Subgroups — C₂×C₉×#886 #13152352

Order 1728.

1158 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₉×#67	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₉×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₉×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
5	C₂×C₉×C₄⋊Dic₃	C₂	1	2	yes	maximal, complemented
6	C₉×#886	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₃×#886	C₃	1	1	yes	maximal, characteristic
8	C₂×C₉×#123	—	3	1	no	maximal
9	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
10	C₂³×D₃×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄×C₉	C₂²	1	2	yes	—
12	C₂×C₉×#67	—	2	4	no	—
13	C₂×C₉×#67	C₂²	1	4	yes	—
14	C₂²×C₉×Dic₃	—	2	4	no	—
15	C₂²×C₉×Dic₃	C₂²	1	1	yes	characteristic
16	C₂²×C₉×Dic₃	C₂²	1	2	yes	—
17	C₂²×C₉×Dic₃	C₂²	1	4	yes	complemented
18	C₃×C₉×C₂²⋊C₄	C₂²	1	4	yes	complemented
19	C₉×(C₂×D₃)⋊C₄	C₂²	1	8	yes	complemented
20	C₉×C₄⋊Dic₃	C₂²	1	8	yes	complemented
21	C₂²×C₃×#67	C₂×C₃	1	1	yes	characteristic
22	C₂³×C₃×Dic₃	C₂×C₃	1	1	yes	characteristic
23	C₂×C₃²×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×(C₂×D₃)⋊C₄	C₂×C₃	1	2	yes	—
25	C₂×C₃×C₄⋊Dic₃	C₂×C₃	1	2	yes	—
26	C₃×#886	C₂×C₃	1	8	yes	—
27	C₂²×D₄×C₉	—	3	1	no	—
28	C₂³×C₄×C₉	—	3	1	no	—
29	C₉×#123	—	3	8	no	—
30	C₂×C₉×C₄⋊C₄	—	3	2	no	—
31	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
32	C₂×C₉×C₂²⋊C₄	—	3	2	no	—
33	C₂×C₉×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
34	C₂³×C₃×C₉	—	2	4	no	—
35	C₂³×C₃×C₉	D₄	1	4	yes	—
36	C₂³×C₃×C₉	C₂³	1	2	yes	—
37	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
38	C₂²×D₃×C₉	—	2	2	no	—
39	C₂²×D₃×C₉	—	2	4	no	—
40	C₂²×D₃×C₉	C₂³	1	2	yes	—
41	C₂×C₃×C₄×C₉	—	2	4	no	—
42	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
43	C₉×#67	—	2	8	no	—
44	C₂×C₉×Dic₃	—	2	4	no	—
45	C₂×C₉×Dic₃	—	2	8	no	—
46	C₂×C₉×Dic₃	—	2	2	no	—
47	C₂×C₉×Dic₃	C₂³	1	4	yes	—
48	C₂×C₉×Dic₃	C₂³	1	2	yes	—
49	C₂×C₃×#123	—	3	1	no	—
50	C₂×#886	C₉	1	1	yes	characteristic, direct product factor
51	C₂⁴×C₃²	C₂²×C₃	1	1	yes	characteristic
52	C₂³×C₃×D₃	C₂²×C₃	1	1	yes	characteristic
53	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
