Subgroups — C₃×#70721 #11785606

Order 1152.

581 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	C₂×C₃×#901	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5133	C₂	1	2	yes	maximal
4	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#4554	C₂	1	2	yes	maximal, complemented
6	C₃×#1816	—	3	1	no	maximal
7	#70721	C₃	1	1	yes	maximal, characteristic, direct product factor
8	C₂×C₃×#235	C₂²	1	1	yes	characteristic
9	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
12	C₂×C₃×#208	C₂²	1	1	yes	characteristic
13	C₃×#901	—	2	2	no	—
14	C₃×#901	C₄	1	4	yes	complemented
15	C₂×C₃×ΓL(1,𝔽₂₅)	—	2	1	no	—
16	C₂×C₃×D₃×C₈	—	2	1	no	—
17	C₃²×#108	—	2	2	no	—
18	C₃×#821	—	2	2	no	—
19	C₃×#818	—	2	1	no	—
20	C₃×#818	—	2	1	no	—
21	C₃×#816	—	2	2	no	—
22	C₂×C₃×#131	—	3	1	no	—
23	C₂×#901	C₂×C₃	1	1	yes	characteristic
24	C₂×C₃×#108	—	2	1	no	—
25	C₂×C₃×#108	D₃	1	1	yes	characteristic, complemented
26	C₂×C₃×#108	C₂×C₃	1	1	yes	characteristic, complemented
27	C₂×C₃×#107	—	3	1	no	—
28	C₃×#417	—	3	2	no	—
29	#5133	C₂×C₃	1	2	yes	—
30	C₂×#818	C₂×C₃	1	1	yes	characteristic, complemented
31	C₃×#343	—	3	2	no	—
32	#4554	C₂×C₃	1	2	yes	complemented
33	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₂×C₃×#67	—	2	1	no	—
35	C₂²×C₃×Dic₃	—	2	2	no	—
36	C₃×#235	—	2	1	no	—
37	C₃×#235	—	2	1	no	—
38	C₃×#235	C₂×C₄	1	2	yes	—
39	C₃×#235	Q₈	1	2	yes	—
40	C₂×C₃×D₁₂	D₄	1	1	yes	characteristic
41	C₂×C₃×C₄×D₃	—	2	1	no	—
42	C₂×C₃×Dic₆	D₄	1	1	yes	characteristic
43	C₃²×M₁₆	—	2	2	no	—
44	C₃²×M₁₆	—	2	2	no	—
45	C₂×C₃²×C₈	—	2	2	no	—
46	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
47	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
48	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
49	C₂×C₃²×C₈	D₄	1	2	yes	—
50	C₃×C₄⋊Dic₃	—	2	2	no	—
51	C₃×C₄⋊Dic₃	—	2	2	no	—
52	C₃×#208	—	2	1	no	—
53	C₃×#208	C₂×C₄	1	2	yes	—
54	C₂×C₃×C₃⋊C₈	—	2	1	no	—
55	C₃×ΓL(1,𝔽₂₅)	—	2	4	no	—
56	C₃×D₃×C₈	—	2	4	no	—
57	#1816	—	3	1	no	Sylow
58	C₂×C₃×#41	—	3	1	no	—
59	C₂×#235	C₂²×C₃	1	1	yes	characteristic
60	C₃×#131	—	3	4	no	—
61	C₃×#131	—	6	2	no	—
62	C₂×C₃×M₁₆	—	2	2	no	—
63	C₂×C₃×M₁₆	—	3	1	no	—
64	C₂×C₃×M₁₆	—	6	1	no	—
65	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
66	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
67	C₂²×C₃×C₈	—	2	1	no	—
68	C₂²×C₃×C₈	—	6	1	no	—
69	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
70	C₂²×C₃×C₈	C₂²×C₃	1	1	yes	characteristic
71	C₂×C₃×C₄⋊C₄	—	3	2	no	—
72	C₂×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
