Subgroups — C₃×#70772 #11776122

Order 1152.

571 conjugacy classes of subgroups.

The subgroup lattice has 389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5477	C₂	1	1	yes	maximal, characteristic
2	C₃²×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#4486	C₂	1	2	yes	maximal, complemented
5	C₃×#4485	C₂	1	2	yes	maximal, complemented
6	C₃×#1540	—	3	1	no	maximal
7	#70772	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#235	—	2	1	no	—
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₃×#930	—	2	1	no	—
11	C₃×#930	C₄	1	2	yes	—
12	C₂²×C₃×C₃⋊C₈	—	2	1	no	—
13	C₃×#875	—	2	1	no	—
14	C₃×#874	C₂²	1	1	yes	characteristic
15	C₃×C₄×D₁₂	—	2	1	no	—
16	C₃×C₄×D₁₂	C₄	1	2	yes	—
17	C₃×#869	C₂²	1	1	yes	characteristic
18	C₃²×C₄⋊C₈	C₂²	1	2	yes	—
19	C₃²×C₂²⋊C₈	—	2	1	no	—
20	C₃²×C₄×C₈	—	2	1	no	—
21	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
22	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
23	C₃×#532	—	3	1	no	—
24	#5477	C₂×C₃	1	1	yes	characteristic
25	C₃×#431	—	2	1	no	—
26	C₃×#431	D₃	1	1	yes	characteristic, complemented
27	C₃×#431	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×C₃×C₄⋊C₈	—	3	1	no	—
29	C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
30	C₃×#332	—	3	2	no	—
31	C₃×#331	—	3	2	no	—
32	#4486	C₂×C₃	1	2	yes	complemented
33	#4485	C₂×C₃	1	2	yes	complemented
34	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
36	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
37	C₂×C₃×#67	—	2	2	no	—
38	C₃×#235	—	4	2	no	—
39	C₃×#235	—	4	2	no	—
40	C₂×C₃×D₁₂	—	2	1	no	—
41	C₂×C₃×D₁₂	—	2	1	no	—
42	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
43	C₂×C₃×C₄×D₃	—	2	2	no	—
44	C₂×C₃×Dic₆	—	2	1	no	—
45	C₂×C₃²×C₈	—	2	2	no	—
46	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
47	C₃²×C₄²	D₄	1	1	yes	characteristic
48	C₃²×C₄²	D₄	1	1	yes	characteristic
49	C₃²×C₄²	C₂³	1	1	yes	characteristic
50	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
51	C₃×(C₂×D₃)⋊C₄	—	2	2	no	—
52	C₃×C₄⋊Dic₃	—	2	1	no	—
53	C₃×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₃⋊C₈	—	2	2	no	—
55	C₂×C₃×C₃⋊C₈	—	4	2	no	—
56	#1540	—	3	1	no	Sylow
57	C₂×C₃×#41	—	6	1	no	—
58	C₂×#235	—	2	1	no	—
59	C₂²×C₃×C₈	—	6	1	no	—
60	C₃×C₄⋊Q₈	—	3	1	no	—
61	C₃×#127	—	3	1	no	—
62	C₃×#124	—	6	1	no	—
63	C₃×#121	—	3	2	no	—
64	C₃×#121	—	6	1	no	—
65	C₃×C₄×D₄	—	3	2	no	—
66	C₃×C₄×D₄	—	6	1	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	#930	—	2	1	no	—
71	#930	C₃×C₄	1	2	yes	—
72	C₂²×C₃⋊C₈	—	2	1	no	—
73	#875	—	2	1	no	—
74	#874	C₂²×C₃	1	1	yes	characteristic
75	C₄×D₁₂	—	2	1	no	—
76	C₄×D₁₂	C₃×C₄	1	2	yes	—
77	#869	C₂²×C₃	1	1	yes	characteristic
78	C₃×C₄⋊C₈	—	2	2	no	—
79	C₃×C₄⋊C₈	—	3	2	no	—
80	C₃×C₄⋊C₈	—	6	1	no	—
81	C₃×C₄⋊C₈	C₂×D₃	1	2	yes	—
82	C₃×C₄⋊C₈	C₂²×C₃	1	2	yes	—
83	C₃×C₂²⋊C₈	—	2	2	no	—
84	C₃×C₂²⋊C₈	—	2	1	no	—
85	C₃×C₂²⋊C₈	—	2	1	no	—
86	C₃×C₄×C₈	—	2	2	no	—
87	C₃×C₄×C₈	—	2	1	no	—
88	C₃×C₄×C₈	—	2	1	no	—
89	C₄⋊(C₃⋊C₈)	—	2	1	no	—
90	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
91	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₃×D₃	—	2	2	no	—
93	C₂×C₃²×C₄	—	2	2	no	—
