Subgroups — C₉×#5837 #13153753

Order 1728.

920 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₉×#1009	C₂	1	1	yes	maximal, characteristic, complemented
3	C₉×#950	C₂	1	3	yes	maximal, complemented
4	C₉×#949	C₂	1	3	yes	maximal, complemented
5	C₉×#948	C₂	1	1	yes	maximal, characteristic, complemented
6	C₉×#942	C₂	1	3	yes	maximal, complemented
7	C₂×C₉×#215	C₂	1	3	yes	maximal, complemented
8	C₃×#5837	C₃	1	1	yes	maximal, characteristic
9	C₉×#577	—	3	1	no	maximal
10	C₃×C₉×#41	—	2	3	no	—
11	C₃×C₉×#41	C₂²	1	1	yes	characteristic
12	C₃×C₉×#41	C₂²	1	3	yes	complemented
13	C₂×C₃×Q₈×C₉	—	2	1	no	—
14	C₂×C₃×Q₈×C₉	C₂²	1	3	yes	complemented
15	C₉×#239	—	2	1	no	—
16	D₃×D₄×C₉	—	2	3	no	—
17	C₉×#235	C₂²	1	3	yes	—
18	C₂×C₉×D₁₂	C₂²	1	3	yes	—
19	C₉×#216	C₂²	1	3	yes	complemented
20	C₉×#215	C₂²	1	3	yes	complemented
21	C₉×#215	C₂²	1	6	yes	complemented
22	C₉×#214	C₂²	1	1	yes	characteristic, complemented
23	C₉×#213	C₂²	1	3	yes	complemented
24	C₉×#208	C₂²	1	3	yes	complemented
25	C₂×C₉×C₃⋊C₈	C₂²	1	3	yes	complemented
26	C₃²×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic
27	C₃×#1009	C₂×C₃	1	1	yes	characteristic
28	C₃×#950	C₂×C₃	1	3	yes	—
29	C₃×#949	C₂×C₃	1	3	yes	—
30	C₃×#948	C₂×C₃	1	1	yes	characteristic
31	C₃×#942	C₂×C₃	1	3	yes	—
32	C₂×C₃×#215	C₂×C₃	1	3	yes	—
33	C₉×2₋¹⁺⁴	—	2	1	no	—
34	C₉×2₋¹⁺⁴	D₃	1	1	yes	characteristic, complemented
35	C₉×H(5,𝔽₂)	—	3	1	no	—
36	C₉×#137	—	3	3	no	—
37	C₉×AGL(1,ℤ/8)	—	3	3	no	—
38	C₉×#135	—	3	3	no	—
39	C₂×C₉×SD₁₆	—	3	3	no	—
40	C₉×#131	—	3	1	no	—
41	C₂²×D₃×C₉	—	2	3	no	—
42	C₃×Q₈×C₉	—	2	3	no	—
43	C₃×Q₈×C₉	D₄	1	1	yes	characteristic
44	C₃×Q₈×C₉	C₂³	1	3	yes	—
45	C₃×D₄×C₉	—	2	3	no	—
46	C₃×D₄×C₉	D₄	1	3	yes	—
47	C₃×D₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	—	2	3	no	—
49	C₂×C₃×C₄×C₉	—	2	3	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	3	yes	—
51	C₉×#67	—	2	3	no	—
52	C₉×D₁₂	—	2	3	no	—
53	C₉×D₁₂	C₂³	1	3	yes	—
54	C₄×D₃×C₉	—	2	3	no	—
55	C₉×Dic₆	C₂³	1	1	yes	characteristic
56	C₉×C₃⋊C₈	C₂³	1	1	yes	characteristic
57	C₉×C₃⋊C₈	C₂³	1	3	yes	—
58	C₃×#577	—	3	1	no	—
59	#5837	C₉	1	1	yes	characteristic, direct product factor
