Subgroups — C₉×#5212 #13143521

Order 1728.

938 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉×#217	C₂	1	2	yes	maximal
3	C₂×C₉×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
4	C₉×C₃⋊#95	C₂	1	2	yes	maximal, complemented
5	C₃×#5212	C₃	1	1	yes	maximal, characteristic
6	C₉×#380	—	3	1	no	maximal
7	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄×C₉	—	2	4	no	—
9	C₂²×C₃×C₄×C₉	C₄	1	4	yes	complemented
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₉×Dic₃	C₂²	1	4	yes	—
13	C₉×#217	—	2	4	no	—
14	C₉×C₄⋊Dic₃	—	2	4	no	—
15	C₂³×C₃²×C₄	C₂×C₃	1	1	yes	characteristic
16	C₂×C₃×#217	C₂×C₃	1	2	yes	—
17	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	2	yes	—
18	C₂³×C₄×C₉	—	2	1	no	—
19	C₂³×C₄×C₉	D₃	1	1	yes	characteristic
20	C₃×C₃⋊#95	C₂×C₃	1	2	yes	—
21	C₂×C₉×C₄⋊C₄	—	3	2	no	—
22	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
23	C₉×#95	—	3	2	no	—
24	C₂³×C₃×C₉	—	2	2	no	—
25	C₂³×C₃×C₉	—	2	2	no	—
26	C₂³×C₃×C₉	C₂×C₄	1	2	yes	—
27	C₂³×C₃×C₉	D₄	1	2	yes	—
28	C₂³×C₃×C₉	Q₈	1	2	yes	—
29	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
30	C₂×C₃×C₄×C₉	—	2	2	no	—
31	C₂×C₃×C₄×C₉	—	2	8	no	—
32	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
33	C₂×C₃×C₄×C₉	C₂×C₄	1	2	yes	—
34	C₂×C₃×C₄×C₉	D₄	1	4	yes	—
35	C₂×C₉×Dic₃	—	2	4	no	—
36	C₂×C₉×Dic₃	—	2	4	no	—
37	C₂×C₉×Dic₃	—	2	4	no	—
38	C₃×#380	—	3	1	no	—
39	#5212	C₉	1	1	yes	characteristic, direct product factor
40	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
41	C₂²×C₃²×C₄	—	2	4	no	—
42	C₂²×C₃²×C₄	C₃×C₄	1	4	yes	—
43	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
44	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
45	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
46	C₂⁴×C₉	—	2	1	no	—
47	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
48	C₃×#217	—	2	4	no	—
49	C₃×C₄⋊Dic₃	—	2	4	no	—
50	C₂²×C₄×C₉	—	2	8	no	—
51	C₂²×C₄×C₉	—	2	4	no	—
52	C₂²×C₄×C₉	—	2	1	no	—
53	C₂²×C₄×C₉	—	2	1	no	—
54	C₂²×C₄×C₉	—	2	4	no	—
55	C₂²×C₄×C₉	—	3	4	no	—
56	C₂²×C₄×C₉	Dic₃	1	4	yes	complemented
57	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
58	C₂²×C₄×C₉	C₂×D₃	1	1	yes	characteristic
59	C₉×C₄⋊C₄	—	6	4	no	—
60	C₉×C₂²⋊C₄	—	6	4	no	—
61	C₂²×C₃×C₉	—	2	2	no	—
62	C₂²×C₃×C₉	—	2	2	no	—
63	C₂²×C₃×C₉	—	2	4	no	—
64	C₂²×C₃×C₉	—	2	4	no	—
65	C₂²×C₃×C₉	C₄⋊C₄	1	4	yes	complemented
66	C₂²×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
68	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₃×C₉	#41	1	2	yes	—
