Subgroups — C₉×#5732 #13153313

Order 1728.

704 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	2	yes	maximal
3	Q₈×C₉×Dic₃	C₂	1	2	yes	maximal, complemented
4	C₉×#898	C₂	1	4	yes	maximal, complemented
5	C₉×#897	C₂	1	2	yes	maximal, complemented
6	C₉×#892	C₂	1	2	yes	maximal, complemented
7	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
8	C₄×C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5732	C₃	1	1	yes	maximal, characteristic
10	C₉×#556	—	3	1	no	maximal
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
14	C₂×C₉×Dic₆	C₂²	1	1	yes	characteristic
15	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
16	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
18	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
19	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
20	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
22	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₉×C₄⋊Dic₃	C₂²	1	4	yes	—
24	C₉×Dic₃⋊C₄	C₂²	1	2	yes	—
25	C₄×C₉×Dic₃	C₂²	1	2	yes	—
26	C₄×C₉×Dic₃	C₂²	1	4	yes	—
27	C₃²×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
28	C₃×#947	C₂×C₃	1	2	yes	—
29	C₃×Q₈×Dic₃	C₂×C₃	1	2	yes	—
30	C₃×#898	C₂×C₃	1	4	yes	—
31	C₃×#897	C₂×C₃	1	2	yes	—
32	C₃×#892	C₂×C₃	1	2	yes	—
33	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
34	C₃×C₄×Dic₆	C₂×C₃	1	1	yes	characteristic
35	C₉×C₄⋊Q₈	—	2	1	no	—
36	C₉×C₄⋊Q₈	D₃	1	1	yes	characteristic, complemented
37	C₉×#126	—	3	4	no	—
38	C₉×#124	—	3	2	no	—
39	C₉×C₂²⋊Q₈	—	3	2	no	—
40	C₄×Q₈×C₉	—	3	2	no	—
41	C₄×Q₈×C₉	—	3	1	no	—
42	C₄×D₄×C₉	—	3	1	no	—
43	C₉×#117	—	3	2	no	—
44	C₂²×D₃×C₉	C₂³	1	2	yes	—
45	C₃×Q₈×C₉	—	2	4	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₉×Dic₃	C₂³	1	2	yes	—
51	C₂×C₉×Dic₃	C₂³	1	2	yes	—
52	C₂×C₉×Dic₃	C₂³	1	2	yes	—
53	C₉×D₁₂	—	2	2	no	—
54	C₄×D₃×C₉	—	2	4	no	—
55	C₉×Dic₆	—	2	2	no	—
56	C₃×#556	—	3	1	no	—
57	#5732	C₉	1	1	yes	characteristic, direct product factor
58	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
59	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃×C₄×D₃	C₂²×C₃	1	2	yes	—
61	C₂×C₃×Dic₆	C₂²×C₃	1	1	yes	characteristic
62	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
63	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
65	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
66	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
67	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
68	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
69	C₃×C₄⋊Dic₃	C₂²×C₃	1	4	yes	—
70	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
71	C₃×Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
72	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
73	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
74	C₂×Q₈×C₉	—	2	2	no	—
75	C₂×Q₈×C₉	—	3	1	no	—
76	C₂×Q₈×C₉	C₂×D₃	1	2	yes	—
77	C₂×D₄×C₉	—	3	1	no	—
78	C₂²×C₄×C₉	—	3	2	no	—
79	C₉×C₄⋊C₄	—	2	2	no	—
80	C₉×C₄⋊C₄	—	2	2	no	—
81	C₉×C₄⋊C₄	—	3	1	no	—
82	C₉×C₄⋊C₄	—	3	1	no	—
83	C₉×C₄⋊C₄	—	3	4	no	—
84	C₉×C₄⋊C₄	—	3	2	no	—
85	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
86	C₉×C₄⋊C₄	C₂×D₃	1	2	yes	—