73	C₂×#208	C₂²×C₃	1	1	yes	characteristic
74	#901	—	2	2	no	—
75	#901	C₃×C₄	1	4	yes	complemented
76	C₂×ΓL(1,𝔽₂₅)	—	2	1	no	—
77	C₂×D₃×C₈	—	2	1	no	—
78	C₃×#108	—	2	4	no	—
79	C₃×#108	—	2	2	no	—
80	C₃×#108	—	2	2	no	—
81	C₃×#107	—	6	1	no	—
82	C₃×#107	—	6	1	no	—
83	C₃×#103	—	6	2	no	—
84	C₃×#102	—	6	2	no	—
85	#821	—	2	2	no	—
86	#818	—	2	1	no	—
87	#818	—	2	1	no	—
88	#816	—	2	2	no	—
89	C₂³×C₃²	#41	1	1	yes	characteristic
90	C₂²×C₃×D₃	—	2	1	no	—
91	C₂×C₃²×C₄	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
96	C₂×C₃²×C₄	#41	1	1	yes	characteristic
97	C₃×#67	—	2	2	no	—
98	C₃×#67	—	2	2	no	—
99	C₂×C₃×Dic₃	—	2	1	no	—
100	C₂×C₃×Dic₃	—	4	2	no	—
101	C₂×C₃×Dic₃	—	8	2	no	—
102	C₃×D₁₂	—	2	1	no	—
103	C₃×D₁₂	C₄⋊C₄	1	2	yes	—
104	C₃×C₄×D₃	—	2	2	no	—
105	C₃×C₄×D₃	—	2	2	no	—
106	C₃×Dic₆	—	2	1	no	—
107	C₃×Dic₆	C₄⋊C₄	1	2	yes	—
108	C₃²×C₈	—	4	2	no	—
109	C₃²×C₈	C₂²⋊C₄	1	2	yes	—
110	C₃²×C₈	C₂²⋊C₄	1	2	yes	—
111	C₃×C₃⋊C₈	—	2	2	no	—
112	C₂×#131	—	3	1	no	—
113	C₂×#108	C₃×D₃	1	1	yes	characteristic, complemented
114	C₂×#107	—	3	1	no	—
115	#417	—	3	2	no	—
116	#343	—	3	2	no	—
117	C₃×#41	—	3	2	no	—
118	C₃×#41	—	3	2	no	—
119	C₃×#41	—	6	1	no	—
120	C₃×#41	—	6	1	no	—
121	C₂×C₃×Q₈	—	3	1	no	—
122	C₂×C₃×D₄	—	3	1	no	—
123	C₂×C₃×D₄	—	6	1	no	—
124	C₂²×C₃×C₄	—	2	1	no	—
125	C₂²×C₃×C₄	—	6	1	no	—
126	C₂²×C₃×C₄	—	6	2	no	—
127	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
129	C₂×#67	—	2	1	no	—
130	C₂²×Dic₃	—	2	2	no	—
131	#235	—	2	1	no	—
132	#235	—	2	1	no	—
133	#235	C₂×C₃×C₄	1	2	yes	—
134	#235	C₃×Q₈	1	2	yes	—
135	C₂×D₁₂	C₃×D₄	1	1	yes	characteristic
136	C₂×C₄×D₃	—	2	1	no	—
137	C₂×Dic₆	C₃×D₄	1	1	yes	characteristic
138	C₃×M₁₆	—	2	4	no	—
139	C₃×M₁₆	—	2	2	no	—
140	C₃×M₁₆	—	2	2	no	—
141	C₃×M₁₆	—	2	2	no	—
142	C₃×M₁₆	—	2	2	no	—
143	C₃×M₁₆	—	3	2	no	—
144	C₃×M₁₆	—	4	2	no	—
145	C₃×M₁₆	—	6	1	no	—
146	C₃×M₁₆	—	6	4	no	—
147	C₂×C₃×C₈	—	2	2	no	—
148	C₂×C₃×C₈	—	2	2	no	—
149	C₂×C₃×C₈	—	2	2	no	—
150	C₂×C₃×C₈	—	2	1	no	—
151	C₂×C₃×C₈	—	2	1	no	—
152	C₂×C₃×C₈	—	2	2	no	—
153	C₂×C₃×C₈	—	4	2	no	—
154	C₂×C₃×C₈	—	6	1	no	—
155	C₂×C₃×C₈	—	6	4	no	—
156	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
157	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
158	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
159	C₂×C₃×C₈	#67	1	2	yes	—
160	C₂×C₃×C₈	C₂×C₃×C₄	1	2	yes	—
161	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
162	C₂×C₃×C₈	C₃×D₄	1	1	yes	characteristic
163	C₂×C₃×C₈	C₃×D₄	1	2	yes	—
164	C₃×C₄⋊C₄	—	6	2	no	—
165	C₃×C₄⋊C₄	—	6	2	no	—