71	C₃×C₄×C₉	—	2	2	no	—
72	C₃×C₄×C₉	C₂²⋊C₄	1	4	yes	complemented
73	C₉×Dic₃	—	4	4	no	—
74	C₂³×C₃×C₄	—	2	1	no	—
75	C₂³×C₃×C₄	C₂×C₉	1	1	yes	characteristic
76	C₂³×C₃×C₄	C₃×D₃	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	—	3	2	no	—
78	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
79	C₂×#217	C₂×C₉	1	2	yes	—
80	C₂×C₄⋊Dic₃	C₂×C₉	1	2	yes	complemented
81	C₃×#95	—	3	2	no	—
82	C₃⋊#95	C₂×C₉	1	2	yes	complemented
83	C₂³×C₃²	—	2	2	no	—
84	C₂³×C₃²	—	2	2	no	—
85	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
86	C₂³×C₃²	C₃×D₄	1	2	yes	—
87	C₂³×C₃²	C₃×Q₈	1	2	yes	—
88	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
89	C₂×C₃²×C₄	—	2	2	no	—
90	C₂×C₃²×C₄	—	2	8	no	—
91	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
92	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
93	C₂×C₃²×C₄	C₃×D₄	1	4	yes	—
94	C₂×C₃×Dic₃	—	2	4	no	—
95	C₂×C₃×Dic₃	—	2	4	no	—
96	C₂×C₃×Dic₃	—	2	4	no	—
97	C₂³×C₉	—	2	4	no	—
98	C₂³×C₉	—	2	4	no	—
99	C₂³×C₉	—	2	2	no	—
100	C₂³×C₉	—	2	2	no	—
101	C₂³×C₉	—	2	2	no	—
102	C₂³×C₉	—	2	2	no	—
103	C₂³×C₉	—	2	2	no	—
104	C₂³×C₉	—	2	1	no	—
105	C₂³×C₉	Dic₆	1	2	yes	—
106	C₂³×C₉	D₁₂	1	2	yes	—
107	C₂³×C₉	C₂×Dic₃	1	2	yes	—
108	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
109	C₂×C₄×C₉	—	2	4	no	—
110	C₂×C₄×C₉	—	2	16	no	—
111	C₂×C₄×C₉	—	2	2	no	—
112	C₂×C₄×C₉	—	2	8	no	—
113	C₂×C₄×C₉	—	2	2	no	—
114	C₂×C₄×C₉	—	2	2	no	—
115	C₂×C₄×C₉	—	2	4	no	—
116	C₂×C₄×C₉	—	6	4	no	—
117	C₂×C₄×C₉	—	6	4	no	—
118	C₂×C₄×C₉	—	6	4	no	—
119	C₂×C₄×C₉	C₂×Dic₃	1	2	yes	—
120	C₂×C₄×C₉	C₂×Dic₃	1	2	yes	—
121	C₂×C₄×C₉	#67	1	4	yes	—
122	#380	—	3	1	no	Sylow
123	C₂×C₃×C₉	—	2	4	no	—
124	C₂×C₃×C₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
125	C₂×C₃×C₉	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₃×C₉	#117	1	1	yes	characteristic
127	C₂×C₃×C₉	#121	1	2	yes	—
128	C₂×C₃×C₉	C₂²⋊Q₈	1	2	yes	—
129	C₂⁴×C₃	—	2	1	no	—
130	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
131	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₄	—	2	8	no	—
133	C₂²×C₃×C₄	—	2	4	no	—
134	C₂²×C₃×C₄	—	2	4	no	—
135	C₂²×C₃×C₄	—	2	4	no	—
136	C₂²×C₃×C₄	—	2	1	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	3	4	no	—
139	C₂²×C₃×C₄	C₄×C₉	1	4	yes	complemented
140	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
141	C₂²×C₃×C₄	C₂²×C₉	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₃×Dic₃	1	4	yes	—
143	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
144	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