60	C₃²×#41	—	2	3	no	—
61	C₃²×#41	C₂²×C₃	1	3	yes	—
62	C₃²×#41	C₂²×C₃	1	1	yes	characteristic
63	C₂×C₃²×Q₈	—	2	1	no	—
64	C₂×C₃²×Q₈	C₂²×C₃	1	3	yes	—
65	C₃×#239	—	2	1	no	—
66	C₃×D₃×D₄	—	2	3	no	—
67	C₃×#235	C₂²×C₃	1	3	yes	—
68	C₂×C₃×D₁₂	C₂²×C₃	1	3	yes	—
69	C₃×#216	C₂²×C₃	1	3	yes	—
70	C₃×#215	C₂²×C₃	1	3	yes	—
71	C₃×#215	C₂²×C₃	1	6	yes	—
72	C₃×#214	C₂²×C₃	1	1	yes	characteristic
73	C₃×#213	C₂²×C₃	1	3	yes	—
74	C₃×#208	C₂²×C₃	1	3	yes	—
75	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	3	yes	—
76	C₉×#41	—	2	6	no	—
77	C₉×#41	—	2	1	no	—
78	C₉×#41	—	2	3	no	—
79	C₉×#41	—	2	3	no	—
80	C₉×#41	—	3	3	no	—
81	C₉×#41	—	6	1	no	—
82	C₉×#41	C₂×D₃	1	1	yes	characteristic
83	C₉×#41	C₂×D₃	1	3	yes	complemented
84	C₂×Q₈×C₉	—	2	2	no	—
85	C₂×Q₈×C₉	—	2	3	no	—
86	C₂×Q₈×C₉	—	2	1	no	—
87	C₂×Q₈×C₉	C₂×D₃	1	3	yes	complemented
88	C₂×D₄×C₉	—	3	3	no	—
89	C₂×D₄×C₉	—	6	3	no	—
90	C₉×Q₁₆	—	3	3	no	—
91	C₉×SD₁₆	—	3	3	no	—
92	C₉×SD₁₆	—	3	6	no	—
93	C₉×SD₁₆	—	3	1	no	—
94	C₉×D₈	—	3	3	no	—
95	C₉×M₁₆	—	3	3	no	—
96	C₂×C₈×C₉	—	3	3	no	—
97	C₂²×C₃×C₉	—	2	1	no	—
98	C₂²×C₃×C₉	C₂×D₄	1	3	yes	—
99	C₂×D₃×C₉	—	2	3	no	—
100	C₂×D₃×C₉	—	8	3	no	—
101	C₃×C₄×C₉	—	2	3	no	—
102	C₃×C₄×C₉	C₂×D₄	1	3	yes	—
103	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
104	C₉×Dic₃	—	2	1	no	—
105	C₃×2₋¹⁺⁴	—	2	1	no	—
106	C₃×2₋¹⁺⁴	C₂×C₉	1	1	yes	characteristic, complemented
107	C₃×2₋¹⁺⁴	C₃×D₃	1	1	yes	characteristic
108	C₃×H(5,𝔽₂)	—	3	1	no	—
109	#1009	C₂×C₉	1	1	yes	characteristic, complemented
110	C₃×#137	—	3	3	no	—
111	C₃×AGL(1,ℤ/8)	—	3	3	no	—
112	C₃×#135	—	3	3	no	—
113	C₂×C₃×SD₁₆	—	3	3	no	—
114	C₃×#131	—	3	1	no	—
115	#950	C₂×C₉	1	3	yes	complemented
116	#949	C₂×C₉	1	3	yes	complemented
117	#948	C₂×C₉	1	1	yes	characteristic, complemented
118	#942	C₂×C₉	1	3	yes	complemented
119	C₂×#215	C₂×C₉	1	3	yes	complemented
120	C₂²×C₃×D₃	—	2	3	no	—
121	C₃²×Q₈	—	2	3	no	—
122	C₃²×Q₈	C₃×D₄	1	1	yes	characteristic
123	C₃²×Q₈	C₂³×C₃	1	3	yes	—
124	C₃²×D₄	—	2	3	no	—
125	C₃²×D₄	C₃×D₄	1	3	yes	—
126	C₃²×D₄	C₂³×C₃	1	1	yes	characteristic
127	C₂×C₃²×C₄	—	2	3	no	—
128	C₂×C₃²×C₄	—	2	3	no	—
