Subgroups — C₃×#5596 #10595693

Order 576.

667 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#237	C₂	1	2	yes	maximal, complemented
2	C₃²×#121	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#940	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#939	C₂	1	2	yes	maximal, complemented
5	C₃×D₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#930	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#888	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#885	C₂	1	2	yes	maximal, complemented
11	C₃×#67⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#532	—	3	1	no	maximal
13	#5596	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×D₄	C₂²	1	1	yes	characteristic
15	C₂×C₃²×D₄	C₂²	1	2	yes	—
16	C₂²×C₃²×C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×#67	C₂²	1	2	yes	—
18	C₂×C₃×#67	C₂²	1	2	yes	—
19	C₂×C₃×#67	C₂²	1	2	yes	—
20	C₂²×C₃×Dic₃	C₂²	1	2	yes	—
21	C₂²×C₃×Dic₃	C₂²	1	1	yes	characteristic
22	C₂²×C₃×Dic₃	C₂²	1	1	yes	characteristic
23	C₃×#237	—	2	8	no	—
24	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄×D₃	C₂²	1	2	yes	—
26	C₂×C₃×Dic₆	C₂²	1	2	yes	—
27	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
28	C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₃×#217	C₂²	1	2	yes	—
30	C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
32	C₃×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
33	C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
35	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
36	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
37	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
38	C₂×C₃×#41	—	3	2	no	—
39	C₂×#237	C₂×C₃	1	2	yes	complemented
40	C₃×C₄⋊Q₈	—	3	1	no	—
41	C₃×#127	—	3	1	no	—
42	C₃×#124	—	3	2	no	—
43	C₃×#121	—	2	1	no	—
44	C₃×#121	—	3	2	no	—
45	C₃×#121	—	3	1	no	—
46	C₃×#121	D₃	1	1	yes	characteristic, complemented
47	C₃×#121	C₂×C₃	1	1	yes	characteristic, complemented
48	C₃×C₄×D₄	—	3	1	no	—
49	C₃×C₄×D₄	—	3	1	no	—
50	C₃×C₄×D₄	—	3	2	no	—
51	C₂×C₃×C₄²	—	3	1	no	—
52	#940	C₂×C₃	1	1	yes	characteristic, complemented
53	#939	C₂×C₃	1	2	yes	complemented
54	D₄×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
55	#930	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₄×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
57	#893	C₂×C₃	1	1	yes	characteristic, complemented
58	#888	C₂×C₃	1	1	yes	characteristic, complemented
59	#885	C₂×C₃	1	2	yes	complemented
60	#67⋊C₄	C₂×C₃	1	2	yes	complemented
61	C₂³×C₃²	C₂³	1	2	yes	—
62	C₂³×C₃²	C₂³	1	1	yes	characteristic