145	C₂²×Dic₃	C₂²×C₉	1	4	yes	—
146	C₃×C₄⋊C₄	—	6	4	no	—
147	C₃×C₂²⋊C₄	—	6	4	no	—
148	#217	—	2	4	no	—
149	C₄⋊Dic₃	—	2	4	no	—
150	C₂²×C₃²	—	2	2	no	—
151	C₂²×C₃²	—	2	2	no	—
152	C₂²×C₃²	—	2	4	no	—
153	C₂²×C₃²	—	2	4	no	—
154	C₂²×C₃²	C₃×C₄⋊C₄	1	4	yes	—
155	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
156	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
157	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
158	C₂²×C₃²	C₂×C₃×Q₈	1	1	yes	characteristic
159	C₂²×C₃²	C₃×#41	1	2	yes	—
160	C₃²×C₄	—	2	2	no	—
161	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	—
162	C₃×Dic₃	—	4	4	no	—
163	C₂²×C₉	—	2	4	no	—
164	C₂²×C₉	—	2	8	no	—
165	C₂²×C₉	—	2	4	no	—
166	C₂²×C₉	—	2	8	no	—
167	C₂²×C₉	—	2	4	no	—
168	C₂²×C₉	—	2	2	no	—
169	C₂²×C₉	—	2	4	no	—
170	C₂²×C₉	—	2	2	no	—
171	C₂²×C₉	—	2	4	no	—
172	C₂²×C₉	—	2	1	no	—
173	C₂²×C₉	—	2	1	no	—
174	C₂²×C₉	—	2	2	no	—
175	C₂²×C₉	—	2	1	no	—
176	C₂²×C₉	—	2	2	no	—
177	C₂²×C₉	C₄⋊Dic₃	1	4	yes	complemented
178	C₂²×C₉	C₂×Dic₆	1	1	yes	characteristic
179	C₂²×C₉	C₂×D₁₂	1	1	yes	characteristic
180	C₂²×C₉	#235	1	2	yes	—
181	C₂²×C₉	C₂²×Dic₃	1	1	yes	characteristic
182	C₂²×C₉	C₂×#67	1	2	yes	—
183	C₄×C₉	—	2	4	no	—
184	C₄×C₉	—	2	2	no	—
185	C₄×C₉	—	2	4	no	—
186	C₄×C₉	—	12	4	no	—
187	C₄×C₉	#217	1	4	yes	complemented
188	C₂³×C₄	D₃×C₉	1	1	yes	characteristic
189	C₂×C₄⋊C₄	—	3	2	no	—
190	C₂×C₂²⋊C₄	—	3	2	no	—
191	#95	—	3	2	no	—
192	C₃×C₉	#380	1	1	yes	characteristic, complemented, Sylow
193	C₂³×C₃	—	2	4	no	—
194	C₂³×C₃	—	2	4	no	—
195	C₂³×C₃	—	2	2	no	—
196	C₂³×C₃	—	2	2	no	—
197	C₂³×C₃	—	2	2	no	—
198	C₂³×C₃	—	2	2	no	—
199	C₂³×C₃	—	2	2	no	—
200	C₂³×C₃	—	2	2	no	—
201	C₂³×C₃	—	2	2	no	—
202	C₂³×C₃	—	2	1	no	—
203	C₂³×C₃	C₂×C₄×C₉	1	2	yes	—
204	C₂³×C₃	D₄×C₉	1	2	yes	—
205	C₂³×C₃	Q₈×C₉	1	2	yes	—
206	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
207	C₂³×C₃	C₃×Dic₆	1	2	yes	—
208	C₂³×C₃	C₃×D₁₂	1	2	yes	—
209	C₂³×C₃	C₂×C₃×Dic₃	1	2	yes	—
210	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	16	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	8	no	—
216	C₂×C₃×C₄	—	2	8	no	—
217	C₂×C₃×C₄	—	2	2	no	—
218	C₂×C₃×C₄	—	2	2	no	—
219	C₂×C₃×C₄	—	2	4	no	—
220	C₂×C₃×C₄	—	6	4	no	—
221	C₂×C₃×C₄	—	6	4	no	—
222	C₂×C₃×C₄	—	6	4	no	—
223	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
224	C₂×C₃×C₄	C₂×C₄×C₉	1	2	yes	—
225	C₂×C₃×C₄	D₄×C₉	1	4	yes	—
226	C₂×C₃×C₄	C₂×C₃×Dic₃	1	2	yes	—
227	C₂×C₃×C₄	C₂×C₃×Dic₃	1	2	yes	—
228	C₂×C₃×C₄	C₃×#67	1	4	yes	—
