Subgroups — C₃×#10596013 #13179295

Order 1728.

1648 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic
2	C₃×#64145	C₂	1	2	yes	maximal
3	C₃×#64135	C₂	1	2	yes	maximal, complemented
4	C₃×#64133	C₂	1	2	yes	maximal, complemented
5	C₃×#64096	C₂	1	2	yes	maximal, complemented
6	C₃×#64088	C₂	1	4	yes	maximal, complemented
7	C₃×#64078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596013	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5542	—	3	4	no	maximal
11	C₂×C₃³×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃³×C₄	C₂²	1	2	yes	—
13	C₂×C₃×#634	C₂²	1	1	yes	characteristic
14	C₂×C₃×#634	C₂²	1	2	yes	—
15	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃³×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₃³×C₄²	C₂²	1	1	yes	characteristic
18	C₃×#3757	C₂²	1	4	yes	—
19	C₃×#3757	C₂²	1	4	yes	—
20	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
21	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
22	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
23	C₃×#3750	C₂²	1	2	yes	—
24	C₃×#3750	C₂²	1	4	yes	—
25	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	yes	—
26	C₃×C₄×C₃⋊Dic₃	C₂²	1	4	yes	—
27	C₃²×C₄×D₄	—	2	4	no	—
28	C₃²×C₄×D₄	D₃	1	4	yes	—
29	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
30	#64145	C₂×C₃	1	2	yes	—
31	#64135	C₂×C₃	1	2	yes	complemented
32	#64133	C₂×C₃	1	2	yes	complemented
33	#64096	C₂×C₃	1	2	yes	complemented
34	#64088	C₂×C₃	1	4	yes	complemented
35	#64078	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×#936	—	3	8	no	—
38	C₃×#926	—	3	8	no	—
39	C₃×#924	—	3	8	no	—
40	C₃×#887	—	3	8	no	—
41	C₃×#879	—	3	16	no	—
42	C₃×#869	—	3	4	no	—
43	C₃×C₄×Dic₆	—	3	4	no	—
44	C₂³×C₃³	C₂³	1	2	yes	—
45	C₃³×D₄	—	2	2	no	—
46	C₂×C₃³×C₄	—	2	4	no	—
47	C₂×C₃³×C₄	C₂³	1	2	yes	—
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
53	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
54	C₃×#634	—	2	4	no	—
55	C₃×#634	—	2	2	no	—
56	C₃×#556	—	9	1	no	—
57	#5542	—	3	4	no	—
58	C₂×C₃²×D₄	—	2	4	no	—
59	C₂×C₃²×D₄	C₂×D₃	1	4	yes	—
60	C₂×C₃²×D₄	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₃²×C₄	—	2	8	no	—
62	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
63	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
64	C₂×#634	C₂²×C₃	1	1	yes	characteristic
65	C₂×#634	C₂²×C₃	1	2	yes	—
66	C₂×C₃×Dic₆	—	3	8	no	—
67	C₂×C₃×Dic₆	—	3	4	no	—
68	C₃²×C₄⋊C₄	—	2	4	no	—
69	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
70	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
71	C₃²×C₂²⋊C₄	—	2	8	no	—
72	C₃²×C₂²⋊C₄	C₂×D₃	1	8	yes	—
73	C₃²×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
74	C₃²×C₄²	—	2	4	no	—
75	C₃²×C₄²	C₂×D₃	1	4	yes	—
76	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
77	#3757	C₂²×C₃	1	4	yes	—
78	#3757	C₂²×C₃	1	4	yes	—
79	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
80	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
81	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
82	#3750	C₂²×C₃	1	2	yes	—
83	#3750	C₂²×C₃	1	4	yes	—
84	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
85	C₄×C₃⋊Dic₃	C₂²×C₃	1	4	yes	—
