Subgroups — C₃×#5599 #10595696

Order 576.

671 conjugacy classes of subgroups.

The subgroup lattice has 390 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	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#235	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×#121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#940	C₂	1	2	yes	maximal, complemented
5	C₃×#940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#939	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×#67	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#895	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#884	C₂	1	2	yes	maximal, complemented
11	C₃×#67⋊C₄	C₂	1	2	yes	maximal, complemented
12	C₃×#550	—	3	1	no	maximal
13	#5599	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	1	yes	characteristic
20	C₂×C₃×#67	C₂²	1	2	yes	—
21	C₂×C₃×#67	C₂²	1	2	yes	—
22	C₂²×C₃×Dic₃	C₂²	1	2	yes	—
23	C₃×#237	—	2	4	no	—
24	C₃×#235	—	2	4	no	—
25	C₂×C₃×D₁₂	C₂²	1	1	yes	characteristic
26	C₂×C₃×D₁₂	C₂²	1	2	yes	—
27	C₂×C₃×C₄×D₃	C₂²	1	2	yes	—
28	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
29	C₂×C₃×Dic₆	C₂²	1	1	yes	characteristic
30	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
31	C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
32	C₃×#217	C₂²	1	1	yes	characteristic
33	C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
34	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
37	C₃×C₄×Dic₃	C₂²	1	2	yes	—
38	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
39	C₂×C₃×#41	—	3	1	no	—
40	C₂×C₃×#41	—	3	1	no	—
41	C₂×#237	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#235	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×#127	—	3	2	no	—
44	C₃×#127	—	3	1	no	—
45	C₃×#121	—	2	1	no	—
46	C₃×#121	—	3	2	no	—
47	C₃×#121	—	3	1	no	—
48	C₃×#121	—	3	2	no	—
49	C₃×#121	D₃	1	1	yes	characteristic, complemented
50	C₃×#121	C₂×C₃	1	1	yes	characteristic, complemented
51	C₃×C₄×Q₈	—	3	1	no	—
52	C₃×C₄×D₄	—	3	1	no	—
53	C₃×C₄×D₄	—	3	2	no	—
54	#940	C₂×C₃	1	2	yes	complemented
55	#940	C₂×C₃	1	1	yes	characteristic, complemented
56	#939	C₂×C₃	1	2	yes	complemented
57	C₄×#67	C₂×C₃	1	1	yes	characteristic, complemented
58	#895	C₂×C₃	1	1	yes	characteristic, complemented
59	#887	C₂×C₃	1	1	yes	characteristic, complemented
60	#884	C₂×C₃	1	2	yes	complemented
61	#67⋊C₄	C₂×C₃	1	2	yes	complemented
62	C₂³×C₃²	C₂³	1	1	yes	characteristic
63	C₂³×C₃²	C₂³	1	2	yes	—
64	C₂²×C₃×D₃	C₂³	1	2	yes	—
65	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
66	C₃²×D₄	—	2	2	no	—
67	C₃²×D₄	—	4	2	no	—