129	C₂×C₃²×C₄	C₂³×C₃	1	3	yes	—
130	C₃×#67	—	2	3	no	—
131	C₃×D₁₂	—	2	3	no	—
132	C₃×D₁₂	C₂³×C₃	1	3	yes	—
133	C₃×C₄×D₃	—	2	3	no	—
134	C₃×Dic₆	C₂³×C₃	1	1	yes	characteristic
135	C₂³×C₉	—	6	3	no	—
136	C₃×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
137	C₃×C₃⋊C₈	C₂³×C₃	1	3	yes	—
138	Q₈×C₉	—	2	6	no	—
139	Q₈×C₉	—	2	3	no	—
140	Q₈×C₉	—	2	1	no	—
141	Q₈×C₉	—	2	3	no	—
142	Q₈×C₉	—	3	1	no	—
143	Q₈×C₉	#67	1	1	yes	characteristic
144	Q₈×C₉	C₂²×D₃	1	3	yes	—
145	D₄×C₉	—	2	6	no	—
146	D₄×C₉	—	2	3	no	—
147	D₄×C₉	—	2	3	no	—
148	D₄×C₉	—	2	1	no	—
149	D₄×C₉	—	3	3	no	—
150	D₄×C₉	—	6	3	no	—
151	D₄×C₉	—	6	3	no	—
152	D₄×C₉	#67	1	3	yes	—
153	D₄×C₉	C₂²×D₃	1	1	yes	characteristic
154	C₂×C₄×C₉	—	2	6	no	—
155	C₂×C₄×C₉	—	2	6	no	—
156	C₂×C₄×C₉	—	2	3	no	—
157	C₂×C₄×C₉	—	2	3	no	—
158	C₂×C₄×C₉	—	2	3	no	—
159	C₂×C₄×C₉	—	6	3	no	—
160	C₂×C₄×C₉	C₂²×D₃	1	3	yes	—
161	C₈×C₉	—	3	1	no	—
162	C₈×C₉	—	3	3	no	—
163	#577	—	3	1	no	Sylow
164	C₂×C₃×C₉	—	2	3	no	—
165	C₂×C₃×C₉	—	4	1	no	—
166	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
167	D₃×C₉	—	4	3	no	—
168	C₃×#41	—	2	6	no	—
169	C₃×#41	—	2	3	no	—
170	C₃×#41	—	2	3	no	—
171	C₃×#41	—	2	1	no	—
172	C₃×#41	—	2	3	no	—
173	C₃×#41	—	3	3	no	—
174	C₃×#41	—	6	1	no	—
175	C₃×#41	C₂²×C₉	1	1	yes	characteristic
176	C₃×#41	C₂²×C₉	1	3	yes	complemented
177	C₃×#41	C₂×C₃×D₃	1	1	yes	characteristic
178	C₃×#41	C₂×C₃×D₃	1	3	yes	—
179	C₂×C₃×Q₈	—	2	2	no	—
180	C₂×C₃×Q₈	—	2	1	no	—
181	C₂×C₃×Q₈	—	2	1	no	—
182	C₂×C₃×Q₈	—	2	3	no	—
183	C₂×C₃×Q₈	C₂²×C₉	1	3	yes	complemented
184	C₂×C₃×Q₈	C₂×C₃×D₃	1	3	yes	—
185	C₂×C₃×D₄	—	3	3	no	—
186	C₂×C₃×D₄	—	6	3	no	—
187	#239	—	2	1	no	—
188	D₃×D₄	—	2	3	no	—
189	#235	C₂²×C₉	1	3	yes	—
190	C₂×D₁₂	C₂²×C₉	1	3	yes	—
191	C₃×Q₁₆	—	3	3	no	—
192	C₃×SD₁₆	—	3	3	no	—
193	C₃×SD₁₆	—	3	6	no	—
194	C₃×SD₁₆	—	3	1	no	—
195	C₃×D₈	—	3	3	no	—
196	C₃×M₁₆	—	3	3	no	—
197	C₂×C₃×C₈	—	3	3	no	—
198	#216	C₂²×C₉	1	3	yes	complemented
199	#215	C₂²×C₉	1	3	yes	complemented
200	#215	C₂²×C₉	1	6	yes	complemented
201	#214	C₂²×C₉	1	1	yes	characteristic, complemented
202	#213	C₂²×C₉	1	3	yes	complemented
203	#208	C₂²×C₉	1	3	yes	complemented
