Subgroups — C₃×#10592832 #13163170

Order 1728.

1244 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3828	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#63648	C₂	1	2	yes	maximal, complemented
5	C₃×#63643	C₂	1	2	yes	maximal, complemented
6	#10592832	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₃×#5133	—	3	4	no	maximal
8	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
9	C₂×C₃×#638	—	2	1	no	—
10	C₂²×C₃×C₃⋊Dic₃	—	2	1	no	—
11	C₃×#3828	—	2	2	no	—
12	C₃×#3828	C₄	1	4	yes	complemented
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×C₃⋊D₃	—	2	1	no	—
15	C₂×C₃×#634	C₂²	1	1	yes	characteristic
16	C₃³×M₁₆	—	2	2	no	—
17	C₂×C₃³×C₈	C₂²	1	2	yes	—
18	C₃×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
19	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
20	C₂×#3828	C₂×C₃	1	1	yes	characteristic
21	C₂×C₃×#235	—	3	4	no	—
22	C₂×C₃²×M₁₆	—	2	4	no	—
23	C₂×C₃²×M₁₆	D₃	1	4	yes	complemented
24	C₂×C₃²×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
27	#63648	C₂×C₃	1	2	yes	complemented
28	#63643	C₂×C₃	1	2	yes	complemented
29	C₃×#821	—	3	8	no	—
30	C₃×#816	—	3	8	no	—
31	C₂³×C₃³	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₃⋊D₃	—	2	1	no	—
33	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
34	C₂×C₃³×C₄	D₄	1	1	yes	characteristic
35	C₂×C₃³×C₄	D₄	1	2	yes	—
36	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
37	C₃×#638	—	2	4	no	—
38	C₂×C₃×C₃⋊Dic₃	—	2	1	no	—
39	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
40	C₂×C₃×C₃⋊Dic₃	—	4	2	no	—
41	C₃×C₄⋊(C₃⋊D₃)	—	2	1	no	—
42	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	2	yes	complemented
43	C₃×C₄×C₃⋊D₃	—	2	4	no	—
44	C₃×#634	—	2	1	no	—
45	C₃×#634	C₂×C₄	1	2	yes	complemented
46	C₃³×C₈	—	2	2	no	—
47	C₃×#417	—	9	1	no	—
48	#5133	—	3	4	no	—
49	C₂²×C₃²×C₄	—	2	4	no	—
50	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
51	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
52	C₂×#638	—	2	1	no	—
53	C₂²×C₃⋊Dic₃	—	2	1	no	—
54	#3828	—	2	2	no	—
55	#3828	C₃×C₄	1	4	yes	complemented
56	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₄×C₃⋊D₃	—	2	1	no	—
58	C₂×#634	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃×#67	—	6	4	no	—
60	C₂²×C₃×Dic₃	—	6	4	no	—
61	C₃×#235	—	3	16	no	—
62	C₃×#235	—	6	8	no	—
63	C₂×C₃×D₁₂	—	3	4	no	—
64	C₂×C₃×C₄×D₃	—	6	4	no	—
65	C₂×C₃×Dic₆	—	3	4	no	—
66	C₃²×M₁₆	—	2	16	no	—
67	C₃²×M₁₆	—	2	8	no	—
68	C₃²×M₁₆	—	2	2	no	—
69	C₂×C₃²×C₈	—	2	8	no	—
70	C₂×C₃²×C₈	C₂×D₃	1	8	yes	—
71	C₂×C₃²×C₈	C₂²×C₃	1	2	yes	—
72	C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
73	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
74	C₃×C₄⋊Dic₃	—	3	8	no	—
75	C₃×C₄⋊Dic₃	—	6	4	no	—
76	C₂²×C₃³	—	2	1	no	—
77	C₂²×C₃³	—	2	1	no	—
78	C₂²×C₃³	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
80	C₂×C₃×C₃⋊D₃	—	2	2	no	—
81	C₂×C₃×C₃⋊D₃	—	4	1	no	—
82	C₂×C₃×C₃⋊D₃	—	4	1	no	—
83	C₃³×C₄	C₂²⋊C₄	1	2	yes	—
84	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
85	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
86	C₃×C₃⋊Dic₃	—	2	2	no	—
87	C₃×C₃⋊Dic₃	—	4	2	no	—
88	C₂×C₃×#41	—	9	1	no	—
89	C₂×#235	—	3	4	no	—
90	C₂×C₃×M₁₆	—	2	4	no	—
91	C₂×C₃×M₁₆	C₃×D₃	1	4	yes	complemented
