Subgroups — C₃×#69825 #11791096

Order 1152.

825 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	C₂²×C₃×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#821	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#817	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4939	C₂	1	2	yes	maximal, complemented
6	C₃×#1972	—	3	1	no	maximal
7	#69825	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂²×C₃×D₁₂	C₂²	1	2	yes	—
9	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
12	C₂×C₃×(C₂×D₃)⋊C₄	—	2	4	no	—
13	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₂×C₃×D₂₄	—	2	2	no	—
15	C₂×C₃×D₂₄	—	2	2	no	—
16	C₂×C₃×D₂₄	C₄	1	4	yes	complemented
17	C₃²×#97	—	2	2	no	—
18	C₃×#821	—	2	4	no	—
19	C₃×#817	—	2	2	no	—
20	C₂²×C₃×D₈	—	3	1	no	—
21	C₂²×D₂₄	C₂×C₃	1	1	yes	characteristic
22	C₂×C₃×#106	—	3	1	no	—
23	C₂×C₃×#102	—	3	2	no	—
24	C₂×C₃×#97	—	2	1	no	—
25	C₂×C₃×#97	D₃	1	1	yes	characteristic, complemented
26	C₂×C₃×#97	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×#390	—	3	2	no	—
28	C₂×#821	C₂×C₃	1	2	yes	complemented
29	C₂×#817	C₂×C₃	1	1	yes	characteristic, complemented
30	#4939	C₂×C₃	1	2	yes	complemented
31	C₂³×C₃×D₃	—	2	2	no	—
32	C₂²×C₃²×C₄	D₄	1	2	yes	—
33	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₂²×C₃×Dic₃	—	2	2	no	—
35	C₂×C₃×D₁₂	—	2	2	no	—
36	C₂×C₃×D₁₂	—	2	2	no	—
37	C₂×C₃×D₁₂	—	2	2	no	—
38	C₂×C₃×D₁₂	—	2	2	no	—
39	C₂×C₃×D₁₂	—	2	2	no	—
40	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
41	C₂×C₃²×C₈	—	2	1	no	—
42	C₂×C₃²×C₈	—	2	1	no	—
43	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
44	C₂×C₃²×C₈	D₄	1	2	yes	—
45	C₂×C₃²×C₈	D₄	1	2	yes	—
46	C₂×C₃²×C₈	D₄	1	2	yes	—
47	C₃²×C₄²	—	2	1	no	—
48	C₃²×C₄²	—	2	1	no	—
49	C₃×(C₂×D₃)⋊C₄	—	4	8	no	—
50	C₃×C₄⋊Dic₃	—	2	2	no	—
51	C₃×C₄⋊Dic₃	—	2	2	no	—
52	C₃×D₂₄	—	2	8	no	—
53	#1972	—	3	1	no	Sylow
54	C₂²×C₃×D₄	—	3	2	no	—
55	C₂²×D₁₂	C₂²×C₃	1	2	yes	—
56	C₂×C₃×D₈	—	3	4	no	—
57	C₂×C₃×D₈	—	6	2	no	—
58	C₂×C₃×D₈	—	6	2	no	—
59	C₂²×C₃×C₈	—	2	1	no	—
60	C₂²×C₃×C₈	—	2	1	no	—
61	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
62	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
64	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
65	C₂×C₃×C₄⋊C₄	—	3	2	no	—
66	C₂×C₃×C₂²⋊C₄	—	6	4	no	—
67	C₂×C₃×C₄²	—	2	1	no	—
68	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
69	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
70	C₂×(C₂×D₃)⋊C₄	—	2	4	no	—
71	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
72	C₂×D₂₄	—	2	2	no	—
