Subgroups — C₃×#33783 #10652390

Order 768.

688 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#493	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2250	C₂	1	2	yes	maximal, complemented
4	C₃×#2244	C₂	1	2	yes	maximal, complemented
5	C₃×#2207	C₂	1	2	yes	maximal, complemented
6	C₃×#2206	C₂	1	2	yes	maximal, complemented
7	C₃×#2187	C₂	1	2	yes	maximal, complemented
8	C₃×#2184	C₂	1	2	yes	maximal, complemented
9	C₃×#2163	C₂	1	1	yes	maximal, characteristic, complemented
10	#33783	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂²×C₃×D₈	—	2	1	no	—
12	C₂²×C₃×D₈	C₂²	1	2	yes	—
13	C₂×C₃×#127	—	2	1	no	—
14	C₃×#529	—	2	1	no	—
15	C₂×C₃×SD₃₂	C₂²	1	4	yes	complemented
16	C₂×C₃×D₁₆	C₂²	1	4	yes	complemented
17	C₃×#499	C₂²	1	1	yes	characteristic, complemented
18	C₃×#495	C₂²	1	1	yes	characteristic, complemented
19	C₃×#493	—	2	1	no	—
20	C₃×#493	—	2	1	no	—
21	C₃×#493	C₂²	1	2	yes	—
22	C₃×#493	C₂²	1	2	yes	—
23	C₃×#488	—	2	1	no	—
24	C₃×#467	C₂²	1	1	yes	characteristic
25	C₃×#466	C₂²	1	1	yes	characteristic
26	C₃×#465	—	2	1	no	—
27	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₄×SD₁₆	—	2	1	no	—
29	C₃×C₄×D₈	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊C₁₆	C₂²	1	2	yes	complemented
32	C₃×#357	C₂²	1	4	yes	complemented
33	C₃×#357	C₂²	1	4	yes	complemented
34	C₃×C₂²⋊C₁₆	C₂²	1	2	yes	—
35	C₃×#346	C₂²	1	2	yes	complemented
36	#3168	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#493	C₂×C₃	1	1	yes	characteristic, complemented
38	#2250	C₂×C₃	1	2	yes	complemented
39	#2244	C₂×C₃	1	2	yes	complemented
40	#2207	C₂×C₃	1	2	yes	complemented
41	#2206	C₂×C₃	1	2	yes	complemented
42	#2187	C₂×C₃	1	2	yes	complemented
43	#2184	C₂×C₃	1	2	yes	complemented
44	#2163	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂²×C₃×D₄	—	2	2	no	—
46	C₂²×C₃×D₄	—	4	1	no	—
47	C₂²×C₃×D₄	—	4	1	no	—
48	C₂×C₃×Q₁₆	C₂³	1	1	yes	characteristic
49	C₂×C₃×SD₁₆	—	2	1	no	—
50	C₂×C₃×D₈	—	2	2	no	—
51	C₂×C₃×D₈	—	2	2	no	—
52	C₂×C₃×D₈	—	2	2	no	—
53	C₂×C₃×D₈	—	4	4	no	—
54	C₂×C₃×D₈	—	4	4	no	—
55	C₂×C₃×D₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×D₈	C₂³	1	4	yes	—
57	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
59	C₃×#127	—	2	2	no	—
60	C₃×#127	—	2	2	no	—
61	C₃×#127	—	4	1	no	—
62	C₃×#127	—	4	1	no	—
63	C₃×#126	—	4	1	no	—
64	C₃×#125	—	2	1	no	—
65	C₃×#124	—	2	1	no	—
66	C₃×#123	—	4	1	no	—
67	C₃×C₂²⋊Q₈	—	2	1	no	—
68	C₃×#121	—	2	1	no	—
69	C₃×C₄×Q₈	—	2	1	no	—
70	C₃×C₄×D₄	—	2	1	no	—
71	C₃×C₄×D₄	—	4	1	no	—
72	C₃×#117	—	4	1	no	—