229	C₂×Dic₃	—	2	4	no	—
230	C₂×Dic₃	—	2	4	no	—
231	C₂×Dic₃	—	2	4	no	—
232	C₂×C₃²	—	2	4	no	—
233	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
234	C₂×C₃²	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
235	C₂×C₃²	C₃×#117	1	1	yes	characteristic
236	C₂×C₃²	C₃×#121	1	2	yes	—
237	C₂×C₃²	C₃×C₂²⋊Q₈	1	2	yes	—
238	C₂×C₉	—	2	8	no	—
239	C₂×C₉	—	2	4	no	—
240	C₂×C₉	—	2	2	no	—
241	C₂×C₉	—	2	1	no	—
242	C₂×C₉	—	2	1	no	—
243	C₂×C₉	—	2	2	no	—
244	C₂×C₉	—	2	1	no	—
245	C₂×C₉	#924	1	2	yes	—
246	C₂×C₉	C₂×C₄⋊Dic₃	1	1	yes	characteristic
247	C₂×C₉	#926	1	1	yes	characteristic
248	C₂×C₉	#930	1	2	yes	—
249	C₂×C₉	C₂×#217	1	1	yes	characteristic
250	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	3	4	no	—
253	C₂²×C₄	C₉×Dic₃	1	4	yes	complemented
254	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₃×C₉	1	1	yes	characteristic
256	C₄⋊C₄	—	6	4	no	—
257	C₂²⋊C₄	—	6	4	no	—
258	C₂²×C₃	—	2	4	no	—
259	C₂²×C₃	—	2	8	no	—
260	C₂²×C₃	—	2	4	no	—
261	C₂²×C₃	—	2	8	no	—
262	C₂²×C₃	—	2	2	no	—
263	C₂²×C₃	—	2	2	no	—
264	C₂²×C₃	—	2	4	no	—
265	C₂²×C₃	—	2	4	no	—
266	C₂²×C₃	—	2	4	no	—
267	C₂²×C₃	—	2	2	no	—
268	C₂²×C₃	—	2	4	no	—
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	2	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	4	no	—
276	C₂²×C₃	C₉×C₄⋊C₄	1	4	yes	complemented
277	C₂²×C₃	C₂²×C₄×C₉	1	1	yes	characteristic
278	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
279	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
280	C₂²×C₃	C₂×Q₈×C₉	1	1	yes	characteristic
281	C₂²×C₃	C₉×#41	1	2	yes	—
282	C₂²×C₃	C₃×C₄⋊Dic₃	1	4	yes	—
283	C₂²×C₃	C₂×C₃×Dic₆	1	1	yes	characteristic
284	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
285	C₂²×C₃	C₃×#235	1	2	yes	—
286	C₂²×C₃	C₂²×C₃×Dic₃	1	1	yes	characteristic
287	C₂²×C₃	C₂×C₃×#67	1	2	yes	—
288	C₃×C₄	—	2	4	no	—
289	C₃×C₄	—	2	2	no	—
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	2	4	no	—
292	C₃×C₄	—	12	4	no	—
293	C₃×C₄	C₉×C₂²⋊C₄	1	4	yes	complemented
294	C₃×C₄	C₃×#217	1	4	yes	—
295	Dic₃	—	4	4	no	—
296	C₃²	C₃×#380	1	1	yes	characteristic
297	C₉	—	2	1	no	—
298	C₉	#5212	1	1	yes	characteristic, direct product factor
299	C₂³	—	2	2	no	—
300	C₂³	—	2	2	no	—
301	C₂³	C₉×Dic₆	1	2	yes	—
302	C₂³	C₉×D₁₂	1	2	yes	—
303	C₂³	C₂×C₉×Dic₃	1	2	yes	—
304	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	6	4	no	—
308	C₂×C₄	—	6	4	no	—
309	C₂×C₄	—	6	4	no	—
310	C₂×C₄	C₂×C₉×Dic₃	1	2	yes	—
311	C₂×C₄	C₂×C₉×Dic₃	1	2	yes	—
312	C₂×C₄	C₉×#67	1	4	yes	—
313	C₂×C₃	—	2	8	no	—
