Subgroups — C₃×C₉×#468 #13145162

Order 1728.

600 conjugacy classes of subgroups.

The subgroup lattice has 336 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	C₂×C₃×C₉×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₉×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₉×#121	C₂	1	1	yes	maximal, characteristic
5	C₃×C₉×#107	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₉×#103	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₉×#102	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃²×#468	C₃	1	1	yes	maximal, characteristic
9	C₉×#468	C₃	1	3	yes	maximal, direct product factor
10	C₂×C₃×Q₈×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₃×D₄×C₉	—	2	1	no	—
12	C₂×C₃×D₄×C₉	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
14	C₃×C₉×SD₁₆	—	2	2	no	—
15	C₃×C₉×M₁₆	—	2	2	no	—
16	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
18	C₃×C₉×C₄⋊C₄	—	2	1	no	—
19	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₃×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₃×C₉×C₂²⋊C₄	—	2	1	no	—
22	C₃×C₉×C₂²⋊C₄	—	2	1	no	—
23	C₂×C₃²×SD₁₆	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃²×M₁₆	C₂×C₃	1	1	yes	characteristic
25	C₃²×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
26	C₃²×#121	C₂×C₃	1	1	yes	characteristic
27	C₃²×#107	C₂×C₃	1	1	yes	characteristic
28	C₃²×#103	C₂×C₃	1	1	yes	characteristic
29	C₃²×#102	C₂×C₃	1	1	yes	characteristic
30	C₂×C₉×SD₁₆	C₂×C₃	1	3	yes	complemented
31	C₂×C₉×M₁₆	C₂×C₃	1	3	yes	complemented
32	C₉×C₂²⋊Q₈	C₂×C₃	1	3	yes	complemented
33	C₉×#121	C₂×C₃	1	3	yes	—
34	C₉×#107	C₂×C₃	1	3	yes	complemented
35	C₉×#103	C₂×C₃	1	3	yes	complemented
36	C₉×#102	C₂×C₃	1	3	yes	complemented
37	C₂³×C₃×C₉	—	2	1	no	—
38	C₂³×C₃×C₉	D₄	1	1	yes	characteristic
39	C₃×Q₈×C₉	—	2	1	no	—
40	C₃×Q₈×C₉	—	2	1	no	—
41	C₃×D₄×C₉	—	2	1	no	—
42	C₃×D₄×C₉	—	2	1	no	—
43	C₃×D₄×C₉	—	4	2	no	—
44	C₂×C₃×C₄×C₉	—	2	1	no	—
45	C₂×C₃×C₄×C₉	—	2	1	no	—
46	C₂×C₃×C₄×C₉	—	2	1	no	—
47	C₂×C₃×C₄×C₉	—	2	1	no	—
48	C₂×C₃×C₄×C₉	—	2	1	no	—
49	C₂×C₃×C₄×C₉	D₄	1	1	yes	characteristic
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₃×C₈×C₉	—	2	1	no	—
52	C₃×C₈×C₉	D₄	1	2	yes	complemented
53	C₃×#468	C₉	1	3	yes	direct product factor
54	C₃×#468	C₃²	1	1	yes	characteristic
55	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₃²×D₄	—	2	1	no	—
57	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
58	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
59	C₃²×SD₁₆	—	2	2	no	—
60	C₃²×M₁₆	—	2	2	no	—
