Subgroups — C₉×#3137 #11767858

Order 1152.

558 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#536	C₂	1	1	yes	maximal, characteristic
3	C₉×#491	C₂	1	2	yes	maximal, complemented
4	C₉×#489	C₂	1	2	yes	maximal, complemented
5	C₉×#488	C₂	1	2	yes	maximal, complemented
6	C₉×#487	C₂	1	2	yes	maximal, complemented
7	C₉×#419	C₂	1	1	yes	maximal, characteristic, complemented
8	C₉×#417	C₂	1	1	yes	maximal, characteristic
9	C₉×#416	C₂	1	1	yes	maximal, characteristic
10	C₂×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₉×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×#3137	C₃	1	1	yes	maximal, characteristic
13	C₂×C₉×#41	C₂²	1	1	yes	characteristic
14	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
15	C₂×C₉×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
17	C₉×C₄⋊Q₈	—	2	1	no	—
18	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₉×C₄⋊Q₈	C₂²	1	2	yes	—
20	C₉×#125	—	2	1	no	—
21	C₉×#125	C₂²	1	2	yes	—
22	C₉×#124	C₂²	1	2	yes	—
23	C₉×#123	—	2	2	no	—
24	C₉×C₂²⋊Q₈	—	2	1	no	—
25	C₉×C₂²⋊Q₈	—	2	1	no	—
26	C₉×C₂²⋊Q₈	—	2	2	no	—
27	C₉×#117	C₂²	1	1	yes	characteristic
28	C₉×#117	C₂²	1	1	yes	characteristic
29	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₉×#103	C₂²	1	2	yes	—
31	C₉×#103	C₂²	1	2	yes	—
32	C₉×#103	C₂²	1	1	yes	characteristic
33	C₉×#103	C₂²	1	1	yes	characteristic
34	C₉×#103	C₂²	1	2	yes	—
35	C₉×#103	C₂²	1	2	yes	—
36	C₉×#103	C₂²	1	2	yes	—
37	C₉×#102	C₂²	1	1	yes	characteristic
38	C₉×#102	C₂²	1	1	yes	characteristic
39	C₉×#102	C₂²	1	2	yes	—
40	C₉×#97	C₂²	1	2	yes	—
41	C₄×C₈×C₉	C₂²	1	2	yes	—
42	C₃×#544	C₂×C₃	1	1	yes	characteristic
43	C₃×#536	C₂×C₃	1	1	yes	characteristic
44	C₃×#491	C₂×C₃	1	2	yes	—
45	C₃×#489	C₂×C₃	1	2	yes	—
46	C₃×#488	C₂×C₃	1	2	yes	—
47	C₃×#487	C₂×C₃	1	2	yes	—
48	C₃×#419	C₂×C₃	1	1	yes	characteristic
49	C₃×#417	C₂×C₃	1	1	yes	characteristic
50	C₃×#416	C₂×C₃	1	1	yes	characteristic
51	C₂×C₃×#103	C₂×C₃	1	1	yes	characteristic
52	C₃×#405	C₂×C₃	1	1	yes	characteristic
53	C₉×#41	—	2	2	no	—
54	C₉×#41	—	2	2	no	—
55	C₂×Q₈×C₉	—	2	1	no	—
56	C₂×Q₈×C₉	—	2	2	no	—
57	C₂×Q₈×C₉	—	2	2	no	—
58	C₂×Q₈×C₉	—	2	2	no	—
59	C₂×Q₈×C₉	C₂³	1	2	yes	—
60	C₂×Q₈×C₉	C₂³	1	1	yes	characteristic
61	C₂×D₄×C₉	—	2	1	no	—
62	C₂×D₄×C₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₉	—	2	1	no	—
64	C₂²×C₄×C₉	—	2	1	no	—
65	C₂²×C₄×C₉	—	2	1	no	—
66	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
67	C₉×M₁₆	—	2	2	no	—
68	C₂×C₈×C₉	—	2	2	no	—
69	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
70	C₂×C₈×C₉	C₂³	1	1	yes	characteristic
71	C₂×C₈×C₉	C₂³	1	2	yes	—
