Subgroups — C₉×#5165 #13143343

Order 1728.

440 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₉×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#947	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×#213	C₂	1	1	yes	maximal, characteristic
5	C₉×#835	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#821	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#5165	C₃	1	1	yes	maximal, characteristic
9	C₉×#463	—	3	1	no	maximal
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
12	C₂²×C₉×Dic₃	—	2	1	no	—
13	C₂×C₉×D₁₂	C₂²	1	1	yes	characteristic
14	C₃×C₉×SD₁₆	—	2	2	no	—
15	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
16	C₉×#217	—	2	1	no	—
17	C₉×#213	—	2	2	no	—
18	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
19	C₉×(C₂×D₃)⋊C₄	—	2	1	no	—
20	C₉×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
21	C₄×C₉×Dic₃	C₂²	1	1	yes	characteristic
22	C₂×C₉×C₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₃²×SD₁₆	C₂×C₃	1	1	yes	characteristic
24	C₃×#947	C₂×C₃	1	1	yes	characteristic
25	C₃×D₄×Dic₃	C₂×C₃	1	1	yes	characteristic
26	C₂×C₃×#213	C₂×C₃	1	1	yes	characteristic
27	C₃×#835	C₂×C₃	1	1	yes	characteristic
28	C₃×#821	C₂×C₃	1	1	yes	characteristic
29	C₃×Dic₃⋊C₈	C₂×C₃	1	1	yes	characteristic
30	C₂×C₉×SD₁₆	—	2	1	no	—
31	C₂×C₉×SD₁₆	D₃	1	1	yes	characteristic, complemented
32	C₂×C₉×D₈	—	3	1	no	—
33	C₉×#124	—	3	1	no	—
34	C₄×D₄×C₉	—	3	1	no	—
35	C₉×C₄⋊C₈	—	3	1	no	—
36	C₉×#103	—	3	1	no	—
37	C₉×#102	—	3	1	no	—
38	C₂³×C₃×C₉	—	2	1	no	—
39	C₂²×D₃×C₉	—	2	1	no	—
40	C₃×Q₈×C₉	—	2	1	no	—
41	C₃×Q₈×C₉	—	2	1	no	—
42	C₃×D₄×C₉	—	2	1	no	—
43	C₃×D₄×C₉	D₄	1	2	yes	—
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
46	C₂×C₉×Dic₃	—	2	1	no	—
47	C₂×C₉×Dic₃	—	4	2	no	—
48	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
49	C₂×C₉×Dic₃	D₄	1	1	yes	characteristic
50	C₉×D₁₂	—	2	1	no	—
51	C₉×D₁₂	—	2	1	no	—
52	C₃×C₈×C₉	—	2	1	no	—
53	C₉×C₃⋊C₈	—	2	1	no	—
54	C₃×#463	—	3	1	no	—
55	#5165	C₉	1	1	yes	characteristic, direct product factor
56	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
58	C₂²×C₃×Dic₃	—	2	1	no	—
59	C₂×C₃×D₁₂	C₂²×C₃	1	1	yes	characteristic
60	C₃²×SD₁₆	—	2	2	no	—
61	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
62	C₃×#217	—	2	1	no	—
63	C₃×#213	—	2	2	no	—
64	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
65	C₃×(C₂×D₃)⋊C₄	—	2	1	no	—
66	C₃×C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
67	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
69	C₂×Q₈×C₉	—	2	1	no	—
70	C₂×Q₈×C₉	C₂×D₃	1	1	yes	characteristic