61	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
63	C₃²×C₄⋊C₄	—	2	1	no	—
64	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
65	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
66	C₃²×C₂²⋊C₄	—	2	1	no	—
67	C₃²×C₂²⋊C₄	—	2	1	no	—
68	C₂×Q₈×C₉	C₂²×C₃	1	3	yes	—
69	C₂×D₄×C₉	—	2	3	no	—
70	C₂×D₄×C₉	C₂²×C₃	1	3	yes	—
71	C₂²×C₄×C₉	C₂²×C₃	1	3	yes	—
72	C₉×SD₁₆	—	2	6	no	—
73	C₉×M₁₆	—	2	6	no	—
74	C₂×C₈×C₉	C₂²×C₃	1	3	yes	—
75	C₂×C₈×C₉	C₂²×C₃	1	3	yes	—
76	C₉×C₄⋊C₄	—	2	3	no	—
77	C₉×C₄⋊C₄	C₂²×C₃	1	3	yes	—
78	C₉×C₄⋊C₄	C₂²×C₃	1	3	yes	—
79	C₉×C₂²⋊C₄	—	2	3	no	—
80	C₉×C₂²⋊C₄	—	2	3	no	—
81	C₂²×C₃×C₉	—	2	1	no	—
82	C₂²×C₃×C₉	—	2	1	no	—
83	C₂²×C₃×C₉	—	2	1	no	—
84	C₂²×C₃×C₉	—	4	1	no	—
85	C₂²×C₃×C₉	—	4	1	no	—
86	C₂²×C₃×C₉	—	4	1	no	—
87	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
88	C₃×C₄×C₉	—	2	1	no	—
89	C₃×C₄×C₉	—	4	1	no	—
90	C₃×C₄×C₉	—	4	1	no	—
91	C₃×C₄×C₉	—	4	1	no	—
92	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
93	C₃×C₄×C₉	#41	1	1	yes	characteristic
94	C₂×C₃×SD₁₆	C₂×C₉	1	3	yes	complemented
95	C₂×C₃×SD₁₆	C₂×C₃²	1	1	yes	characteristic
96	C₂×C₃×M₁₆	C₂×C₉	1	3	yes	complemented
97	C₂×C₃×M₁₆	C₂×C₃²	1	1	yes	characteristic
98	C₃×C₂²⋊Q₈	C₂×C₉	1	3	yes	complemented
99	C₃×C₂²⋊Q₈	C₂×C₃²	1	1	yes	characteristic
100	C₃×#121	C₂×C₉	1	3	yes	—
101	C₃×#121	C₂×C₃²	1	1	yes	characteristic
102	C₃×#107	C₂×C₉	1	3	yes	complemented
103	C₃×#107	C₂×C₃²	1	1	yes	characteristic
104	C₃×#103	C₂×C₉	1	3	yes	complemented
105	C₃×#103	C₂×C₃²	1	1	yes	characteristic
106	C₃×#102	C₂×C₉	1	3	yes	complemented
107	C₃×#102	C₂×C₃²	1	1	yes	characteristic
108	C₂³×C₃²	—	2	1	no	—
109	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
110	C₃²×Q₈	—	2	1	no	—
111	C₃²×Q₈	—	2	1	no	—
112	C₃²×D₄	—	2	1	no	—
113	C₃²×D₄	—	2	1	no	—
114	C₃²×D₄	—	4	2	no	—
115	C₂×C₃²×C₄	—	2	1	no	—
116	C₂×C₃²×C₄	—	2	1	no	—
117	C₂×C₃²×C₄	—	2	1	no	—
118	C₂×C₃²×C₄	—	2	1	no	—
119	C₂×C₃²×C₄	—	2	1	no	—
120	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
121	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
122	C₂³×C₉	—	2	3	no	—
123	C₂³×C₉	C₃×D₄	1	3	yes	—
124	C₃²×C₈	—	2	1	no	—
125	C₃²×C₈	C₃×D₄	1	2	yes	—
126	Q₈×C₉	—	2	3	no	—
127	Q₈×C₉	—	2	3	no	—
128	D₄×C₉	—	2	3	no	—
129	D₄×C₉	—	2	3	no	—
130	D₄×C₉	—	4	6	no	—
131	C₂×C₄×C₉	—	2	3	no	—
132	C₂×C₄×C₉	—	2	3	no	—
133	C₂×C₄×C₉	—	2	3	no	—
134	C₂×C₄×C₉	—	2	3	no	—
135	C₂×C₄×C₉	—	2	3	no	—
136	C₂×C₄×C₉	C₃×D₄	1	3	yes	—
137	C₂×C₄×C₉	C₂³×C₃	1	3	yes	—
138	C₈×C₉	—	2	3	no	—
139	C₈×C₉	C₃×D₄	1	6	yes	complemented
140	#468	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
