Subgroups — C₃×D₃×#362 #11796902

Order 1152.

459 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₃×D₃×M₃₂	C₂	1	1	yes	maximal, characteristic
3	C₃×D₃×#108	C₂	1	1	yes	maximal, characteristic
4	C₃²×#362	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4565	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4517	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4496	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#362	—	3	1	no	maximal
9	D₃×#362	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×D₃×Q₈	—	2	1	no	—
11	C₂×C₃²×Q₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×#216	—	2	1	no	—
13	C₃×D₃×Q₁₆	—	2	1	no	—
14	C₃×D₃×Q₁₆	—	2	1	no	—
15	C₃×D₃×Q₁₆	C₄	1	2	yes	—
16	C₃×D₃×Q₁₆	C₄	1	2	yes	—
17	C₃×D₃×M₁₆	—	2	1	no	—
18	C₂×C₃×Dic₁₂	C₂²	1	1	yes	characteristic
19	C₂×C₃×D₃×C₈	C₂²	1	1	yes	characteristic
20	C₃²×M₃₂	C₂²	1	1	yes	characteristic
21	C₃²×#108	C₂²	1	1	yes	characteristic
22	C₃×#822	—	2	1	no	—
23	C₃×#819	C₂²	1	1	yes	characteristic
24	C₃×#812	C₂²	1	1	yes	characteristic
25	C₃×#798	—	2	1	no	—
26	C₃×D₃×C₁₆	—	2	1	no	—
27	C₂²×C₃×Q₁₆	—	3	1	no	—
28	C₂×D₃×Q₁₆	C₂×C₃	1	1	yes	characteristic
29	C₂×C₃×M₃₂	—	3	1	no	—
30	C₂×C₃×#108	—	3	1	no	—
31	D₃×M₃₂	C₂×C₃	1	1	yes	characteristic
32	D₃×#108	C₂×C₃	1	1	yes	characteristic
33	C₃×#362	—	2	1	no	—
34	C₃×#362	—	3	1	no	—
35	C₃×#362	—	3	1	no	—
36	C₃×#362	—	3	1	no	—
37	C₃×#362	D₃	1	1	yes	characteristic, direct product factor
38	C₃×#362	C₂×C₃	1	1	yes	characteristic, complemented
39	#4565	C₂×C₃	1	1	yes	characteristic, complemented
40	#4517	C₂×C₃	1	1	yes	characteristic, complemented
41	#4496	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×C₃²×Q₈	—	2	1	no	—
43	C₃×D₃×Q₈	—	2	2	no	—
44	C₃×D₃×Q₈	—	2	2	no	—
45	C₃×D₃×Q₈	—	4	1	no	—
46	C₃×D₃×Q₈	—	4	1	no	—
47	C₂×C₃×C₄×D₃	—	4	1	no	—
48	C₂×C₃×C₄×D₃	D₄	1	1	yes	characteristic
49	C₂×C₃×Dic₆	—	2	1	no	—
50	C₂×C₃×Dic₆	—	4	1	no	—
51	C₃²×Q₁₆	—	2	1	no	—
52	C₃²×Q₁₆	C₂×C₄	1	2	yes	—
53	C₃²×M₁₆	—	2	1	no	—
54	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
55	C₃×#216	—	2	2	no	—
56	C₃×#216	—	2	2	no	—
57	C₃×#208	—	2	1	no	—
58	C₂×C₃×C₃⋊C₈	D₄	1	1	yes	characteristic
59	C₃×Dic₁₂	—	2	1	no	—
60	C₃×Dic₁₂	C₂×C₄	1	2	yes	—
61	C₃×ΓL(1,𝔽₂₅)	—	4	1	no	—
62	C₃×D₃×C₈	—	4	1	no	—
63	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
64	C₃×D₃×C₈	C₂×C₄	1	1	yes	characteristic
65	C₃×D₃×C₈	D₄	1	1	yes	characteristic
66	C₃×D₃×C₈	D₄	1	1	yes	characteristic
67	C₃²×C₁₆	—	2	1	no	—
68	C₃×C₃⋊C₁₆	—	2	1	no	—
69	C₂×#362	—	3	1	no	Sylow
70	C₂²×C₃×Q₈	—	6	1	no	—
71	C₂×D₃×Q₈	—	2	1	no	—
