Subgroups — C₉×#5683 #13153107

Order 1728.

856 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	2	yes	maximal, complemented
3	C₉×#937	C₂	1	2	yes	maximal, complemented
4	C₉×#885	C₂	1	4	yes	maximal, complemented
5	C₉×#882	C₂	1	4	yes	maximal, complemented
6	C₉×#875	C₂	1	2	yes	maximal, complemented
7	C₃×#5683	C₃	1	1	yes	maximal, characteristic
8	C₉×H(3,𝔽₄)	—	3	1	no	maximal
9	C₂³×D₃×C₉	C₂²	1	2	yes	complemented
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic, complemented
11	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×#67	C₂²	1	4	yes	—
13	C₂×C₉×D₁₂	C₂²	1	2	yes	—
14	C₂×C₉×D₁₂	C₂²	1	2	yes	—
15	C₂×C₉×Dic₆	C₂²	1	2	yes	complemented
16	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
17	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic, complemented
18	C₉×#217	C₂²	1	2	yes	complemented
19	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
20	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	complemented
22	C₄×C₉×Dic₃	C₂²	1	2	yes	complemented
23	C₃²×#124	C₂×C₃	1	1	yes	characteristic
24	C₃×#947	C₂×C₃	1	2	yes	—
25	C₃×#937	C₂×C₃	1	2	yes	—
26	C₃×#885	C₂×C₃	1	4	yes	—
27	C₃×#882	C₂×C₃	1	4	yes	—
28	C₃×#875	C₂×C₃	1	2	yes	—
29	C₉×#124	—	2	1	no	—
30	C₉×#124	—	3	2	no	—
31	C₉×#124	—	3	4	no	—
32	C₉×#124	—	3	2	no	—
33	C₉×#124	D₃	1	1	yes	characteristic, complemented
34	C₉×#120	—	3	2	no	—
35	C₉×#120	—	3	4	no	—
36	C₂³×C₃×C₉	C₂³	1	2	yes	—
37	C₂²×D₃×C₉	—	4	2	no	—
38	C₂²×D₃×C₉	—	4	4	no	—
39	C₂²×D₃×C₉	C₂³	1	4	yes	—
40	C₃×Q₈×C₉	—	4	1	no	—
41	C₃×D₄×C₉	—	4	1	no	—
42	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
43	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
44	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
45	C₉×#67	—	4	4	no	—
46	C₂×C₉×Dic₃	C₂³	1	4	yes	—
47	C₉×D₁₂	—	4	2	no	—
48	C₉×D₁₂	—	4	2	no	—
49	C₉×Dic₆	—	4	2	no	—
50	C₃×H(3,𝔽₄)	—	3	1	no	—
51	#5683	C₉	1	1	yes	characteristic, direct product factor
52	C₂³×C₃×D₃	C₂²×C₃	1	2	yes	—
53	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
54	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
55	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
56	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
57	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
58	C₂×C₃×Dic₆	C₂²×C₃	1	2	yes	—
59	C₂⁴×C₉	—	3	2	no	—
60	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
61	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
62	C₃×#217	C₂²×C₃	1	2	yes	—
63	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
64	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
65	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
66	C₃×C₄×Dic₃	C₂²×C₃	1	2	yes	—
67	C₂×Q₈×C₉	—	2	1	no	—
68	C₂×Q₈×C₉	—	3	2	no	—
69	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic, complemented
70	C₂×D₄×C₉	—	2	1	no	—
71	C₂×D₄×C₉	—	3	4	no	—
72	C₂×D₄×C₉	—	3	2	no	—
73	C₂×D₄×C₉	—	3	2	no	—
74	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
75	C₉×C₂²⋊C₄	—	2	4	no	—
76	C₉×C₂²⋊C₄	—	3	2	no	—
77	C₉×C₂²⋊C₄	—	3	4	no	—
78	C₉×C₂²⋊C₄	—	3	4	no	—
79	C₉×C₂²⋊C₄	—	3	4	no	—
80	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
81	C₄²×C₉	—	2	1	no	—
82	C₄²×C₉	—	3	2	no	—
83	C₄²×C₉	C₂×D₃	1	1	yes	characteristic, complemented
84	C₂²×C₃×C₉	—	2	4	no	—
85	C₂²×C₃×C₉	—	2	2	no	—
86	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