87	C₉×C₂²⋊C₄	—	3	4	no	—
88	C₉×C₂²⋊C₄	—	3	2	no	—
89	C₉×C₂²⋊C₄	—	3	4	no	—
90	C₄²×C₉	—	2	1	no	—
91	C₄²×C₉	—	3	4	no	—
92	C₄²×C₉	—	3	2	no	—
93	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
94	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
95	C₂×D₃×C₉	—	2	2	no	—
96	C₂×D₃×C₉	—	2	2	no	—
97	C₂×D₃×C₉	—	2	2	no	—
98	C₃×C₄×C₉	—	2	4	no	—
99	C₃×C₄×C₉	—	2	1	no	—
100	C₃×C₄×C₉	#41	1	2	yes	—
101	C₃×C₄×C₉	#41	1	2	yes	—
102	C₉×Dic₃	—	2	2	no	—
103	C₉×Dic₃	—	2	2	no	—
104	C₉×Dic₃	—	2	2	no	—
105	C₃×C₄⋊Q₈	—	2	1	no	—
106	C₃×C₄⋊Q₈	C₂×C₉	1	1	yes	characteristic, complemented
107	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
108	C₃×#126	—	3	4	no	—
109	C₃×#124	—	3	2	no	—
110	C₃×C₂²⋊Q₈	—	3	2	no	—
111	C₃×C₄×Q₈	—	3	2	no	—
112	C₃×C₄×Q₈	—	3	1	no	—
113	C₃×C₄×D₄	—	3	1	no	—
114	C₃×#117	—	3	2	no	—
115	#947	C₂×C₉	1	2	yes	—
116	Q₈×Dic₃	C₂×C₉	1	2	yes	complemented
117	#898	C₂×C₉	1	4	yes	complemented
118	#897	C₂×C₉	1	2	yes	complemented
119	#892	C₂×C₉	1	2	yes	complemented
120	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic
121	C₄×Dic₆	C₂×C₉	1	1	yes	characteristic, complemented
122	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
123	C₃²×Q₈	—	2	4	no	—
124	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
125	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
127	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
128	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
129	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
130	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
131	C₃×D₁₂	—	2	2	no	—
132	C₃×C₄×D₃	—	2	4	no	—
133	C₃×Dic₆	—	2	2	no	—
134	C₂³×C₉	—	3	2	no	—
135	Q₈×C₉	—	2	4	no	—
136	Q₈×C₉	—	4	4	no	—
137	Q₈×C₉	—	6	2	no	—
138	D₄×C₉	—	6	2	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	4	no	—
143	C₂×C₄×C₉	—	3	2	no	—
144	C₂×C₄×C₉	—	3	2	no	—
145	C₂×C₄×C₉	—	3	2	no	—
146	C₂×C₄×C₉	—	6	4	no	—
147	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
148	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
149	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
150	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
151	#556	—	3	1	no	Sylow
152	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
153	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
154	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
155	D₃×C₉	—	4	2	no	—
156	C₂×C₃×Q₈	—	2	2	no	—
157	C₂×C₃×Q₈	—	3	1	no	—
158	C₂×C₃×Q₈	C₂²×C₉	1	2	yes	—
159	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
160	C₂×C₃×D₄	—	3	1	no	—
161	C₂²×C₃×C₄	—	3	2	no	—
162	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
163	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
164	C₂×Dic₆	C₂²×C₉	1	1	yes	characteristic
165	C₃×C₄⋊C₄	—	2	2	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	—	3	2	no	—
168	C₃×C₄⋊C₄	—	3	1	no	—
169	C₃×C₄⋊C₄	—	3	1	no	—
170	C₃×C₄⋊C₄	—	3	4	no	—
171	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
172	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
173	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
174	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