63	C₂²×C₃×D₃	C₂³	1	2	yes	—
64	C₃²×D₄	—	2	4	no	—
65	C₃²×D₄	—	2	2	no	—
66	C₂×C₃²×C₄	—	2	2	no	—
67	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
68	C₂×C₃²×C₄	C₂³	1	2	yes	—
69	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
70	C₃×#67	—	2	4	no	—
71	C₃×#67	—	2	4	no	—
72	C₃×#67	—	2	4	no	—
73	C₂×C₃×Dic₃	—	2	4	no	—
74	C₂×C₃×Dic₃	—	2	2	no	—
75	C₂×C₃×Dic₃	D₄	1	4	yes	complemented
76	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
77	C₂×C₃×Dic₃	C₂³	1	2	yes	—
78	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
81	C₃×D₁₂	—	2	2	no	—
82	C₃×C₄×D₃	—	2	4	no	—
83	C₃×Dic₆	—	2	4	no	—
84	#532	—	3	1	no	Sylow
85	C₃×#41	—	6	8	no	—
86	C₂×C₃×Q₈	—	3	2	no	—
87	C₂×C₃×D₄	—	2	1	no	—
88	C₂×C₃×D₄	—	2	2	no	—
89	C₂×C₃×D₄	—	3	2	no	—
90	C₂×C₃×D₄	—	3	2	no	—
91	C₂×C₃×D₄	—	3	2	no	—
92	C₂×C₃×D₄	—	3	1	no	—
93	C₂×C₃×D₄	C₂×D₃	1	1	yes	characteristic
94	C₂×C₃×D₄	C₂×D₃	1	2	yes	—
95	C₂×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₃×D₄	C₂²×C₃	1	2	yes	—
97	C₂²×C₃×C₄	—	2	1	no	—
98	C₂²×C₃×C₄	—	3	1	no	—
99	C₂²×C₃×C₄	—	3	1	no	—
100	C₂²×C₃×C₄	—	3	2	no	—
101	C₂²×C₃×C₄	—	3	2	no	—
102	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
103	C₂²×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×#67	C₂²×C₃	1	2	yes	—
105	C₂×#67	C₂²×C₃	1	2	yes	—
106	C₂×#67	C₂²×C₃	1	2	yes	—
107	C₂²×Dic₃	C₂²×C₃	1	2	yes	—
108	C₂²×Dic₃	C₂²×C₃	1	1	yes	characteristic
109	C₂²×Dic₃	C₂²×C₃	1	1	yes	characteristic
110	#237	—	2	8	no	—
111	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₄×D₃	C₂²×C₃	1	2	yes	—
113	C₂×Dic₆	C₂²×C₃	1	2	yes	—
114	C₃×C₄⋊C₄	—	2	1	no	—
115	C₃×C₄⋊C₄	—	3	2	no	—
116	C₃×C₄⋊C₄	—	3	1	no	—
117	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
119	C₃×C₂²⋊C₄	—	2	2	no	—
120	C₃×C₂²⋊C₄	—	3	2	no	—
121	C₃×C₂²⋊C₄	—	3	2	no	—
122	C₃×C₂²⋊C₄	—	3	2	no	—
123	C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
124	C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
125	C₃×C₄²	—	3	1	no	—
126	C₃×C₄²	—	3	1	no	—
127	C₃×C₄²	—	3	1	no	—
128	C₃×C₄²	—	3	1	no	—
129	#217	C₂²×C₃	1	2	yes	—
130	(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
131	(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
132	C₄⋊Dic₃	C₂²×C₃	1	1	yes	characteristic
133	Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
134	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
135	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
136	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
137	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
138	C₂²×C₃²	—	2	1	no	—
139	C₂²×C₃²	—	2	1	no	—
140	C₂²×C₃²	—	2	2	no	—