94	C₂×C₃²×C₄	—	4	1	no	—
95	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₃²×C₄	D₈	1	2	yes	—
99	C₂×C₃²×C₄	SD₁₆	1	2	yes	—
100	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
103	C₃×#67	—	4	4	no	—
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₃×D₁₂	—	4	2	no	—
106	C₃×D₁₂	—	4	1	no	—
107	C₃×D₁₂	—	4	1	no	—
108	C₃×D₁₂	—	4	2	no	—
109	C₃×C₄×D₃	—	4	4	no	—
110	C₃×Dic₆	—	4	1	no	—
111	C₃×Dic₆	—	4	1	no	—
112	C₃²×C₈	—	4	2	no	—
113	C₃×C₃⋊C₈	—	4	2	no	—
114	#532	—	3	1	no	—
115	#431	C₃×D₃	1	1	yes	characteristic, complemented
116	C₂×C₄⋊C₈	—	3	1	no	—
117	#332	—	3	2	no	—
118	#331	—	3	2	no	—
119	C₃×#41	—	12	2	no	—
120	C₃×#41	—	12	2	no	—
121	C₂×C₃×Q₈	—	6	1	no	—
122	C₂×C₃×D₄	—	3	2	no	—
123	C₂×C₃×D₄	—	6	2	no	—
124	C₂×C₃×D₄	—	6	1	no	—
125	C₂×C₃×D₄	—	6	1	no	—
126	C₂²×C₃×C₄	—	2	1	no	—
127	C₂²×C₃×C₄	—	2	1	no	—
128	C₂²×C₃×C₄	—	2	1	no	—
129	C₂²×C₃×C₄	—	6	2	no	—
130	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
131	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
132	C₂²×C₃×C₄	#67	1	1	yes	characteristic
133	C₂²×C₃×C₄	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
135	C₂²×C₃×C₄	C₃×D₄	1	1	yes	characteristic
136	C₂×#67	—	2	2	no	—
137	#235	—	4	2	no	—
138	#235	—	4	2	no	—
139	C₂×D₁₂	—	2	1	no	—
140	C₂×D₁₂	—	2	1	no	—
141	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
142	C₂×C₄×D₃	—	2	2	no	—
143	C₂×Dic₆	—	2	1	no	—
144	C₂×C₃×C₈	—	2	4	no	—
145	C₂×C₃×C₈	—	2	2	no	—
146	C₂×C₃×C₈	—	2	2	no	—
147	C₂×C₃×C₈	—	6	2	no	—
148	C₂×C₃×C₈	—	12	2	no	—
149	C₃×C₄⋊C₄	—	3	2	no	—
150	C₃×C₄⋊C₄	—	6	1	no	—
151	C₃×C₂²⋊C₄	—	6	2	no	—
152	C₃×C₂²⋊C₄	—	6	2	no	—
153	C₃×C₄²	—	2	1	no	—
154	C₃×C₄²	—	2	1	no	—
155	C₃×C₄²	—	2	1	no	—
156	C₃×C₄²	—	2	1	no	—
157	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
158	C₃×C₄²	D₁₂	1	1	yes	characteristic
159	C₃×C₄²	#67	1	1	yes	characteristic
160	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
161	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
162	C₃×C₄²	C₃×D₄	1	1	yes	characteristic
163	C₃×C₄²	C₂²×D₃	1	1	yes	characteristic
164	C₃×C₄²	C₂³×C₃	1	1	yes	characteristic
165	(C₂×D₃)⋊C₄	—	2	2	no	—
166	(C₂×D₃)⋊C₄	—	2	2	no	—
167	C₄⋊Dic₃	—	2	1	no	—
168	C₄⋊Dic₃	C₂×C₃×C₄	1	2	yes	—
169	C₂×C₃⋊C₈	—	2	2	no	—
170	C₂×C₃⋊C₈	—	4	2	no	—
171	C₂²×C₃²	—	2	1	no	—
172	C₂²×C₃²	—	2	1	no	—
173	C₂²×C₃²	#102	1	2	yes	—
174	C₂²×C₃²	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂×C₃×D₃	—	4	2	no	—
176	C₂×C₃×D₃	—	4	2	no	—
177	C₂×C₃×D₃	—	4	2	no	—
178	C₃²×C₄	—	2	1	no	—
179	C₃²×C₄	—	2	1	no	—
180	C₃²×C₄	—	2	1	no	—
181	C₃²×C₄	#102	1	2	yes	—
182	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
183	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
184	C₃²×C₄	#135	1	2	yes	—
185	C₃×Dic₃	—	4	2	no	—
186	C₂×#41	—	6	1	no	—
187	C₂²×C₈	—	6	1	no	—
188	C₄⋊Q₈	—	3	1	no	—
189	#127	—	3	1	no	—
190	#124	—	6	1	no	—
191	#121	—	3	2	no	—
192	#121	—	6	1	no	—
193	C₄×D₄	—	3	2	no	—
194	C₄×D₄	—	6	1	no	—
195	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
196	C₄⋊C₈	—	3	2	no	—
197	C₄⋊C₈	—	6	1	no	—
198	C₄⋊C₈	C₂×C₃×D₃	1	2	yes	—
199	C₂²⋊C₈	—	2	1	no	—
200	C₄×C₈	—	2	1	no	—