175	C₃×C₂²⋊C₄	—	3	4	no	—
176	C₃×C₂²⋊C₄	—	3	2	no	—
177	C₃×C₂²⋊C₄	—	3	4	no	—
178	C₃×C₄²	—	2	1	no	—
179	C₃×C₄²	—	3	4	no	—
180	C₃×C₄²	—	3	2	no	—
181	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
182	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
183	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
184	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
185	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
186	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
187	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
188	C₄⋊Dic₃	C₂²×C₉	1	4	yes	—
189	Dic₃⋊C₄	C₂²×C₉	1	2	yes	—
190	C₄×Dic₃	C₂²×C₉	1	2	yes	—
191	C₄×Dic₃	C₂²×C₉	1	4	yes	—
192	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
193	C₂×C₃×D₃	—	2	2	no	—
194	C₂×C₃×D₃	—	2	2	no	—
195	C₂×C₃×D₃	—	2	2	no	—
196	C₃²×C₄	—	2	1	no	—
197	C₃²×C₄	—	2	4	no	—
198	C₃²×C₄	C₃×#41	1	2	yes	—
199	C₃²×C₄	C₃×#41	1	2	yes	—
200	C₃×Dic₃	—	2	2	no	—
201	C₃×Dic₃	—	2	2	no	—
202	C₃×Dic₃	—	2	2	no	—
203	C₂²×C₉	—	2	1	no	—
204	C₂²×C₉	—	6	2	no	—
205	C₂²×C₉	—	6	2	no	—
206	C₂²×C₉	—	6	2	no	—
207	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
208	C₄×C₉	—	2	2	no	—
209	C₄×C₉	—	2	4	no	—
210	C₄×C₉	—	2	1	no	—
211	C₄×C₉	—	2	2	no	—
212	C₄×C₉	—	2	2	no	—
213	C₄×C₉	—	4	4	no	—
214	C₄×C₉	—	6	2	no	—
215	C₄×C₉	—	6	2	no	—
216	C₄×C₉	—	6	2	no	—
217	C₄×C₉	#237	1	2	yes	—
218	C₄×C₉	#239	1	2	yes	—
219	C₄⋊Q₈	D₃×C₉	1	1	yes	characteristic, complemented
220	#126	—	3	4	no	—
221	#124	—	3	2	no	—
222	C₂²⋊Q₈	—	3	2	no	—
223	C₄×Q₈	—	3	2	no	—
224	C₄×Q₈	—	3	1	no	—
225	C₄×D₄	—	3	1	no	—
226	#117	—	3	2	no	—
227	C₃×C₉	#556	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₃	—	3	2	no	—
229	C₂²×D₃	C₂³×C₉	1	2	yes	—
230	C₃×Q₈	—	2	4	no	—
231	C₃×Q₈	—	2	4	no	—
232	C₃×Q₈	—	4	4	no	—
233	C₃×Q₈	—	6	2	no	—
234	C₃×D₄	—	6	2	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	4	no	—
239	C₂×C₃×C₄	—	3	2	no	—
240	C₂×C₃×C₄	—	3	2	no	—
241	C₂×C₃×C₄	—	3	2	no	—
242	C₂×C₃×C₄	—	6	4	no	—
243	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
244	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
248	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
251	C₂×Dic₃	C₂³×C₉	1	2	yes	—
252	C₂×Dic₃	C₂³×C₉	1	2	yes	—
253	C₂×Dic₃	C₂³×C₉	1	2	yes	—
254	D₁₂	—	2	2	no	—
255	C₄×D₃	—	2	4	no	—
256	Dic₆	—	2	2	no	—
257	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
258	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
259	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
260	C₃×D₃	—	4	2	no	—
261	C₂×C₉	—	2	1	no	—
262	C₂×C₉	—	2	1	no	—
263	C₂×C₉	—	2	1	no	—
264	C₂×C₉	—	12	2	no	—
265	C₂×C₉	C₂×#237	1	1	yes	characteristic
266	C₂×C₉	C₂×#239	1	1	yes	characteristic
267	C₂×C₉	#1007	1	1	yes	characteristic
268	C₂×Q₈	—	3	1	no	—
269	C₂×Q₈	C₂×D₃×C₉	1	2	yes	—
270	C₂×D₄	—	3	1	no	—
271	C₂²×C₄	—	3	2	no	—
272	C₄⋊C₄	—	3	1	no	—
273	C₄⋊C₄	—	3	1	no	—
274	C₄⋊C₄	—	3	4	no	—
275	C₄⋊C₄	—	3	2	no	—
276	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
277	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
278	C₂²⋊C₄	—	3	4	no	—
279	C₂²⋊C₄	—	3	2	no	—