86	C₃×#217	—	3	16	no	—
87	C₃×#217	—	3	16	no	—
88	C₃×C₄⋊Dic₃	—	3	8	no	—
89	C₃×C₄⋊Dic₃	—	3	8	no	—
90	C₃×C₄⋊Dic₃	—	3	4	no	—
91	C₃×Dic₃⋊C₄	—	3	8	no	—
92	C₃×Dic₃⋊C₄	—	3	16	no	—
93	C₃×C₄×Dic₃	—	3	16	no	—
94	C₃×C₄×Dic₃	—	3	8	no	—
95	C₂²×C₃³	—	2	2	no	—
96	C₂²×C₃³	—	2	2	no	—
97	C₂²×C₃³	—	2	2	no	—
98	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
99	C₃³×C₄	—	2	2	no	—
100	C₃³×C₄	—	2	1	no	—
101	C₃³×C₄	#41	1	2	yes	—
102	C₃³×C₄	#41	1	2	yes	—
103	C₃×C₃⋊Dic₃	—	2	4	no	—
104	C₃×C₃⋊Dic₃	—	2	2	no	—
105	C₃×C₃⋊Dic₃	—	2	2	no	—
106	C₃×C₄⋊Q₈	—	9	1	no	—
107	C₃×#126	—	9	4	no	—
108	C₃×#124	—	9	2	no	—
109	C₃×C₂²⋊Q₈	—	9	2	no	—
110	C₃×C₄×Q₈	—	9	2	no	—
111	C₃×C₄×Q₈	—	9	1	no	—
112	C₃×C₄×D₄	—	2	4	no	—
113	C₃×C₄×D₄	C₃×D₃	1	4	yes	—
114	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic
115	C₃×#117	—	9	2	no	—
116	#936	—	3	8	no	—
117	#926	—	3	8	no	—
118	#924	—	3	8	no	—
119	#887	—	3	8	no	—
120	#879	—	3	16	no	—
121	#869	—	3	4	no	—
122	C₄×Dic₆	—	3	4	no	—
123	C₂³×C₃²	—	2	8	no	—
124	C₂³×C₃²	C₂²×D₃	1	8	yes	—
125	C₂³×C₃²	C₂³×C₃	1	2	yes	—
126	C₃²×D₄	—	2	16	no	—
127	C₃²×D₄	—	2	8	no	—
128	C₃²×D₄	—	2	2	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	2	4	no	—
132	C₂×C₃²×C₄	—	2	4	no	—
133	C₂×C₃²×C₄	—	2	8	no	—
134	C₂×C₃²×C₄	—	2	16	no	—
135	C₂×C₃²×C₄	—	4	16	no	—
136	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
137	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
138	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
139	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
140	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
141	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
145	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
146	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
147	#634	—	2	4	no	—
148	#634	—	2	2	no	—
149	C₂×C₃×Dic₃	—	3	8	no	—
150	C₂×C₃×Dic₃	—	3	8	no	—
151	C₂×C₃×Dic₃	—	3	16	no	—
152	C₃×Dic₆	—	6	16	no	—
153	C₃×Dic₆	—	6	8	no	—
154	#556	—	9	1	no	Sylow
155	C₂×C₃³	—	4	2	no	—
156	C₂×C₃³	C₂×#41	1	1	yes	characteristic
157	C₂×C₃³	C₂×#41	1	1	yes	characteristic
158	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
159	C₂×C₃×Q₈	—	9	1	no	—
160	C₂×C₃×Q₈	—	9	2	no	—
161	C₂×C₃×D₄	—	2	4	no	—
162	C₂×C₃×D₄	C₂×C₃×D₃	1	4	yes	—
163	C₂×C₃×D₄	C₂×C₃⋊D₃	1	1	yes	characteristic
164	C₂²×C₃×C₄	—	2	8	no	—
165	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
166	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
167	C₂×Dic₆	—	3	4	no	—
168	C₂×Dic₆	—	3	8	no	—
169	C₃×C₄⋊C₄	—	2	4	no	—
170	C₃×C₄⋊C₄	—	9	4	no	—
171	C₃×C₄⋊C₄	—	9	2	no	—
172	C₃×C₄⋊C₄	—	9	1	no	—
173	C₃×C₄⋊C₄	—	9	2	no	—
174	C₃×C₄⋊C₄	—	9	2	no	—
175	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
176	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
177	C₃×C₂²⋊C₄	—	2	8	no	—
178	C₃×C₂²⋊C₄	—	9	4	no	—
179	C₃×C₂²⋊C₄	—	9	4	no	—
180	C₃×C₂²⋊C₄	C₂×C₃×D₃	1	8	yes	—
181	C₃×C₂²⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
182	C₃×C₄²	—	2	4	no	—
183	C₃×C₄²	—	9	4	no	—
184	C₃×C₄²	—	9	2	no	—
185	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
186	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