141	C₂×C₃×C₉	—	4	1	no	—
142	C₂×C₃×C₉	—	8	1	no	—
143	C₂×C₃×C₉	#121	1	1	yes	characteristic
144	C₂×C₃×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₃×C₉	#137	1	1	yes	characteristic
146	C₂×C₃×Q₈	C₂²×C₉	1	3	yes	—
147	C₂×C₃×Q₈	C₂²×C₃²	1	1	yes	characteristic
148	C₂×C₃×D₄	—	2	3	no	—
149	C₂×C₃×D₄	—	2	1	no	—
150	C₂×C₃×D₄	C₂²×C₉	1	3	yes	—
151	C₂×C₃×D₄	C₂²×C₃²	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂²×C₉	1	3	yes	—
153	C₂²×C₃×C₄	C₂²×C₃²	1	1	yes	characteristic
154	C₃×SD₁₆	—	2	6	no	—
155	C₃×SD₁₆	—	2	2	no	—
156	C₃×M₁₆	—	2	6	no	—
157	C₃×M₁₆	—	2	2	no	—
158	C₂×C₃×C₈	C₂²×C₉	1	3	yes	—
159	C₂×C₃×C₈	C₂²×C₉	1	3	yes	—
160	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
161	C₂×C₃×C₈	C₂²×C₃²	1	1	yes	characteristic
162	C₃×C₄⋊C₄	—	2	3	no	—
163	C₃×C₄⋊C₄	—	2	1	no	—
164	C₃×C₄⋊C₄	C₂²×C₉	1	3	yes	—
165	C₃×C₄⋊C₄	C₂²×C₉	1	3	yes	—
166	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
167	C₃×C₄⋊C₄	C₂²×C₃²	1	1	yes	characteristic
168	C₃×C₂²⋊C₄	—	2	3	no	—
169	C₃×C₂²⋊C₄	—	2	1	no	—
170	C₃×C₂²⋊C₄	—	2	3	no	—
171	C₃×C₂²⋊C₄	—	2	1	no	—
172	C₂²×C₃²	—	2	1	no	—
173	C₂²×C₃²	—	2	1	no	—
174	C₂²×C₃²	—	2	1	no	—
175	C₂²×C₃²	—	4	1	no	—
176	C₂²×C₃²	—	4	1	no	—
177	C₂²×C₃²	—	4	1	no	—
178	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
179	C₃²×C₄	—	2	1	no	—
180	C₃²×C₄	—	4	1	no	—
181	C₃²×C₄	—	4	1	no	—
182	C₃²×C₄	—	4	1	no	—
183	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
184	C₃²×C₄	C₃×#41	1	1	yes	characteristic
185	C₂²×C₉	—	2	3	no	—
186	C₂²×C₉	—	2	3	no	—
187	C₂²×C₉	—	2	3	no	—
188	C₂²×C₉	—	4	3	no	—
189	C₂²×C₉	—	4	3	no	—
190	C₂²×C₉	—	4	3	no	—
191	C₂²×C₉	C₂×C₃×D₄	1	3	yes	—
192	C₄×C₉	—	2	3	no	—
193	C₄×C₉	—	4	3	no	—
194	C₄×C₉	—	4	3	no	—
195	C₄×C₉	—	4	3	no	—
196	C₄×C₉	C₂×C₃×D₄	1	3	yes	—
197	C₄×C₉	C₃×#41	1	3	yes	—
198	C₂×SD₁₆	C₂×C₃×C₉	1	1	yes	characteristic, complemented
199	C₂×M₁₆	C₂×C₃×C₉	1	1	yes	characteristic, complemented
200	C₂²⋊Q₈	C₂×C₃×C₉	1	1	yes	characteristic, complemented
201	#121	C₂×C₃×C₉	1	1	yes	characteristic
202	#107	C₂×C₃×C₉	1	1	yes	characteristic, complemented
203	#103	C₂×C₃×C₉	1	1	yes	characteristic, complemented
204	#102	C₂×C₃×C₉	1	1	yes	characteristic, complemented
205	C₃×C₉	#468	1	1	yes	characteristic, direct product factor, Sylow
206	C₂³×C₃	—	2	3	no	—
207	C₂³×C₃	—	2	1	no	—
208	C₂³×C₃	D₄×C₉	1	3	yes	—
209	C₂³×C₃	C₃²×D₄	1	1	yes	characteristic
210	C₃×Q₈	—	2	3	no	—
211	C₃×Q₈	—	2	3	no	—
212	C₃×Q₈	—	2	1	no	—
213	C₃×Q₈	—	2	1	no	—
214	C₃×D₄	—	2	3	no	—
215	C₃×D₄	—	2	3	no	—
216	C₃×D₄	—	2	1	no	—