166	C₄⋊Dic₃	—	2	2	no	—
167	C₄⋊Dic₃	—	2	2	no	—
168	#208	—	2	1	no	—
169	#208	C₂×C₃×C₄	1	2	yes	—
170	C₂×C₃⋊C₈	—	2	1	no	—
171	ΓL(1,𝔽₂₅)	—	2	4	no	—
172	D₃×C₈	—	2	4	no	—
173	C₂²×C₃²	—	2	1	no	—
174	C₂²×C₃²	—	2	1	no	—
175	C₂²×C₃²	#117	1	1	yes	characteristic
176	C₂²×C₃²	#121	1	1	yes	characteristic
177	C₂²×C₃²	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₃×D₃	—	2	2	no	—
179	C₂×C₃×D₃	—	4	1	no	—
180	C₂×C₃×D₃	—	4	1	no	—
181	C₃²×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₃²×C₄	#121	1	1	yes	characteristic
184	C₃²×C₄	C₂²⋊Q₈	1	1	yes	characteristic
185	C₃×Dic₃	—	2	2	no	—
186	C₃×Dic₃	—	8	2	no	—
187	C₂×#41	—	3	1	no	—
188	#131	—	3	4	no	—
189	#131	—	6	2	no	—
190	C₂×M₁₆	—	3	1	no	—
191	C₂×M₁₆	—	6	1	no	—
192	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
193	C₂²×C₈	—	6	1	no	—
194	C₂²×C₈	C₂×C₃×D₃	1	1	yes	characteristic
195	C₂×C₄⋊C₄	—	3	2	no	—
196	#108	—	2	2	no	—
197	#107	—	6	1	no	—
198	#107	—	6	1	no	—
199	#103	—	6	2	no	—
200	#102	—	6	2	no	—
201	C₂³×C₃	—	2	1	no	—
202	C₂³×C₃	—	6	1	no	—
203	C₂³×C₃	#239	1	1	yes	characteristic
204	C₂³×C₃	C₃×#41	1	1	yes	characteristic
205	C₂²×D₃	—	2	1	no	—
206	C₃×Q₈	—	3	2	no	—
207	C₃×Q₈	—	6	1	no	—
208	C₃×D₄	—	3	2	no	—
209	C₃×D₄	—	6	2	no	—
210	C₃×D₄	—	6	2	no	—
211	C₃×D₄	—	6	1	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	—	6	1	no	—
219	C₂×C₃×C₄	—	6	2	no	—
220	C₂×C₃×C₄	—	6	2	no	—
221	C₂×C₃×C₄	—	12	2	no	—
222	C₂×C₃×C₄	—	24	2	no	—
223	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
224	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
225	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
226	C₂×C₃×C₄	#237	1	1	yes	characteristic
227	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
229	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
230	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
231	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
232	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
233	C₂×C₃×C₄	C₂×C₃×Q₈	1	1	yes	characteristic
234	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
235	#67	—	2	2	no	—
236	#67	—	2	2	no	—
237	C₂×Dic₃	—	2	1	no	—
238	C₂×Dic₃	—	4	2	no	—
239	C₂×Dic₃	—	8	2	no	—
240	D₁₂	—	2	1	no	—
241	D₁₂	C₃×C₄⋊C₄	1	2	yes	—
242	C₄×D₃	—	2	2	no	—
243	C₄×D₃	—	2	2	no	—
244	Dic₆	—	2	1	no	—
245	Dic₆	C₃×C₄⋊C₄	1	2	yes	—
246	C₃×C₈	—	2	2	no	—
247	C₃×C₈	—	2	2	no	—
248	C₃×C₈	—	4	4	no	—
249	C₃×C₈	—	4	2	no	—
250	C₃×C₈	—	4	2	no	—
251	C₃×C₈	—	6	2	no	—
252	C₃×C₈	(C₂×D₃)⋊C₄	1	2	yes	—
253	C₃×C₈	(C₂×D₃)⋊C₄	1	2	yes	—