68	C₂×C₃²×C₄	—	2	2	no	—
69	C₂×C₃²×C₄	C₂³	1	2	yes	—
70	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
71	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
72	C₃×#67	—	2	4	no	—
73	C₃×#67	—	2	4	no	—
74	C₃×#67	—	2	4	no	—
75	C₃×#67	—	2	2	no	—
76	C₃×#67	—	4	2	no	—
77	C₂×C₃×Dic₃	—	2	4	no	—
78	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
79	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
80	C₂×C₃×Dic₃	C₂³	1	2	yes	—
81	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
82	C₃×D₁₂	—	2	2	no	—
83	C₃×D₁₂	—	4	2	no	—
84	C₃×C₄×D₃	—	2	2	no	—
85	C₃×C₄×D₃	—	2	4	no	—
86	C₃×Dic₆	D₄	1	4	yes	complemented
87	#550	—	3	1	no	Sylow
88	C₃×#41	—	6	4	no	—
89	C₃×#41	—	6	4	no	—
90	C₂×C₃×Q₈	—	3	1	no	—
91	C₂×C₃×D₄	—	2	1	no	—
92	C₂×C₃×D₄	—	2	2	no	—
93	C₂×C₃×D₄	—	3	1	no	—
94	C₂×C₃×D₄	—	3	2	no	—
95	C₂×C₃×D₄	—	3	2	no	—
96	C₂×C₃×D₄	—	3	2	no	—
97	C₂×C₃×D₄	—	3	2	no	—
98	C₂×C₃×D₄	—	3	1	no	—
99	C₂×C₃×D₄	—	3	2	no	—
100	C₂×C₃×D₄	C₂×D₃	1	1	yes	characteristic
101	C₂×C₃×D₄	C₂×D₃	1	2	yes	—
102	C₂×C₃×D₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₃×D₄	C₂²×C₃	1	2	yes	—
104	C₂²×C₃×C₄	—	2	1	no	—
105	C₂²×C₃×C₄	—	3	2	no	—
106	C₂²×C₃×C₄	—	3	2	no	—
107	C₂²×C₃×C₄	—	3	1	no	—
108	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
109	C₂²×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×#67	C₂²×C₃	1	2	yes	—
111	C₂×#67	C₂²×C₃	1	2	yes	—
112	C₂×#67	C₂²×C₃	1	1	yes	characteristic
113	C₂×#67	C₂²×C₃	1	2	yes	—
114	C₂×#67	C₂²×C₃	1	2	yes	—
115	C₂²×Dic₃	C₂²×C₃	1	2	yes	—
116	#237	—	2	4	no	—
117	#235	—	2	4	no	—
118	C₂×D₁₂	C₂²×C₃	1	1	yes	characteristic
119	C₂×D₁₂	C₂²×C₃	1	2	yes	—
120	C₂×C₄×D₃	C₂²×C₃	1	2	yes	—
121	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
122	C₂×Dic₆	C₂²×C₃	1	1	yes	characteristic
123	C₃×C₄⋊C₄	—	2	1	no	—
124	C₃×C₄⋊C₄	—	3	1	no	—
125	C₃×C₄⋊C₄	—	3	2	no	—
126	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
127	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
128	C₃×C₂²⋊C₄	—	2	2	no	—
129	C₃×C₂²⋊C₄	—	3	1	no	—
130	C₃×C₂²⋊C₄	—	3	1	no	—
131	C₃×C₂²⋊C₄	—	3	2	no	—
132	C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
133	C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
134	C₃×C₄²	—	3	2	no	—
135	C₃×C₄²	—	3	1	no	—
136	#217	C₂²×C₃	1	1	yes	characteristic
137	(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
138	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
139	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
140	Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
141	C₄×Dic₃	C₂²×C₃	1	2	yes	—
142	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