87	C₂×D₃×C₉	—	2	4	no	—
88	C₂×D₃×C₉	—	2	4	no	—
89	C₂×D₃×C₉	—	2	4	no	—
90	C₂×D₃×C₉	—	4	8	no	—
91	C₃×C₄×C₉	—	2	1	no	—
92	C₃×C₄×C₉	—	2	2	no	—
93	C₃×C₄×C₉	—	2	2	no	—
94	C₉×Dic₃	—	2	4	no	—
95	C₃×#124	—	2	1	no	—
96	C₃×#124	—	3	2	no	—
97	C₃×#124	—	3	4	no	—
98	C₃×#124	—	3	2	no	—
99	C₃×#124	C₂×C₉	1	1	yes	characteristic, complemented
100	C₃×#124	C₃×D₃	1	1	yes	characteristic
101	C₃×#120	—	3	2	no	—
102	C₃×#120	—	3	4	no	—
103	#947	C₂×C₉	1	2	yes	complemented
104	#937	C₂×C₉	1	2	yes	complemented
105	#885	C₂×C₉	1	4	yes	complemented
106	#882	C₂×C₉	1	4	yes	complemented
107	#875	C₂×C₉	1	2	yes	complemented
108	C₂³×C₃²	C₂³×C₃	1	2	yes	—
109	C₂²×C₃×D₃	—	4	2	no	—
110	C₂²×C₃×D₃	—	4	4	no	—
111	C₂²×C₃×D₃	C₂³×C₃	1	4	yes	—
112	C₃²×Q₈	—	4	1	no	—
113	C₃²×D₄	—	4	1	no	—
114	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
115	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
116	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
117	C₃×#67	—	4	4	no	—
118	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
119	C₃×D₁₂	—	4	2	no	—
120	C₃×D₁₂	—	4	2	no	—
121	C₃×Dic₆	—	4	2	no	—
122	C₂³×C₉	—	2	2	no	—
123	C₂³×C₉	—	3	4	no	—
124	C₂³×C₉	—	12	2	no	—
125	C₂³×C₉	—	12	4	no	—
126	C₂³×C₉	C₂²×D₃	1	2	yes	—
127	Q₈×C₉	—	4	1	no	—
128	Q₈×C₉	—	4	2	no	—
129	Q₈×C₉	—	12	2	no	—
130	D₄×C₉	—	4	1	no	—
131	D₄×C₉	—	4	2	no	—
132	D₄×C₉	—	12	2	no	—
133	D₄×C₉	—	12	2	no	—
134	D₄×C₉	—	12	4	no	—
135	C₂×C₄×C₉	—	2	1	no	—
136	C₂×C₄×C₉	—	2	2	no	—
137	C₂×C₄×C₉	—	2	2	no	—
138	C₂×C₄×C₉	—	3	4	no	—
139	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
140	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
141	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
142	H(3,𝔽₄)	—	3	1	no	Sylow
143	C₂×C₃×C₉	—	4	2	no	—
144	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂×C₃×C₉	H(5,𝔽₂)	1	2	yes	—
146	D₃×C₉	—	4	4	no	—
147	C₂⁴×C₃	—	3	2	no	—
148	C₂³×D₃	C₂²×C₉	1	2	yes	complemented
149	C₂×C₃×Q₈	—	2	1	no	—
150	C₂×C₃×Q₈	—	3	2	no	—
151	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic, complemented
152	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
153	C₂×C₃×D₄	—	2	1	no	—
154	C₂×C₃×D₄	—	3	4	no	—
155	C₂×C₃×D₄	—	3	2	no	—
156	C₂×C₃×D₄	—	3	2	no	—
157	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
158	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
159	C₂×#67	C₂²×C₉	1	4	yes	—
160	C₂×D₁₂	C₂²×C₉	1	2	yes	—
161	C₂×D₁₂	C₂²×C₉	1	2	yes	—
162	C₂×Dic₆	C₂²×C₉	1	2	yes	complemented
163	C₃×C₂²⋊C₄	—	2	4	no	—
164	C₃×C₂²⋊C₄	—	3	2	no	—
165	C₃×C₂²⋊C₄	—	3	4	no	—
166	C₃×C₂²⋊C₄	—	3	4	no	—
167	C₃×C₂²⋊C₄	—	3	4	no	—
168	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
169	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
170	C₃×C₄²	—	2	1	no	—
171	C₃×C₄²	—	3	2	no	—
172	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic, complemented
173	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
174	#217	C₂²×C₉	1	2	yes	complemented
175	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
176	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
177	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	complemented
178	C₄×Dic₃	C₂²×C₉	1	2	yes	complemented
179	C₂²×C₃²	—	2	4	no	—
180	C₂²×C₃²	—	2	2	no	—
181	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
182	C₂×C₃×D₃	—	2	4	no	—