71	C₂×D₄×C₉	—	2	1	no	—
72	C₂×D₄×C₉	—	3	1	no	—
73	C₂×D₄×C₉	C₂×D₃	1	1	yes	characteristic
74	C₂²×C₄×C₉	—	6	1	no	—
75	C₉×SD₁₆	—	2	4	no	—
76	C₉×SD₁₆	—	2	2	no	—
77	C₉×D₈	—	6	2	no	—
78	C₂×C₈×C₉	—	2	1	no	—
79	C₂×C₈×C₉	—	3	1	no	—
80	C₂×C₈×C₉	C₂×D₃	1	1	yes	characteristic
81	C₉×C₄⋊C₄	—	3	1	no	—
82	C₉×C₂²⋊C₄	—	6	1	no	—
83	C₉×C₂²⋊C₄	—	6	1	no	—
84	C₉×C₂²⋊C₄	—	6	1	no	—
85	C₄²×C₉	—	3	1	no	—
86	C₂²×C₃×C₉	—	2	2	no	—
87	C₂²×C₃×C₉	—	4	1	no	—
88	C₂²×C₃×C₉	—	4	1	no	—
89	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
90	C₂×D₃×C₉	—	4	1	no	—
91	C₂×D₃×C₉	—	4	1	no	—
92	C₂×D₃×C₉	—	4	1	no	—
93	C₃×C₄×C₉	—	4	1	no	—
94	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
95	C₃×C₄×C₉	#41	1	1	yes	characteristic
96	C₉×Dic₃	—	2	1	no	—
97	C₉×Dic₃	—	2	1	no	—
98	C₉×Dic₃	—	4	1	no	—
99	C₂×C₃×SD₁₆	—	2	1	no	—
100	C₂×C₃×SD₁₆	C₂×C₉	1	1	yes	characteristic, complemented
101	C₂×C₃×SD₁₆	C₃×D₃	1	1	yes	characteristic
102	C₂×C₃×D₈	—	3	1	no	—
103	C₃×#124	—	3	1	no	—
104	C₃×C₄×D₄	—	3	1	no	—
105	#947	C₂×C₉	1	1	yes	characteristic, complemented
106	D₄×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
107	C₂×#213	C₂×C₉	1	1	yes	characteristic
108	C₃×C₄⋊C₈	—	3	1	no	—
109	C₃×#103	—	3	1	no	—
110	C₃×#102	—	3	1	no	—
111	#835	C₂×C₉	1	1	yes	characteristic, complemented
112	#821	C₂×C₉	1	1	yes	characteristic, complemented
113	Dic₃⋊C₈	C₂×C₉	1	1	yes	characteristic, complemented
114	C₂³×C₃²	—	2	1	no	—
115	C₂²×C₃×D₃	—	2	1	no	—
116	C₃²×Q₈	—	2	1	no	—
117	C₃²×Q₈	—	2	1	no	—
118	C₃²×D₄	—	2	1	no	—
119	C₃²×D₄	C₃×D₄	1	2	yes	—
120	C₂×C₃²×C₄	—	2	1	no	—
121	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
122	C₂×C₃×Dic₃	—	2	1	no	—
123	C₂×C₃×Dic₃	—	4	2	no	—
124	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
125	C₂×C₃×Dic₃	C₃×D₄	1	1	yes	characteristic
126	C₃×D₁₂	—	2	1	no	—
127	C₃×D₁₂	—	2	1	no	—
128	C₂³×C₉	—	2	1	no	—
129	C₂³×C₉	—	4	1	no	—
130	C₂³×C₉	—	6	1	no	—
131	C₃²×C₈	—	2	1	no	—
132	C₃×C₃⋊C₈	—	2	1	no	—
133	Q₈×C₉	—	2	2	no	—
134	Q₈×C₉	—	2	1	no	—
135	Q₈×C₉	—	2	1	no	—
136	Q₈×C₉	—	4	1	no	—
137	D₄×C₉	—	2	1	no	—
138	D₄×C₉	—	2	2	no	—
139	D₄×C₉	—	4	1	no	—
140	D₄×C₉	—	6	1	no	—
141	D₄×C₉	—	6	1	no	—
142	D₄×C₉	#67	1	2	yes	—
143	C₂×C₄×C₉	—	2	1	no	—
144	C₂×C₄×C₉	—	2	1	no	—
145	C₂×C₄×C₉	—	3	1	no	—
146	C₂×C₄×C₉	—	3	1	no	—
147	C₂×C₄×C₉	—	4	1	no	—
148	C₂×C₄×C₉	—	6	1	no	—
149	C₂×C₄×C₉	—	12	2	no	—
150	C₂×C₄×C₉	C₂²×D₃	1	1	yes	characteristic
151	C₈×C₉	—	2	2	no	—
152	C₈×C₉	—	2	1	no	—
153	C₈×C₉	—	6	1	no	—
154	#463	—	3	1	no	Sylow
155	C₂×C₃×C₉	—	4	2	no	—
156	C₂×C₃×C₉	#121	1	1	yes	characteristic