73	C₂×D₂₄	—	2	2	no	—
74	C₂×D₂₄	C₃×C₄	1	4	yes	complemented
75	C₃×#106	—	6	2	no	—
76	C₃×#102	—	6	4	no	—
77	C₃×#97	—	2	4	no	—
78	C₃×#97	—	2	2	no	—
79	C₃×#97	—	2	2	no	—
80	#821	—	2	4	no	—
81	#817	—	2	2	no	—
82	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₃×D₃	—	2	4	no	—
84	C₂²×C₃×D₃	—	4	2	no	—
85	C₂²×C₃×D₃	—	4	2	no	—
86	C₂²×C₃×D₃	—	4	4	no	—
87	C₂²×C₃×D₃	—	4	4	no	—
88	C₂×C₃²×C₄	—	2	2	no	—
89	C₂×C₃²×C₄	—	2	4	no	—
90	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
92	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
94	C₂×C₃²×C₄	#41	1	1	yes	characteristic
95	C₂×C₃²×C₄	#41	1	1	yes	characteristic
96	C₂×C₃×Dic₃	—	4	2	no	—
97	C₂×C₃×Dic₃	—	4	4	no	—
98	C₃×D₁₂	—	2	4	no	—
99	C₃×D₁₂	—	2	4	no	—
100	C₃×D₁₂	—	4	2	no	—
101	C₃×D₁₂	—	4	2	no	—
102	C₃²×C₈	—	2	2	no	—
103	C₃²×C₈	C₂²⋊C₄	1	4	yes	complemented
104	C₂²×D₈	—	3	1	no	—
105	C₂×#106	—	3	1	no	—
106	C₂×#102	—	3	2	no	—
107	C₂×#97	C₃×D₃	1	1	yes	characteristic, complemented
108	#390	—	3	2	no	—
109	C₂⁴×C₃	—	6	2	no	—
110	C₂³×D₃	—	2	2	no	—
111	C₂×C₃×D₄	—	3	4	no	—
112	C₂×C₃×D₄	—	6	2	no	—
113	C₂×C₃×D₄	—	6	2	no	—
114	C₂×C₃×D₄	—	6	2	no	—
115	C₂×C₃×D₄	—	6	2	no	—
116	C₂×C₃×D₄	—	6	2	no	—
117	C₂²×C₃×C₄	—	2	2	no	—
118	C₂²×C₃×C₄	—	2	1	no	—
119	C₂²×C₃×C₄	—	6	2	no	—
120	C₂²×C₃×C₄	D₁₂	1	2	yes	—
121	C₂²×C₃×C₄	C₃×D₄	1	2	yes	—
122	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
123	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
124	C₂²×Dic₃	—	2	2	no	—
125	C₂×D₁₂	—	2	2	no	—
126	C₂×D₁₂	—	2	2	no	—
127	C₂×D₁₂	—	2	2	no	—
128	C₂×D₁₂	—	2	2	no	—
129	C₂×D₁₂	—	2	2	no	—
130	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
131	C₃×D₈	—	6	8	no	—
132	C₂×C₃×C₈	—	2	2	no	—
133	C₂×C₃×C₈	—	2	2	no	—
134	C₂×C₃×C₈	—	2	1	no	—
135	C₂×C₃×C₈	—	2	1	no	—
136	C₂×C₃×C₈	—	2	1	no	—
137	C₂×C₃×C₈	—	2	1	no	—
138	C₂×C₃×C₈	—	2	2	no	—
139	C₂×C₃×C₈	—	2	2	no	—
140	C₂×C₃×C₈	—	2	2	no	—
141	C₂×C₃×C₈	—	2	2	no	—
142	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
143	C₂×C₃×C₈	D₁₂	1	2	yes	—
144	C₂×C₃×C₈	D₁₂	1	2	yes	—
145	C₂×C₃×C₈	#67	1	2	yes	—
146	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
147	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
148	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
149	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
150	C₃×C₄⋊C₄	—	6	2	no	—
151	C₃×C₄⋊C₄	—	6	2	no	—
152	C₃×C₂²⋊C₄	—	12	8	no	—
153	C₃×C₄²	—	2	2	no	—
154	C₃×C₄²	—	2	2	no	—
155	C₃×C₄²	—	2	1	no	—
156	C₃×C₄²	—	2	1	no	—
157	C₃×C₄²	—	2	1	no	—