217	C₃×D₄	—	2	1	no	—
218	C₃×D₄	—	4	2	no	—
219	C₃×D₄	—	4	6	no	—
220	C₂×C₃×C₄	—	2	3	no	—
221	C₂×C₃×C₄	—	2	3	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	3	no	—
225	C₂×C₃×C₄	—	2	3	no	—
226	C₂×C₃×C₄	—	2	3	no	—
227	C₂×C₃×C₄	—	2	1	no	—
228	C₂×C₃×C₄	—	2	1	no	—
229	C₂×C₃×C₄	—	2	1	no	—
230	C₂×C₃×C₄	D₄×C₉	1	3	yes	—
231	C₂×C₃×C₄	C₂³×C₉	1	3	yes	—
232	C₂×C₃×C₄	C₃²×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂³×C₃²	1	1	yes	characteristic
234	C₃×C₈	—	2	3	no	—
235	C₃×C₈	—	2	1	no	—
236	C₃×C₈	D₄×C₉	1	6	yes	complemented
237	C₃×C₈	C₃²×D₄	1	2	yes	—
238	C₂×C₃²	—	4	1	no	—
239	C₂×C₃²	—	8	1	no	—
240	C₂×C₃²	C₃×#121	1	1	yes	characteristic
241	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
242	C₂×C₃²	C₃×#137	1	1	yes	characteristic
243	C₂×C₉	—	4	3	no	—
244	C₂×C₉	—	8	3	no	—
245	C₂×C₉	C₃×#121	1	3	yes	—
246	C₂×C₉	C₃×AGL(1,ℤ/8)	1	3	yes	—
247	C₂×C₉	C₃×#137	1	3	yes	—
248	C₂×Q₈	C₂²×C₃×C₉	1	1	yes	characteristic
249	C₂×D₄	—	2	1	no	—
250	C₂×D₄	C₂²×C₃×C₉	1	1	yes	characteristic
251	C₂²×C₄	C₂²×C₃×C₉	1	1	yes	characteristic
252	SD₁₆	—	2	2	no	—
253	M₁₆	—	2	2	no	—
254	C₂×C₈	C₂²×C₃×C₉	1	1	yes	characteristic
255	C₂×C₈	C₂²×C₃×C₉	1	1	yes	characteristic
256	C₄⋊C₄	—	2	1	no	—
257	C₄⋊C₄	C₂²×C₃×C₉	1	1	yes	characteristic
258	C₄⋊C₄	C₂²×C₃×C₉	1	1	yes	characteristic
259	C₂²⋊C₄	—	2	1	no	—
260	C₂²⋊C₄	—	2	1	no	—
261	C₂²×C₃	—	2	3	no	—
262	C₂²×C₃	—	2	3	no	—
263	C₂²×C₃	—	2	3	no	—
264	C₂²×C₃	—	2	1	no	—
265	C₂²×C₃	—	2	1	no	—
266	C₂²×C₃	—	2	1	no	—
267	C₂²×C₃	—	4	3	no	—
268	C₂²×C₃	—	4	3	no	—
269	C₂²×C₃	—	4	3	no	—
270	C₂²×C₃	—	4	1	no	—
271	C₂²×C₃	—	4	1	no	—
272	C₂²×C₃	—	4	1	no	—
273	C₂²×C₃	C₂×D₄×C₉	1	3	yes	—
274	C₂²×C₃	C₂×C₃²×D₄	1	1	yes	characteristic
275	C₃×C₄	—	2	3	no	—
276	C₃×C₄	—	2	1	no	—
277	C₃×C₄	—	4	3	no	—
278	C₃×C₄	—	4	3	no	—
279	C₃×C₄	—	4	3	no	—
280	C₃×C₄	—	4	1	no	—
281	C₃×C₄	—	4	1	no	—
282	C₃×C₄	—	4	1	no	—
283	C₃×C₄	C₂×D₄×C₉	1	3	yes	—
284	C₃×C₄	C₉×#41	1	3	yes	—
285	C₃×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
286	C₃×C₄	C₃²×#41	1	1	yes	characteristic
287	C₃²	C₃×#468	1	1	yes	characteristic
288	C₉	C₃×#468	1	3	yes	direct product factor
289	C₂³	—	2	1	no	—
290	C₂³	C₃×D₄×C₉	1	1	yes	characteristic
291	Q₈	—	2	1	no	—
292	Q₈	—	2	1	no	—
293	D₄	—	2	1	no	—
294	D₄	—	2	1	no	—
295	D₄	—	4	2	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	1	no	—
298	C₂×C₄	—	2	1	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	C₃×D₄×C₉	1	1	yes	characteristic
302	C₂×C₄	C₂³×C₃×C₉	1	1	yes	characteristic
303	C₈	—	2	1	no	—
304	C₈	C₃×D₄×C₉	1	2	yes	complemented
