Subgroups — C₉×#5584 #13152705

Order 1728.

706 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#946	C₂	1	2	yes	maximal, complemented
3	C₉×#898	C₂	1	4	yes	maximal, complemented
4	C₉×#892	C₂	1	2	yes	maximal, complemented
5	C₉×#875	C₂	1	2	yes	maximal
6	C₄×C₉×D₁₂	C₂	1	1	yes	maximal, characteristic
7	C₉×#869	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₉×Dic₆	C₂	1	2	yes	maximal, complemented
9	C₃×#5584	C₃	1	1	yes	maximal, characteristic
10	C₉×#556	—	3	1	no	maximal
11	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃×C₉	C₂²	1	2	yes	—
14	C₂×C₉×Dic₆	C₂²	1	2	yes	—
15	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃×C₄²×C₉	C₂²	1	2	yes	—
18	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
19	C₉×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
21	C₉×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
22	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
24	C₉×C₄⋊Dic₃	C₂²	1	2	yes	—
25	C₉×Dic₃⋊C₄	C₂²	1	4	yes	—
26	C₄×C₉×Dic₃	C₂²	1	4	yes	—
27	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic
28	C₃×#946	C₂×C₃	1	2	yes	—
29	C₃×#898	C₂×C₃	1	4	yes	—
30	C₃×#892	C₂×C₃	1	2	yes	—
31	C₃×#875	C₂×C₃	1	2	yes	—
32	C₃×C₄×D₁₂	C₂×C₃	1	1	yes	characteristic
33	C₃×#869	C₂×C₃	1	1	yes	characteristic
34	C₃×C₄×Dic₆	C₂×C₃	1	2	yes	—
35	C₉×C₄⋊Q₈	—	3	1	no	—
36	C₉×#126	—	3	4	no	—
37	C₉×#124	—	3	2	no	—
38	C₉×C₂²⋊Q₈	—	3	2	no	—
39	C₄×Q₈×C₉	—	2	1	no	—
40	C₄×Q₈×C₉	—	3	2	no	—
41	C₄×Q₈×C₉	D₃	1	1	yes	characteristic, complemented
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	2	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	2	yes	—
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₂×C₉×Dic₃	C₂³	1	4	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	4	no	—
56	C₃×#556	—	3	1	no	—
57	#5584	C₉	1	1	yes	characteristic, direct product factor
58	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
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	2	yes	—
62	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
63	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
64	C₃²×C₄²	C₂²×C₃	1	2	yes	—
65	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
66	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
67	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
68	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	4	yes	—
69	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
70	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
71	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
72	C₃×Dic₃⋊C₄	C₂²×C₃	1	4	yes	—
73	C₃×C₄×Dic₃	C₂²×C₃	1	4	yes	—
74	C₂×Q₈×C₉	—	2	1	no	—
75	C₂×Q₈×C₉	—	3	2	no	—
76	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
77	C₂×D₄×C₉	—	3	1	no	—
78	C₂²×C₄×C₉	—	3	2	no	—
79	C₉×C₄⋊C₄	—	2	1	no	—
80	C₉×C₄⋊C₄	—	2	2	no	—
81	C₉×C₄⋊C₄	—	3	2	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	1	yes	characteristic
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	—	2	2	no	—
92	C₄²×C₉	—	3	4	no	—
93	C₄²×C₉	C₂×D₃	1	1	yes	characteristic
94	C₄²×C₉	C₂×D₃	1	2	yes	—
95	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