141	C₂²×C₃²	—	2	2	no	—
142	C₂²×C₃²	—	2	2	no	—
143	C₂²×C₃²	C₂×D₄	1	2	yes	—
144	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
145	C₂×C₃×D₃	—	2	2	no	—
146	C₂×C₃×D₃	—	2	2	no	—
147	C₂×C₃×D₃	—	2	2	no	—
148	C₃²×C₄	—	2	2	no	—
149	C₃²×C₄	—	2	1	no	—
150	C₃²×C₄	#41	1	2	yes	complemented
151	C₃×Dic₃	—	2	2	no	—
152	C₃×Dic₃	—	2	1	no	—
153	C₃×Dic₃	C₂×D₄	1	2	yes	—
154	C₃×Dic₃	C₂×D₄	1	2	yes	—
155	C₃×Dic₃	#41	1	2	yes	complemented
156	C₂×#41	—	3	2	no	—
157	C₄⋊Q₈	—	3	1	no	—
158	#127	—	3	1	no	—
159	#124	—	3	2	no	—
160	#121	—	3	2	no	—
161	#121	—	3	1	no	—
162	#121	C₃×D₃	1	1	yes	characteristic, complemented
163	C₄×D₄	—	3	1	no	—
164	C₄×D₄	—	3	1	no	—
165	C₄×D₄	—	3	2	no	—
166	C₂×C₄²	—	3	1	no	—
167	C₂³×C₃	—	2	1	no	—
168	C₂³×C₃	—	2	2	no	—
169	C₂³×C₃	—	3	2	no	—
170	C₂³×C₃	C₂²×D₃	1	2	yes	—
171	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
172	C₂³×C₃	C₂³×C₃	1	2	yes	—
173	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
174	C₂²×D₃	C₂³×C₃	1	2	yes	—
175	C₃×Q₈	—	6	4	no	—
176	C₃×D₄	—	2	4	no	—
177	C₃×D₄	—	2	4	no	—
178	C₃×D₄	—	2	2	no	—
179	C₃×D₄	—	2	2	no	—
180	C₃×D₄	—	4	2	no	—
181	C₃×D₄	—	4	4	no	—
182	C₃×D₄	—	6	4	no	—
183	C₃×D₄	—	6	4	no	—
184	C₃×D₄	—	6	4	no	—
185	C₃×D₄	—	6	2	no	—
186	C₂×C₃×C₄	—	2	2	no	—
187	C₂×C₃×C₄	—	2	2	no	—
188	C₂×C₃×C₄	—	2	1	no	—
189	C₂×C₃×C₄	—	2	1	no	—
190	C₂×C₃×C₄	—	2	2	no	—
191	C₂×C₃×C₄	—	3	4	no	—
192	C₂×C₃×C₄	—	3	1	no	—
193	C₂×C₃×C₄	—	3	1	no	—
194	C₂×C₃×C₄	—	3	1	no	—
195	C₂×C₃×C₄	—	3	1	no	—
196	C₂×C₃×C₄	—	3	2	no	—
197	C₂×C₃×C₄	—	4	2	no	—
198	C₂×C₃×C₄	—	6	4	no	—
199	C₂×C₃×C₄	—	6	2	no	—
200	C₂×C₃×C₄	—	6	4	no	—
201	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
202	C₂×C₃×C₄	C₂²×D₃	1	2	yes	—
203	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₃×C₄	C₂³×C₃	1	2	yes	—
206	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
207	#67	—	2	4	no	—
208	#67	—	2	4	no	—
209	#67	—	2	4	no	—
210	C₂×Dic₃	—	2	4	no	—
211	C₂×Dic₃	—	2	2	no	—
212	C₂×Dic₃	C₃×D₄	1	4	yes	complemented
213	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
214	C₂×Dic₃	C₂³×C₃	1	2	yes	—
215	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
216	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
217	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
218	D₁₂	—	2	2	no	—
219	C₄×D₃	—	2	4	no	—
220	Dic₆	—	2	4	no	—
221	C₂×C₃²	—	2	2	no	—
222	C₂×C₃²	—	4	2	no	—
223	C₂×C₃²	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₃²	C₂×#41	1	1	yes	characteristic
225	C₂×C₃²	C₂×#41	1	1	yes	characteristic
226	C₃×D₃	—	4	2	no	—
227	#41	—	6	8	no	—
228	C₂×Q₈	—	3	2	no	—
229	C₂×D₄	—	3	2	no	—