73	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
74	C₃×SD₃₂	—	4	4	no	—
75	C₃×D₁₆	—	4	4	no	—
76	C₂×C₃×C₁₆	C₂³	1	4	yes	—
77	C₃×#107	C₂³	1	1	yes	characteristic
78	C₃×#107	C₂³	1	1	yes	characteristic
79	C₃×#106	—	2	1	no	—
80	C₃×#103	—	2	1	no	—
81	C₃×#103	—	2	1	no	—
82	C₃×#102	—	2	1	no	—
83	C₃×#102	—	2	1	no	—
84	C₃×C₄×C₈	D₄	1	1	yes	characteristic
85	C₃×C₄×C₈	D₄	1	1	yes	characteristic
86	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
87	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
88	C₂²×D₈	—	2	1	no	—
89	C₂²×D₈	C₂²×C₃	1	2	yes	—
90	C₂×#127	—	2	1	no	—
91	#529	—	2	1	no	—
92	C₂×SD₃₂	C₂²×C₃	1	4	yes	complemented
93	C₂×D₁₆	C₂²×C₃	1	4	yes	complemented
94	#499	C₂²×C₃	1	1	yes	characteristic, complemented
95	#495	C₂²×C₃	1	1	yes	characteristic, complemented
96	#493	—	2	1	no	—
97	#493	—	2	1	no	—
98	#493	C₂²×C₃	1	2	yes	—
99	#493	C₂²×C₃	1	2	yes	—
100	#488	—	2	1	no	—
101	#467	C₂²×C₃	1	1	yes	characteristic
102	#466	C₂²×C₃	1	1	yes	characteristic
103	#465	—	2	1	no	—
104	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
105	C₄×SD₁₆	—	2	1	no	—
106	C₄×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
107	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
108	C₄⋊C₁₆	C₂²×C₃	1	2	yes	complemented
109	#357	C₂²×C₃	1	4	yes	complemented
110	#357	C₂²×C₃	1	4	yes	complemented
111	C₂²⋊C₁₆	C₂²×C₃	1	2	yes	—
112	#346	C₂²×C₃	1	2	yes	complemented
113	C₂⁴×C₃	—	4	2	no	—
114	C₂×C₃×Q₈	—	2	1	no	—
115	C₂×C₃×D₄	—	2	1	no	—
116	C₂×C₃×D₄	—	2	4	no	—
117	C₂×C₃×D₄	—	4	4	no	—
118	C₂×C₃×D₄	—	4	4	no	—
119	C₂×C₃×D₄	—	4	1	no	—
120	C₂×C₃×D₄	—	4	2	no	—
121	C₂×C₃×D₄	—	4	2	no	—
122	C₂×C₃×D₄	—	4	2	no	—
123	C₂×C₃×D₄	—	4	2	no	—
124	C₂×C₃×D₄	—	4	2	no	—
125	C₂×C₃×D₄	—	8	4	no	—
126	C₂×C₃×D₄	—	8	4	no	—
127	C₂²×C₃×C₄	—	4	1	no	—
128	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
129	C₂²×C₃×C₄	D₈	1	1	yes	characteristic
130	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
131	C₃×Q₁₆	—	2	2	no	—
132	C₃×SD₁₆	—	4	2	no	—
133	C₃×D₈	—	2	2	no	—
134	C₃×D₈	—	2	4	no	—
135	C₃×D₈	—	2	4	no	—
136	C₃×D₈	—	4	4	no	—
137	C₃×D₈	—	4	4	no	—
138	C₃×D₈	—	4	4	no	—
139	C₂×C₃×C₈	—	2	2	no	—
140	C₂×C₃×C₈	—	2	2	no	—
141	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₈	C₂⁴	1	1	yes	characteristic
145	C₃×C₄⋊C₄	—	2	1	no	—
146	C₃×C₄⋊C₄	—	2	1	no	—
147	C₃×C₄⋊C₄	—	4	1	no	—
148	C₃×C₄⋊C₄	—	4	1	no	—
149	C₃×C₄⋊C₄	—	4	1	no	—
150	C₃×C₄⋊C₄	—	4	1	no	—
151	C₃×C₂²⋊C₄	—	4	1	no	—
152	C₃×C₂²⋊C₄	—	4	1	no	—
153	C₃×C₂²⋊C₄	—	4	1	no	—