96	C₂×D₃×C₉	—	2	2	no	—
97	C₂×D₃×C₉	—	2	2	no	—
98	C₂×D₃×C₉	—	2	2	no	—
99	C₃×C₄×C₉	—	2	2	no	—
100	C₃×C₄×C₉	—	2	2	no	—
101	C₃×C₄×C₉	—	2	1	no	—
102	C₃×C₄×C₉	#41	1	2	yes	—
103	C₃×C₄×C₉	#41	1	2	yes	—
104	C₉×Dic₃	—	2	4	no	—
105	C₉×Dic₃	—	2	2	no	—
106	C₃×C₄⋊Q₈	—	3	1	no	—
107	C₃×#126	—	3	4	no	—
108	C₃×#124	—	3	2	no	—
109	C₃×C₂²⋊Q₈	—	3	2	no	—
110	C₃×C₄×Q₈	—	2	1	no	—
111	C₃×C₄×Q₈	—	3	2	no	—
112	C₃×C₄×Q₈	C₂×C₉	1	1	yes	characteristic, complemented
113	C₃×C₄×Q₈	C₃×D₃	1	1	yes	characteristic
114	C₃×C₄×D₄	—	3	1	no	—
115	C₃×#117	—	3	2	no	—
116	#946	C₂×C₉	1	2	yes	complemented
117	#898	C₂×C₉	1	4	yes	complemented
118	#892	C₂×C₉	1	2	yes	complemented
119	#875	C₂×C₉	1	2	yes	—
120	C₄×D₁₂	C₂×C₉	1	1	yes	characteristic
121	#869	C₂×C₉	1	1	yes	characteristic, complemented
122	C₄×Dic₆	C₂×C₉	1	2	yes	complemented
123	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
124	C₃²×Q₈	—	2	2	no	—
125	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
126	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
127	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
129	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
130	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
131	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
132	C₃×D₁₂	—	2	2	no	—
133	C₃×C₄×D₃	—	2	4	no	—
134	C₃×Dic₆	—	2	4	no	—
135	C₂³×C₉	—	3	2	no	—
136	Q₈×C₉	—	2	4	no	—
137	Q₈×C₉	—	2	2	no	—
138	Q₈×C₉	—	6	4	no	—
139	D₄×C₉	—	6	2	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	2	no	—
142	C₂×C₄×C₉	—	2	1	no	—
143	C₂×C₄×C₉	—	2	2	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	3	2	no	—
146	C₂×C₄×C₉	—	3	4	no	—
147	C₂×C₄×C₉	—	6	4	no	—
148	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
149	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
150	C₂×C₄×C₉	C₂²×D₃	1	2	yes	—
151	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
152	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
153	#556	—	3	1	no	Sylow
154	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
155	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
156	C₂×C₃×C₉	2₋¹⁺⁴	1	1	yes	characteristic
157	D₃×C₉	—	4	2	no	—
158	C₂×C₃×Q₈	—	2	1	no	—
159	C₂×C₃×Q₈	—	3	2	no	—
160	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
161	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
162	C₂×C₃×D₄	—	3	1	no	—
163	C₂²×C₃×C₄	—	3	2	no	—
164	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
165	C₂×C₄×D₃	C₂²×C₉	1	2	yes	—
166	C₂×Dic₆	C₂²×C₉	1	2	yes	—
167	C₃×C₄⋊C₄	—	2	1	no	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	3	4	no	—
170	C₃×C₄⋊C₄	—	3	2	no	—
171	C₃×C₄⋊C₄	—	3	1	no	—
172	C₃×C₄⋊C₄	—	3	2	no	—
173	C₃×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
174	C₃×C₄⋊C₄	C₂²×C₉	1	2	yes	—
175	C₃×C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
176	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
177	C₃×C₂²⋊C₄	—	3	4	no	—
178	C₃×C₂²⋊C₄	—	3	2	no	—
179	C₃×C₂²⋊C₄	—	3	4	no	—
180	C₃×C₄²	—	2	1	no	—
181	C₃×C₄²	—	2	2	no	—
182	C₃×C₄²	—	3	4	no	—
183	C₃×C₄²	C₂²×C₉	1	2	yes	—