54	C₂×C₃×#67	—	2	4	no	—
55	C₂×C₃×#67	C₂²×C₃	1	4	yes	—
56	C₂²×C₃×Dic₃	—	2	4	no	—
57	C₂²×C₃×Dic₃	C₂²×C₃	1	1	yes	characteristic
58	C₂²×C₃×Dic₃	C₂²×C₃	1	2	yes	—
59	C₂²×C₃×Dic₃	C₂²×C₃	1	4	yes	—
60	C₂⁴×C₉	—	2	1	no	—
61	C₂⁴×C₉	—	3	1	no	—
62	C₂⁴×C₉	C₂×D₃	1	1	yes	characteristic
63	C₃²×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
64	C₃×(C₂×D₃)⋊C₄	C₂²×C₃	1	8	yes	—
65	C₃×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
66	C₂×D₄×C₉	—	3	4	no	—
67	C₂×D₄×C₉	—	6	4	no	—
68	C₂²×C₄×C₉	—	2	2	no	—
69	C₂²×C₄×C₉	—	3	4	no	—
70	C₂²×C₄×C₉	—	3	2	no	—
71	C₂²×C₄×C₉	—	3	1	no	—
72	C₂²×C₄×C₉	—	6	4	no	—
73	C₂²×C₄×C₉	C₂×D₃	1	2	yes	—
74	C₉×C₄⋊C₄	—	3	8	no	—
75	C₉×C₂²⋊C₄	—	2	4	no	—
76	C₉×C₂²⋊C₄	—	3	8	no	—
77	C₉×C₂²⋊C₄	C₂×D₃	1	4	yes	complemented
78	C₂²×C₃×C₉	—	2	8	no	—
79	C₂²×C₃×C₉	—	2	4	no	—
80	C₂²×C₃×C₉	C₂×D₄	1	4	yes	—
81	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
82	C₂²×C₃×C₉	#41	1	4	yes	—
83	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
84	C₂×D₃×C₉	—	2	2	no	—
85	C₂×D₃×C₉	—	2	4	no	—
86	C₂×D₃×C₉	—	4	4	no	—
87	C₃×C₄×C₉	—	2	4	no	—
88	C₉×Dic₃	—	2	4	no	—
89	C₉×Dic₃	—	2	2	no	—
90	C₂²×C₃×D₄	—	3	1	no	—
91	C₂³×C₃×C₄	—	3	1	no	—
92	C₂²×#67	C₂×C₉	1	1	yes	characteristic
93	C₂³×Dic₃	C₂×C₉	1	1	yes	characteristic, complemented
94	C₃×#123	—	3	8	no	—
95	C₂×C₃×C₄⋊C₄	—	3	2	no	—
96	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
97	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
98	C₂×C₃×C₂²⋊C₄	C₂×C₉	1	1	yes	characteristic, complemented
99	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
100	C₂×(C₂×D₃)⋊C₄	C₂×C₉	1	2	yes	complemented
101	C₂×C₄⋊Dic₃	C₂×C₉	1	2	yes	complemented
102	#886	C₂×C₉	1	8	yes	direct product factor
103	C₂³×C₃²	—	2	4	no	—
104	C₂³×C₃²	C₃×D₄	1	4	yes	—
105	C₂³×C₃²	C₂³×C₃	1	2	yes	—
106	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
107	C₂²×C₃×D₃	—	2	2	no	—
108	C₂²×C₃×D₃	—	2	4	no	—
109	C₂²×C₃×D₃	C₂³×C₃	1	2	yes	—
110	C₂×C₃²×C₄	—	2	4	no	—
111	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
112	C₃×#67	—	2	8	no	—
113	C₂×C₃×Dic₃	—	2	4	no	—
114	C₂×C₃×Dic₃	—	2	8	no	—
115	C₂×C₃×Dic₃	—	2	2	no	—