204	C₂×C₃⋊C₈	C₂²×C₉	1	3	yes	complemented
205	C₂²×C₃²	—	2	1	no	—
206	C₂²×C₃²	C₂×C₃×D₄	1	3	yes	—
207	C₂×C₃×D₃	—	2	3	no	—
208	C₂×C₃×D₃	—	8	3	no	—
209	C₃²×C₄	—	2	3	no	—
210	C₃²×C₄	C₂×C₃×D₄	1	3	yes	—
211	C₃²×C₄	C₂⁴×C₃	1	1	yes	characteristic
212	C₃×Dic₃	—	2	1	no	—
213	C₂²×C₉	—	2	2	no	—
214	C₂²×C₉	—	2	1	no	—
215	C₂²×C₉	—	2	3	no	—
216	C₂²×C₉	—	6	3	no	—
217	C₂²×C₉	—	24	3	no	—
218	C₂²×C₉	C₂×#67	1	3	yes	—
219	C₄×C₉	—	2	6	no	—
220	C₄×C₉	—	2	3	no	—
221	C₄×C₉	—	2	1	no	—
222	C₄×C₉	—	2	3	no	—
223	C₄×C₉	—	6	1	no	—
224	C₄×C₉	C₂×#67	1	3	yes	—
225	C₄×C₉	C₂³×D₃	1	1	yes	characteristic
226	2₋¹⁺⁴	D₃×C₉	1	1	yes	characteristic, complemented
227	H(5,𝔽₂)	—	3	1	no	—
228	#137	—	3	3	no	—
229	AGL(1,ℤ/8)	—	3	3	no	—
230	#135	—	3	3	no	—
231	C₂×SD₁₆	—	3	3	no	—
232	#131	—	3	1	no	—
233	C₃×C₉	#577	1	1	yes	characteristic, complemented, Sylow
234	C₂³×C₃	—	6	3	no	—
235	C₂²×D₃	—	2	3	no	—
236	C₃×Q₈	—	2	6	no	—
237	C₃×Q₈	—	2	3	no	—
238	C₃×Q₈	—	2	3	no	—
239	C₃×Q₈	—	2	1	no	—
240	C₃×Q₈	—	2	3	no	—
241	C₃×Q₈	—	3	1	no	—
242	C₃×Q₈	D₄×C₉	1	1	yes	characteristic
243	C₃×Q₈	C₂³×C₉	1	3	yes	—
244	C₃×Q₈	C₃×#67	1	1	yes	characteristic
245	C₃×Q₈	C₂²×C₃×D₃	1	3	yes	—
246	C₃×D₄	—	2	6	no	—
247	C₃×D₄	—	2	3	no	—
248	C₃×D₄	—	2	3	no	—
249	C₃×D₄	—	2	3	no	—
250	C₃×D₄	—	2	1	no	—
251	C₃×D₄	—	3	3	no	—
252	C₃×D₄	—	6	3	no	—
253	C₃×D₄	—	6	3	no	—
254	C₃×D₄	D₄×C₉	1	3	yes	—
255	C₃×D₄	C₂³×C₉	1	1	yes	characteristic
256	C₃×D₄	C₃×#67	1	3	yes	—
257	C₃×D₄	C₂²×C₃×D₃	1	1	yes	characteristic
258	C₂×C₃×C₄	—	2	6	no	—
259	C₂×C₃×C₄	—	2	6	no	—
260	C₂×C₃×C₄	—	2	3	no	—
261	C₂×C₃×C₄	—	2	3	no	—
262	C₂×C₃×C₄	—	2	3	no	—
263	C₂×C₃×C₄	—	2	3	no	—
264	C₂×C₃×C₄	—	2	3	no	—
265	C₂×C₃×C₄	—	6	3	no	—
266	C₂×C₃×C₄	C₂³×C₉	1	3	yes	—
267	C₂×C₃×C₄	C₂²×C₃×D₃	1	3	yes	—
268	#67	—	2	3	no	—
269	D₁₂	—	2	3	no	—
270	D₁₂	C₂³×C₉	1	3	yes	—
271	C₄×D₃	—	2	3	no	—
272	Dic₆	C₂³×C₉	1	1	yes	characteristic
273	C₃×C₈	—	3	1	no	—
274	C₃×C₈	—	3	3	no	—
275	C₃⋊C₈	C₂³×C₉	1	1	yes	characteristic
276	C₃⋊C₈	C₂³×C₉	1	3	yes	—
277	C₂×C₃²	—	2	3	no	—
278	C₂×C₃²	—	4	1	no	—
279	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
280	C₃×D₃	—	4	3	no	—
281	C₂×C₉	—	2	3	no	—