184	C₃×C₄²	C₂²×C₉	1	1	yes	characteristic
185	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
186	C₃×C₄²	C₂×C₃×D₃	1	2	yes	—
187	(C₂×D₃)⋊C₄	C₂²×C₉	1	2	yes	—
188	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
189	(C₂×D₃)⋊C₄	C₂²×C₉	1	4	yes	—
190	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
191	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
192	C₄⋊Dic₃	C₂²×C₉	1	2	yes	—
193	Dic₃⋊C₄	C₂²×C₉	1	4	yes	—
194	C₄×Dic₃	C₂²×C₉	1	4	yes	—
195	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
196	C₂×C₃×D₃	—	2	2	no	—
197	C₂×C₃×D₃	—	2	2	no	—
198	C₂×C₃×D₃	—	2	2	no	—
199	C₃²×C₄	—	2	2	no	—
200	C₃²×C₄	—	2	2	no	—
201	C₃²×C₄	—	2	1	no	—
202	C₃²×C₄	C₃×#41	1	2	yes	—
203	C₃²×C₄	C₃×#41	1	2	yes	—
204	C₃×Dic₃	—	2	4	no	—
205	C₃×Dic₃	—	2	2	no	—
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	—	6	2	no	—
208	C₂²×C₉	—	6	2	no	—
209	C₂²×C₉	—	6	2	no	—
210	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
211	C₄×C₉	—	2	4	no	—
212	C₄×C₉	—	2	2	no	—
213	C₄×C₉	—	2	2	no	—
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	2	2	no	—
217	C₄×C₉	—	4	2	no	—
218	C₄×C₉	—	4	1	no	—
219	C₄×C₉	—	6	2	no	—
220	C₄×C₉	—	6	4	no	—
221	C₄×C₉	#235	1	2	yes	—
222	C₄×C₉	#239	1	2	yes	—
223	C₄⋊Q₈	—	3	1	no	—
224	#126	—	3	4	no	—
225	#124	—	3	2	no	—
226	C₂²⋊Q₈	—	3	2	no	—
227	C₄×Q₈	—	3	2	no	—
228	C₄×Q₈	D₃×C₉	1	1	yes	characteristic, complemented
229	C₄×D₄	—	3	1	no	—
230	#117	—	3	2	no	—
231	C₃×C₉	#556	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₃	—	3	2	no	—
233	C₂²×D₃	C₂³×C₉	1	2	yes	—
234	C₃×Q₈	—	2	4	no	—
235	C₃×Q₈	—	2	2	no	—
236	C₃×Q₈	—	2	2	no	—
237	C₃×Q₈	—	6	4	no	—
238	C₃×D₄	—	6	2	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	2	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	3	2	no	—
245	C₂×C₃×C₄	—	3	4	no	—
246	C₂×C₃×C₄	—	6	4	no	—
247	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
248	C₂×C₃×C₄	C₂³×C₉	1	2	yes	—
249	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×C₃×D₃	1	2	yes	—
255	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
257	C₂×Dic₃	C₂³×C₉	1	2	yes	—
258	C₂×Dic₃	C₂³×C₉	1	4	yes	—
259	D₁₂	—	2	2	no	—
260	C₄×D₃	—	2	4	no	—
261	Dic₆	—	2	4	no	—
262	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
263	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
264	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
265	C₃×D₃	—	4	2	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	—	2	1	no	—
268	C₂×C₉	—	2	1	no	—
269	C₂×C₉	—	12	2	no	—
270	C₂×C₉	C₂×#235	1	1	yes	characteristic
271	C₂×C₉	C₂×#239	1	1	yes	characteristic
272	C₂×C₉	#1010	1	1	yes	characteristic
273	C₂×Q₈	—	3	2	no	—
274	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
275	C₂×D₄	—	3	1	no	—
276	C₂²×C₄	—	3	2	no	—
277	C₄⋊C₄	—	3	2	no	—
278	C₄⋊C₄	—	3	1	no	—
279	C₄⋊C₄	—	3	4	no	—
280	C₄⋊C₄	—	3	2	no	—
281	C₄⋊C₄	C₂×D₃×C₉	1	1	yes	characteristic
282	C₄⋊C₄	C₂×D₃×C₉	1	2	yes	—
283	C₂²⋊C₄	—	3	4	no	—
284	C₂²⋊C₄	—	3	2	no	—
285	C₂²⋊C₄	—	3	4	no	—
286	C₄²	—	3	4	no	—
287	C₄²	C₂×D₃×C₉	1	1	yes	characteristic
288	C₄²	C₂×D₃×C₉	1	2	yes	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	6	2	no	—