254	C₃×C₈	C₃×C₂²⋊C₄	1	2	yes	—
255	C₃×C₈	C₃×C₂²⋊C₄	1	2	yes	—
256	C₃⋊C₈	—	2	2	no	—
257	C₂×C₃²	—	2	1	no	—
258	C₂×C₃²	—	2	1	no	—
259	C₂×C₃²	#380	1	1	yes	characteristic
260	C₂×C₃²	#472	1	1	yes	characteristic
261	C₂×C₃²	#473	1	1	yes	characteristic
262	C₃×D₃	—	4	2	no	—
263	#41	—	3	2	no	—
264	#41	—	3	2	no	—
265	#41	—	6	1	no	—
266	#41	—	6	1	no	—
267	C₂×Q₈	—	3	1	no	—
268	C₂×D₄	—	3	1	no	—
269	C₂×D₄	—	6	1	no	—
270	C₂²×C₄	—	6	1	no	—
271	C₂²×C₄	—	6	2	no	—
272	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
273	M₁₆	—	2	2	no	—
274	M₁₆	—	2	2	no	—
275	M₁₆	—	3	2	no	—
276	M₁₆	—	6	1	no	—
277	M₁₆	—	6	4	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	6	1	no	—
280	C₂×C₈	—	6	4	no	—
281	C₂×C₈	C₃×C₄×D₃	1	2	yes	—
282	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
283	C₂×C₈	C₃×D₁₂	1	1	yes	characteristic
284	C₂×C₈	C₃×#67	1	2	yes	—
285	C₄⋊C₄	—	6	2	no	—
286	C₄⋊C₄	—	6	2	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	1	no	—
292	C₂²×C₃	—	2	1	no	—
293	C₂²×C₃	—	2	1	no	—
294	C₂²×C₃	—	4	1	no	—
295	C₂²×C₃	—	4	1	no	—
296	C₂²×C₃	—	6	2	no	—
297	C₂²×C₃	—	12	1	no	—
298	C₂²×C₃	—	12	1	no	—
299	C₂²×C₃	#892	1	1	yes	characteristic
300	C₂²×C₃	#895	1	1	yes	characteristic
301	C₂²×C₃	#946	1	1	yes	characteristic
302	C₂²×C₃	C₃×#117	1	1	yes	characteristic
303	C₂²×C₃	C₃×#121	1	1	yes	characteristic
304	C₂²×C₃	C₃×C₂²⋊Q₈	1	1	yes	characteristic
305	C₂×D₃	—	2	2	no	—
306	C₂×D₃	—	4	1	no	—
307	C₂×D₃	—	4	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	—	6	2	no	—
313	C₃×C₄	—	24	2	no	—
314	C₃×C₄	D₃×C₄⋊C₄	1	1	yes	characteristic
315	C₃×C₄	#897	1	1	yes	characteristic
316	C₃×C₄	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
317	C₃×C₄	#938	1	1	yes	characteristic
318	C₃×C₄	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
319	C₃×C₄	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
320	C₃×C₄	C₃×#121	1	1	yes	characteristic
321	C₃×C₄	C₃×C₂²⋊Q₈	1	1	yes	characteristic
322	Dic₃	—	2	2	no	—
323	Dic₃	—	8	2	no	—
324	C₃²	#1816	1	1	yes	characteristic, complemented, Sylow
325	C₂³	—	6	1	no	—
326	C₂³	C₃×#239	1	1	yes	characteristic
327	Q₈	—	3	2	no	—
328	Q₈	—	6	1	no	—
329	D₄	—	3	2	no	—
330	D₄	—	6	2	no	—
331	D₄	—	6	2	no	—
332	D₄	—	6	1	no	—
333	C₂×C₄	—	6	1	no	—
334	C₂×C₄	—	6	2	no	—
335	C₂×C₄	—	6	2	no	—
336	C₂×C₄	—	12	2	no	—
337	C₂×C₄	—	24	2	no	—
338	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
339	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
340	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