314	C₂×C₃	—	2	4	no	—
315	C₂×C₃	—	2	4	no	—
316	C₂×C₃	—	2	2	no	—
317	C₂×C₃	—	2	1	no	—
318	C₂×C₃	—	2	1	no	—
319	C₂×C₃	—	2	2	no	—
320	C₂×C₃	—	2	1	no	—
321	C₂×C₃	C₂×C₉×C₂²⋊C₄	1	1	yes	characteristic
322	C₂×C₃	C₂×C₉×C₄⋊C₄	1	1	yes	characteristic
323	C₂×C₃	C₉×#117	1	1	yes	characteristic
324	C₂×C₃	C₉×#121	1	2	yes	—
325	C₂×C₃	C₉×C₂²⋊Q₈	1	2	yes	—
326	C₂×C₃	C₃×#924	1	2	yes	—
327	C₂×C₃	C₂×C₃×C₄⋊Dic₃	1	1	yes	characteristic
328	C₂×C₃	C₃×#926	1	1	yes	characteristic
329	C₂×C₃	C₃×#930	1	2	yes	—
330	C₂×C₃	C₂×C₃×#217	1	1	yes	characteristic
331	C₂²	—	2	4	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	2	no	—
335	C₂²	C₉×C₄⋊Dic₃	1	4	yes	complemented
336	C₂²	C₂×C₉×Dic₆	1	1	yes	characteristic
337	C₂²	C₂×C₉×D₁₂	1	1	yes	characteristic
338	C₂²	C₉×#235	1	2	yes	—
339	C₂²	C₂²×C₉×Dic₃	1	1	yes	characteristic
340	C₂²	C₂×C₉×#67	1	2	yes	—
341	C₄	—	2	2	no	—
342	C₄	—	12	4	no	—
343	C₄	C₉×#217	1	4	yes	complemented
344	C₃	—	2	1	no	—
345	C₃	C₉×#380	1	1	yes	characteristic, complemented
346	C₃	C₃×#5212	1	1	yes	characteristic
347	C₂	—	2	4	no	—
348	C₂	C₉×#924	1	2	yes	—
349	C₂	C₂×C₉×C₄⋊Dic₃	1	1	yes	characteristic
350	C₂	C₉×#926	1	1	yes	characteristic
351	C₂	C₉×#930	1	2	yes	—
352	C₂	C₂×C₉×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄×C₉
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₂³×C₃×C₄×C₉	C₂
socle, cosocle	C₂³×C₃²	C₂³×C₃
prime radical	C₂⁴×C₃²	C₂²×C₃
hypercenter	C₂³×C₄×C₉	D₃
hypocenter	C₃	C₉×#380
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂³×C₄×C₉

Complements

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

N	H ≅ G/N	type
3. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
4. C₉×C₃⋊#95	C₂	semidirect
9. C₂²×C₃×C₄×C₉	C₄	semidirect
39. #5212	C₉	direct (N × H)
56. C₂²×C₄×C₉	Dic₃	semidirect
65. C₂²×C₃×C₉	C₄⋊C₄	semidirect
72. C₃×C₄×C₉	C₂²⋊C₄	semidirect
80. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
82. C₃⋊#95	C₂×C₉	semidirect
139. C₂²×C₃×C₄	C₄×C₉	semidirect
177. C₂²×C₉	C₄⋊Dic₃	semidirect
187. C₄×C₉	#217	semidirect
192. C₃×C₉	#380	semidirect
253. C₂²×C₄	C₉×Dic₃	semidirect
276. C₂²×C₃	C₉×C₄⋊C₄	semidirect
293. C₃×C₄	C₉×C₂²⋊C₄	semidirect
298. C₉	#5212	direct (N × H)
335. C₂²	C₉×C₄⋊Dic₃	semidirect
343. C₄	C₉×#217	semidirect
345. C₃	C₉×#380	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×C₉	2
C₂×C₉×#217	2
C₂×C₉×C₄⋊Dic₃	2
C₉×C₃⋊#95	2
C₃×#5212	3
C₉×#380	3

Subgroups — C9×#5212 #13143521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5212 #13143521