72	C₂×C₃×Q₁₆	—	2	1	no	—
73	C₂×C₃×Q₁₆	—	3	2	no	—
74	C₂×C₃×Q₁₆	—	3	2	no	—
75	C₂×C₃×Q₁₆	—	3	1	no	—
76	C₂×C₃×Q₁₆	—	6	1	no	—
77	C₂×C₃×Q₁₆	—	6	1	no	—
78	C₂×C₃×Q₁₆	—	6	1	no	—
79	C₂×C₃×Q₁₆	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃×Q₁₆	C₂²×C₃	1	1	yes	characteristic
81	C₂×C₃×M₁₆	—	6	1	no	—
82	C₂²×C₃×C₈	—	3	1	no	—
83	C₂×#216	—	2	1	no	—
84	D₃×Q₁₆	—	2	1	no	—
85	D₃×Q₁₆	—	2	1	no	—
86	D₃×Q₁₆	C₃×C₄	1	2	yes	—
87	D₃×Q₁₆	C₃×C₄	1	2	yes	—
88	D₃×M₁₆	—	2	1	no	—
89	C₂×Dic₁₂	C₂²×C₃	1	1	yes	characteristic
90	C₂×D₃×C₈	C₂²×C₃	1	1	yes	characteristic
91	C₃×M₃₂	—	2	1	no	—
92	C₃×M₃₂	—	3	1	no	—
93	C₃×M₃₂	—	6	1	no	—
94	C₃×M₃₂	C₂×D₃	1	1	yes	characteristic
95	C₃×M₃₂	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×C₁₆	—	6	1	no	—
97	C₃×#108	—	2	1	no	—
98	C₃×#108	—	3	1	no	—
99	C₃×#108	—	6	1	no	—
100	C₃×#108	C₂×D₃	1	1	yes	characteristic
101	C₃×#108	C₂²×C₃	1	1	yes	characteristic
102	#822	—	2	1	no	—
103	#819	C₂²×C₃	1	1	yes	characteristic
104	#812	C₂²×C₃	1	1	yes	characteristic
105	#798	—	2	1	no	—
106	D₃×C₁₆	—	2	1	no	—
107	C₂²×C₃×D₃	SD₁₆	1	1	yes	characteristic
108	C₃²×Q₈	—	2	2	no	—
109	C₃²×Q₈	—	4	1	no	—
110	C₂×C₃²×C₄	—	4	1	no	—
111	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×Dic₃	—	4	1	no	—
113	C₂×C₃×Dic₃	SD₁₆	1	1	yes	characteristic
114	C₃×C₄×D₃	—	4	2	no	—
115	C₃×C₄×D₃	—	4	2	no	—
116	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₃×C₄×D₃	C₂²⋊C₄	1	1	yes	characteristic
118	C₃×C₄×D₃	D₈	1	1	yes	characteristic
119	C₃×C₄×D₃	D₈	1	1	yes	characteristic
120	C₃×Dic₆	—	2	2	no	—
121	C₃×Dic₆	—	4	1	no	—
122	C₃×Dic₆	—	4	2	no	—
123	C₃×Dic₆	—	4	2	no	—
124	C₃²×C₈	—	4	1	no	—
125	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
126	C₃²×C₈	C₂×D₄	1	1	yes	characteristic
127	C₃×C₃⋊C₈	—	4	1	no	—
128	C₃×C₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
129	C₃×C₃⋊C₈	C₂²⋊C₄	1	1	yes	characteristic
130	C₂²×Q₁₆	—	3	1	no	—
131	C₂×M₃₂	—	3	1	no	—
132	C₂×#108	—	3	1	no	—
133	#362	—	3	1	no	—
134	#362	—	3	1	no	—
135	#362	—	3	1	no	—
136	#362	C₃×D₃	1	1	yes	characteristic, direct product factor
137	C₂×C₃×Q₈	—	2	1	no	—
138	C₂×C₃×Q₈	—	2	1	no	—
139	C₂×C₃×Q₈	—	4	1	no	—
140	C₂×C₃×Q₈	—	6	2	no	—
141	C₂×C₃×Q₈	—	6	2	no	—
142	C₂×C₃×Q₈	—	6	1	no	—
143	C₂×C₃×Q₈	—	12	1	no	—
144	C₂×C₃×Q₈	—	12	1	no	—
145	C₂×C₃×Q₈	—	12	1	no	—
146	C₂²×C₃×C₄	—	3	1	no	—
147	C₂²×C₃×C₄	—	12	1	no	—
148	D₃×Q₈	—	2	2	no	—
149	D₃×Q₈	—	2	2	no	—
150	D₃×Q₈	—	4	1	no	—
151	D₃×Q₈	—	4	1	no	—
152	C₂×C₄×D₃	—	4	1	no	—
153	C₂×C₄×D₃	C₃×D₄	1	1	yes	characteristic
154	C₂×Dic₆	—	2	1	no	—
155	C₂×Dic₆	—	4	1	no	—
156	C₃×Q₁₆	—	2	1	no	—