187	#217	—	3	16	no	—
188	#217	—	3	16	no	—
189	C₄⋊Dic₃	—	3	4	no	—
190	C₄⋊Dic₃	—	3	8	no	—
191	C₄⋊Dic₃	—	3	8	no	—
192	Dic₃⋊C₄	—	3	8	no	—
193	Dic₃⋊C₄	—	3	16	no	—
194	C₄×Dic₃	—	3	8	no	—
195	C₄×Dic₃	—	3	16	no	—
196	C₂²×C₃²	—	2	16	no	—
197	C₂²×C₃²	—	2	8	no	—
198	C₂²×C₃²	—	2	2	no	—
199	C₂²×C₃²	—	2	2	no	—
200	C₂²×C₃²	—	2	2	no	—
201	C₂²×C₃²	—	2	4	no	—
202	C₂²×C₃²	—	2	8	no	—
203	C₂²×C₃²	—	2	8	no	—
204	C₂²×C₃²	—	4	8	no	—
205	C₂²×C₃²	—	4	8	no	—
206	C₂²×C₃²	C₂³×D₃	1	4	yes	—
207	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
208	C₃²×C₄	—	2	2	no	—
209	C₃²×C₄	—	2	1	no	—
210	C₃²×C₄	—	2	8	no	—
211	C₃²×C₄	—	2	8	no	—
212	C₃²×C₄	—	2	8	no	—
213	C₃²×C₄	—	2	4	no	—
214	C₃²×C₄	—	4	4	no	—
215	C₃²×C₄	—	4	8	no	—
216	C₃²×C₄	#235	1	8	yes	—
217	C₃²×C₄	#237	1	8	yes	—
218	C₃²×C₄	C₃×#41	1	2	yes	—
219	C₃²×C₄	C₃×#41	1	2	yes	—
220	C₃⋊Dic₃	—	2	4	no	—
221	C₃⋊Dic₃	—	2	2	no	—
222	C₃⋊Dic₃	—	2	2	no	—
223	C₃×Dic₃	—	6	16	no	—
224	C₃×Dic₃	—	6	8	no	—
225	C₃×Dic₃	—	6	8	no	—
226	C₄⋊Q₈	—	9	1	no	—
227	#126	—	9	4	no	—
228	#124	—	9	2	no	—
229	C₂²⋊Q₈	—	9	2	no	—
230	C₄×Q₈	—	9	2	no	—
231	C₄×Q₈	—	9	1	no	—
232	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic
233	#117	—	9	2	no	—
234	C₃³	#556	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₃	—	2	8	no	—
236	C₂³×C₃	C₂²×C₃×D₃	1	8	yes	—
237	C₂³×C₃	C₂²×C₃⋊D₃	1	2	yes	—
238	C₃×Q₈	—	18	4	no	—
239	C₃×Q₈	—	18	2	no	—
240	C₃×D₄	—	2	16	no	—
241	C₃×D₄	—	2	8	no	—
242	C₃×D₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	16	no	—
244	C₂×C₃×C₄	—	2	4	no	—
245	C₂×C₃×C₄	—	2	4	no	—
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	4	no	—
248	C₂×C₃×C₄	—	2	8	no	—
249	C₂×C₃×C₄	—	4	16	no	—
250	C₂×C₃×C₄	—	9	2	no	—
251	C₂×C₃×C₄	—	9	4	no	—
252	C₂×C₃×C₄	—	9	2	no	—
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
254	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
255	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
256	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
257	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
258	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
259	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
260	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
261	C₂×Dic₃	—	3	8	no	—
262	C₂×Dic₃	—	3	8	no	—
263	C₂×Dic₃	—	3	16	no	—
264	Dic₆	—	6	16	no	—
265	Dic₆	—	6	8	no	—
266	C₂×C₃²	—	2	4	no	—
267	C₂×C₃²	—	2	4	no	—
268	C₂×C₃²	—	2	4	no	—
269	C₂×C₃²	—	4	16	no	—
270	C₂×C₃²	—	4	8	no	—
271	C₂×C₃²	—	4	2	no	—
272	C₂×C₃²	C₂×#235	1	4	yes	—
273	C₂×C₃²	C₂×#237	1	4	yes	—
274	C₂×C₃²	#1010	1	4	yes	—
275	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
276	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
277	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
278	C₂×Q₈	—	9	1	no	—
279	C₂×Q₈	—	9	2	no	—
280	C₂×D₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
282	C₄⋊C₄	—	9	1	no	—
283	C₄⋊C₄	—	9	2	no	—
284	C₄⋊C₄	—	9	4	no	—
285	C₄⋊C₄	—	9	2	no	—
286	C₄⋊C₄	—	9	2	no	—
287	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
288	C₂²⋊C₄	—	9	4	no	—
289	C₂²⋊C₄	—	9	4	no	—
290	C₂²⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
291	C₄²	—	9	4	no	—