158	C₃×C₄²	—	2	1	no	—
159	(C₂×D₃)⋊C₄	—	4	8	no	—
160	C₄⋊Dic₃	—	2	2	no	—
161	C₄⋊Dic₃	—	2	2	no	—
162	D₂₄	—	2	8	no	—
163	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
164	C₂²×C₃²	#121	1	1	yes	characteristic
165	C₂²×C₃²	#127	1	1	yes	characteristic
166	C₂²×C₃²	AGL(1,ℤ/8)	1	4	yes	—
167	C₂×C₃×D₃	—	4	4	no	—
168	C₂×C₃×D₃	—	4	8	no	—
169	C₂×C₃×D₃	—	8	4	no	—
170	C₂×C₃×D₃	—	8	2	no	—
171	C₂×C₃×D₃	—	8	2	no	—
172	C₃²×C₄	—	4	2	no	—
173	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
175	C₃²×C₄	#121	1	1	yes	characteristic
176	C₃²×C₄	#124	1	1	yes	characteristic
177	C₃×Dic₃	—	8	2	no	—
178	C₂²×D₄	—	3	2	no	—
179	C₂×D₈	—	3	4	no	—
180	C₂×D₈	—	6	2	no	—
181	C₂×D₈	—	6	2	no	—
182	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
183	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
184	C₂×C₄⋊C₄	—	3	2	no	—
185	C₂×C₂²⋊C₄	—	6	4	no	—
186	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
187	#106	—	6	2	no	—
188	#102	—	6	4	no	—
189	#97	—	2	2	no	—
190	C₂³×C₃	—	2	1	no	—
191	C₂³×C₃	—	6	4	no	—
192	C₂³×C₃	—	12	2	no	—
193	C₂³×C₃	—	12	4	no	—
194	C₂³×C₃	—	12	4	no	—
195	C₂³×C₃	—	12	2	no	—
196	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
197	C₂³×C₃	C₂×C₃×D₄	1	1	yes	characteristic
198	C₂²×D₃	—	2	4	no	—
199	C₂²×D₃	—	4	2	no	—
200	C₂²×D₃	—	4	2	no	—
201	C₂²×D₃	—	4	4	no	—
202	C₂²×D₃	—	4	4	no	—
203	C₃×D₄	—	6	4	no	—
204	C₃×D₄	—	6	4	no	—
205	C₃×D₄	—	12	2	no	—
206	C₃×D₄	—	12	2	no	—
207	C₂×C₃×C₄	—	2	4	no	—
208	C₂×C₃×C₄	—	2	4	no	—
209	C₂×C₃×C₄	—	2	2	no	—
210	C₂×C₃×C₄	—	2	2	no	—
211	C₂×C₃×C₄	—	2	4	no	—
212	C₂×C₃×C₄	—	2	1	no	—
213	C₂×C₃×C₄	—	2	1	no	—
214	C₂×C₃×C₄	—	2	1	no	—
215	C₂×C₃×C₄	—	2	1	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	4	4	no	—
219	C₂×C₃×C₄	—	12	2	no	—
220	C₂×C₃×C₄	—	12	4	no	—
221	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
224	C₂×C₃×C₄	#235	1	1	yes	characteristic
225	C₂×C₃×C₄	#235	1	1	yes	characteristic
226	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
227	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
232	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
233	C₂×Dic₃	—	4	2	no	—
234	C₂×Dic₃	—	4	4	no	—
235	D₁₂	—	2	4	no	—
236	D₁₂	—	2	4	no	—
237	D₁₂	—	4	2	no	—
238	D₁₂	—	4	2	no	—
239	C₃×C₈	—	2	4	no	—
240	C₃×C₈	—	2	2	no	—
241	C₃×C₈	—	2	2	no	—
242	C₃×C₈	—	2	4	no	—
243	C₃×C₈	(C₂×D₃)⋊C₄	1	4	yes	complemented
244	C₃×C₈	C₃×C₂²⋊C₄	1	4	yes	complemented
245	C₂×C₃²	#390	1	1	yes	characteristic
246	C₂×C₃²	#442	1	2	yes	—
247	C₂×C₃²	#469	1	2	yes	—
