Subgroups — C₃×#10588627 #13142454

Order 1728.

738 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	C₂²×C₃×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₉×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#3676	C₂	1	2	yes	maximal
4	C₃×C₉⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₉⋊#95	C₂	1	2	yes	maximal, complemented
6	C₃×#4947	—	3	1	no	maximal
7	#10588627	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂⁴×C₃×C₉	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₃×Dic₉	C₂²	1	2	yes	—
12	C₂²×C₃×Dic₉	C₂²	1	2	yes	—
13	C₂×C₃×Dic₁₈	—	2	2	no	—
14	C₂×C₃×Dic₁₈	—	2	4	no	—
15	C₃×C₉×C₂²⋊C₄	—	2	2	no	—
16	C₃×#3676	—	2	4	no	—
17	C₂²×C₃×Dic₆	—	3	1	no	—
18	C₂×C₃²×C₂²⋊C₄	D₃	1	1	yes	characteristic
19	C₂×C₃×#217	—	3	2	no	—
20	C₂²×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
21	C₃×C₃⋊#95	—	3	2	no	—
22	C₃×C₃⋊#95	—	3	1	no	—
23	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
24	C₂×C₉×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
25	C₂×#3676	C₂×C₃	1	2	yes	—
26	C₉⋊#95	C₂×C₃	1	1	yes	characteristic, complemented
27	C₉⋊#95	C₂×C₃	1	2	yes	complemented
28	C₂³×C₃×C₉	—	2	1	no	—
29	C₂³×C₃×C₉	—	2	2	no	—
30	C₂³×C₃×C₉	—	2	1	no	—
31	C₂³×C₃×C₉	—	2	2	no	—
32	C₂³×C₃×C₉	Q₈	1	2	yes	complemented
33	C₂³×C₃×C₉	C₂³	1	1	yes	characteristic
34	C₂×C₃×C₄×C₉	—	2	2	no	—
35	C₂×C₃×C₄×C₉	—	2	1	no	—
36	C₂×C₃×C₄×C₉	—	2	2	no	—
37	C₂×C₃×C₄×C₉	D₄	1	2	yes	—
38	C₂×C₃×Dic₉	—	2	2	no	—
39	C₂×C₃×Dic₉	—	2	2	no	—
40	C₂×C₃×Dic₉	—	2	2	no	—
41	C₂×C₃×Dic₉	—	2	2	no	—
42	C₂×C₃×Dic₉	—	2	2	no	—
43	C₂×C₃×Dic₉	D₄	1	4	yes	—
44	C₃×Dic₁₈	—	2	8	no	—
45	C₃×#393	—	9	1	no	—
46	#4947	—	3	1	no	—
47	C₂⁴×C₃²	C₂×D₃	1	1	yes	characteristic
48	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
49	C₂²×C₃²×C₄	C₂×D₃	1	1	yes	characteristic
50	C₂²×C₃×Dic₃	—	3	2	no	—
51	C₂²×C₃×Dic₃	—	3	2	no	—
52	C₂×C₃×Dic₆	—	6	4	no	—
53	C₂×C₃×Dic₆	—	6	2	no	—
54	C₂⁴×C₉	—	2	1	no	—
55	C₂⁴×C₉	C₂²×C₃	1	1	yes	characteristic
56	C₃²×C₂²⋊C₄	—	2	2	no	—
57	C₃×#217	—	6	4	no	—
58	C₂²×C₄×C₉	—	2	1	no	—
59	C₂²×C₄×C₉	—	2	1	no	—
60	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₄×C₉	C₂²×C₃	1	1	yes	characteristic
62	C₂²×Dic₉	C₂²×C₃	1	2	yes	—
63	C₂²×Dic₉	C₂²×C₃	1	2	yes	—
64	C₂×Dic₁₈	—	2	2	no	—
65	C₂×Dic₁₈	—	2	4	no	—
66	C₉×C₂²⋊C₄	—	2	4	no	—
67	C₉×C₂²⋊C₄	—	2	2	no	—
68	#3676	—	2	4	no	—
69	C₂²×C₃×C₉	—	2	2	no	—
70	C₂²×C₃×C₉	—	2	4	no	—