116	C₂×C₃×Dic₃	C₂³×C₃	1	2	yes	—
117	C₂×C₃×Dic₃	C₂³×C₃	1	4	yes	—
118	C₂³×C₉	—	2	4	no	—
119	C₂³×C₉	—	2	4	no	—
120	C₂³×C₉	—	2	1	no	—
121	C₂³×C₉	—	2	2	no	—
122	C₂³×C₉	—	3	2	no	—
123	C₂³×C₉	—	4	4	no	—
124	C₂³×C₉	—	6	2	no	—
125	C₂³×C₉	—	6	4	no	—
126	C₂³×C₉	D₁₂	1	4	yes	—
127	C₂³×C₉	C₂²×D₃	1	2	yes	—
128	C₂³×C₉	C₂²×D₃	1	1	yes	characteristic
129	D₄×C₉	—	6	8	no	—
130	C₂×C₄×C₉	—	2	4	no	—
131	C₂×C₄×C₉	—	2	4	no	—
132	C₂×C₄×C₉	—	3	4	no	—
133	C₂×C₄×C₉	—	3	2	no	—
134	C₂×C₄×C₉	—	4	4	no	—
135	C₂×C₄×C₉	—	6	8	no	—
136	C₂×C₄×C₉	—	6	4	no	—
137	C₂×C₄×C₉	—	6	2	no	—
138	C₂×C₄×C₉	C₂²×D₃	1	4	yes	—
139	C₂×#123	—	3	1	no	Sylow
140	C₂×C₃×C₉	—	2	4	no	—
141	C₂×C₃×C₉	#123	1	4	yes	complemented
142	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
143	C₂×C₃×C₉	C₂×#41	1	2	yes	—
144	D₃×C₉	—	4	2	no	—
145	C₂⁴×C₃	—	2	1	no	—
146	C₂⁴×C₃	—	3	1	no	—
147	C₂⁴×C₃	C₂²×C₉	1	1	yes	characteristic
148	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
149	C₂³×D₃	C₂²×C₉	1	1	yes	characteristic
150	C₂×C₃×D₄	—	3	4	no	—
151	C₂×C₃×D₄	—	6	4	no	—
152	C₂²×C₃×C₄	—	2	2	no	—
153	C₂²×C₃×C₄	—	3	2	no	—
154	C₂²×C₃×C₄	—	3	1	no	—
155	C₂²×C₃×C₄	—	3	4	no	—
156	C₂²×C₃×C₄	—	6	4	no	—
157	C₂²×C₃×C₄	C₂²×C₉	1	2	yes	—
158	C₂²×C₃×C₄	C₂×C₃×D₃	1	2	yes	—
159	C₂×#67	—	2	4	no	—
160	C₂×#67	C₂²×C₉	1	4	yes	—
161	C₂²×Dic₃	—	2	4	no	—
162	C₂²×Dic₃	C₂²×C₉	1	1	yes	characteristic
163	C₂²×Dic₃	C₂²×C₉	1	2	yes	—
164	C₂²×Dic₃	C₂²×C₉	1	4	yes	complemented
165	C₃×C₄⋊C₄	—	3	8	no	—
166	C₃×C₂²⋊C₄	—	2	4	no	—
167	C₃×C₂²⋊C₄	—	3	8	no	—
168	C₃×C₂²⋊C₄	C₂²×C₉	1	4	yes	complemented
169	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	4	yes	—
170	(C₂×D₃)⋊C₄	C₂²×C₉	1	8	yes	complemented
171	C₄⋊Dic₃	C₂²×C₉	1	8	yes	complemented
172	C₂²×C₃²	—	2	8	no	—
173	C₂²×C₃²	—	2	4	no	—
174	C₂²×C₃²	C₂×C₃×D₄	1	4	yes	—
175	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
176	C₂²×C₃²	C₃×#41	1	4	yes	—
177	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
178	C₂×C₃×D₃	—	2	2	no	—
179	C₂×C₃×D₃	—	2	4	no	—
180	C₂×C₃×D₃	—	4	4	no	—
181	C₃²×C₄	—	2	4	no	—
182	C₃×Dic₃	—	2	4	no	—
183	C₃×Dic₃	—	2	2	no	—
184	C₂²×C₉	—	2	8	no	—
185	C₂²×C₉	—	2	4	no	—