154	C₃×C₂²⋊C₄	—	4	1	no	—
155	C₃×C₂²⋊C₄	—	4	1	no	—
156	C₃×C₄²	—	4	1	no	—
157	C₃×C₄²	D₈	1	1	yes	characteristic
158	C₃×C₄²	D₈	1	1	yes	characteristic
159	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
160	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
161	C₃×C₁₆	—	2	4	no	—
162	C₂²×D₄	—	2	2	no	—
163	C₂²×D₄	—	4	1	no	—
164	C₂²×D₄	—	4	1	no	—
165	C₂×Q₁₆	C₂³×C₃	1	1	yes	characteristic
166	C₂×SD₁₆	—	2	1	no	—
167	C₂×D₈	—	2	2	no	—
168	C₂×D₈	—	2	2	no	—
169	C₂×D₈	—	2	2	no	—
170	C₂×D₈	—	4	4	no	—
171	C₂×D₈	—	4	4	no	—
172	C₂×D₈	C₂³×C₃	1	4	yes	—
173	C₂×D₈	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
175	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
176	#127	—	2	2	no	—
177	#127	—	2	2	no	—
178	#127	—	4	1	no	—
179	#127	—	4	1	no	—
180	#126	—	4	1	no	—
181	#125	—	2	1	no	—
182	#124	—	2	1	no	—
183	#123	—	4	1	no	—
184	C₂²⋊Q₈	—	2	1	no	—
185	#121	—	2	1	no	—
186	C₄×Q₈	—	2	1	no	—
187	C₄×D₄	—	2	1	no	—
188	C₄×D₄	—	4	1	no	—
189	#117	—	4	1	no	—
190	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
191	SD₃₂	—	4	4	no	—
192	D₁₆	—	4	4	no	—
193	C₂×C₁₆	C₂³×C₃	1	4	yes	—
194	#107	C₂³×C₃	1	1	yes	characteristic
195	#107	C₂³×C₃	1	1	yes	characteristic
196	#106	—	2	1	no	—
197	#103	—	2	1	no	—
198	#103	—	2	1	no	—
199	#102	—	2	1	no	—
200	#102	—	2	1	no	—
201	C₄×C₈	C₃×D₄	1	1	yes	characteristic
202	C₄×C₈	C₃×D₄	1	1	yes	characteristic
203	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
204	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₂³×C₃	—	4	1	no	—
206	C₂³×C₃	—	4	4	no	—
207	C₂³×C₃	—	8	4	no	—
208	C₂³×C₃	—	8	4	no	—
209	C₂³×C₃	—	8	4	no	—
210	C₂³×C₃	C₂×D₈	1	1	yes	characteristic
211	C₃×Q₈	—	4	1	no	—
212	C₃×Q₈	—	4	1	no	—
213	C₃×D₄	—	4	4	no	—
214	C₃×D₄	—	4	1	no	—
215	C₃×D₄	—	4	4	no	—
216	C₃×D₄	—	4	1	no	—
217	C₃×D₄	—	8	4	no	—
218	C₃×D₄	—	8	4	no	—
219	C₃×D₄	—	8	4	no	—
220	C₃×D₄	—	8	4	no	—
221	C₃×D₄	—	8	2	no	—
222	C₃×D₄	—	8	4	no	—
223	C₂×C₃×C₄	—	2	2	no	—
224	C₂×C₃×C₄	—	2	1	no	—
225	C₂×C₃×C₄	—	2	1	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	4	1	no	—
228	C₂×C₃×C₄	—	4	1	no	—
229	C₂×C₃×C₄	—	4	1	no	—
230	C₂×C₃×C₄	—	8	2	no	—
231	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
235	C₂×C₃×C₄	C₂×D₈	1	1	yes	characteristic
236	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
237	C₃×C₈	—	2	1	no	—
238	C₃×C₈	—	2	1	no	—
239	C₃×C₈	AGL(1,ℤ/8)	1	2	yes	—
240	C₃×C₈	H(5,𝔽₂)	1	2	yes	—
241	C₂⁴	—	4	2	no	—
242	C₂×Q₈	—	2	1	no	—
243	C₂×D₄	—	2	1	no	—
244	C₂×D₄	—	2	4	no	—
245	C₂×D₄	—	4	4	no	—