230	C₂×D₄	—	3	2	no	—
231	C₂×D₄	—	3	2	no	—
232	C₂×D₄	—	3	1	no	—
233	C₂×D₄	C₂×C₃×D₃	1	1	yes	characteristic
234	C₂×D₄	C₂×C₃×D₃	1	2	yes	—
235	C₂²×C₄	—	3	1	no	—
236	C₂²×C₄	—	3	1	no	—
237	C₂²×C₄	—	3	2	no	—
238	C₂²×C₄	—	3	2	no	—
239	C₂²×C₄	C₂×C₃×D₃	1	1	yes	characteristic
240	C₄⋊C₄	—	3	2	no	—
241	C₄⋊C₄	—	3	1	no	—
242	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
243	C₂²⋊C₄	—	3	2	no	—
244	C₂²⋊C₄	—	3	2	no	—
245	C₂²⋊C₄	—	3	2	no	—
246	C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
247	C₄²	—	3	1	no	—
248	C₄²	—	3	1	no	—
249	C₄²	—	3	1	no	—
250	C₄²	—	3	1	no	—
251	C₂²×C₃	—	2	1	no	—
252	C₂²×C₃	—	2	1	no	—
253	C₂²×C₃	—	2	1	no	—
254	C₂²×C₃	—	2	1	no	—
255	C₂²×C₃	—	2	2	no	—
256	C₂²×C₃	—	2	2	no	—
257	C₂²×C₃	—	2	2	no	—
258	C₂²×C₃	—	2	2	no	—
259	C₂²×C₃	—	2	2	no	—
260	C₂²×C₃	—	2	2	no	—
261	C₂²×C₃	—	2	1	no	—
262	C₂²×C₃	—	2	2	no	—
263	C₂²×C₃	—	4	1	no	—
264	C₂²×C₃	—	4	1	no	—
265	C₂²×C₃	—	4	2	no	—
266	C₂²×C₃	—	4	2	no	—
267	C₂²×C₃	—	4	2	no	—
268	C₂²×C₃	—	6	2	no	—
269	C₂²×C₃	—	6	2	no	—
270	C₂²×C₃	—	6	2	no	—
271	C₂²×C₃	D₃×D₄	1	2	yes	—
272	C₂²×C₃	C₂×C₃×D₄	1	2	yes	—
273	C₂²×C₃	C₂³×D₃	1	1	yes	characteristic
274	C₂²×C₃	C₂⁴×C₃	1	1	yes	characteristic
275	C₂×D₃	—	2	2	no	—
276	C₂×D₃	—	2	2	no	—
277	C₂×D₃	—	2	2	no	—
278	C₃×C₄	—	2	2	no	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	2	2	no	—
281	C₃×C₄	—	2	1	no	—
282	C₃×C₄	—	2	2	no	—
283	C₃×C₄	—	3	2	no	—
284	C₃×C₄	—	3	2	no	—
285	C₃×C₄	—	3	2	no	—
286	C₃×C₄	—	4	1	no	—
287	C₃×C₄	—	4	2	no	—
288	C₃×C₄	—	6	2	no	—
289	C₃×C₄	—	6	1	no	—
290	C₃×C₄	#237	1	2	yes	complemented
291	C₃×C₄	C₃×#41	1	2	yes	complemented
292	Dic₃	—	2	2	no	—
293	Dic₃	—	2	1	no	—
294	Dic₃	C₂×C₃×D₄	1	2	yes	—
295	Dic₃	C₂×C₃×D₄	1	2	yes	—
296	Dic₃	C₃×#41	1	2	yes	complemented
297	C₃²	#532	1	1	yes	characteristic, complemented, Sylow
298	C₂³	—	3	2	no	—
299	C₂³	C₂²×C₃×D₃	1	2	yes	—
300	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
301	Q₈	—	6	4	no	—
302	D₄	—	2	4	no	—
303	D₄	—	2	2	no	—
304	D₄	—	6	4	no	—
305	D₄	—	6	4	no	—
306	D₄	—	6	4	no	—
307	D₄	—	6	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	3	1	no	—
310	C₂×C₄	—	3	1	no	—
311	C₂×C₄	—	3	1	no	—
312	C₂×C₄	—	3	4	no	—
313	C₂×C₄	—	3	1	no	—
314	C₂×C₄	—	3	2	no	—
315	C₂×C₄	—	6	4	no	—
316	C₂×C₄	—	6	4	no	—
317	C₂×C₄	—	6	2	no	—
318	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
319	C₂×C₄	C₂²×C₃×D₃	1	2	yes	—
320	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
321	C₂×C₃	—	2	2	no	—
322	C₂×C₃	—	2	2	no	—
323	C₂×C₃	—	2	1	no	—
324	C₂×C₃	—	2	1	no	—
325	C₂×C₃	—	2	1	no	—
326	C₂×C₃	—	4	2	no	—