72	C₉×C₄⋊C₄	—	2	1	no	—
73	C₉×C₄⋊C₄	—	2	2	no	—
74	C₉×C₄⋊C₄	—	2	2	no	—
75	C₉×C₄⋊C₄	—	2	2	no	—
76	C₉×C₄⋊C₄	—	2	2	no	—
77	C₉×C₄⋊C₄	—	2	2	no	—
78	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
79	C₉×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₉×C₄⋊C₄	C₂³	1	2	yes	—
81	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₉×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₉×C₂²⋊C₄	—	2	1	no	—
84	C₉×C₂²⋊C₄	—	2	2	no	—
85	C₉×C₂²⋊C₄	—	2	2	no	—
86	C₉×C₂²⋊C₄	D₄	1	2	yes	—
87	C₄²×C₉	—	2	1	no	—
88	C₄²×C₉	C₂³	1	2	yes	—
89	#3137	C₉	1	1	yes	characteristic, direct product factor, Sylow
90	C₂×C₃×#41	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
93	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
94	C₃×C₄⋊Q₈	—	2	1	no	—
95	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
96	C₃×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
97	C₃×#125	—	2	1	no	—
98	C₃×#125	C₂²×C₃	1	2	yes	—
99	C₃×#124	C₂²×C₃	1	2	yes	—
100	C₃×#123	—	2	2	no	—
101	C₃×C₂²⋊Q₈	—	2	1	no	—
102	C₃×C₂²⋊Q₈	—	2	1	no	—
103	C₃×C₂²⋊Q₈	—	2	2	no	—
104	C₃×#117	C₂²×C₃	1	1	yes	characteristic
105	C₃×#117	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₃×#103	C₂²×C₃	1	2	yes	—
108	C₃×#103	C₂²×C₃	1	2	yes	—
109	C₃×#103	C₂²×C₃	1	1	yes	characteristic
110	C₃×#103	C₂²×C₃	1	1	yes	characteristic
111	C₃×#103	C₂²×C₃	1	2	yes	—
112	C₃×#103	C₂²×C₃	1	2	yes	—
113	C₃×#103	C₂²×C₃	1	2	yes	—
114	C₃×#102	C₂²×C₃	1	1	yes	characteristic
115	C₃×#102	C₂²×C₃	1	1	yes	characteristic
116	C₃×#102	C₂²×C₃	1	2	yes	—
117	C₃×#97	C₂²×C₃	1	2	yes	—
118	C₃×C₄×C₈	C₂²×C₃	1	2	yes	—
119	C₂³×C₉	—	2	1	no	—
120	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
121	Q₈×C₉	—	2	2	no	—
122	Q₈×C₉	—	2	2	no	—
123	Q₈×C₉	—	2	1	no	—
124	Q₈×C₉	—	2	1	no	—
125	Q₈×C₉	—	4	2	no	—
126	Q₈×C₉	—	8	2	no	—
127	D₄×C₉	—	2	1	no	—
128	D₄×C₉	—	2	1	no	—
129	D₄×C₉	—	4	2	no	—
130	C₂×C₄×C₉	—	2	1	no	—
131	C₂×C₄×C₉	—	2	1	no	—
132	C₂×C₄×C₉	—	2	2	no	—
133	C₂×C₄×C₉	—	2	2	no	—
134	C₂×C₄×C₉	—	2	1	no	—
135	C₂×C₄×C₉	—	4	2	no	—
136	C₂×C₄×C₉	—	4	2	no	—
137	C₂×C₄×C₉	—	8	1	no	—
138	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
139	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₉	#41	1	2	yes	—
142	C₂×C₄×C₉	#41	1	2	yes	—
143	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
144	C₈×C₉	—	2	1	no	—
145	C₈×C₉	—	2	1	no	—
146	C₈×C₉	—	2	2	no	—
147	#544	C₂×C₉	1	1	yes	characteristic, complemented
148	#536	C₂×C₉	1	1	yes	characteristic
149	#491	C₂×C₉	1	2	yes	complemented
150	#489	C₂×C₉	1	2	yes	complemented
151	#488	C₂×C₉	1	2	yes	complemented