71	C₂²×C₃×C₉	—	4	1	no	—
72	C₂²×C₃×C₉	—	4	2	no	—
73	C₂²×C₃×C₉	—	4	1	no	—
74	C₂²×C₃×C₉	C₂×D₄	1	2	yes	—
75	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
77	C₂²×C₃×C₉	#41	1	1	yes	characteristic
78	C₂²×C₃×C₉	#41	1	2	yes	—
79	C₃×C₄×C₉	—	2	2	no	—
80	C₃×C₄×C₉	—	4	1	no	—
81	C₃×Dic₉	—	2	4	no	—
82	C₃×Dic₉	—	4	2	no	—
83	C₂²×C₃×Q₈	—	9	1	no	—
84	C₂²×Dic₆	—	3	1	no	—
85	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
86	C₂×C₃×C₂²⋊C₄	—	9	2	no	—
87	C₂×C₃×C₂²⋊C₄	D₉	1	1	yes	characteristic
88	C₂×C₃×C₂²⋊C₄	C₃×D₃	1	1	yes	characteristic
89	C₂×#217	—	3	2	no	—
90	C₃×#95	—	9	2	no	—
91	C₃×#95	—	9	1	no	—
92	C₃⋊#95	—	3	2	no	—
93	C₃⋊#95	—	3	1	no	—
94	C₂³×C₃²	—	2	1	no	—
95	C₂³×C₃²	—	2	1	no	—
96	C₂³×C₃²	—	2	2	no	—
97	C₂³×C₃²	—	2	2	no	—
98	C₂³×C₃²	Dic₆	1	2	yes	—
99	C₂³×C₃²	C₂²×D₃	1	1	yes	characteristic
100	C₂×C₃²×C₄	—	2	1	no	—
101	C₂×C₃²×C₄	—	2	2	no	—
102	C₂×C₃²×C₄	—	2	2	no	—
103	C₂×C₃²×C₄	#67	1	2	yes	—
104	C₂×C₃×Dic₃	—	3	4	no	—
105	C₂×C₃×Dic₃	—	6	2	no	—
106	C₂×C₃×Dic₃	—	6	2	no	—
107	C₂×C₃×Dic₃	—	6	2	no	—
108	C₂×C₃×Dic₃	—	6	2	no	—
109	C₂×C₃×Dic₃	—	6	2	no	—
110	C₃×Dic₆	—	6	8	no	—
111	C₂³×C₉	—	2	2	no	—
112	C₂³×C₉	—	2	2	no	—
113	C₂³×C₉	—	2	2	no	—
114	C₂³×C₉	—	2	1	no	—
115	C₂³×C₉	—	2	1	no	—
116	C₂³×C₉	—	2	2	no	—
117	C₂³×C₉	—	2	2	no	—
118	C₂³×C₉	—	2	1	no	—
119	C₂³×C₉	—	4	2	no	—
120	C₂³×C₉	—	4	2	no	—
121	C₂³×C₉	C₃×Q₈	1	2	yes	complemented
122	C₂³×C₉	C₂³×C₃	1	1	yes	characteristic
123	C₂×C₄×C₉	—	2	2	no	—
124	C₂×C₄×C₉	—	2	2	no	—
125	C₂×C₄×C₉	—	2	1	no	—
126	C₂×C₄×C₉	—	2	2	no	—
127	C₂×C₄×C₉	—	2	2	no	—
128	C₂×C₄×C₉	—	4	2	no	—
129	C₂×C₄×C₉	—	4	2	no	—
130	C₂×C₄×C₉	C₃×D₄	1	2	yes	—
131	C₂×Dic₉	—	2	2	no	—
132	C₂×Dic₉	—	2	2	no	—
133	C₂×Dic₉	—	2	2	no	—
134	C₂×Dic₉	—	2	2	no	—
135	C₂×Dic₉	—	2	2	no	—
136	C₂×Dic₉	C₃×D₄	1	4	yes	—
137	Dic₁₈	—	2	8	no	—
138	#393	—	9	1	no	Sylow
139	C₂×C₃×C₉	—	4	2	no	—
140	C₂×C₃×C₉	#120	1	1	yes	characteristic
141	C₂×C₃×C₉	C₂²⋊Q₈	1	2	yes	—
142	C₂×C₃×C₉	C₂²⋊Q₈	1	1	yes	characteristic
143	C₂×C₃×C₉	#124	1	2	yes	—
144	C₂×C₃×C₉	#124	1	1	yes	characteristic
145	C₂⁴×C₃	—	2	1	no	—
146	C₂⁴×C₃	C₂×D₉	1	1	yes	characteristic
147	C₂⁴×C₃	C₂×C₃×D₃	1	1	yes	characteristic
148	C₂×C₃×Q₈	—	18	4	no	—
149	C₂×C₃×Q₈	—	18	2	no	—
150	C₂²×C₃×C₄	—	2	1	no	—
151	C₂²×C₃×C₄	—	2	1	no	—
152	C₂²×C₃×C₄	—	9	2	no	—
153	C₂²×C₃×C₄	—	9	2	no	—
154	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
155	C₂²×C₃×C₄	C₂×D₉	1	1	yes	characteristic