327	C₂×C₃	—	4	2	no	—
328	C₂×C₃	—	4	2	no	—
329	C₂×C₃	—	8	2	no	—
330	C₂×C₃	—	12	2	no	—
331	C₂×C₃	C₂×D₃×D₄	1	1	yes	characteristic
332	C₂×C₃	C₂×#237	1	1	yes	characteristic
333	C₂×C₃	D₃×#41	1	1	yes	characteristic
334	C₂×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
335	C₂×C₃	C₂×C₃×#41	1	1	yes	characteristic
336	C₂×C₃	C₂×C₃×#41	1	1	yes	characteristic
337	D₃	—	4	2	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	6	2	no	—
344	C₂²	—	6	2	no	—
345	C₂²	—	6	2	no	—
346	C₂²	C₃×D₃×D₄	1	2	yes	—
347	C₂²	C₂³×C₃×D₃	1	1	yes	characteristic
348	C₄	—	2	2	no	—
349	C₄	—	2	1	no	—
350	C₄	—	3	2	no	—
351	C₄	—	3	2	no	—
352	C₄	—	3	2	no	—
353	C₄	—	6	2	no	—
354	C₄	—	6	1	no	—
355	C₄	C₃×#237	1	2	yes	complemented
356	C₃	—	2	1	no	—
357	C₃	#5596	1	1	yes	characteristic, direct product factor
358	C₃	C₃×#532	1	1	yes	characteristic, complemented
359	C₂	—	2	2	no	—
360	C₂	—	4	2	no	—
361	C₂	—	12	2	no	—
362	C₂	C₂×C₃×D₃×D₄	1	1	yes	characteristic
363	C₂	C₂×C₃×#237	1	1	yes	characteristic
364	C₂	C₃×D₃×#41	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₃
Fitting	C₃²×#121	C₂
socle	C₂²×C₃²	C₂⁴
hypercenter	C₃×#121	D₃
hypocenter	C₃	C₃×#532
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#121

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#237	C₂	semidirect
2. C₃²×#121	C₂	semidirect
3. C₃×#940	C₂	semidirect
4. C₃×#939	C₂	semidirect
5. C₃×D₄×Dic₃	C₂	semidirect
6. C₃×#930	C₂	semidirect
7. C₂×C₃×C₄×Dic₃	C₂	semidirect
8. C₃×#893	C₂	semidirect
9. C₃×#888	C₂	semidirect
10. C₃×#885	C₂	semidirect
11. C₃×#67⋊C₄	C₂	semidirect
13. #5596	C₃	direct (N × H)
39. C₂×#237	C₂×C₃	semidirect
46. C₃×#121	D₃	semidirect
47. C₃×#121	C₂×C₃	semidirect
52. #940	C₂×C₃	semidirect
53. #939	C₂×C₃	semidirect
54. D₄×Dic₃	C₂×C₃	semidirect
55. #930	C₂×C₃	semidirect
56. C₂×C₄×Dic₃	C₂×C₃	semidirect
57. #893	C₂×C₃	semidirect
58. #888	C₂×C₃	semidirect
59. #885	C₂×C₃	semidirect
60. #67⋊C₄	C₂×C₃	semidirect
75. C₂×C₃×Dic₃	D₄	semidirect
150. C₃²×C₄	#41	semidirect
155. C₃×Dic₃	#41	semidirect
162. #121	C₃×D₃	semidirect
212. C₂×Dic₃	C₃×D₄	semidirect
290. C₃×C₄	#237	semidirect
291. C₃×C₄	C₃×#41	semidirect
296. Dic₃	C₃×#41	semidirect
297. C₃²	#532	semidirect
355. C₄	C₃×#237	semidirect
357. C₃	#5596	direct (N × H)
358. C₃	C₃×#532	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#237	2
C₃²×#121	2
C₃×#940	2
C₃×#939	2
C₃×D₄×Dic₃	2
C₃×#930	2
C₂×C₃×C₄×Dic₃	2
C₃×#893	2
C₃×#888	2
C₃×#885	2
C₃×#67⋊C₄	2
C₃×#532	3
#5596	3

Subgroups — C3×#5596 #10595693

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#5596 #10595693