282	C₂×C₉	—	2	1	no	—
283	C₂×C₉	—	4	3	no	—
284	C₂×C₉	—	4	2	no	—
285	C₂×C₉	—	4	1	no	—
286	C₂×C₉	—	12	3	no	—
287	C₂×C₉	C₂²×#67	1	1	yes	characteristic
288	#41	—	2	3	no	—
289	#41	—	3	3	no	—
290	#41	—	6	1	no	—
291	#41	C₂×D₃×C₉	1	1	yes	characteristic
292	#41	C₂×D₃×C₉	1	3	yes	complemented
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	C₂×D₃×C₉	1	3	yes	complemented
295	C₂×D₄	—	3	3	no	—
296	C₂×D₄	—	6	3	no	—
297	Q₁₆	—	3	3	no	—
298	SD₁₆	—	3	3	no	—
299	SD₁₆	—	3	6	no	—
300	SD₁₆	—	3	1	no	—
301	D₈	—	3	3	no	—
302	M₁₆	—	3	3	no	—
303	C₂×C₈	—	3	3	no	—
304	C₂²×C₃	—	2	2	no	—
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	2	3	no	—
308	C₂²×C₃	—	6	3	no	—
309	C₂²×C₃	—	24	3	no	—
310	C₂²×C₃	C₂×D₄×C₉	1	3	yes	—
311	C₂²×C₃	C₂×C₃×#67	1	3	yes	—
312	C₂×D₃	—	2	3	no	—
313	C₂×D₃	—	8	3	no	—
314	C₃×C₄	—	2	6	no	—
315	C₃×C₄	—	2	3	no	—
316	C₃×C₄	—	2	3	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	3	no	—
319	C₃×C₄	—	6	1	no	—
320	C₃×C₄	C₂×D₄×C₉	1	3	yes	—
321	C₃×C₄	C₂⁴×C₉	1	1	yes	characteristic
322	C₃×C₄	C₂×C₃×#67	1	3	yes	—
323	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
324	Dic₃	—	2	1	no	—
325	C₃²	C₃×#577	1	1	yes	characteristic
326	C₉	—	2	1	no	—
327	C₉	#5837	1	1	yes	characteristic, direct product factor
328	C₂³	—	6	3	no	—
329	Q₈	—	2	3	no	—
330	Q₈	—	3	1	no	—
331	Q₈	C₉×#67	1	1	yes	characteristic
332	Q₈	C₂²×D₃×C₉	1	3	yes	—
333	D₄	—	2	3	no	—
334	D₄	—	3	3	no	—
335	D₄	—	6	3	no	—
336	D₄	—	6	3	no	—
337	D₄	C₉×#67	1	3	yes	—
338	D₄	C₂²×D₃×C₉	1	1	yes	characteristic
339	C₂×C₄	—	2	3	no	—
340	C₂×C₄	—	2	3	no	—
341	C₂×C₄	—	6	3	no	—
342	C₂×C₄	C₂²×D₃×C₉	1	3	yes	—
343	C₈	—	3	1	no	—
344	C₈	—	3	3	no	—
345	C₂×C₃	—	2	3	no	—
346	C₂×C₃	—	2	3	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	4	3	no	—
349	C₂×C₃	—	4	2	no	—
350	C₂×C₃	—	4	1	no	—
351	C₂×C₃	—	4	1	no	—
352	C₂×C₃	—	12	3	no	—
353	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
354	C₂×C₃	C₂²×C₃×#67	1	1	yes	characteristic
355	D₃	—	4	3	no	—
356	C₂²	—	2	1	no	—
357	C₂²	—	6	3	no	—
358	C₂²	—	24	3	no	—
359	C₂²	C₂×C₉×#67	1	3	yes	—
360	C₄	—	2	3	no	—
361	C₄	—	6	1	no	—