156	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
157	C₂²×C₃×C₄	C₂×C₃×D₃	1	1	yes	characteristic
158	C₂²×Dic₃	—	3	2	no	—
159	C₂²×Dic₃	—	3	2	no	—
160	C₂×Dic₆	—	6	4	no	—
161	C₂×Dic₆	—	6	2	no	—
162	C₃×C₂²⋊C₄	—	2	4	no	—
163	C₃×C₂²⋊C₄	—	2	2	no	—
164	C₃×C₂²⋊C₄	—	2	2	no	—
165	C₃×C₂²⋊C₄	—	18	4	no	—
166	#217	—	6	4	no	—
167	C₂²×C₃²	—	2	2	no	—
168	C₂²×C₃²	—	2	4	no	—
169	C₂²×C₃²	—	4	2	no	—
170	C₂²×C₃²	—	4	1	no	—
171	C₂²×C₃²	—	4	1	no	—
172	C₂²×C₃²	C₂×Dic₆	1	1	yes	characteristic
173	C₂²×C₃²	#235	1	1	yes	characteristic
174	C₂²×C₃²	D₃×D₄	1	2	yes	—
175	C₂²×C₃²	#237	1	2	yes	—
176	C₂²×C₃²	C₂×#67	1	1	yes	characteristic
177	C₃²×C₄	—	2	2	no	—
178	C₃²×C₄	—	4	1	no	—
179	C₃×Dic₃	—	6	4	no	—
180	C₃×Dic₃	—	12	2	no	—
181	C₂²×C₉	—	2	4	no	—
182	C₂²×C₉	—	2	4	no	—
183	C₂²×C₉	—	2	2	no	—
184	C₂²×C₉	—	2	1	no	—
185	C₂²×C₉	—	2	1	no	—
186	C₂²×C₉	—	2	2	no	—
187	C₂²×C₉	—	2	2	no	—
188	C₂²×C₉	—	2	1	no	—
189	C₂²×C₉	—	4	4	no	—
190	C₂²×C₉	—	4	4	no	—
191	C₂²×C₉	—	4	2	no	—
192	C₂²×C₉	—	4	2	no	—
193	C₂²×C₉	—	4	1	no	—
194	C₂²×C₉	—	4	2	no	—
195	C₂²×C₉	—	4	1	no	—
196	C₂²×C₉	C₂×C₃×D₄	1	2	yes	—
197	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
198	C₂²×C₉	C₂×C₃×Q₈	1	1	yes	characteristic
199	C₂²×C₉	C₃×#41	1	1	yes	characteristic
200	C₂²×C₉	C₃×#41	1	2	yes	—
201	C₄×C₉	—	2	2	no	—
202	C₄×C₉	—	4	2	no	—
203	C₄×C₉	—	4	2	no	—
204	C₄×C₉	—	4	1	no	—
205	Dic₉	—	2	4	no	—
206	Dic₉	—	4	2	no	—
207	C₂²×Q₈	—	9	1	no	—
208	C₂×C₂²⋊C₄	—	9	2	no	—
209	C₂×C₂²⋊C₄	C₃×D₉	1	1	yes	characteristic
210	#95	—	9	2	no	—
211	#95	—	9	1	no	—
212	C₃×C₉	#393	1	1	yes	characteristic, complemented, Sylow
213	C₂³×C₃	—	2	2	no	—
214	C₂³×C₃	—	2	2	no	—
215	C₂³×C₃	—	2	1	no	—
216	C₂³×C₃	—	2	2	no	—
217	C₂³×C₃	—	2	2	no	—
218	C₂³×C₃	—	2	1	no	—
219	C₂³×C₃	—	2	1	no	—
220	C₂³×C₃	—	2	2	no	—
221	C₂³×C₃	—	2	2	no	—
222	C₂³×C₃	—	2	1	no	—
223	C₂³×C₃	—	2	2	no	—
224	C₂³×C₃	—	2	1	no	—
225	C₂³×C₃	—	4	2	no	—
226	C₂³×C₃	—	4	2	no	—
227	C₂³×C₃	Dic₁₈	1	2	yes	complemented
228	C₂³×C₃	C₂²×D₉	1	1	yes	characteristic
229	C₂³×C₃	C₃×Dic₆	1	2	yes	—
230	C₂³×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
231	C₃×Q₈	—	18	8	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	—	9	4	no	—
243	C₂×C₃×C₄	—	18	2	no	—
244	C₂×C₃×C₄	—	18	2	no	—
245	C₂×C₃×C₄	—	18	2	no	—
246	C₂×C₃×C₄	—	18	2	no	—
247	C₂×C₃×C₄	—	18	2	no	—
248	C₂×C₃×C₄	#611	1	2	yes	—
249	C₂×C₃×C₄	C₃×#67	1	2	yes	—