341	C₂×C₄	C₃×#237	1	1	yes	characteristic
342	C₂×C₄	C₃×D₃×Q₈	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×#67	1	1	yes	characteristic
344	C₈	—	4	2	no	—
345	C₈	—	6	2	no	—
346	C₈	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
347	C₈	C₃×(C₂×D₃)⋊C₄	1	2	yes	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	2	1	no	—
350	C₂×C₃	—	2	1	no	—
351	C₂×C₃	—	2	1	no	—
352	C₂×C₃	—	2	1	no	—
353	C₂×C₃	—	2	1	no	—
354	C₂×C₃	—	2	1	no	—
355	C₂×C₃	—	4	1	no	—
356	C₂×C₃	—	4	1	no	—
357	C₂×C₃	—	12	2	no	—
358	C₂×C₃	#4896	1	1	yes	characteristic
359	C₂×C₃	#4897	1	1	yes	characteristic
360	C₂×C₃	#4987	1	1	yes	characteristic
361	C₂×C₃	C₃×#380	1	1	yes	characteristic
362	C₂×C₃	C₃×#472	1	1	yes	characteristic
363	C₂×C₃	C₃×#473	1	1	yes	characteristic
364	D₃	—	4	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	6	2	no	—
368	C₂²	—	12	1	no	—
369	C₂²	—	12	1	no	—
370	C₂²	C₃×#892	1	1	yes	characteristic
371	C₂²	C₃×#895	1	1	yes	characteristic
372	C₂²	C₃×#946	1	1	yes	characteristic
373	C₄	—	6	2	no	—
374	C₄	—	24	2	no	—
375	C₄	C₃×D₃×C₄⋊C₄	1	1	yes	characteristic
376	C₄	C₃×#897	1	1	yes	characteristic
377	C₄	C₂×C₃×(C₂×D₃)⋊C₄	1	1	yes	characteristic
378	C₄	C₃×#938	1	1	yes	characteristic
379	C₃	—	2	1	no	—
380	C₃	#70721	1	1	yes	characteristic, direct product factor
381	C₃	C₃×#1816	1	1	yes	characteristic, complemented
382	C₂	—	2	1	no	—
383	C₂	—	2	1	no	—
384	C₂	—	12	2	no	—
385	C₂	C₃×#4896	1	1	yes	characteristic
386	C₂	C₃×#4897	1	1	yes	characteristic
387	C₂	C₃×#4987	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#895
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₂×C₃²×#108	C₂
socle	C₂²×C₃²	#121
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₂×C₃×#108	D₃
hypocenter	C₃	C₃×#1816
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#108

Complements

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

N	H ≅ G/N	type
2. C₂×C₃²×#108	C₂	semidirect
4. C₂×C₃×#818	C₂	semidirect
5. C₃×#4554	C₂	semidirect
7. #70721	C₃	direct (N × H)
14. C₃×#901	C₄	semidirect
25. C₂×C₃×#108	D₃	semidirect
26. C₂×C₃×#108	C₂×C₃	semidirect
30. C₂×#818	C₂×C₃	semidirect
32. #4554	C₂×C₃	semidirect
75. #901	C₃×C₄	semidirect
113. C₂×#108	C₃×D₃	semidirect
324. C₃²	#1816	semidirect
380. C₃	#70721	direct (N × H)
381. C₃	C₃×#1816	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#901	2
C₂×C₃²×#108	2
C₃×#5133	2
C₂×C₃×#818	2
C₃×#4554	2
C₃×#1816	3
#70721	3

Subgroups — C3×#70721 #11785606

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#70721 #11785606