183	C₂×C₃×D₃	—	2	4	no	—
184	C₂×C₃×D₃	—	2	4	no	—
185	C₂×C₃×D₃	—	4	8	no	—
186	C₃²×C₄	—	2	1	no	—
187	C₃²×C₄	—	2	2	no	—
188	C₃²×C₄	—	2	2	no	—
189	C₃×Dic₃	—	2	4	no	—
190	C₂²×C₉	—	2	2	no	—
191	C₂²×C₉	—	2	4	no	—
192	C₂²×C₉	—	2	1	no	—
193	C₂²×C₉	—	4	2	no	—
194	C₂²×C₉	—	4	4	no	—
195	C₂²×C₉	—	6	4	no	—
196	C₂²×C₉	—	6	4	no	—
197	C₂²×C₉	—	6	4	no	—
198	C₂²×C₉	—	12	8	no	—
199	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
200	C₄×C₉	—	2	2	no	—
201	C₄×C₉	—	2	1	no	—
202	C₄×C₉	—	2	2	no	—
203	C₄×C₉	—	2	2	no	—
204	C₄×C₉	—	4	2	no	—
205	C₄×C₉	—	4	2	no	—
206	C₄×C₉	—	6	4	no	—
207	#124	—	3	2	no	—
208	#124	—	3	4	no	—
209	#124	—	3	2	no	—
210	#124	D₃×C₉	1	1	yes	characteristic, complemented
211	#120	—	3	2	no	—
212	#120	—	3	4	no	—
213	C₃×C₉	H(3,𝔽₄)	1	1	yes	characteristic, complemented, Sylow
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	3	4	no	—
216	C₂³×C₃	—	12	2	no	—
217	C₂³×C₃	—	12	4	no	—
218	C₂³×C₃	C₂³×C₉	1	2	yes	—
219	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
220	C₂²×D₃	—	4	2	no	—
221	C₂²×D₃	—	4	4	no	—
222	C₂²×D₃	C₂³×C₉	1	4	yes	—
223	C₃×Q₈	—	4	1	no	—
224	C₃×Q₈	—	4	1	no	—
225	C₃×Q₈	—	4	2	no	—
226	C₃×Q₈	—	12	2	no	—
227	C₃×D₄	—	4	1	no	—
228	C₃×D₄	—	4	1	no	—
229	C₃×D₄	—	4	2	no	—
230	C₃×D₄	—	12	2	no	—
231	C₃×D₄	—	12	2	no	—
232	C₃×D₄	—	12	4	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	3	4	no	—
237	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
238	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
240	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
241	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
243	#67	—	4	4	no	—
244	C₂×Dic₃	C₂³×C₉	1	4	yes	—
245	D₁₂	—	4	2	no	—
246	D₁₂	—	4	2	no	—
247	Dic₆	—	4	2	no	—
248	C₂×C₃²	—	4	2	no	—
249	C₂×C₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic
250	C₂×C₃²	C₃×H(5,𝔽₂)	1	2	yes	—
251	C₃×D₃	—	4	4	no	—
252	C₂×C₉	—	2	1	no	—
253	C₂×C₉	—	2	2	no	—
254	C₂×C₉	—	4	2	no	—
255	C₂×C₉	—	8	2	no	—
256	C₂×C₉	—	12	4	no	—
257	C₂×C₉	#1004	1	1	yes	characteristic
258	C₂×C₉	#1009	1	2	yes	—
259	C₂⁴	—	3	2	no	—
260	C₂×Q₈	—	3	2	no	—
261	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic, complemented
262	C₂×D₄	—	3	4	no	—
263	C₂×D₄	—	3	2	no	—
264	C₂×D₄	—	3	2	no	—
265	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
266	C₂²⋊C₄	—	3	2	no	—
267	C₂²⋊C₄	—	3	4	no	—
268	C₂²⋊C₄	—	3	4	no	—
269	C₂²⋊C₄	—	3	4	no	—
270	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
271	C₄²	—	3	2	no	—
272	C₄²	C₂×D₃×C₉	1	1	yes	characteristic, complemented
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	4	no	—
275	C₂²×C₃	—	2	4	no	—
276	C₂²×C₃	—	2	2	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	4	2	no	—
279	C₂²×C₃	—	4	4	no	—
280	C₂²×C₃	—	6	4	no	—
281	C₂²×C₃	—	6	4	no	—
282	C₂²×C₃	—	6	4	no	—
283	C₂²×C₃	—	12	8	no	—
284	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
285	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
286	C₂×D₃	—	2	4	no	—
287	C₂×D₃	—	2	4	no	—
288	C₂×D₃	—	2	4	no	—
289	C₂×D₃	—	4	8	no	—
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	2	1	no	—
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	2	no	—
295	C₃×C₄	—	2	2	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	4	2	no	—
298	C₃×C₄	—	4	2	no	—
299	C₃×C₄	—	6	4	no	—
300	Dic₃	—	2	4	no	—
301	C₃²	C₃×H(3,𝔽₄)	1	1	yes	characteristic
