1	no	—
190	C₃×Dic₃	—	4	1	no	—
191	C₂²×C₉	—	2	2	no	—
192	C₂²×C₉	—	2	1	no	—
193	C₂²×C₉	—	4	2	no	—
194	C₂²×C₉	—	4	1	no	—
195	C₂²×C₉	—	4	1	no	—
196	C₂²×C₉	—	6	2	no	—
197	C₂²×C₉	—	8	1	no	—
198	C₂²×C₉	—	8	1	no	—
199	C₂²×C₉	—	12	1	no	—
200	C₂²×C₉	—	12	1	no	—
201	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
202	C₄×C₉	—	2	1	no	—
203	C₄×C₉	—	2	1	no	—
204	C₄×C₉	—	4	1	no	—
205	C₄×C₉	—	6	1	no	—
206	C₄×C₉	—	6	1	no	—
207	C₄×C₉	—	8	1	no	—
208	C₄×C₉	—	12	1	no	—
209	C₄×C₉	C₂×C₄×D₃	1	1	yes	characteristic
210	C₄×C₉	#237	1	1	yes	characteristic
211	C₂×D₈	—	3	1	no	—
212	C₄×D₄	—	3	1	no	—
213	C₄×D₄	—	3	1	no	—
214	#106	—	3	1	no	—
215	#102	—	3	1	no	—
216	#102	D₃×C₉	1	1	yes	characteristic, complemented
217	#97	—	3	1	no	—
218	C₃×C₉	#442	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₃	—	2	1	no	—
220	C₂³×C₃	—	2	1	no	—
221	C₂³×C₃	—	4	1	no	—
222	C₂³×C₃	—	6	1	no	—
223	C₂²×D₃	—	2	1	no	—
224	C₃×D₄	—	2	1	no	—
225	C₃×D₄	—	2	1	no	—
226	C₃×D₄	—	2	2	no	—
227	C₃×D₄	—	3	2	no	—
228	C₃×D₄	—	4	1	no	—
229	C₃×D₄	—	6	1	no	—
230	C₃×D₄	C₂×C₄×C₉	1	2	yes	complemented
231	C₃×D₄	C₃×C₄×D₃	1	2	yes	—
232	C₂×C₃×C₄	—	2	1	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	3	1	no	—
236	C₂×C₃×C₄	—	3	1	no	—
237	C₂×C₃×C₄	—	4	1	no	—
238	C₂×C₃×C₄	—	6	1	no	—
239	C₂×C₃×C₄	—	12	2	no	—
240	C₂×C₃×C₄	—	12	2	no	—
241	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
243	C₂×Dic₃	—	2	1	no	—
244	C₂×Dic₃	—	4	2	no	—
245	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
246	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
247	D₁₂	—	2	1	no	—
248	D₁₂	C₂×C₄×C₉	1	2	yes	complemented
249	C₄×D₃	—	4	2	no	—
250	C₃×C₈	—	2	1	no	—
251	C₃×C₈	—	2	1	no	—
252	C₃×C₈	—	3	2	no	—
253	C₃×C₈	—	4	1	no	—
254	C₃⋊C₈	C₂×C₄×C₉	1	2	yes	complemented
255	C₂×C₃²	—	4	2	no	—
256	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
257	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₃×D₃	—	4	2	no	—
260	C₂×C₉	—	2	1	no	—
261	C₂×C₉	—	2	1	no	—
262	C₂×C₉	—	2	1	no	—
263	C₂×C₉	—	4	2	no	—
264	C₂×C₉	—	8	2	no	—
265	C₂×C₉	—	12	2	no	—
266	C₂×C₉	#67⋊C₄	1	1	yes	characteristic
267	C₂×C₉	#911	1	1	yes	characteristic
268	C₂×C₉	#914	1	1	yes	characteristic
269	C₂×D₄	—	3	1	no	—
270	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
271	C₂²×C₄	—	6	1	no	—
272	C₂²×C₄	—	6	1	no	—
273	D₈	—	3	4	no	—
274	C₂×C₈	—	3	1	no	—
275	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
276	C₄⋊C₄	—	3	1	no	—
277	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
278	C₂²⋊C₄	—	6	1	no	—
279	C₂²⋊C₄	—	6	1	no	—
280	C₄²	—	3	1	no	—
281	C₂²×C₃	—	2	2	no	—
282	C₂²×C₃	—	2	2	no	—
283	C₂²×C₃	—	2	1	no	—
284	C₂²×C₃	—	4	2	no	—
285	C₂²×C₃	—	4	1	no	—
286	C₂²×C₃	—	4	1	no	—
287	C₂²×C₃	—	4	1	no	—
288	C₂²×C₃	—	4	1	no	—
289	C₂²×C₃	—	6	2	no	—
290	C₂²×C₃	—	8	1	no	—
291	C₂²×C₃	—	8	1	no	—
292	C₂²×C₃	—	12	1	no	—
293	C₂²×C₃	—	12	1	no	—
294	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
295	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
296	C₂×D₃	—	2	2	no	—
297	C₂×D₃	—	4	1	no	—
298	C₂×D₃	—	4	1	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	4	1	no	—
302	C₃×C₄	—	4	1	no	—
303	C₃×C₄	—	6	1	no	—
304	C₃×C₄	—	6	1	no	—
305	C₃×C₄	—	8	1	no	—
306	C₃×C₄	—	12	1	no	—
307	C₃×C₄	C₂²×C₄×C₉	1	1	yes	characteristic
308	C₃×C₄	C₉×#41	1	1	yes	characteristic
309	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
310	C₃×C₄	C₃×#237	1	1	yes	characteristic
311	Dic₃	—	2	1	no	—
312	Dic₃	—	2	1	no	—
313	Dic₃	—	4	1	no	—
314	C₃²	C₃×#442	1	1	yes	characteristic
315	C₉	—	2	1	no	—
316	C₉	#4785	1	1	yes	characteristic, direct product factor
317	C₂³	—	2	1	no	—
318	C₂³	—	6	1	no	—
319	D₄	—	2	1	no	—
320	D₄	—	3	2	no	—
321	D₄	—	6	1	no	—
322	D₄	C₄×D₃×C₉	1	2	yes	complemented
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	3	1	no	—
325	C₂×C₄	—	3	1	no	—
326	C₂×C₄	—	6	1	no	—
327	C₂×C₄	—	12	2	no	—
328	C₂×C₄	—	12	2	no	—
329	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
330	C₈	—	2	1	no	—
331	C₈	—	3	2	no	—
332	C₂×C₃	—	2	1	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	—	4	2	no	—
336	C₂×C₃	—	4	2	no	—
337	C₂×C₃	—	8	2	no	—
338	C₂×C₃	—	12	2	no	—
339	C₂×C₃	C₄×D₄×C₉	1	1	yes	characteristic
340	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
341	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
342	C₂×C₃	C₃×#67⋊C₄	1	1	yes	characteristic
343	C₂×C₃	C₃×#911	1	1	yes	characteristic
344	C₂×C₃	C₃×#914	1	1	yes	characteristic
345	D₃	—	4	2	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	6	2	no	—
350	C₂²	—	12	1	no	—
351	C₂²	—	12	1	no	—
352	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
353	C₄	—	4	1	no	—
354	C₄	—	6	1	no	—
355	C₄	—	6	1	no	—
356	C₄	—	12	1	no	—
357	C₄	C₂×C₄×D₃×C₉	1	1	yes	characteristic
358	C₄	C₉×#237	1	1	yes	characteristic
359	C₃	—	2	1	no	—
360	C₃	C₉×#442	1	1	yes	characteristic, complemented
361	C₃	C₃×#4785	1	1	yes	characteristic
362	C₂	—	4	2	no	—
363	C₂	—	12	2	no	—
364	C₂	C₉×#67⋊C₄	1	1	yes	characteristic
365	C₂	C₉×#911	1	1	yes	characteristic
366	C₂	C₉×#914	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₃×C₄	C₂²×C₄×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₃×C₉×#102	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#213	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₉×#102	D₃
hypocenter	C₃	C₉×#442
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₉×#102