186	C₂²×C₉	—	2	1	no	—
187	C₂²×C₉	—	2	2	no	—
188	C₂²×C₉	—	2	4	no	—
189	C₂²×C₉	—	2	4	no	—
190	C₂²×C₉	—	4	8	no	—
191	C₂²×C₉	—	4	4	no	—
192	C₂²×C₉	—	6	2	no	—
193	C₂²×C₉	—	6	4	no	—
194	C₂²×C₉	—	12	4	no	—
195	C₂²×C₉	C₂×D₁₂	1	4	yes	—
196	C₂²×C₉	C₂×D₁₂	1	2	yes	—
197	C₂²×C₉	#237	1	4	yes	—
198	C₂²×C₉	C₂³×D₃	1	1	yes	characteristic
199	C₄×C₉	—	2	4	no	—
200	C₄×C₉	—	4	4	no	—
201	C₄×C₉	—	6	4	no	—
202	C₄×C₉	—	6	2	no	—
203	C₂²×D₄	—	3	1	no	—
204	C₂³×C₄	—	3	1	no	—
205	#123	—	3	8	no	—
206	C₂×C₄⋊C₄	—	3	2	no	—
207	C₂×C₂²⋊C₄	—	3	2	no	—
208	C₂×C₂²⋊C₄	D₃×C₉	1	1	yes	characteristic, complemented
209	C₃×C₉	C₂×#123	1	1	yes	characteristic, complemented, Sylow
210	C₂³×C₃	—	2	4	no	—
211	C₂³×C₃	—	2	4	no	—
212	C₂³×C₃	—	2	4	no	—
213	C₂³×C₃	—	2	1	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	3	2	no	—
216	C₂³×C₃	—	4	4	no	—
217	C₂³×C₃	—	6	2	no	—
218	C₂³×C₃	—	6	4	no	—
219	C₂³×C₃	D₄×C₉	1	4	yes	—
220	C₂³×C₃	C₂³×C₉	1	2	yes	—
221	C₂³×C₃	C₂³×C₉	1	1	yes	characteristic
222	C₂³×C₃	C₃×D₁₂	1	4	yes	—
223	C₂³×C₃	C₂²×C₃×D₃	1	2	yes	—
224	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
225	C₂²×D₃	—	2	2	no	—
226	C₂²×D₃	—	2	4	no	—
227	C₂²×D₃	C₂³×C₉	1	2	yes	—
228	C₃×D₄	—	6	8	no	—
229	C₂×C₃×C₄	—	2	4	no	—
230	C₂×C₃×C₄	—	2	4	no	—
231	C₂×C₃×C₄	—	2	4	no	—
232	C₂×C₃×C₄	—	3	4	no	—
233	C₂×C₃×C₄	—	3	2	no	—
234	C₂×C₃×C₄	—	4	4	no	—
235	C₂×C₃×C₄	—	6	8	no	—
236	C₂×C₃×C₄	—	6	4	no	—
237	C₂×C₃×C₄	—	6	2	no	—
238	C₂×C₃×C₄	C₂³×C₉	1	4	yes	—
239	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
240	#67	—	2	8	no	—
241	C₂×Dic₃	—	2	4	no	—
242	C₂×Dic₃	—	2	8	no	—
243	C₂×Dic₃	—	2	2	no	—
244	C₂×Dic₃	C₂³×C₉	1	2	yes	—
245	C₂×Dic₃	C₂³×C₉	1	4	yes	—
246	C₂×C₃²	—	2	4	no	—
247	C₂×C₃²	C₃×#123	1	4	yes	—
248	C₂×C₃²	C₂²×C₃×D₄	1	1	yes	characteristic
249	C₂×C₃²	C₂×C₃×#41	1	2	yes	—
250	C₃×D₃	—	4	2	no	—
251	C₂×C₉	—	2	4	no	—
252	C₂×C₉	—	2	4	no	—
253	C₂×C₉	—	2	1	no	—
254	C₂×C₉	—	2	2	no	—
255	C₂×C₉	—	4	4	no	—
256	C₂×C₉	—	12	2	no	—
257	C₂×C₉	#886	1	4	yes	direct product factor
258	C₂×C₉	C₂²×D₁₂	1	1	yes	characteristic
259	C₂×C₉	C₂×#237	1	2	yes	—
260	C₂⁴	—	3	1	no	—
261	C₂⁴	C₂×D₃×C₉	1	1	yes	characteristic