248	C₂×C₃²	#496	1	2	yes	—
249	C₃×D₃	—	8	4	no	—
250	C₂⁴	—	6	2	no	—
251	C₂×D₄	—	3	4	no	—
252	C₂×D₄	—	6	2	no	—
253	C₂×D₄	—	6	2	no	—
254	C₂×D₄	—	6	2	no	—
255	C₂×D₄	—	6	2	no	—
256	C₂×D₄	—	6	2	no	—
257	C₂²×C₄	—	6	2	no	—
258	C₂²×C₄	C₃×D₁₂	1	2	yes	—
259	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
260	D₈	—	6	8	no	—
261	C₂×C₈	—	2	1	no	—
262	C₂×C₈	—	2	1	no	—
263	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
264	C₂×C₈	C₃×D₁₂	1	2	yes	—
265	C₂×C₈	C₃×D₁₂	1	2	yes	—
266	C₂×C₈	C₃×#67	1	2	yes	—
267	C₄⋊C₄	—	6	2	no	—
268	C₄⋊C₄	—	6	2	no	—
269	C₂²⋊C₄	—	12	8	no	—
270	C₄²	—	2	1	no	—
271	C₄²	—	2	1	no	—
272	C₂²×C₃	—	2	4	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	1	no	—
276	C₂²×C₃	—	12	4	no	—
277	C₂²×C₃	—	12	8	no	—
278	C₂²×C₃	—	24	4	no	—
279	C₂²×C₃	—	24	2	no	—
280	C₂²×C₃	—	24	2	no	—
281	C₂²×C₃	C₄×D₁₂	1	1	yes	characteristic
282	C₂²×C₃	#874	1	1	yes	characteristic
283	C₂²×C₃	#908	1	4	yes	—
284	C₂²×C₃	#930	1	1	yes	characteristic
285	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
286	C₂²×C₃	C₃×#121	1	1	yes	characteristic
287	C₂²×C₃	C₃×#127	1	1	yes	characteristic
288	C₂²×C₃	C₃×AGL(1,ℤ/8)	1	4	yes	—
289	C₂×D₃	—	4	4	no	—
290	C₂×D₃	—	4	8	no	—
291	C₂×D₃	—	8	4	no	—
292	C₂×D₃	—	8	2	no	—
293	C₂×D₃	—	8	2	no	—
294	C₃×C₄	—	2	1	no	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	2	1	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	4	4	no	—
299	C₃×C₄	—	4	2	no	—
300	C₃×C₄	—	4	2	no	—
301	C₃×C₄	—	24	2	no	—
302	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
303	C₃×C₄	#875	1	1	yes	characteristic
304	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
305	C₃×C₄	#930	1	1	yes	characteristic
306	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
307	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
308	C₃×C₄	C₃×#121	1	1	yes	characteristic
309	C₃×C₄	C₃×#124	1	1	yes	characteristic
310	Dic₃	—	8	2	no	—
311	C₃²	#1972	1	1	yes	characteristic, complemented, Sylow
312	C₂³	—	6	4	no	—
313	C₂³	—	12	4	no	—
314	C₂³	—	12	4	no	—
315	C₂³	—	12	2	no	—
316	C₂³	—	12	2	no	—
317	C₂³	C₂×C₃×D₁₂	1	1	yes	characteristic
318	D₄	—	6	4	no	—
319	D₄	—	6	4	no	—
320	D₄	—	12	2	no	—
321	D₄	—	12	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	12	4	no	—
325	C₂×C₄	—	12	2	no	—
326	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
327	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
328	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
329	C₂×C₄	C₃×#235	1	1	yes	characteristic