250	C₂×Dic₃	—	3	4	no	—
251	C₂×Dic₃	—	6	2	no	—
252	C₂×Dic₃	—	6	2	no	—
253	C₂×Dic₃	—	6	2	no	—
254	C₂×Dic₃	—	6	2	no	—
255	C₂×Dic₃	—	6	2	no	—
256	Dic₆	—	6	8	no	—
257	C₂×C₃²	—	4	2	no	—
258	C₂×C₃²	#878	1	2	yes	—
259	C₂×C₃²	#885	1	2	yes	—
260	C₂×C₃²	#924	1	1	yes	characteristic
261	C₂×C₃²	#936	1	1	yes	characteristic
262	C₂×C₃²	#937	1	1	yes	characteristic
263	C₂×C₉	—	2	2	no	—
264	C₂×C₉	—	2	2	no	—
265	C₂×C₉	—	2	1	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	—	2	1	no	—
268	C₂×C₉	—	4	4	no	—
269	C₂×C₉	—	4	2	no	—
270	C₂×C₉	C₃×#120	1	1	yes	characteristic
271	C₂×C₉	C₃×C₂²⋊Q₈	1	2	yes	—
272	C₂×C₉	C₃×C₂²⋊Q₈	1	1	yes	characteristic
273	C₂×C₉	C₃×#124	1	2	yes	—
274	C₂×C₉	C₃×#124	1	1	yes	characteristic
275	C₂⁴	C₂×C₃×D₉	1	1	yes	characteristic
276	C₂×Q₈	—	18	4	no	—
277	C₂×Q₈	—	18	2	no	—
278	C₂²×C₄	—	9	2	no	—
279	C₂²×C₄	—	9	2	no	—
280	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₃×D₉	1	1	yes	characteristic
282	C₂²⋊C₄	—	2	2	no	—
283	C₂²⋊C₄	—	18	4	no	—
284	C₂²×C₃	—	2	4	no	—
285	C₂²×C₃	—	2	4	no	—
286	C₂²×C₃	—	2	2	no	—
287	C₂²×C₃	—	2	4	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	2	2	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	4	4	no	—
295	C₂²×C₃	—	4	2	no	—
296	C₂²×C₃	—	4	2	no	—
297	C₂²×C₃	—	4	4	no	—
298	C₂²×C₃	—	4	2	no	—
299	C₂²×C₃	—	4	1	no	—
300	C₂²×C₃	—	4	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	4	1	no	—
303	C₂²×C₃	—	4	2	no	—
304	C₂²×C₃	C₂×Dic₁₈	1	1	yes	characteristic
305	C₂²×C₃	#3697	1	1	yes	characteristic
306	C₂²×C₃	D₄×D₉	1	2	yes	—
307	C₂²×C₃	#3699	1	2	yes	—
308	C₂²×C₃	C₂×#611	1	1	yes	characteristic
309	C₂²×C₃	C₂×C₃×Dic₆	1	1	yes	characteristic
310	C₂²×C₃	C₃×#235	1	1	yes	characteristic
311	C₂²×C₃	C₃×D₃×D₄	1	2	yes	—
312	C₂²×C₃	C₃×#237	1	2	yes	—
313	C₂²×C₃	C₂×C₃×#67	1	1	yes	characteristic
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	2	2	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	—	4	2	no	—
318	C₃×C₄	—	4	1	no	—
319	C₃×C₄	—	4	1	no	—
320	C₃×C₄	—	18	4	no	—
321	C₃×C₄	—	36	2	no	—
322	Dic₃	—	6	4	no	—
323	Dic₃	—	12	2	no	—
324	C₃²	#4947	1	1	yes	characteristic
325	C₉	—	2	1	no	—
326	C₉	C₃×#393	1	1	yes	characteristic, complemented
327	C₂³	—	2	1	no	—
328	C₂³	—	2	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	2	1	no	—
331	C₂³	C₃×Dic₁₈	1	2	yes	complemented
332	C₂³	C₂²×C₃×D₉	1	1	yes	characteristic