302	C₉	—	2	1	no	—
303	C₉	#5683	1	1	yes	characteristic, direct product factor
304	C₂³	—	3	4	no	—
305	C₂³	—	12	2	no	—
306	C₂³	—	12	4	no	—
307	C₂³	C₂²×D₃×C₉	1	2	yes	—
308	Q₈	—	4	1	no	—
309	Q₈	—	12	2	no	—
310	D₄	—	4	1	no	—
311	D₄	—	12	2	no	—
312	D₄	—	12	2	no	—
313	D₄	—	12	4	no	—
314	C₂×C₄	—	3	4	no	—
315	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
316	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
317	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
318	C₂×C₃	—	2	1	no	—
319	C₂×C₃	—	2	2	no	—
320	C₂×C₃	—	4	2	no	—
321	C₂×C₃	—	4	2	no	—
322	C₂×C₃	—	8	2	no	—
323	C₂×C₃	—	12	4	no	—
324	C₂×C₃	C₉×H(5,𝔽₂)	1	1	yes	characteristic
325	C₂×C₃	C₉×H(5,𝔽₂)	1	2	yes	—
326	C₂×C₃	C₃×#1004	1	1	yes	characteristic
327	C₂×C₃	C₃×#1009	1	2	yes	—
328	D₃	—	4	4	no	—
329	C₂²	—	2	2	no	—
330	C₂²	—	2	4	no	—
331	C₂²	—	6	4	no	—
332	C₂²	—	6	4	no	—
333	C₂²	—	6	4	no	—
334	C₂²	—	12	8	no	—
335	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	—	2	2	no	—
339	C₄	—	6	4	no	—
340	C₃	—	2	1	no	—
341	C₃	C₉×H(3,𝔽₄)	1	1	yes	characteristic, complemented
342	C₃	C₃×#5683	1	1	yes	characteristic
343	C₂	—	4	2	no	—
344	C₂	—	12	4	no	—
345	C₂	C₉×#1004	1	1	yes	characteristic
346	C₂	C₉×#1009	1	2	yes	—

	subgroup	G/H
center	C₂²×C₉	C₂³×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×#124	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₃×#5683	C₃
hypercenter	C₉×#124	D₃
hypocenter	C₃	C₉×H(3,𝔽₄)
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#124

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×#124	C₂	semidirect
2. C₉×#947	C₂	semidirect
3. C₉×#937	C₂	semidirect
4. C₉×#885	C₂	semidirect
5. C₉×#882	C₂	semidirect
6. C₉×#875	C₂	semidirect
9. C₂³×D₃×C₉	C₂²	semidirect
10. C₂×C₃×Q₈×C₉	C₂²	semidirect
15. C₂×C₉×Dic₆	C₂²	semidirect
16. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
17. C₃×C₄²×C₉	C₂²	semidirect
18. C₉×#217	C₂²	semidirect
19. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
20. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
21. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
22. C₄×C₉×Dic₃	C₂²	semidirect
33. C₉×#124	D₃	semidirect
51. #5683	C₉	direct (N × H)
69. C₂×Q₈×C₉	C₂×D₃	semidirect
80. C₉×C₂²⋊C₄	C₂×D₃	semidirect
83. C₄²×C₉	C₂×D₃	semidirect
99. C₃×#124	C₂×C₉	semidirect
103. #947	C₂×C₉	semidirect
104. #937	C₂×C₉	semidirect
105. #885	C₂×C₉	semidirect
106. #882	C₂×C₉	semidirect
107. #875	C₂×C₉	semidirect
148. C₂³×D₃	C₂²×C₉	semidirect
151. C₂×C₃×Q₈	C₂²×C₉	semidirect
162. C₂×Dic₆	C₂²×C₉	semidirect
168. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
172. C₃×C₄²	C₂²×C₉	semidirect
174. #217	C₂²×C₉	semidirect
175. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
176. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
177. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
178. C₄×Dic₃	C₂²×C₉	semidirect
210. #124	D₃×C₉	semidirect
213. C₃×C₉	H(3,𝔽₄)	semidirect
261. C₂×Q₈	C₂×D₃×C₉	semidirect
270. C₂²⋊C₄	C₂×D₃×C₉	semidirect
272. C₄²	C₂×D₃×C₉	semidirect
303. C₉	#5683	direct (N × H)
341. C₃	C₉×H(3,𝔽₄)	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×#124	2
C₉×#947	2
C₉×#937	2
C₉×#885	2
C₉×#882	2
C₉×#875	2
C₃×#5683	3
C₉×H(3,𝔽₄)	3

Subgroups — C9×#5683 #13153107

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5683 #13153107