292	C₄²	—	9	2	no	—
293	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
294	C₂²×C₃	—	2	16	no	—
295	C₂²×C₃	—	2	8	no	—
296	C₂²×C₃	—	2	8	no	—
297	C₂²×C₃	—	2	8	no	—
298	C₂²×C₃	—	2	2	no	—
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	2	4	no	—
302	C₂²×C₃	—	4	8	no	—
303	C₂²×C₃	—	4	8	no	—
304	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
305	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
306	C₃×C₄	—	2	8	no	—
307	C₃×C₄	—	2	4	no	—
308	C₃×C₄	—	2	2	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	8	no	—
311	C₃×C₄	—	2	8	no	—
312	C₃×C₄	—	4	8	no	—
313	C₃×C₄	—	4	4	no	—
314	C₃×C₄	—	18	4	no	—
315	C₃×C₄	—	18	2	no	—
316	C₃×C₄	—	18	2	no	—
317	C₃×C₄	C₃×#235	1	8	yes	—
318	C₃×C₄	C₃×#237	1	8	yes	—
319	C₃×C₄	#3828	1	2	yes	—
320	C₃×C₄	#3830	1	2	yes	—
321	Dic₃	—	6	16	no	—
322	Dic₃	—	6	8	no	—
323	Dic₃	—	6	8	no	—
324	C₃²	—	2	4	no	—
325	C₃²	#5542	1	4	yes	complemented
326	C₃²	C₃×#556	1	1	yes	characteristic, complemented
327	C₂³	C₂²×C₃×C₃⋊D₃	1	2	yes	—
328	Q₈	—	18	4	no	—
329	Q₈	—	18	2	no	—
330	D₄	—	2	2	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	9	2	no	—
333	C₂×C₄	—	9	4	no	—
334	C₂×C₄	—	9	2	no	—
335	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
336	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
339	C₂×C₃	—	2	4	no	—
340	C₂×C₃	—	2	4	no	—
341	C₂×C₃	—	2	4	no	—
342	C₂×C₃	—	4	16	no	—
343	C₂×C₃	—	4	8	no	—
344	C₂×C₃	—	4	2	no	—
345	C₂×C₃	C₂×C₃×#235	1	4	yes	—
346	C₂×C₃	C₂×C₃×#237	1	4	yes	—
347	C₂×C₃	C₃×#1010	1	4	yes	—
348	C₂×C₃	C₂×#3828	1	1	yes	characteristic
349	C₂×C₃	C₂×#3830	1	1	yes	characteristic
350	C₂×C₃	#64367	1	1	yes	characteristic
351	C₂²	—	2	2	no	—
352	C₂²	—	2	2	no	—
353	C₂²	—	2	2	no	—
354	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
355	C₄	—	2	2	no	—
356	C₄	—	2	1	no	—
357	C₄	—	18	4	no	—
358	C₄	—	18	2	no	—
359	C₄	—	18	2	no	—
360	C₄	C₃×#3828	1	2	yes	—
361	C₄	C₃×#3830	1	2	yes	—
362	C₃	—	2	4	no	—
363	C₃	C₃×#5542	1	4	yes	complemented
364	C₃	#10596013	1	1	yes	characteristic, direct product factor
365	C₂	—	4	2	no	—
366	C₂	C₂×C₃×#3828	1	1	yes	characteristic
367	C₂	C₂×C₃×#3830	1	1	yes	characteristic
368	C₂	C₃×#64367	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃³×D₄	C₂²
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×#556
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
3. C₃×#64135	C₂	semidirect
4. C₃×#64133	C₂	semidirect
5. C₃×#64096	C₂	semidirect
6. C₃×#64088	C₂	semidirect
7. C₃×#64078	C₂	semidirect
8. C₃×C₄×#634	C₂	semidirect
9. #10596013	C₃	direct (N × H)
31. #64135	C₂×C₃	semidirect
32. #64133	C₂×C₃	semidirect
33. #64096	C₂×C₃	semidirect
34. #64088	C₂×C₃	semidirect
35. #64078	C₂×C₃	semidirect
36. C₄×#634	C₂×C₃	semidirect
234. C₃³	#556	semidirect
325. C₃²	#5542	semidirect
326. C₃²	C₃×#556	semidirect
363. C₃	C₃×#5542	semidirect
364. C₃	#10596013	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×D₄	2
C₃×#64145	2
C₃×#64135	2
C₃×#64133	2
C₃×#64096	2
C₃×#64088	2
C₃×#64078	2
C₃×C₄×#634	2
#10596013	3
C₃×#5542	3

Subgroups — C3×#10596013 #13179295

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596013 #13179295