330	C₂×C₄	C₃×#235	1	1	yes	characteristic
331	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
332	C₈	—	2	2	no	—
333	C₈	C₃×(C₂×D₃)⋊C₄	1	4	yes	complemented
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	—	2	2	no	—
336	C₂×C₃	—	2	2	no	—
337	C₂×C₃	—	2	2	no	—
338	C₂×C₃	—	24	4	no	—
339	C₂×C₃	#4711	1	2	yes	—
340	C₂×C₃	#4712	1	2	yes	—
341	C₂×C₃	#4939	1	1	yes	characteristic
342	C₂×C₃	#5135	1	2	yes	—
343	C₂×C₃	C₃×#390	1	1	yes	characteristic
344	C₂×C₃	C₃×#442	1	2	yes	—
345	C₂×C₃	C₃×#469	1	2	yes	—
346	C₂×C₃	C₃×#496	1	2	yes	—
347	D₃	—	8	4	no	—
348	C₂²	—	12	4	no	—
349	C₂²	—	12	8	no	—
350	C₂²	—	24	2	no	—
351	C₂²	—	24	2	no	—
352	C₂²	—	24	4	no	—
353	C₂²	C₃×C₄×D₁₂	1	1	yes	characteristic
354	C₂²	C₃×#874	1	1	yes	characteristic
355	C₂²	C₃×#908	1	4	yes	—
356	C₂²	C₃×#930	1	1	yes	characteristic
357	C₄	—	4	2	no	—
358	C₄	—	24	2	no	—
359	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
360	C₄	C₃×#875	1	1	yes	characteristic
361	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
362	C₄	C₃×#930	1	1	yes	characteristic
363	C₃	—	2	1	no	—
364	C₃	#69825	1	1	yes	characteristic, direct product factor
365	C₃	C₃×#1972	1	1	yes	characteristic, complemented
366	C₂	—	24	4	no	—
367	C₂	C₃×#4711	1	2	yes	—
368	C₂	C₃×#4712	1	2	yes	—
369	C₂	C₃×#4939	1	1	yes	characteristic
370	C₂	C₃×#5135	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂×D₁₂
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×#97	C₂
socle	C₂³×C₃²	C₂×D₄
prime radical	C₂²×C₃×D₂₄	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×#97	D₃
hypocenter	C₃	C₃×#1972
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#97

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×#97	C₂	semidirect
3. C₂×C₃×#821	C₂	semidirect
4. C₂×C₃×#817	C₂	semidirect
5. C₃×#4939	C₂	semidirect
7. #69825	C₃	direct (N × H)
16. C₂×C₃×D₂₄	C₄	semidirect
25. C₂×C₃×#97	D₃	semidirect
26. C₂×C₃×#97	C₂×C₃	semidirect
28. C₂×#821	C₂×C₃	semidirect
29. C₂×#817	C₂×C₃	semidirect
30. #4939	C₂×C₃	semidirect
74. C₂×D₂₄	C₃×C₄	semidirect
103. C₃²×C₈	C₂²⋊C₄	semidirect
107. C₂×#97	C₃×D₃	semidirect
243. C₃×C₈	(C₂×D₃)⋊C₄	semidirect
244. C₃×C₈	C₃×C₂²⋊C₄	semidirect
311. C₃²	#1972	semidirect
333. C₈	C₃×(C₂×D₃)⋊C₄	semidirect
364. C₃	#69825	direct (N × H)
365. C₃	C₃×#1972	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₂₄	2
C₂×C₃²×#97	2
C₂×C₃×#821	2
C₂×C₃×#817	2
C₃×#4939	2
C₃×#1972	3
#69825	3

Subgroups — C3×#69825 #11791096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#69825 #11791096