246	C₂×D₄	—	4	4	no	—
247	C₂×D₄	—	4	1	no	—
248	C₂×D₄	—	4	2	no	—
249	C₂×D₄	—	4	2	no	—
250	C₂×D₄	—	4	2	no	—
251	C₂×D₄	—	4	2	no	—
252	C₂×D₄	—	4	2	no	—
253	C₂×D₄	—	8	4	no	—
254	C₂×D₄	—	8	4	no	—
255	C₂²×C₄	—	4	1	no	—
256	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
257	C₂²×C₄	C₃×D₈	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
259	Q₁₆	—	2	2	no	—
260	SD₁₆	—	4	2	no	—
261	D₈	—	2	2	no	—
262	D₈	—	2	4	no	—
263	D₈	—	2	4	no	—
264	D₈	—	4	4	no	—
265	D₈	—	4	4	no	—
266	D₈	—	4	4	no	—
267	C₂×C₈	—	2	2	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
271	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
272	C₂×C₈	C₂⁴×C₃	1	1	yes	characteristic
273	C₄⋊C₄	—	2	1	no	—
274	C₄⋊C₄	—	2	1	no	—
275	C₄⋊C₄	—	4	1	no	—
276	C₄⋊C₄	—	4	1	no	—
277	C₄⋊C₄	—	4	1	no	—
278	C₄⋊C₄	—	4	1	no	—
279	C₂²⋊C₄	—	4	1	no	—
280	C₂²⋊C₄	—	4	1	no	—
281	C₂²⋊C₄	—	4	1	no	—
282	C₂²⋊C₄	—	4	1	no	—
283	C₂²⋊C₄	—	4	1	no	—
284	C₄²	—	4	1	no	—
285	C₄²	C₃×D₈	1	1	yes	characteristic
286	C₄²	C₃×D₈	1	1	yes	characteristic
287	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
288	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
289	C₁₆	—	2	4	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	2	1	no	—
292	C₂²×C₃	—	8	1	no	—
293	C₂²×C₃	—	8	4	no	—
294	C₂²×C₃	—	8	4	no	—
295	C₂²×C₃	—	8	1	no	—
296	C₂²×C₃	—	8	4	no	—
297	C₂²×C₃	—	8	1	no	—
298	C₂²×C₃	—	16	8	no	—
299	C₂²×C₃	#509	1	2	yes	—
300	C₂²×C₃	C₂²×D₈	1	1	yes	characteristic
301	C₃×C₄	—	2	1	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	1	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	8	1	no	—
306	C₃×C₄	—	8	1	no	—
307	C₃×C₄	—	8	1	no	—
308	C₃×C₄	#509	1	2	yes	—
309	C₃×C₄	#535	1	1	yes	characteristic
310	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
311	C₂³	—	4	1	no	—
312	C₂³	—	4	4	no	—
313	C₂³	—	8	4	no	—
314	C₂³	—	8	4	no	—
315	C₂³	—	8	4	no	—
316	C₂³	C₂×C₃×D₈	1	1	yes	characteristic
317	Q₈	—	4	1	no	—
318	Q₈	—	4	1	no	—
319	D₄	—	4	4	no	—
320	D₄	—	4	1	no	—
321	D₄	—	4	4	no	—
322	D₄	—	4	1	no	—
323	D₄	—	8	4	no	—
324	D₄	—	8	4	no	—
325	D₄	—	8	4	no	—
326	D₄	—	8	4	no	—
327	D₄	—	8	2	no	—
328	D₄	—	8	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	8	2	no	—
337	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
338	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
339	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
340	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
341	C₂×C₄	C₂×C₃×D₈	1	1	yes	characteristic
342	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