143	C₂²×C₃²	—	2	1	no	—
144	C₂²×C₃²	—	2	2	no	—
145	C₂²×C₃²	—	2	1	no	—
146	C₂²×C₃²	—	2	1	no	—
147	C₂²×C₃²	—	2	2	no	—
148	C₂²×C₃²	—	2	2	no	—
149	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
150	C₂×C₃×D₃	—	2	2	no	—
151	C₂×C₃×D₃	—	2	1	no	—
152	C₂×C₃×D₃	—	2	2	no	—
153	C₂×C₃×D₃	—	2	1	no	—
154	C₂×C₃×D₃	—	2	1	no	—
155	C₂×C₃×D₃	—	2	2	no	—
156	C₃²×C₄	—	2	1	no	—
157	C₃²×C₄	—	2	2	no	—
158	C₃²×C₄	C₂×D₄	1	2	yes	—
159	C₃×Dic₃	—	2	1	no	—
160	C₃×Dic₃	—	2	1	no	—
161	C₃×Dic₃	C₂×D₄	1	4	yes	—
162	C₃×Dic₃	#41	1	2	yes	complemented
163	C₂×#41	—	3	1	no	—
164	C₂×#41	—	3	1	no	—
165	#127	—	3	2	no	—
166	#127	—	3	1	no	—
167	#121	—	3	2	no	—
168	#121	—	3	1	no	—
169	#121	—	3	2	no	—
170	#121	C₃×D₃	1	1	yes	characteristic, complemented
171	C₄×Q₈	—	3	1	no	—
172	C₄×D₄	—	3	1	no	—
173	C₄×D₄	—	3	2	no	—
174	C₂³×C₃	—	2	1	no	—
175	C₂³×C₃	—	2	2	no	—
176	C₂³×C₃	—	3	1	no	—
177	C₂³×C₃	—	3	2	no	—
178	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
179	C₂³×C₃	C₂²×D₃	1	2	yes	—
180	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
181	C₂³×C₃	C₂³×C₃	1	2	yes	—
182	C₂²×D₃	C₂³×C₃	1	2	yes	—
183	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
184	C₃×Q₈	—	3	4	no	—
185	C₃×D₄	—	2	2	no	—
186	C₃×D₄	—	2	2	no	—
187	C₃×D₄	—	4	2	no	—
188	C₃×D₄	—	4	2	no	—
189	C₃×D₄	—	4	2	no	—
190	C₃×D₄	—	4	4	no	—
191	C₃×D₄	—	6	2	no	—
192	C₃×D₄	—	6	4	no	—
193	C₃×D₄	—	6	4	no	—
194	C₃×D₄	—	6	4	no	—
195	C₃×D₄	—	6	2	no	—
196	C₃×D₄	—	12	2	no	—
197	C₃×D₄	—	12	2	no	—
198	C₂×C₃×C₄	—	2	2	no	—
199	C₂×C₃×C₄	—	2	2	no	—
200	C₂×C₃×C₄	—	2	1	no	—
201	C₂×C₃×C₄	—	2	1	no	—
202	C₂×C₃×C₄	—	2	2	no	—
203	C₂×C₃×C₄	—	3	1	no	—
204	C₂×C₃×C₄	—	3	2	no	—
205	C₂×C₃×C₄	—	3	1	no	—
206	C₂×C₃×C₄	—	3	1	no	—
207	C₂×C₃×C₄	—	4	2	no	—
208	C₂×C₃×C₄	—	6	4	no	—
209	C₂×C₃×C₄	—	6	4	no	—
210	C₂×C₃×C₄	—	6	2	no	—
211	C₂×C₃×C₄	C₂²×D₃	1	2	yes	—
212	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
213	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
214	C₂×C₃×C₄	C₂³×C₃	1	2	yes	—
215	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
217	#67	—	2	4	no	—
218	#67	—	2	4	no	—
219	#67	—	2	4	no	—
220	#67	—	2	2	no	—
221	#67	—	4	2	no	—
222	C₂×Dic₃	—	2	4	no	—
223	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
224	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
225	C₂×Dic₃	C₂³×C₃	1	2	yes	—
226	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
227	D₁₂	—	2	2	no	—
228	D₁₂	—	4	2	no	—
229	C₄×D₃	—	2	2	no	—
230	C₄×D₃	—	2	4	no	—
231	Dic₆	C₃×D₄	1	4	yes	complemented
232	C₂×C₃²	—	4	1	no	—
233	C₂×C₃²	—	4	2	no	—