157	C₂×C₃×C₉	#135	1	1	yes	characteristic
158	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	D₃×C₉	—	8	1	no	—
160	C₂×C₃×Q₈	—	2	1	no	—
161	C₂×C₃×Q₈	C₂²×C₉	1	1	yes	characteristic
162	C₂×C₃×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
163	C₂×C₃×D₄	—	2	1	no	—
164	C₂×C₃×D₄	—	3	1	no	—
165	C₂×C₃×D₄	C₂²×C₉	1	1	yes	characteristic
166	C₂×C₃×D₄	C₂×C₃×D₃	1	1	yes	characteristic
167	C₂²×C₃×C₄	—	6	1	no	—
168	C₂²×Dic₃	—	2	1	no	—
169	C₂×D₁₂	C₂²×C₉	1	1	yes	characteristic
170	C₃×SD₁₆	—	2	4	no	—
171	C₃×SD₁₆	—	2	2	no	—
172	C₃×SD₁₆	—	2	2	no	—
173	C₃×D₈	—	6	2	no	—
174	C₂×C₃×C₈	—	2	1	no	—
175	C₂×C₃×C₈	—	3	1	no	—
176	C₂×C₃×C₈	C₂²×C₉	1	1	yes	characteristic
177	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
178	C₃×C₄⋊C₄	—	3	1	no	—
179	C₃×C₂²⋊C₄	—	6	1	no	—
180	C₃×C₂²⋊C₄	—	6	1	no	—
181	C₃×C₂²⋊C₄	—	6	1	no	—
182	C₃×C₄²	—	3	1	no	—
183	#217	—	2	1	no	—
184	#213	—	2	2	no	—
185	(C₂×D₃)⋊C₄	—	2	1	no	—
186	(C₂×D₃)⋊C₄	—	2	1	no	—
187	C₄⋊Dic₃	C₂²×C₉	1	1	yes	characteristic
188	C₄×Dic₃	C₂²×C₉	1	1	yes	characteristic
189	C₂×C₃⋊C₈	C₂²×C₉	1	1	yes	characteristic
190	C₂²×C₃²	—	2	2	no	—
191	C₂²×C₃²	—	4	1	no	—
192	C₂²×C₃²	—	4	1	no	—
193	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
194	C₂×C₃×D₃	—	4	1	no	—
195	C₂×C₃×D₃	—	4	1	no	—
196	C₂×C₃×D₃	—	4	1	no	—
197	C₃²×C₄	—	4	1	no	—
198	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
199	C₃²×C₄	C₃×#41	1	1	yes	characteristic
200	C₃×Dic₃	—	2	1	no	—
201	C₃×Dic₃	—	2	1	no	—
202	C₃×Dic₃	—	4	1	no	—
203	C₂²×C₉	—	2	2	no	—
204	C₂²×C₉	—	2	1	no	—
205	C₂²×C₉	—	4	2	no	—
206	C₂²×C₉	—	4	1	no	—
207	C₂²×C₉	—	4	1	no	—
208	C₂²×C₉	—	8	1	no	—
209	C₂²×C₉	—	8	1	no	—
210	C₂²×C₉	—	12	1	no	—
211	C₂²×C₉	—	12	1	no	—
212	C₂²×C₉	—	12	1	no	—
213	C₂²×C₉	D₃×D₄	1	1	yes	characteristic
214	C₄×C₉	—	2	1	no	—
215	C₄×C₉	—	2	1	no	—
216	C₄×C₉	—	4	2	no	—
217	C₄×C₉	—	4	1	no	—
218	C₄×C₉	—	6	1	no	—
219	C₄×C₉	—	6	1	no	—
220	C₄×C₉	—	12	1	no	—
221	C₄×C₉	#237	1	1	yes	characteristic
222	C₄×C₉	C₂×#67	1	1	yes	characteristic
223	C₂×SD₁₆	D₃×C₉	1	1	yes	characteristic, complemented
224	C₂×D₈	—	3	1	no	—
225	#124	—	3	1	no	—
226	C₄×D₄	—	3	1	no	—
227	C₄⋊C₈	—	3	1	no	—
228	#103	—	3	1	no	—
229	#102	—	3	1	no	—
230	C₃×C₉	#463	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₃	—	2	1	no	—
232	C₂³×C₃	—	2	1	no	—
233	C₂³×C₃	—	4	1	no	—
234	C₂³×C₃	—	6	1	no	—
235	C₂²×D₃	—	2	1	no	—
236	C₃×Q₈	—	2	2	no	—
237	C₃×Q₈	—	2	1	no	—
238	C₃×Q₈	—	2	1	no	—
239	C₃×Q₈	—	2	1	no	—
240	C₃×Q₈	—	2	1	no	—
241	C₃×Q₈	—	4	1	no	—
242	C₃×D₄	—	2	1	no	—
243	C₃×D₄	—	2	1	no	—