Complements

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

N	H ≅ G/N	type
1. D₄×C₉×Dic₃	C₂	semidirect
3. C₉×#893	C₂	semidirect
4. C₃×C₉×#102	C₂	semidirect
5. C₉×#821	C₂	semidirect
6. C₉×#815	C₂	semidirect
7. C₉×#808	C₂	semidirect
17. C₉×#213	C₄	semidirect
35. C₉×#102	D₃	semidirect
40. C₃×D₄×C₉	C₂×C₄	semidirect
48. C₉×D₁₂	C₂×C₄	semidirect
51. C₉×C₃⋊C₈	C₂×C₄	semidirect
53. #4785	C₉	direct (N × H)
97. D₄×Dic₃	C₂×C₉	semidirect
99. #893	C₂×C₉	semidirect
103. C₃×#102	C₂×C₉	semidirect
106. #821	C₂×C₉	semidirect
107. #815	C₂×C₉	semidirect
108. #808	C₂×C₉	semidirect
132. D₄×C₉	C₄×D₃	semidirect
173. #213	C₄×C₉	semidirect
216. #102	D₃×C₉	semidirect
218. C₃×C₉	#442	semidirect
230. C₃×D₄	C₂×C₄×C₉	semidirect
248. D₁₂	C₂×C₄×C₉	semidirect
254. C₃⋊C₈	C₂×C₄×C₉	semidirect
316. C₉	#4785	direct (N × H)
322. D₄	C₄×D₃×C₉	semidirect
360. C₃	C₉×#442	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₉×Dic₃	2
C₂×C₉×#213	2
C₉×#893	2
C₃×C₉×#102	2
C₉×#821	2
C₉×#815	2
C₉×#808	2
C₃×#4785	3
C₉×#442	3

Subgroups — C9×#4785 #13141768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#4785 #13141768