280	C₂²⋊C₄	—	3	4	no	—
281	C₄²	—	3	4	no	—
282	C₄²	—	3	2	no	—
283	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
284	C₂²×C₃	—	2	1	no	—
285	C₂²×C₃	—	6	2	no	—
286	C₂²×C₃	—	6	2	no	—
287	C₂²×C₃	—	6	2	no	—
288	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
289	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
290	C₂×D₃	—	2	2	no	—
291	C₂×D₃	—	2	2	no	—
292	C₂×D₃	—	2	2	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	2	no	—
300	C₃×C₄	—	4	4	no	—
301	C₃×C₄	—	6	2	no	—
302	C₃×C₄	—	6	2	no	—
303	C₃×C₄	—	6	2	no	—
304	C₃×C₄	C₉×#41	1	2	yes	—
305	C₃×C₄	C₉×#41	1	2	yes	—
306	C₃×C₄	C₃×#237	1	2	yes	—
307	C₃×C₄	C₃×#239	1	2	yes	—
308	Dic₃	—	2	2	no	—
309	Dic₃	—	2	2	no	—
310	Dic₃	—	2	2	no	—
311	C₃²	C₃×#556	1	1	yes	characteristic
312	C₉	—	2	1	no	—
313	C₉	#5732	1	1	yes	characteristic, direct product factor
314	C₂³	—	3	2	no	—
315	Q₈	—	2	4	no	—
316	Q₈	—	6	2	no	—
317	D₄	—	6	2	no	—
318	C₂×C₄	—	3	2	no	—
319	C₂×C₄	—	3	2	no	—
320	C₂×C₄	—	3	2	no	—
321	C₂×C₄	—	6	4	no	—
322	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
323	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
324	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
325	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
326	C₂×C₃	—	2	1	no	—
327	C₂×C₃	—	2	1	no	—
328	C₂×C₃	—	2	1	no	—
329	C₂×C₃	—	12	2	no	—
330	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
331	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
332	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
333	C₂×C₃	C₂×C₃×#237	1	1	yes	characteristic
334	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
335	C₂×C₃	C₃×#1007	1	1	yes	characteristic
336	D₃	—	4	2	no	—
337	C₂²	—	6	2	no	—
338	C₂²	—	6	2	no	—
339	C₂²	—	6	2	no	—
340	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	1	no	—
343	C₄	—	6	2	no	—
344	C₄	—	6	2	no	—
345	C₄	—	6	2	no	—
346	C₄	C₉×#237	1	2	yes	—
347	C₄	C₉×#239	1	2	yes	—
348	C₃	—	2	1	no	—
349	C₃	C₉×#556	1	1	yes	characteristic, complemented
350	C₃	C₃×#5732	1	1	yes	characteristic
351	C₂	—	12	2	no	—
352	C₂	C₂×C₉×#237	1	1	yes	characteristic
353	C₂	C₂×C₉×#239	1	1	yes	characteristic
354	C₂	C₉×#1007	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₄⋊Q₈	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₉×C₄⋊Q₈	D₃
hypocenter	C₃	C₉×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₄⋊Q₈	C₂	semidirect
3. Q₈×C₉×Dic₃	C₂	semidirect
4. C₉×#898	C₂	semidirect
5. C₉×#897	C₂	semidirect
6. C₉×#892	C₂	semidirect
8. C₄×C₉×Dic₆	C₂	semidirect
36. C₉×C₄⋊Q₈	D₃	semidirect
57. #5732	C₉	direct (N × H)
106. C₃×C₄⋊Q₈	C₂×C₉	semidirect
116. Q₈×Dic₃	C₂×C₉	semidirect
117. #898	C₂×C₉	semidirect
118. #897	C₂×C₉	semidirect
119. #892	C₂×C₉	semidirect
121. C₄×Dic₆	C₂×C₉	semidirect
219. C₄⋊Q₈	D₃×C₉	semidirect
227. C₃×C₉	#556	semidirect
313. C₉	#5732	direct (N × H)
349. C₃	C₉×#556	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×C₄⋊Q₈	2
C₉×#947	2
Q₈×C₉×Dic₃	2
C₉×#898	2
C₉×#897	2
C₉×#892	2
C₄×C₉×D₁₂	2
C₄×C₉×Dic₆	2
C₃×#5732	3
C₉×#556	3

Subgroups — C9×#5732 #13153313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5732 #13153313