157	C₃×Q₁₆	—	2	1	no	—
158	C₃×Q₁₆	—	2	2	no	—
159	C₃×Q₁₆	—	3	2	no	—
160	C₃×Q₁₆	—	4	1	no	—
161	C₃×Q₁₆	—	6	2	no	—
162	C₃×Q₁₆	—	6	2	no	—
163	C₃×Q₁₆	—	6	1	no	—
164	C₃×Q₁₆	C₄×D₃	1	2	yes	—
165	C₃×Q₁₆	C₂×C₃×C₄	1	2	yes	—
166	C₃×M₁₆	—	2	1	no	—
167	C₃×M₁₆	—	2	1	no	—
168	C₃×M₁₆	—	4	1	no	—
169	C₃×M₁₆	—	6	1	no	—
170	C₃×M₁₆	—	12	1	no	—
171	C₂×C₃×C₈	—	2	1	no	—
172	C₂×C₃×C₈	—	3	1	no	—
173	C₂×C₃×C₈	—	3	1	no	—
174	C₂×C₃×C₈	—	3	1	no	—
175	C₂×C₃×C₈	—	3	1	no	—
176	C₂×C₃×C₈	—	3	1	no	—
177	C₂×C₃×C₈	—	12	1	no	—
178	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₃×C₈	C₂³×C₃	1	1	yes	characteristic
180	#216	—	2	2	no	—
181	#216	—	2	2	no	—
182	#208	—	2	1	no	—
183	C₂×C₃⋊C₈	C₃×D₄	1	1	yes	characteristic
184	Dic₁₂	—	2	1	no	—
185	Dic₁₂	C₂×C₃×C₄	1	2	yes	—
186	ΓL(1,𝔽₂₅)	—	4	1	no	—
187	D₃×C₈	—	4	1	no	—
188	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
189	D₃×C₈	C₂×C₃×C₄	1	1	yes	characteristic
190	D₃×C₈	C₃×D₄	1	1	yes	characteristic
191	D₃×C₈	C₃×D₄	1	1	yes	characteristic
192	C₃×C₁₆	—	2	1	no	—
193	C₃×C₁₆	—	2	1	no	—
194	C₃×C₁₆	—	4	1	no	—
195	C₃×C₁₆	—	6	1	no	—
196	C₃⋊C₁₆	—	2	1	no	—
197	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
198	C₂×C₃×D₃	—	2	2	no	—
199	C₂×C₃×D₃	#102	1	1	yes	characteristic
200	C₂×C₃×D₃	#102	1	1	yes	characteristic
201	C₃²×C₄	—	4	2	no	—
202	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
203	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
204	C₃×Dic₃	—	4	2	no	—
205	C₃×Dic₃	#102	1	1	yes	characteristic
206	C₃×Dic₃	#102	1	1	yes	characteristic
207	C₂²×Q₈	—	6	1	no	—
208	C₂×Q₁₆	—	3	2	no	—
209	C₂×Q₁₆	—	3	2	no	—
210	C₂×Q₁₆	—	3	1	no	—
211	C₂×Q₁₆	—	6	1	no	—
212	C₂×Q₁₆	—	6	1	no	—
213	C₂×Q₁₆	—	6	1	no	—
214	C₂×Q₁₆	C₂×C₃×D₃	1	1	yes	characteristic
215	C₂×M₁₆	—	6	1	no	—
216	C₂²×C₈	—	3	1	no	—
217	M₃₂	—	3	1	no	—
218	M₃₂	—	6	1	no	—
219	M₃₂	C₂×C₃×D₃	1	1	yes	characteristic
220	C₂×C₁₆	—	6	1	no	—
221	#108	—	3	1	no	—
222	#108	—	6	1	no	—
223	#108	C₂×C₃×D₃	1	1	yes	characteristic
224	C₂³×C₃	—	3	1	no	—
225	C₂²×D₃	C₃×SD₁₆	1	1	yes	characteristic
226	C₃×Q₈	—	2	2	no	—
227	C₃×Q₈	—	2	2	no	—
228	C₃×Q₈	—	4	2	no	—
229	C₃×Q₈	—	4	1	no	—
230	C₃×Q₈	—	4	1	no	—
231	C₃×Q₈	—	6	2	no	—
232	C₃×Q₈	—	8	1	no	—
233	C₃×Q₈	—	12	2	no	—
234	C₃×Q₈	—	12	2	no	—
235	C₃×Q₈	—	12	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	3	1	no	—
238	C₂×C₃×C₄	—	3	1	no	—
239	C₂×C₃×C₄	—	3	1	no	—
240	C₂×C₃×C₄	—	3	1	no	—
241	C₂×C₃×C₄	—	3	1	no	—
242	C₂×C₃×C₄	—	4	1	no	—
243	C₂×C₃×C₄	—	4	1	no	—
244	C₂×C₃×C₄	—	8	1	no	—
245	C₂×C₃×C₄	—	12	2	no	—
246	C₂×C₃×C₄	—	12	2	no	—
247	C₂×C₃×C₄	—	12	1	no	—