262	C₂×D₄	—	3	4	no	—
263	C₂×D₄	—	6	4	no	—
264	C₂²×C₄	—	3	2	no	—
265	C₂²×C₄	—	3	1	no	—
266	C₂²×C₄	—	3	4	no	—
267	C₂²×C₄	—	6	4	no	—
268	C₂²×C₄	C₂×D₃×C₉	1	2	yes	—
269	C₄⋊C₄	—	3	8	no	—
270	C₂²⋊C₄	—	3	8	no	—
271	C₂²⋊C₄	C₂×D₃×C₉	1	4	yes	complemented
272	C₂²×C₃	—	2	8	no	—
273	C₂²×C₃	—	2	8	no	—
274	C₂²×C₃	—	2	4	no	—
275	C₂²×C₃	—	2	4	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	2	no	—
278	C₂²×C₃	—	2	4	no	—
279	C₂²×C₃	—	2	4	no	—
280	C₂²×C₃	—	4	4	no	—
281	C₂²×C₃	—	4	8	no	—
282	C₂²×C₃	—	6	2	no	—
283	C₂²×C₃	—	6	4	no	—
284	C₂²×C₃	—	12	4	no	—
285	C₂²×C₃	C₂×D₄×C₉	1	4	yes	—
286	C₂²×C₃	C₂×D₄×C₉	1	2	yes	—
287	C₂²×C₃	C₉×#41	1	4	yes	—
288	C₂²×C₃	C₂⁴×C₉	1	1	yes	characteristic
289	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
290	C₂²×C₃	C₂×C₃×D₁₂	1	2	yes	—
291	C₂²×C₃	C₃×#237	1	4	yes	—
292	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
293	C₂×D₃	—	2	2	no	—
294	C₂×D₃	—	2	4	no	—
295	C₂×D₃	—	4	4	no	—
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	2	4	no	—
298	C₃×C₄	—	4	4	no	—
299	C₃×C₄	—	6	4	no	—
300	C₃×C₄	—	6	2	no	—
301	Dic₃	—	2	4	no	—
302	Dic₃	—	2	2	no	—
303	C₃²	C₂×C₃×#123	1	1	yes	characteristic
304	C₉	—	2	1	no	—
305	C₉	C₂×#886	1	1	yes	characteristic, direct product factor
306	C₂³	—	2	4	no	—
307	C₂³	—	3	2	no	—
308	C₂³	—	6	2	no	—
309	C₂³	—	6	4	no	—
310	C₂³	C₉×D₁₂	1	4	yes	—
311	C₂³	C₂²×D₃×C₉	1	2	yes	—
312	C₂³	C₂²×D₃×C₉	1	1	yes	characteristic
313	D₄	—	6	8	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	3	4	no	—
316	C₂×C₄	—	3	2	no	—
317	C₂×C₄	—	6	8	no	—
318	C₂×C₄	—	6	4	no	—
319	C₂×C₄	—	6	2	no	—
320	C₂×C₄	C₂²×D₃×C₉	1	4	yes	—
321	C₂×C₃	—	2	4	no	—
322	C₂×C₃	—	2	4	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	—	2	2	no	—
325	C₂×C₃	—	2	4	no	—
326	C₂×C₃	—	4	4	no	—
327	C₂×C₃	—	12	2	no	—
328	C₂×C₃	C₉×#123	1	4	yes	complemented
329	C₂×C₃	C₂²×D₄×C₉	1	1	yes	characteristic
330	C₂×C₃	C₂×C₉×#41	1	2	yes	—
331	C₂×C₃	C₃×#886	1	4	yes	—
332	C₂×C₃	C₂²×C₃×D₁₂	1	1	yes	characteristic
333	C₂×C₃	C₂×C₃×#237	1	2	yes	—
334	D₃	—	4	2	no	—
335	C₂²	—	2	4	no	—
336	C₂²	—	2	8	no	—
337	C₂²	—	6	2	no	—
338	C₂²	—	6	4	no	—
339	C₂²	—	12	4	no	—