201	C₂³×C₃	—	2	1	no	—
202	C₂³×C₃	—	6	2	no	—
203	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
204	C₂³×C₃	C₃×C₂²⋊C₄	1	1	yes	characteristic
205	C₂²×D₃	—	2	2	no	—
206	C₃×Q₈	—	12	1	no	—
207	C₃×Q₈	—	12	1	no	—
208	C₃×D₄	—	12	2	no	—
209	C₃×D₄	—	12	4	no	—
210	C₃×D₄	—	12	1	no	—
211	C₃×D₄	—	12	1	no	—
212	C₃×D₄	—	12	2	no	—
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	2	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	—	2	1	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	4	2	no	—
224	C₂×C₃×C₄	—	4	1	no	—
225	C₂×C₃×C₄	—	4	1	no	—
226	C₂×C₃×C₄	—	4	2	no	—
227	C₂×C₃×C₄	—	6	2	no	—
228	C₂×C₃×C₄	—	12	4	no	—
229	C₂×C₃×C₄	#204	1	2	yes	—
230	C₂×C₃×C₄	D₂₄	1	2	yes	—
231	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
232	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
233	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
234	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
235	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₃×C₄	C₃×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₃×C₄	C₃×D₈	1	2	yes	—
238	C₂×C₃×C₄	C₃×SD₁₆	1	2	yes	—
239	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
240	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
245	#67	—	4	4	no	—
246	C₂×Dic₃	—	2	2	no	—
247	D₁₂	—	4	2	no	—
248	D₁₂	—	4	1	no	—
249	D₁₂	—	4	1	no	—
250	D₁₂	—	4	2	no	—
251	C₄×D₃	—	4	4	no	—
252	Dic₆	—	4	1	no	—
253	Dic₆	—	4	1	no	—
254	C₃×C₈	—	4	4	no	—
255	C₃×C₈	—	4	2	no	—
256	C₃×C₈	—	4	2	no	—
257	C₃×C₈	—	12	2	no	—
258	C₃⋊C₈	—	4	2	no	—
259	C₂×C₃²	—	2	2	no	—
260	C₂×C₃²	#413	1	1	yes	characteristic
261	C₂×C₃²	C₂×#102	1	1	yes	characteristic
262	C₂×C₃²	#416	1	1	yes	characteristic
263	C₃×D₃	—	8	2	no	—
264	#41	—	12	2	no	—
265	#41	—	12	2	no	—
266	C₂×Q₈	—	6	1	no	—
267	C₂×D₄	—	3	2	no	—
268	C₂×D₄	—	6	2	no	—
269	C₂×D₄	—	6	1	no	—
270	C₂×D₄	—	6	1	no	—
271	C₂²×C₄	—	6	2	no	—
272	C₂²×C₄	C₃×C₄×D₃	1	1	yes	characteristic
273	C₂²×C₄	C₃×D₁₂	1	1	yes	characteristic
274	C₂²×C₄	C₃×#67	1	1	yes	characteristic
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	6	2	no	—
277	C₂×C₈	—	12	2	no	—
278	C₄⋊C₄	—	3	2	no	—
279	C₄⋊C₄	—	6	1	no	—
280	C₂²⋊C₄	—	6	2	no	—
281	C₂²⋊C₄	—	6	2	no	—
282	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
283	C₄²	C₃×D₁₂	1	1	yes	characteristic
284	C₄²	C₃×#67	1	1	yes	characteristic
285	C₄²	C₂²×C₃×D₃	1	1	yes	characteristic
286	C₂²×C₃	—	2	1	no	—
287	C₂²×C₃	—	2	1	no	—
288	C₂²×C₃	—	2	1	no	—
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	2	no	—
292	C₂²×C₃	—	4	1	no	—
293	C₂²×C₃	—	4	1	no	—
294	C₂²×C₃	—	12	2	no	—
295	C₂²×C₃	—	12	2	no	—
296	C₂²×C₃	—	12	2	no	—
297	C₂²×C₃	#821	1	2	yes	—
298	C₂²×C₃	C₃×#102	1	2	yes	—
299	C₂²×C₃	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
300	C₂²×C₃	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×D₃	—	4	2	no	—
302	C₂×D₃	—	4	2	no	—
303	C₂×D₃	—	4	2	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	2	1	no	—
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	2	1	no	—
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	2	no	—
314	C₃×C₄	—	2	2	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	1	no	—