152	#487	C₂×C₉	1	2	yes	complemented
153	#419	C₂×C₉	1	1	yes	characteristic, complemented
154	#417	C₂×C₉	1	1	yes	characteristic
155	#416	C₂×C₉	1	1	yes	characteristic
156	C₂×#103	C₂×C₉	1	1	yes	characteristic, complemented
157	#405	C₂×C₉	1	1	yes	characteristic, complemented
158	C₃×#41	—	2	2	no	—
159	C₃×#41	—	2	2	no	—
160	C₂×C₃×Q₈	—	2	1	no	—
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	—	2	2	no	—
163	C₂×C₃×Q₈	—	2	2	no	—
164	C₂×C₃×Q₈	C₂³×C₃	1	2	yes	—
165	C₂×C₃×Q₈	C₂³×C₃	1	1	yes	characteristic
166	C₂×C₃×D₄	—	2	1	no	—
167	C₂×C₃×D₄	C₂³×C₃	1	1	yes	characteristic
168	C₂²×C₃×C₄	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	1	no	—
170	C₂²×C₃×C₄	—	2	1	no	—
171	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
172	C₃×M₁₆	—	2	2	no	—
173	C₂×C₃×C₈	—	2	2	no	—
174	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
175	C₂×C₃×C₈	C₂³×C₃	1	2	yes	—
176	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
177	C₃×C₄⋊C₄	—	2	1	no	—
178	C₃×C₄⋊C₄	—	2	2	no	—
179	C₃×C₄⋊C₄	—	2	2	no	—
180	C₃×C₄⋊C₄	—	2	2	no	—
181	C₃×C₄⋊C₄	—	2	2	no	—
182	C₃×C₄⋊C₄	—	2	2	no	—
183	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
184	C₃×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
185	C₃×C₄⋊C₄	C₂³×C₃	1	2	yes	—
186	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
187	C₃×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
188	C₃×C₂²⋊C₄	—	2	1	no	—
189	C₃×C₂²⋊C₄	—	2	2	no	—
190	C₃×C₂²⋊C₄	—	2	2	no	—
191	C₃×C₂²⋊C₄	C₃×D₄	1	2	yes	—
192	C₃×C₄²	—	2	1	no	—
193	C₃×C₄²	C₂³×C₃	1	2	yes	—
194	C₂²×C₉	—	2	1	no	—
195	C₂²×C₉	—	2	1	no	—
196	C₂²×C₉	—	4	1	no	—
197	C₂²×C₉	—	4	1	no	—
198	C₂²×C₉	—	4	1	no	—
199	C₂²×C₉	#124	1	2	yes	—
200	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
201	C₄×C₉	—	2	2	no	—
202	C₄×C₉	—	2	2	no	—
203	C₄×C₉	—	4	1	no	—
204	C₄×C₉	—	4	2	no	—
205	C₄×C₉	—	4	2	no	—
206	C₄×C₉	—	4	1	no	—
207	C₄×C₉	—	4	1	no	—
208	C₄×C₉	#124	1	2	yes	—
209	C₄×C₉	C₂×#41	1	1	yes	characteristic
210	C₄×C₉	C₂×#41	1	1	yes	characteristic
211	C₂×#41	C₂²×C₉	1	1	yes	characteristic
212	C₂²×Q₈	C₂²×C₉	1	1	yes	characteristic
213	C₂×M₁₆	C₂²×C₉	1	1	yes	characteristic
214	C₂²×C₈	C₂²×C₉	1	1	yes	characteristic
215	C₄⋊Q₈	—	2	1	no	—
216	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
217	C₄⋊Q₈	C₂²×C₉	1	2	yes	—
218	#125	—	2	1	no	—
219	#125	C₂²×C₉	1	2	yes	—
220	#124	C₂²×C₉	1	2	yes	—
221	#123	—	2	2	no	—
222	C₂²⋊Q₈	—	2	1	no	—
223	C₂²⋊Q₈	—	2	1	no	—
224	C₂²⋊Q₈	—	2	2	no	—
225	#117	C₂²×C₉	1	1	yes	characteristic
226	#117	C₂²×C₉	1	1	yes	characteristic
227	C₂×C₄⋊C₄	C₂²×C₉	1	1	yes	characteristic