244	C₃×D₄	—	2	2	no	—
245	C₃×D₄	—	4	1	no	—
246	C₃×D₄	—	6	1	no	—
247	C₃×D₄	—	6	1	no	—
248	C₃×D₄	D₄×C₉	1	2	yes	—
249	C₃×D₄	C₃×#67	1	2	yes	—
250	C₂×C₃×C₄	—	2	1	no	—
251	C₂×C₃×C₄	—	2	1	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	3	1	no	—
254	C₂×C₃×C₄	—	3	1	no	—
255	C₂×C₃×C₄	—	4	1	no	—
256	C₂×C₃×C₄	—	6	1	no	—
257	C₂×C₃×C₄	—	12	2	no	—
258	C₂×C₃×C₄	C₂³×C₉	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
260	C₂×Dic₃	—	2	1	no	—
261	C₂×Dic₃	—	4	2	no	—
262	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
263	C₂×Dic₃	D₄×C₉	1	1	yes	characteristic
264	D₁₂	—	2	1	no	—
265	D₁₂	—	2	1	no	—
266	C₃×C₈	—	2	2	no	—
267	C₃×C₈	—	2	1	no	—
268	C₃×C₈	—	2	1	no	—
269	C₃×C₈	—	6	1	no	—
270	C₃⋊C₈	—	2	1	no	—
271	C₂×C₃²	—	4	2	no	—
272	C₂×C₃²	C₃×#121	1	1	yes	characteristic
273	C₂×C₃²	C₃×#135	1	1	yes	characteristic
274	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
275	C₃×D₃	—	8	1	no	—
276	C₂×C₉	—	2	1	no	—
277	C₂×C₉	—	2	1	no	—
278	C₂×C₉	—	2	1	no	—
279	C₂×C₉	—	4	2	no	—
280	C₂×C₉	—	8	2	no	—
281	C₂×C₉	—	24	1	no	—
282	C₂×C₉	#914	1	1	yes	characteristic
283	C₂×C₉	#916	1	1	yes	characteristic
284	C₂×C₉	#939	1	1	yes	characteristic
285	C₂×Q₈	C₂×D₃×C₉	1	1	yes	characteristic
286	C₂×D₄	—	3	1	no	—
287	C₂×D₄	C₂×D₃×C₉	1	1	yes	characteristic
288	C₂²×C₄	—	6	1	no	—
289	SD₁₆	—	2	2	no	—
290	D₈	—	6	2	no	—
291	C₂×C₈	—	3	1	no	—
292	C₂×C₈	C₂×D₃×C₉	1	1	yes	characteristic
293	C₄⋊C₄	—	3	1	no	—
294	C₂²⋊C₄	—	6	1	no	—
295	C₂²⋊C₄	—	6	1	no	—
296	C₂²⋊C₄	—	6	1	no	—
297	C₄²	—	3	1	no	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	4	2	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	—	4	1	no	—
304	C₂²×C₃	—	4	1	no	—
305	C₂²×C₃	—	4	1	no	—
306	C₂²×C₃	—	8	1	no	—
307	C₂²×C₃	—	8	1	no	—
308	C₂²×C₃	—	12	1	no	—
309	C₂²×C₃	—	12	1	no	—
310	C₂²×C₃	—	12	1	no	—
311	C₂²×C₃	C₂×D₄×C₉	1	1	yes	characteristic
312	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
313	C₂×D₃	—	4	1	no	—
314	C₂×D₃	—	4	1	no	—
315	C₂×D₃	—	4	1	no	—
316	C₃×C₄	—	2	1	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	4	2	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	—	4	1	no	—
321	C₃×C₄	—	6	1	no	—
322	C₃×C₄	—	6	1	no	—
323	C₃×C₄	—	12	1	no	—
324	C₃×C₄	C₂×D₄×C₉	1	1	yes	characteristic
325	C₃×C₄	C₉×#41	1	1	yes	characteristic
326	C₃×C₄	C₃×#237	1	1	yes	characteristic
327	C₃×C₄	C₂×C₃×#67	1	1	yes	characteristic
328	Dic₃	—	2	1	no	—
329	Dic₃	—	2	1	no	—
330	Dic₃	—	4	1	no	—
331	C₃²	C₃×#463	1	1	yes	characteristic
332	C₉	—	2	1	no	—
333	C₉	#5165	1	1	yes	characteristic, direct product factor