343	C₈	—	2	1	no	—
344	C₈	—	2	1	no	—
345	C₈	C₃×AGL(1,ℤ/8)	1	2	yes	—
346	C₈	C₃×H(5,𝔽₂)	1	2	yes	—
347	C₂×C₃	—	2	2	no	—
348	C₂×C₃	—	16	1	no	—
349	C₂×C₃	—	16	4	no	—
350	C₂×C₃	#3205	1	1	yes	characteristic
351	C₂×C₃	C₂×#509	1	1	yes	characteristic
352	C₂×C₃	C₂×#509	1	1	yes	characteristic
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	4	no	—
357	C₂²	—	8	4	no	—
358	C₂²	—	8	1	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	1	no	—
361	C₂²	—	16	8	no	—
362	C₂²	C₃×#509	1	2	yes	—
363	C₂²	C₂²×C₃×D₈	1	1	yes	characteristic
364	C₄	—	2	1	no	—
365	C₄	—	2	1	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	8	1	no	—
369	C₄	—	8	1	no	—
370	C₄	—	8	1	no	—
371	C₄	C₃×#509	1	2	yes	—
372	C₄	C₃×#535	1	1	yes	characteristic
373	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
374	C₃	#33783	1	1	yes	characteristic, direct product factor, Sylow
375	C₂	—	2	2	no	—
376	C₂	—	16	4	no	—
377	C₂	—	16	1	no	—
378	C₂	C₃×#3205	1	1	yes	characteristic
379	C₂	C₂×C₃×#509	1	1	yes	characteristic
380	C₂	C₂×C₃×#509	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#3168	C₂	semidirect
2. C₂×C₃×#493	C₂	semidirect
3. C₃×#2250	C₂	semidirect
4. C₃×#2244	C₂	semidirect
5. C₃×#2207	C₂	semidirect
6. C₃×#2206	C₂	semidirect
7. C₃×#2187	C₂	semidirect
8. C₃×#2184	C₂	semidirect
9. C₃×#2163	C₂	semidirect
10. #33783	C₃	direct (N × H)
15. C₂×C₃×SD₃₂	C₂²	semidirect
16. C₂×C₃×D₁₆	C₂²	semidirect
17. C₃×#499	C₂²	semidirect
18. C₃×#495	C₂²	semidirect
27. C₃×C₄×Q₁₆	C₂²	semidirect
29. C₃×C₄×D₈	C₂²	semidirect
31. C₃×C₄⋊C₁₆	C₂²	semidirect
32. C₃×#357	C₂²	semidirect
33. C₃×#357	C₂²	semidirect
35. C₃×#346	C₂²	semidirect
36. #3168	C₂×C₃	semidirect
37. C₂×#493	C₂×C₃	semidirect
38. #2250	C₂×C₃	semidirect
39. #2244	C₂×C₃	semidirect
40. #2207	C₂×C₃	semidirect
41. #2206	C₂×C₃	semidirect
42. #2187	C₂×C₃	semidirect
43. #2184	C₂×C₃	semidirect
44. #2163	C₂×C₃	semidirect
92. C₂×SD₃₂	C₂²×C₃	semidirect
93. C₂×D₁₆	C₂²×C₃	semidirect
94. #499	C₂²×C₃	semidirect
95. #495	C₂²×C₃	semidirect
104. C₄×Q₁₆	C₂²×C₃	semidirect
106. C₄×D₈	C₂²×C₃	semidirect
108. C₄⋊C₁₆	C₂²×C₃	semidirect
109. #357	C₂²×C₃	semidirect
110. #357	C₂²×C₃	semidirect
112. #346	C₂²×C₃	semidirect
374. C₃	#33783	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#3168	2
C₂×C₃×#493	2
C₃×#2250	2
C₃×#2244	2
C₃×#2207	2
C₃×#2206	2
C₃×#2187	2
C₃×#2184	2
C₃×#2163	2
#33783	3

Subgroups — C3×#33783 #10652390

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33783 #10652390