228	#103	C₂²×C₉	1	2	yes	—
229	#103	C₂²×C₉	1	2	yes	—
230	#103	C₂²×C₉	1	1	yes	characteristic
231	#103	C₂²×C₉	1	1	yes	characteristic
232	#103	C₂²×C₉	1	2	yes	—
233	#103	C₂²×C₉	1	2	yes	—
234	#103	C₂²×C₉	1	2	yes	—
235	#102	C₂²×C₉	1	1	yes	characteristic
236	#102	C₂²×C₉	1	1	yes	characteristic
237	#102	C₂²×C₉	1	2	yes	—
238	#97	C₂²×C₉	1	2	yes	—
239	C₄×C₈	C₂²×C₉	1	2	yes	—
240	C₂³×C₃	—	2	1	no	—
241	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
242	C₃×Q₈	—	2	2	no	—
243	C₃×Q₈	—	2	2	no	—
244	C₃×Q₈	—	2	1	no	—
245	C₃×Q₈	—	2	1	no	—
246	C₃×Q₈	—	4	2	no	—
247	C₃×Q₈	—	8	2	no	—
248	C₃×D₄	—	2	1	no	—
249	C₃×D₄	—	2	1	no	—
250	C₃×D₄	—	4	2	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	4	2	no	—
257	C₂×C₃×C₄	—	4	2	no	—
258	C₂×C₃×C₄	—	8	1	no	—
259	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
260	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
261	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
262	C₂×C₃×C₄	C₃×#41	1	2	yes	—
263	C₂×C₃×C₄	C₃×#41	1	2	yes	—
264	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
265	C₃×C₈	—	2	1	no	—
266	C₃×C₈	—	2	1	no	—
267	C₃×C₈	—	2	2	no	—
268	C₂×C₉	—	2	2	no	—
269	C₂×C₉	—	8	1	no	—
270	C₂×C₉	C₂×#124	1	1	yes	characteristic
271	C₂×C₉	#577	1	1	yes	characteristic
272	C₂×C₉	#578	1	1	yes	characteristic
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	C₂×Q₈	—	2	1	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	C₂³×C₉	1	2	yes	—
280	C₂×Q₈	C₂³×C₉	1	1	yes	characteristic
281	C₂×D₄	—	2	1	no	—
282	C₂×D₄	C₂³×C₉	1	1	yes	characteristic
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	C₂³×C₉	1	1	yes	characteristic
287	M₁₆	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
290	C₂×C₈	C₂³×C₉	1	2	yes	—
291	C₂×C₈	C₂³×C₉	1	1	yes	characteristic
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
299	C₄⋊C₄	D₄×C₉	1	1	yes	characteristic
300	C₄⋊C₄	C₂³×C₉	1	2	yes	—
301	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
302	C₄⋊C₄	C₂³×C₉	1	1	yes	characteristic
303	C₂²⋊C₄	—	2	1	no	—
304	C₂²⋊C₄	—	2	2	no	—
305	C₂²⋊C₄	—	2	2	no	—
306	C₂²⋊C₄	D₄×C₉	1	2	yes	—
307	C₄²	—	2	1	no	—
308	C₄²	C₂³×C₉	1	2	yes	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	4	1	no	—
312	C₂²×C₃	—	4	1	no	—
313	C₂²×C₃	—	4	1	no	—
314	C₂²×C₃	C₃×#124	1	2	yes	—
315	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
316	C₃×C₄	—	2	2	no	—
317	C₃×C₄	—	2	2	no	—
318	C₃×C₄	—	4	2	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	—	4	1	no	—
321	C₃×C₄	—	4	1	no	—
322	C₃×C₄	—	4	2	no	—
323	C₃×C₄	C₃×#124	1	2	yes	—