334	C₂³	—	2	1	no	—
335	C₂³	—	6	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	6	1	no	—
340	D₄	—	6	1	no	—
341	D₄	C₉×#67	1	2	yes	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	3	1	no	—
344	C₂×C₄	—	3	1	no	—
345	C₂×C₄	—	6	1	no	—
346	C₂×C₄	—	12	2	no	—
347	C₂×C₄	C₂²×D₃×C₉	1	1	yes	characteristic
348	C₈	—	2	1	no	—
349	C₈	—	6	1	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	4	2	no	—
354	C₂×C₃	—	4	2	no	—
355	C₂×C₃	—	8	2	no	—
356	C₂×C₃	—	24	1	no	—
357	C₂×C₃	C₉×#121	1	1	yes	characteristic
358	C₂×C₃	C₉×#135	1	1	yes	characteristic
359	C₂×C₃	C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
360	C₂×C₃	C₃×#914	1	1	yes	characteristic
361	C₂×C₃	C₃×#916	1	1	yes	characteristic
362	C₂×C₃	C₃×#939	1	1	yes	characteristic
363	D₃	—	8	1	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	12	1	no	—
368	C₂²	—	12	1	no	—
369	C₂²	—	12	1	no	—
370	C₂²	D₃×D₄×C₉	1	1	yes	characteristic
371	C₄	—	4	1	no	—
372	C₄	—	6	1	no	—
373	C₄	—	6	1	no	—
374	C₄	—	12	1	no	—
375	C₄	C₉×#237	1	1	yes	characteristic
376	C₄	C₂×C₉×#67	1	1	yes	characteristic
377	C₃	—	2	1	no	—
378	C₃	C₉×#463	1	1	yes	characteristic, complemented
379	C₃	C₃×#5165	1	1	yes	characteristic
380	C₂	—	4	2	no	—
381	C₂	—	24	1	no	—
382	C₂	C₉×#914	1	1	yes	characteristic
383	C₂	C₉×#916	1	1	yes	characteristic
384	C₂	C₉×#939	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₉	D₃×D₄
commutator	C₂×C₃×C₄	C₂³×C₉
Frattini	C₂×C₃×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×SD₁₆	C₂
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₂×C₃×#213	C₂×C₃
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₉×SD₁₆	D₃
hypocenter	C₃	C₉×#463
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₉ ◁ C₂×C₄×C₉ ◁ C₂×C₉×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×SD₁₆	C₂	semidirect
2. C₉×#947	C₂	semidirect
3. D₄×C₉×Dic₃	C₂	semidirect
5. C₉×#835	C₂	semidirect
6. C₉×#821	C₂	semidirect
7. C₉×Dic₃⋊C₈	C₂	semidirect
31. C₂×C₉×SD₁₆	D₃	semidirect
55. #5165	C₉	direct (N × H)
100. C₂×C₃×SD₁₆	C₂×C₉	semidirect
105. #947	C₂×C₉	semidirect
106. D₄×Dic₃	C₂×C₉	semidirect
111. #835	C₂×C₉	semidirect
112. #821	C₂×C₉	semidirect
113. Dic₃⋊C₈	C₂×C₉	semidirect
223. C₂×SD₁₆	D₃×C₉	semidirect
230. C₃×C₉	#463	semidirect
333. C₉	#5165	direct (N × H)
378. C₃	C₉×#463	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₉×SD₁₆	2
C₉×#947	2
D₄×C₉×Dic₃	2
C₂×C₉×#213	2
C₉×#835	2
C₉×#821	2
C₉×Dic₃⋊C₈	2
C₃×#5165	3
C₉×#463	3

Subgroups — C9×#5165 #13143343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5165 #13143343