234	C₂×C₃²	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₃²	C₂×#41	1	1	yes	characteristic
236	C₂×C₃²	H(5,𝔽₂)	1	1	yes	characteristic
237	C₃×D₃	—	4	2	no	—
238	C₃×D₃	—	4	1	no	—
239	#41	—	6	4	no	—
240	#41	—	6	4	no	—
241	C₂×Q₈	—	3	1	no	—
242	C₂×D₄	—	3	1	no	—
243	C₂×D₄	—	3	2	no	—
244	C₂×D₄	—	3	2	no	—
245	C₂×D₄	—	3	2	no	—
246	C₂×D₄	—	3	2	no	—
247	C₂×D₄	—	3	1	no	—
248	C₂×D₄	—	3	2	no	—
249	C₂×D₄	C₂×C₃×D₃	1	1	yes	characteristic
250	C₂×D₄	C₂×C₃×D₃	1	2	yes	—
251	C₂²×C₄	—	3	2	no	—
252	C₂²×C₄	—	3	2	no	—
253	C₂²×C₄	—	3	1	no	—
254	C₂²×C₄	C₂×C₃×D₃	1	1	yes	characteristic
255	C₄⋊C₄	—	3	1	no	—
256	C₄⋊C₄	—	3	2	no	—
257	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
258	C₂²⋊C₄	—	3	1	no	—
259	C₂²⋊C₄	—	3	1	no	—
260	C₂²⋊C₄	—	3	2	no	—
261	C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
262	C₄²	—	3	2	no	—
263	C₄²	—	3	1	no	—
264	C₂²×C₃	—	2	2	no	—
265	C₂²×C₃	—	2	1	no	—
266	C₂²×C₃	—	2	2	no	—
267	C₂²×C₃	—	2	1	no	—
268	C₂²×C₃	—	2	2	no	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	2	no	—
271	C₂²×C₃	—	2	2	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	2	1	no	—
278	C₂²×C₃	—	4	1	no	—
279	C₂²×C₃	—	4	1	no	—
280	C₂²×C₃	—	4	2	no	—
281	C₂²×C₃	—	4	2	no	—
282	C₂²×C₃	—	4	2	no	—
283	C₂²×C₃	—	6	2	no	—
284	C₂²×C₃	—	6	1	no	—
285	C₂²×C₃	—	6	1	no	—
286	C₂²×C₃	—	6	2	no	—
287	C₂²×C₃	—	6	1	no	—
288	C₂²×C₃	—	6	2	no	—
289	C₂²×C₃	C₂³×D₃	1	1	yes	characteristic
290	C₂²×C₃	C₂⁴×C₃	1	1	yes	characteristic
291	C₂×D₃	—	2	2	no	—
292	C₂×D₃	—	2	1	no	—
293	C₂×D₃	—	2	2	no	—
294	C₂×D₃	—	2	1	no	—
295	C₂×D₃	—	2	1	no	—
296	C₂×D₃	—	2	2	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	1	no	—
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	3	4	no	—
303	C₃×C₄	—	3	2	no	—
304	C₃×C₄	—	4	1	no	—
305	C₃×C₄	—	4	2	no	—
306	C₃×C₄	—	6	1	no	—
307	C₃×C₄	—	6	1	no	—
308	C₃×C₄	D₃×D₄	1	2	yes	—
309	C₃×C₄	C₂×C₃×D₄	1	2	yes	—
310	Dic₃	—	2	1	no	—
311	Dic₃	—	2	1	no	—
312	Dic₃	C₂×C₃×D₄	1	4	yes	—
313	Dic₃	C₃×#41	1	2	yes	complemented
314	C₃²	#550	1	1	yes	characteristic, complemented, Sylow
315	C₂³	—	3	1	no	—
316	C₂³	—	3	2	no	—
317	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
318	C₂³	C₂²×C₃×D₃	1	2	yes	—
319	Q₈	—	3	4	no	—
320	D₄	—	2	2	no	—
321	D₄	—	4	2	no	—
322	D₄	—	6	4	no	—
323	D₄	—	6	4	no	—
324	D₄	—	6	2	no	—
325	D₄	—	6	4	no	—
326	D₄	—	6	2	no	—
327	D₄	—	12	2	no	—
328	D₄	—	12	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	3	1	no	—
331	C₂×C₄	—	3	2	no	—
332	C₂×C₄	—	3	1	no	—
333	C₂×C₄	—	3	1	no	—
334	C₂×C₄	—	6	4	no	—
335	C₂×C₄	—	6	4	no	—
336	C₂×C₄	—	6	2	no	—
337	C₂×C₄	C₂²×C₃×D₃	1	2	yes	—