324	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
325	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
326	C₉	#3137	1	1	yes	characteristic, direct product factor, Sylow
327	C₂³	—	2	1	no	—
328	C₂³	C₂×D₄×C₉	1	1	yes	characteristic
329	Q₈	—	2	2	no	—
330	Q₈	—	2	2	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	2	1	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	8	2	no	—
335	D₄	—	2	1	no	—
336	D₄	—	2	1	no	—
337	D₄	—	4	2	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	8	1	no	—
346	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
347	C₂×C₄	C₂×D₄×C₉	1	2	yes	—
348	C₂×C₄	C₂×D₄×C₉	1	1	yes	characteristic
349	C₂×C₄	C₉×#41	1	2	yes	—
350	C₂×C₄	C₉×#41	1	2	yes	—
351	C₂×C₄	C₂⁴×C₉	1	1	yes	characteristic
352	C₈	—	2	1	no	—
353	C₈	—	2	1	no	—
354	C₈	—	2	2	no	—
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	8	1	no	—
357	C₂×C₃	C₂×C₃×#124	1	1	yes	characteristic
358	C₂×C₃	C₃×#577	1	1	yes	characteristic
359	C₂×C₃	C₃×#578	1	1	yes	characteristic
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	4	1	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	C₉×#124	1	2	yes	—
366	C₂²	C₂²×D₄×C₉	1	1	yes	characteristic
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	C₉×#124	1	2	yes	—
375	C₄	C₂×C₉×#41	1	1	yes	characteristic
376	C₄	C₂×C₉×#41	1	1	yes	characteristic
377	C₃	C₃×#3137	1	1	yes	characteristic
378	C₂	—	2	2	no	—
379	C₂	—	8	1	no	—
380	C₂	C₂×C₉×#124	1	1	yes	characteristic
381	C₂	C₉×#577	1	1	yes	characteristic
382	C₂	C₉×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	C₂²×D₄
commutator	C₂×C₄	C₂⁴×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂⁴×C₃
socle	C₂²×C₃	C₂²×C₃×D₄
prime radical	C₂×C₃×#41	C₂²×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₉ ◁ C₉×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₉×#544	C₂	semidirect
3. C₉×#491	C₂	semidirect
4. C₉×#489	C₂	semidirect
5. C₉×#488	C₂	semidirect
6. C₉×#487	C₂	semidirect
7. C₉×#419	C₂	semidirect
10. C₂×C₉×#103	C₂	semidirect
11. C₉×#405	C₂	semidirect
89. #3137	C₉	direct (N × H)
147. #544	C₂×C₉	semidirect
149. #491	C₂×C₉	semidirect
150. #489	C₂×C₉	semidirect
151. #488	C₂×C₉	semidirect
152. #487	C₂×C₉	semidirect
153. #419	C₂×C₉	semidirect
156. C₂×#103	C₂×C₉	semidirect
157. #405	C₂×C₉	semidirect
326. C₉	#3137	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#544	2
C₉×#536	2
C₉×#491	2
C₉×#489	2
C₉×#488	2
C₉×#487	2
C₉×#419	2
C₉×#417	2
C₉×#416	2
C₂×C₉×#103	2
C₉×#405	2
C₃×#3137	3

Subgroups — C9×#3137 #11767858

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#3137 #11767858