317	C₃×C₄	—	12	2	no	—
318	C₃×C₄	#821	1	2	yes	—
319	C₃×C₄	C₃×#102	1	2	yes	—
320	C₃×C₄	C₂×#204	1	1	yes	characteristic
321	C₃×C₄	C₂×D₂₄	1	1	yes	characteristic
322	C₃×C₄	#950	1	2	yes	—
323	C₃×C₄	C₂×C₃×D₈	1	1	yes	characteristic
324	C₃×C₄	C₂×C₃×SD₁₆	1	1	yes	characteristic
325	C₃×C₄	C₃×#135	1	2	yes	—
326	Dic₃	—	4	2	no	—
327	C₃²	#1540	1	1	yes	characteristic, complemented, Sylow
328	C₂³	—	6	2	no	—
329	C₂³	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
330	Q₈	—	12	1	no	—
331	Q₈	—	12	1	no	—
332	D₄	—	12	2	no	—
333	D₄	—	12	4	no	—
334	D₄	—	12	1	no	—
335	D₄	—	12	1	no	—
336	D₄	—	12	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	6	2	no	—
340	C₂×C₄	—	12	4	no	—
341	C₂×C₄	C₃×#204	1	2	yes	—
342	C₂×C₄	C₃×D₂₄	1	2	yes	—
343	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
344	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
345	C₂×C₄	C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
346	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
347	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
348	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
349	C₈	—	4	2	no	—
350	C₈	—	12	2	no	—
351	C₂×C₃	—	2	2	no	—
352	C₂×C₃	—	2	2	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	2	1	no	—
356	C₂×C₃	—	4	2	no	—
357	C₂×C₃	—	24	2	no	—
358	C₂×C₃	#5002	1	1	yes	characteristic
359	C₂×C₃	C₂×#821	1	1	yes	characteristic
360	C₂×C₃	#5132	1	1	yes	characteristic
361	C₂×C₃	C₃×#413	1	1	yes	characteristic
362	C₂×C₃	C₂×C₃×#102	1	1	yes	characteristic
363	C₂×C₃	C₃×#416	1	1	yes	characteristic
364	D₃	—	8	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	12	2	no	—
368	C₂²	—	12	2	no	—
369	C₂²	—	12	2	no	—
370	C₂²	C₃×#821	1	2	yes	—
371	C₂²	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	12	2	no	—
376	C₄	C₃×#821	1	2	yes	—
377	C₄	C₂×C₃×#204	1	1	yes	characteristic
378	C₄	C₂×C₃×D₂₄	1	1	yes	characteristic
379	C₄	C₃×#950	1	2	yes	—
380	C₃	—	2	1	no	—
381	C₃	#70772	1	1	yes	characteristic, direct product factor
382	C₃	C₃×#1540	1	1	yes	characteristic, complemented
383	C₂	—	2	2	no	—
384	C₂	—	24	2	no	—
385	C₂	C₃×#5002	1	1	yes	characteristic
386	C₂	C₂×C₃×#821	1	1	yes	characteristic
387	C₂	C₃×#5132	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₄²	C₂²×C₃×D₃
Fitting	C₃²×#431	C₂
socle	C₂²×C₃²	C₂×C₂²⋊C₄
prime radical	C₃×#5477	C₂
cosocle	C₃×C₄²	C₂³×C₃
hypercenter	C₃×#431	D₃
hypocenter	C₃	C₃×#1540
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₃²×#431	C₂	semidirect
3. C₂×C₃×C₄⋊(C₃⋊C₈)	C₂	semidirect
4. C₃×#4486	C₂	semidirect
5. C₃×#4485	C₂	semidirect
7. #70772	C₃	direct (N × H)
26. C₃×#431	D₃	semidirect
27. C₃×#431	C₂×C₃	semidirect
29. C₂×C₄⋊(C₃⋊C₈)	C₂×C₃	semidirect
32. #4486	C₂×C₃	semidirect
33. #4485	C₂×C₃	semidirect
115. #431	C₃×D₃	semidirect
327. C₃²	#1540	semidirect
381. C₃	#70772	direct (N × H)
382. C₃	C₃×#1540	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5477	2
C₃²×#431	2
C₂×C₃×C₄⋊(C₃⋊C₈)	2
C₃×#4486	2
C₃×#4485	2
C₃×#1540	3
#70772	3

Subgroups — C3×#70772 #11776122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70772 #11776122