340	C₂²	C₂×C₉×D₁₂	1	4	yes	—
341	C₂²	C₂×C₉×D₁₂	1	2	yes	—
342	C₂²	C₉×#237	1	4	yes	—
343	C₂²	C₂³×D₃×C₉	1	1	yes	characteristic
344	C₄	—	2	4	no	—
345	C₄	—	6	4	no	—
346	C₄	—	6	2	no	—
347	C₃	—	2	1	no	—
348	C₃	C₂×C₉×#123	1	1	yes	characteristic, complemented
349	C₃	C₂×C₃×#886	1	1	yes	characteristic
350	C₂	—	2	4	no	—
351	C₂	—	12	2	no	—
352	C₂	C₉×#886	1	4	yes	direct product factor
353	C₂	C₂²×C₉×D₁₂	1	1	yes	characteristic
354	C₂	C₂×C₉×#237	1	2	yes	—

	subgroup	G/H
center	C₂³×C₉	C₂²×D₃
commutator	C₂²×C₃	C₂⁴×C₉
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle	C₂³×C₃²	C₂³×C₃
prime radical	C₂²×C₃×#67	C₂×C₃
cosocle	C₂²×C₃²	C₂⁴×C₃
hypercenter	C₂×C₉×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₉×#123
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₉ ◁ C₂×C₉×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂³×C₉×Dic₃	C₂	semidirect
3. C₂×C₃×C₉×C₂²⋊C₄	C₂	semidirect
4. C₂×C₉×(C₂×D₃)⋊C₄	C₂	semidirect
5. C₂×C₉×C₄⋊Dic₃	C₂	semidirect
6. C₉×#886	C₂	direct (N × H)
17. C₂²×C₉×Dic₃	C₂²	semidirect
18. C₃×C₉×C₂²⋊C₄	C₂²	semidirect
19. C₉×(C₂×D₃)⋊C₄	C₂²	semidirect
20. C₉×C₄⋊Dic₃	C₂²	semidirect
33. C₂×C₉×C₂²⋊C₄	D₃	semidirect
50. C₂×#886	C₉	direct (N × H)
77. C₉×C₂²⋊C₄	C₂×D₃	semidirect
93. C₂³×Dic₃	C₂×C₉	semidirect
98. C₂×C₃×C₂²⋊C₄	C₂×C₉	semidirect
100. C₂×(C₂×D₃)⋊C₄	C₂×C₉	semidirect
101. C₂×C₄⋊Dic₃	C₂×C₉	semidirect
102. #886	C₂×C₉	direct (N × H)
141. C₂×C₃×C₉	#123	semidirect
164. C₂²×Dic₃	C₂²×C₉	semidirect
168. C₃×C₂²⋊C₄	C₂²×C₉	semidirect
170. (C₂×D₃)⋊C₄	C₂²×C₉	semidirect
171. C₄⋊Dic₃	C₂²×C₉	semidirect
208. C₂×C₂²⋊C₄	D₃×C₉	semidirect
209. C₃×C₉	C₂×#123	semidirect
257. C₂×C₉	#886	direct (N × H)
271. C₂²⋊C₄	C₂×D₃×C₉	semidirect
305. C₉	C₂×#886	direct (N × H)
328. C₂×C₃	C₉×#123	semidirect
348. C₃	C₂×C₉×#123	semidirect
352. C₂	C₉×#886	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₉×#67	2
C₂³×C₉×Dic₃	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₉×(C₂×D₃)⋊C₄	2
C₂×C₉×C₄⋊Dic₃	2
C₉×#886	2
C₂×C₃×#886	3
C₂×C₉×#123	3

Subgroups — C2×C9×#886 #13152352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₉×#886 #13152352