248	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
250	C₂×Dic₃	—	4	1	no	—
251	C₂×Dic₃	C₃×SD₁₆	1	1	yes	characteristic
252	C₄×D₃	—	4	2	no	—
253	C₄×D₃	—	4	2	no	—
254	C₄×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
255	C₄×D₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
256	C₄×D₃	C₃×D₈	1	1	yes	characteristic
257	C₄×D₃	C₃×D₈	1	1	yes	characteristic
258	Dic₆	—	2	2	no	—
259	Dic₆	—	4	1	no	—
260	Dic₆	—	4	2	no	—
261	Dic₆	—	4	2	no	—
262	C₃×C₈	—	2	1	no	—
263	C₃×C₈	—	2	1	no	—
264	C₃×C₈	—	3	1	no	—
265	C₃×C₈	—	3	1	no	—
266	C₃×C₈	—	4	1	no	—
267	C₃×C₈	—	4	1	no	—
268	C₃×C₈	—	8	1	no	—
269	C₃×C₈	—	12	1	no	—
270	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
271	C₃×C₈	D₃×D₄	1	1	yes	characteristic
272	C₃×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
273	C₃×C₈	C₂×C₃×D₄	1	1	yes	characteristic
274	C₃⋊C₈	—	4	1	no	—
275	C₃⋊C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
276	C₃⋊C₈	C₃×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₃²	—	2	1	no	—
278	C₂×C₃²	C₂×#102	1	1	yes	characteristic
279	C₃×D₃	—	2	1	no	—
280	C₃×D₃	#362	1	2	yes	direct product factor
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	6	2	no	—
283	C₂×Q₈	—	6	2	no	—
284	C₂×Q₈	—	6	1	no	—
285	C₂×Q₈	—	12	1	no	—
286	C₂×Q₈	—	12	1	no	—
287	C₂×Q₈	—	12	1	no	—
288	C₂²×C₄	—	3	1	no	—
289	C₂²×C₄	—	12	1	no	—
290	Q₁₆	—	2	1	no	—
291	Q₁₆	—	3	2	no	—
292	Q₁₆	—	6	2	no	—
293	Q₁₆	—	6	2	no	—
294	Q₁₆	—	6	1	no	—
295	Q₁₆	C₃×C₄×D₃	1	2	yes	—
296	M₁₆	—	2	1	no	—
297	M₁₆	—	6	1	no	—
298	M₁₆	—	12	1	no	—
299	C₂×C₈	—	3	1	no	—
300	C₂×C₈	—	3	1	no	—
301	C₂×C₈	—	3	1	no	—
302	C₂×C₈	—	3	1	no	—
303	C₂×C₈	—	3	1	no	—
304	C₂×C₈	—	12	1	no	—
305	C₂×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
306	C₁₆	—	2	1	no	—
307	C₁₆	—	6	1	no	—
308	C₂²×C₃	—	2	1	no	—
309	C₂²×C₃	—	3	1	no	—
310	C₂²×C₃	—	3	1	no	—
311	C₂²×C₃	—	6	2	no	—
312	C₂²×C₃	D₃×SD₁₆	1	1	yes	characteristic
313	C₂²×C₃	C₂×C₃×SD₁₆	1	1	yes	characteristic
314	C₂×D₃	—	2	2	no	—
315	C₂×D₃	C₃×#102	1	1	yes	characteristic
316	C₂×D₃	C₃×#102	1	1	yes	characteristic
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	3	1	no	—
320	C₃×C₄	—	3	1	no	—
321	C₃×C₄	—	4	2	no	—
322	C₃×C₄	—	4	2	no	—
323	C₃×C₄	—	8	2	no	—
324	C₃×C₄	—	12	2	no	—
325	C₃×C₄	D₃×C₂²⋊C₄	1	1	yes	characteristic
326	C₃×C₄	D₃×D₈	1	1	yes	characteristic
327	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
328	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
329	Dic₃	—	4	2	no	—
330	Dic₃	C₃×#102	1	1	yes	characteristic
331	Dic₃	C₃×#102	1	1	yes	characteristic