362	C₄	C₂×C₉×#67	1	3	yes	—
363	C₄	C₂³×D₃×C₉	1	1	yes	characteristic
364	C₃	—	2	1	no	—
365	C₃	C₉×#577	1	1	yes	characteristic, complemented
366	C₃	C₃×#5837	1	1	yes	characteristic
367	C₂	—	2	3	no	—
368	C₂	—	4	1	no	—
369	C₂	—	12	3	no	—
370	C₂	C₂²×C₉×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉	C₂²×#67
commutator	C₃×C₄	C₂⁴×C₉
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₃×C₉×2₋¹⁺⁴	C₂
socle	C₂×C₃²	C₂²×C₃×D₄
prime radical	C₃×#5837	C₃
cosocle	C₃²×C₄	C₂⁴×C₃
hypercenter	C₉×2₋¹⁺⁴	D₃
hypocenter	C₃	C₉×#577
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉ ◁ C₉×#41 ◁ C₉×2₋¹⁺⁴

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×2₋¹⁺⁴	C₂	semidirect
2. C₉×#1009	C₂	semidirect
3. C₉×#950	C₂	semidirect
4. C₉×#949	C₂	semidirect
5. C₉×#948	C₂	semidirect
6. C₉×#942	C₂	semidirect
7. C₂×C₉×#215	C₂	semidirect
12. C₃×C₉×#41	C₂²	semidirect
14. C₂×C₃×Q₈×C₉	C₂²	semidirect
19. C₉×#216	C₂²	semidirect
20. C₉×#215	C₂²	semidirect
21. C₉×#215	C₂²	semidirect
22. C₉×#214	C₂²	semidirect
23. C₉×#213	C₂²	semidirect
24. C₉×#208	C₂²	semidirect
25. C₂×C₉×C₃⋊C₈	C₂²	semidirect
34. C₉×2₋¹⁺⁴	D₃	semidirect
59. #5837	C₉	direct (N × H)
83. C₉×#41	C₂×D₃	semidirect
87. C₂×Q₈×C₉	C₂×D₃	semidirect
106. C₃×2₋¹⁺⁴	C₂×C₉	semidirect
109. #1009	C₂×C₉	semidirect
115. #950	C₂×C₉	semidirect
116. #949	C₂×C₉	semidirect
117. #948	C₂×C₉	semidirect
118. #942	C₂×C₉	semidirect
119. C₂×#215	C₂×C₉	semidirect
176. C₃×#41	C₂²×C₉	semidirect
183. C₂×C₃×Q₈	C₂²×C₉	semidirect
198. #216	C₂²×C₉	semidirect
199. #215	C₂²×C₉	semidirect
200. #215	C₂²×C₉	semidirect
201. #214	C₂²×C₉	semidirect
202. #213	C₂²×C₉	semidirect
203. #208	C₂²×C₉	semidirect
204. C₂×C₃⋊C₈	C₂²×C₉	semidirect
226. 2₋¹⁺⁴	D₃×C₉	semidirect
233. C₃×C₉	#577	semidirect
292. #41	C₂×D₃×C₉	semidirect
294. C₂×Q₈	C₂×D₃×C₉	semidirect
327. C₉	#5837	direct (N × H)
365. C₃	C₉×#577	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₉×2₋¹⁺⁴	2
C₉×#1009	2
C₉×#950	2
C₉×#949	2
C₉×#948	2
C₉×#942	2
C₂×C₉×#215	2
C₃×#5837	3
C₉×#577	3

Subgroups — C9×#5837 #13153753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#5837 #13153753