291	C₂²×C₃	—	6	2	no	—
292	C₂²×C₃	—	6	2	no	—
293	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
294	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
295	C₂×D₃	—	2	2	no	—
296	C₂×D₃	—	2	2	no	—
297	C₂×D₃	—	2	2	no	—
298	C₃×C₄	—	2	4	no	—
299	C₃×C₄	—	2	2	no	—
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	2	no	—
306	C₃×C₄	—	2	2	no	—
307	C₃×C₄	—	4	2	no	—
308	C₃×C₄	—	4	1	no	—
309	C₃×C₄	—	6	2	no	—
310	C₃×C₄	—	6	4	no	—
311	C₃×C₄	C₉×#41	1	2	yes	—
312	C₃×C₄	C₉×#41	1	2	yes	—
313	C₃×C₄	C₃×#235	1	2	yes	—
314	C₃×C₄	C₃×#239	1	2	yes	—
315	Dic₃	—	2	4	no	—
316	Dic₃	—	2	2	no	—
317	C₃²	C₃×#556	1	1	yes	characteristic
318	C₉	—	2	1	no	—
319	C₉	#5584	1	1	yes	characteristic, direct product factor
320	C₂³	—	3	2	no	—
321	Q₈	—	2	2	no	—
322	Q₈	—	6	4	no	—
323	D₄	—	6	2	no	—
324	C₂×C₄	—	3	2	no	—
325	C₂×C₄	—	3	4	no	—
326	C₂×C₄	—	6	4	no	—
327	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
328	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
329	C₂×C₄	C₂²×D₃×C₉	1	2	yes	—
330	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
331	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
332	C₂×C₃	—	2	1	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	—	12	2	no	—
336	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
337	C₂×C₃	C₂×C₉×#41	1	1	yes	characteristic
338	C₂×C₃	C₉×2₋¹⁺⁴	1	1	yes	characteristic
339	C₂×C₃	C₂×C₃×#235	1	1	yes	characteristic
340	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
341	C₂×C₃	C₃×#1010	1	1	yes	characteristic
342	D₃	—	4	2	no	—
343	C₂²	—	6	2	no	—
344	C₂²	—	6	2	no	—
345	C₂²	—	6	2	no	—
346	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
347	C₄	—	2	2	no	—
348	C₄	—	2	2	no	—
349	C₄	—	2	1	no	—
350	C₄	—	6	2	no	—
351	C₄	—	6	4	no	—
352	C₄	C₉×#235	1	2	yes	—
353	C₄	C₉×#239	1	2	yes	—
354	C₃	—	2	1	no	—
355	C₃	C₉×#556	1	1	yes	characteristic, complemented
356	C₃	C₃×#5584	1	1	yes	characteristic
357	C₂	—	12	2	no	—
358	C₂	C₂×C₉×#235	1	1	yes	characteristic
359	C₂	C₂×C₉×#239	1	1	yes	characteristic
360	C₂	C₉×#1010	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×C₄×Q₈×C₉	C₂
socle, cosocle	C₂²×C₃²	C₂⁴×C₃
prime radical	C₂×C₃×D₁₂	C₂²×C₃
hypercenter	C₄×Q₈×C₉	D₃
hypocenter	C₃	C₉×#556
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₄×Q₈×C₉

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×Q₈×C₉	C₂	semidirect
2. C₉×#946	C₂	semidirect
3. C₉×#898	C₂	semidirect
4. C₉×#892	C₂	semidirect
7. C₉×#869	C₂	semidirect
8. C₄×C₉×Dic₆	C₂	semidirect
41. C₄×Q₈×C₉	D₃	semidirect
57. #5584	C₉	direct (N × H)
112. C₃×C₄×Q₈	C₂×C₉	semidirect
116. #946	C₂×C₉	semidirect
117. #898	C₂×C₉	semidirect
118. #892	C₂×C₉	semidirect
121. #869	C₂×C₉	semidirect
122. C₄×Dic₆	C₂×C₉	semidirect
228. C₄×Q₈	D₃×C₉	semidirect
231. C₃×C₉	#556	semidirect
319. C₉	#5584	direct (N × H)
355. 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×C₄×Q₈×C₉	2
C₉×#946	2
C₉×#898	2
C₉×#892	2
C₉×#875	2
C₄×C₉×D₁₂	2
C₉×#869	2
C₄×C₉×Dic₆	2
C₃×#5584	3
C₉×#556	3

Subgroups — C9×#5584 #13152705

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5584 #13152705