338	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
339	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
340	C₂×C₃	—	2	1	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	2	1	no	—
343	C₂×C₃	—	4	2	no	—
344	C₂×C₃	—	4	1	no	—
345	C₂×C₃	—	4	2	no	—
346	C₂×C₃	—	4	1	no	—
347	C₂×C₃	—	4	2	no	—
348	C₂×C₃	—	8	2	no	—
349	C₂×C₃	—	12	2	no	—
350	C₂×C₃	—	12	1	no	—
351	C₂×C₃	C₂×D₃×D₄	1	1	yes	characteristic
352	C₂×C₃	#1004	1	1	yes	characteristic
353	C₂×C₃	D₃×#41	1	1	yes	characteristic
354	C₂×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
355	C₂×C₃	C₂×C₃×#41	1	1	yes	characteristic
356	C₂×C₃	C₃×H(5,𝔽₂)	1	1	yes	characteristic
357	D₃	—	4	2	no	—
358	D₃	—	4	1	no	—
359	C₂²	—	2	1	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	6	2	no	—
366	C₂²	—	6	1	no	—
367	C₂²	—	6	1	no	—
368	C₂²	—	6	2	no	—
369	C₂²	—	6	1	no	—
370	C₂²	—	6	2	no	—
371	C₂²	C₂³×C₃×D₃	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	2	no	—
374	C₄	—	3	4	no	—
375	C₄	—	3	2	no	—
376	C₄	—	6	1	no	—
377	C₄	—	6	1	no	—
378	C₄	C₃×D₃×D₄	1	2	yes	—
379	C₃	—	2	1	no	—
380	C₃	#5599	1	1	yes	characteristic, direct product factor
381	C₃	C₃×#550	1	1	yes	characteristic, complemented
382	C₂	—	4	1	no	—
383	C₂	—	4	2	no	—
384	C₂	—	12	2	no	—
385	C₂	—	12	1	no	—
386	C₂	C₂×C₃×D₃×D₄	1	1	yes	characteristic
387	C₂	C₃×#1004	1	1	yes	characteristic
388	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×#550
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. C₂×C₃×#235	C₂	semidirect
3. C₃²×#121	C₂	semidirect
4. C₃×#940	C₂	semidirect
5. C₃×#940	C₂	semidirect
6. C₃×#939	C₂	semidirect
7. C₃×C₄×#67	C₂	semidirect
8. C₃×#895	C₂	semidirect
9. C₃×#887	C₂	semidirect
10. C₃×#884	C₂	semidirect
11. C₃×#67⋊C₄	C₂	semidirect
13. #5599	C₃	direct (N × H)
41. C₂×#237	C₂×C₃	semidirect
42. C₂×#235	C₂×C₃	semidirect
49. C₃×#121	D₃	semidirect
50. C₃×#121	C₂×C₃	semidirect
54. #940	C₂×C₃	semidirect
55. #940	C₂×C₃	semidirect
56. #939	C₂×C₃	semidirect
57. C₄×#67	C₂×C₃	semidirect
58. #895	C₂×C₃	semidirect
59. #887	C₂×C₃	semidirect
60. #884	C₂×C₃	semidirect
61. #67⋊C₄	C₂×C₃	semidirect
86. C₃×Dic₆	D₄	semidirect
162. C₃×Dic₃	#41	semidirect
170. #121	C₃×D₃	semidirect
231. Dic₆	C₃×D₄	semidirect
313. Dic₃	C₃×#41	semidirect
314. C₃²	#550	semidirect
380. C₃	#5599	direct (N × H)
381. C₃	C₃×#550	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
C₂×C₃×#235	2
C₃²×#121	2
C₃×#940	2
C₃×#939	2
C₃×C₄×#67	2
C₃×#895	2
C₃×#887	2
C₃×#884	2
C₃×#67⋊C₄	2
C₃×#550	3
#5599	3

Subgroups — C3×#5599 #10595696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#5599 #10595696