305	C₂×C₃	—	4	1	no	—
306	C₂×C₃	—	4	3	no	—
307	C₂×C₃	—	8	1	no	—
308	C₂×C₃	—	8	3	no	—
309	C₂×C₃	C₉×#121	1	3	yes	—
310	C₂×C₃	C₉×AGL(1,ℤ/8)	1	3	yes	—
311	C₂×C₃	C₉×#137	1	3	yes	—
312	C₂×C₃	C₃²×#121	1	1	yes	characteristic
313	C₂×C₃	C₃²×AGL(1,ℤ/8)	1	1	yes	characteristic
314	C₂×C₃	C₃²×#137	1	1	yes	characteristic
315	C₂²	—	2	1	no	—
316	C₂²	—	2	1	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	4	1	no	—
319	C₂²	—	4	1	no	—
320	C₂²	—	4	1	no	—
321	C₂²	C₂×C₃×D₄×C₉	1	1	yes	characteristic
322	C₄	—	2	1	no	—
323	C₄	—	4	1	no	—
324	C₄	—	4	1	no	—
325	C₄	—	4	1	no	—
326	C₄	C₂×C₃×D₄×C₉	1	1	yes	characteristic
327	C₄	C₃×C₉×#41	1	1	yes	characteristic
328	C₃	C₉×#468	1	3	yes	direct product factor
329	C₃	C₃²×#468	1	1	yes	characteristic
330	C₂	—	4	1	no	—
331	C₂	—	8	1	no	—
332	C₂	C₃×C₉×#121	1	1	yes	characteristic
333	C₂	C₃×C₉×AGL(1,ℤ/8)	1	1	yes	characteristic
334	C₂	C₃×C₉×#137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₉	C₂×D₄
commutator	C₂×C₄	C₂³×C₃×C₉
Frattini, cosocle	C₂×C₃×C₄	C₂³×C₃²
socle	C₂²×C₃²	C₂×C₃×D₄
prime radical	C₃²×#121	C₂×C₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₉ ◁ C₂²×C₃×C₄×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₉×SD₁₆	C₂	semidirect
2. C₂×C₃×C₉×M₁₆	C₂	semidirect
3. C₃×C₉×C₂²⋊Q₈	C₂	semidirect
5. C₃×C₉×#107	C₂	semidirect
6. C₃×C₉×#103	C₂	semidirect
7. C₃×C₉×#102	C₂	semidirect
9. C₉×#468	C₃	direct (N × H)
30. C₂×C₉×SD₁₆	C₂×C₃	semidirect
31. C₂×C₉×M₁₆	C₂×C₃	semidirect
32. C₉×C₂²⋊Q₈	C₂×C₃	semidirect
34. C₉×#107	C₂×C₃	semidirect
35. C₉×#103	C₂×C₃	semidirect
36. C₉×#102	C₂×C₃	semidirect
52. C₃×C₈×C₉	D₄	semidirect
53. C₃×#468	C₉	direct (N × H)
94. C₂×C₃×SD₁₆	C₂×C₉	semidirect
96. C₂×C₃×M₁₆	C₂×C₉	semidirect
98. C₃×C₂²⋊Q₈	C₂×C₉	semidirect
102. C₃×#107	C₂×C₉	semidirect
104. C₃×#103	C₂×C₉	semidirect
106. C₃×#102	C₂×C₉	semidirect
139. C₈×C₉	C₃×D₄	semidirect
140. #468	C₃×C₉	direct (N × H)
198. C₂×SD₁₆	C₂×C₃×C₉	semidirect
199. C₂×M₁₆	C₂×C₃×C₉	semidirect
200. C₂²⋊Q₈	C₂×C₃×C₉	semidirect
202. #107	C₂×C₃×C₉	semidirect
203. #103	C₂×C₃×C₉	semidirect
204. #102	C₂×C₃×C₉	semidirect
205. C₃×C₉	#468	direct (N × H)
236. C₃×C₈	D₄×C₉	semidirect
288. C₉	C₃×#468	direct (N × H)
304. C₈	C₃×D₄×C₉	semidirect
328. C₃	C₉×#468	direct (N × H)

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
C₂×C₃×C₉×M₁₆	2
C₃×C₉×C₂²⋊Q₈	2
C₃×C₉×#121	2
C₃×C₉×#107	2
C₃×C₉×#103	2
C₃×C₉×#102	2
C₃²×#468	3
C₉×#468	3

Subgroups — C3×C9×#468 #13145162

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#468 #13145162