333	Q₈	—	18	8	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	9	4	no	—
338	C₂×C₄	—	18	2	no	—
339	C₂×C₄	—	18	2	no	—
340	C₂×C₄	—	18	2	no	—
341	C₂×C₄	—	18	2	no	—
342	C₂×C₄	—	18	2	no	—
343	C₂×C₄	C₃×#611	1	2	yes	—
344	C₂×C₃	—	2	1	no	—
345	C₂×C₃	—	2	1	no	—
346	C₂×C₃	—	2	1	no	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	2	2	no	—
349	C₂×C₃	—	4	4	no	—
350	C₂×C₃	—	4	2	no	—
351	C₂×C₃	—	4	2	no	—
352	C₂×C₃	#63440	1	2	yes	—
353	C₂×C₃	#63447	1	2	yes	—
354	C₂×C₃	#63486	1	1	yes	characteristic
355	C₂×C₃	#63498	1	1	yes	characteristic
356	C₂×C₃	#63499	1	1	yes	characteristic
357	C₂×C₃	C₃×#878	1	2	yes	—
358	C₂×C₃	C₃×#885	1	2	yes	—
359	C₂×C₃	C₃×#924	1	1	yes	characteristic
360	C₂×C₃	C₃×#936	1	1	yes	characteristic
361	C₂×C₃	C₃×#937	1	1	yes	characteristic
362	C₂²	—	2	2	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	2	no	—
367	C₂²	C₂×C₃×Dic₁₈	1	1	yes	characteristic
368	C₂²	C₃×#3697	1	1	yes	characteristic
369	C₂²	C₃×D₄×D₉	1	2	yes	—
370	C₂²	C₃×#3699	1	2	yes	—
371	C₂²	C₂×C₃×#611	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	4	1	no	—
374	C₄	—	18	4	no	—
375	C₄	—	36	2	no	—
376	C₃	—	2	1	no	—
377	C₃	#10588627	1	1	yes	characteristic, direct product factor
378	C₃	C₃×#4947	1	1	yes	characteristic
379	C₂	—	4	2	no	—
380	C₂	C₃×#63440	1	2	yes	—
381	C₂	C₃×#63447	1	2	yes	—
382	C₂	C₃×#63486	1	1	yes	characteristic
383	C₂	C₃×#63498	1	1	yes	characteristic
384	C₂	C₃×#63499	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂²×D₉
commutator, cosocle	C₂³×C₉	C₂³×C₃
Frattini	C₂³×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₉×C₂²⋊C₄	C₂
socle	C₂³×C₃²	C₂²×D₃
prime radical	C₂⁴×C₃²	C₂×D₃
hypercenter	C₂×C₃×C₂²⋊C₄	D₉
hypocenter	C₉	C₃×#393
LCS	G ▷ C₂³×C₉ ▷ C₉
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Dic₁₈	C₂	semidirect
4. C₃×C₉⋊#95	C₂	semidirect
5. C₃×C₉⋊#95	C₂	semidirect
7. #10588627	C₃	direct (N × H)
20. C₂²×Dic₁₈	C₂×C₃	semidirect
26. C₉⋊#95	C₂×C₃	semidirect
27. C₉⋊#95	C₂×C₃	semidirect
32. C₂³×C₃×C₉	Q₈	semidirect
121. C₂³×C₉	C₃×Q₈	semidirect
212. C₃×C₉	#393	semidirect
227. C₂³×C₃	Dic₁₈	semidirect
326. C₉	C₃×#393	semidirect
331. C₂³	C₃×Dic₁₈	semidirect
377. C₃	#10588627	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×C₃×Dic₁₈	2
C₂×C₃×C₉×C₂²⋊C₄	2
C₂×C₃×#3676	2
C₃×C₉⋊#95	2
C₃×#4947	3
#10588627	3

Subgroups — C3×#10588627 #13142454

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10588627 #13142454