332	C₃²	C₂×#362	1	1	yes	characteristic, complemented, Sylow
333	C₂³	—	3	1	no	—
334	Q₈	—	2	2	no	—
335	Q₈	—	4	1	no	—
336	Q₈	—	6	2	no	—
337	Q₈	—	12	2	no	—
338	Q₈	—	12	2	no	—
339	Q₈	—	12	1	no	—
340	C₂×C₄	—	3	1	no	—
341	C₂×C₄	—	3	1	no	—
342	C₂×C₄	—	3	1	no	—
343	C₂×C₄	—	3	1	no	—
344	C₂×C₄	—	3	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	12	2	no	—
347	C₂×C₄	—	12	2	no	—
348	C₂×C₄	—	12	1	no	—
349	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
350	C₈	—	3	1	no	—
351	C₈	—	3	1	no	—
352	C₈	—	4	1	no	—
353	C₈	—	12	1	no	—
354	C₈	C₂×C₃×C₄×D₃	1	1	yes	characteristic
355	C₈	C₃×D₃×D₄	1	1	yes	characteristic
356	C₂×C₃	—	2	1	no	—
357	C₂×C₃	—	2	1	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	3	2	no	—
360	C₂×C₃	—	4	1	no	—
361	C₂×C₃	—	6	1	no	—
362	C₂×C₃	D₃×#102	1	1	yes	characteristic
363	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
364	D₃	—	2	1	no	—
365	D₃	C₃×#362	1	2	yes	direct product factor
366	C₂²	—	3	1	no	—
367	C₂²	—	3	1	no	—
368	C₂²	—	6	2	no	—
369	C₂²	C₃×D₃×SD₁₆	1	1	yes	characteristic
370	C₄	—	3	1	no	—
371	C₄	—	3	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	12	2	no	—
374	C₄	C₃×D₃×C₂²⋊C₄	1	1	yes	characteristic
375	C₄	C₃×D₃×D₈	1	1	yes	characteristic
376	C₃	—	2	1	no	—
377	C₃	D₃×#362	1	1	yes	characteristic, direct product factor
378	C₃	C₂×C₃×#362	1	1	yes	characteristic, complemented
379	C₂	—	2	1	no	—
380	C₂	—	3	2	no	—
381	C₂	—	6	1	no	—
382	C₂	C₃×D₃×#102	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₃×#102
commutator	C₃×C₈	C₂²×C₃×C₄
Frattini	C₂×C₈	C₂²×C₃×D₃
Fitting	C₃²×#362	C₂
socle	C₂×C₃²	C₂×#102
prime radical	C₂²×C₃×D₃	SD₁₆
cosocle	C₂×C₃×C₈	C₂³×C₃
hypercenter	C₃×#362	D₃
hypocenter	C₃	C₂×C₃×#362
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈ ◁ C₃×#362

Complements

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

N	H ≅ G/N	type
4. C₃²×#362	C₂	semidirect
5. C₃×#4565	C₂	semidirect
6. C₃×#4517	C₂	semidirect
7. C₃×#4496	C₂	semidirect
9. D₃×#362	C₃	direct (N × H)
37. C₃×#362	D₃	direct (N × H)
38. C₃×#362	C₂×C₃	semidirect
39. #4565	C₂×C₃	semidirect
40. #4517	C₂×C₃	semidirect
41. #4496	C₂×C₃	semidirect
136. #362	C₃×D₃	direct (N × H)
280. C₃×D₃	#362	direct (N × H)
332. C₃²	C₂×#362	semidirect
365. D₃	C₃×#362	direct (N × H)
377. C₃	D₃×#362	direct (N × H)
378. C₃	C₂×C₃×#362	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×Q₁₆	2
C₃×D₃×M₃₂	2
C₃×D₃×#108	2
C₃²×#362	2
C₃×#4565	2
C₃×#4517	2
C₃×#4496	2
C₂×C₃×#362	3
D₃×#362	3

Subgroups — C3×D3×#362 #11796902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₃×#362 #11796902