92	C₂×C₃×M₁₆	C₃⋊D₃	1	1	yes	characteristic, complemented
93	C₂×C₃×C₄⋊C₄	—	9	1	no	—
94	C₂×C₄⋊Dic₃	—	3	4	no	—
95	C₃×#103	—	9	2	no	—
96	C₃×#102	—	9	2	no	—
97	#821	—	3	8	no	—
98	#816	—	3	8	no	—
99	C₂³×C₃²	—	2	4	no	—
100	C₂³×C₃²	D₁₂	1	4	yes	—
101	C₂³×C₃²	C₃×D₄	1	1	yes	characteristic
102	C₂²×C₃⋊D₃	—	2	1	no	—
103	C₂²×C₃×D₃	—	6	4	no	—
104	C₂×C₃²×C₄	—	2	8	no	—
105	C₂×C₃²×C₄	—	2	4	no	—
106	C₂×C₃²×C₄	—	2	8	no	—
107	C₂×C₃²×C₄	—	2	4	no	—
108	C₂×C₃²×C₄	C₄×D₃	1	8	yes	—
109	C₂×C₃²×C₄	D₁₂	1	4	yes	—
110	C₂×C₃²×C₄	#67	1	8	yes	—
111	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
112	C₂×C₃²×C₄	C₃×D₄	1	1	yes	characteristic
113	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
114	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
115	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
116	#638	—	2	4	no	—
117	C₂×C₃⋊Dic₃	—	2	1	no	—
118	C₂×C₃⋊Dic₃	—	2	2	no	—
119	C₂×C₃⋊Dic₃	—	4	2	no	—
120	C₄⋊(C₃⋊D₃)	—	2	1	no	—
121	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	2	yes	complemented
122	C₄×C₃⋊D₃	—	2	4	no	—
123	#634	—	2	1	no	—
124	#634	C₂×C₃×C₄	1	2	yes	complemented
125	C₃×#67	—	6	16	no	—
126	C₂×C₃×Dic₃	—	6	4	no	—
127	C₂×C₃×Dic₃	—	6	8	no	—
128	C₂×C₃×Dic₃	—	12	8	no	—
129	C₃×D₁₂	—	3	8	no	—
130	C₃×D₁₂	—	6	4	no	—
131	C₃×C₄×D₃	—	6	16	no	—
132	C₃×Dic₆	—	3	8	no	—
133	C₃×Dic₆	—	6	4	no	—
134	C₃²×C₈	—	2	16	no	—
135	C₃²×C₈	—	2	8	no	—
136	C₃²×C₈	—	2	2	no	—
137	#417	—	9	1	no	Sylow
138	C₂×C₃³	—	2	2	no	—
139	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂×C₃³	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂×C₃³	#137	1	1	yes	characteristic
142	C₃×C₃⋊D₃	—	4	2	no	—
143	C₃×#41	—	9	4	no	—
144	C₃×#41	—	18	2	no	—
145	C₂×C₃×Q₈	—	9	1	no	—
146	C₂×C₃×D₄	—	9	1	no	—
147	C₂×C₃×D₄	—	18	1	no	—
148	C₂²×C₃×C₄	—	2	4	no	—
149	C₂²×C₃×C₄	—	18	1	no	—
150	C₂²×C₃×C₄	—	18	1	no	—
151	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
152	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
153	C₂×#67	—	6	4	no	—
154	C₂²×Dic₃	—	6	4	no	—
155	#235	—	3	16	no	—
156	#235	—	6	8	no	—
157	C₂×D₁₂	—	3	4	no	—
158	C₂×C₄×D₃	—	6	4	no	—
159	C₂×Dic₆	—	3	4	no	—
160	C₃×M₁₆	—	2	16	no	—
161	C₃×M₁₆	—	2	8	no	—
162	C₃×M₁₆	—	2	2	no	—
163	C₂×C₃×C₈	—	2	8	no	—
164	C₂×C₃×C₈	C₂×C₃×D₃	1	8	yes	—
165	C₂×C₃×C₈	C₂×C₃⋊D₃	1	2	yes	—
166	C₃×C₄⋊C₄	—	9	2	no	—
167	C₃×C₄⋊C₄	—	18	1	no	—
168	C₄⋊Dic₃	—	3	8	no	—
169	C₄⋊Dic₃	—	6	4	no	—
170	C₂²×C₃²	—	2	1	no	—
171	C₂²×C₃²	—	2	1	no	—
172	C₂²×C₃²	—	2	8	no	—
173	C₂²×C₃²	—	2	4	no	—
174	C₂²×C₃²	—	2	4	no	—
175	C₂²×C₃²	—	2	4	no	—
176	C₂²×C₃²	—	4	4	no	—
177	C₂²×C₃²	—	4	4	no	—
178	C₂²×C₃²	(C₂×D₃)⋊C₄	1	8	yes	—
179	C₂²×C₃²	C₃×C₂²⋊C₄	1	2	yes	—
180	C₂²×C₃²	C₂×D₁₂	1	4	yes	—
181	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
182	C₂×C₃⋊D₃	—	2	2	no	—
183	C₂×C₃⋊D₃	—	4	1	no	—
184	C₂×C₃⋊D₃	—	4	1	no	—
185	C₂×C₃×D₃	—	6	8	no	—
186	C₂×C₃×D₃	—	12	4	no	—
187	C₂×C₃×D₃	—	12	4	no	—
188	C₃²×C₄	—	2	8	no	—
189	C₃²×C₄	—	2	4	no	—
190	C₃²×C₄	—	2	4	no	—
191	C₃²×C₄	(C₂×D₃)⋊C₄	1	8	yes	—
192	C₃²×C₄	C₃×C₂²⋊C₄	1	2	yes	—
193	C₃²×C₄	C₂×C₄×D₃	1	4	yes	—
194	C₃²×C₄	C₂×#67	1	4	yes	—
195	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
196	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
197	C₃⋊Dic₃	—	2	2	no	—
198	C₃⋊Dic₃	—	4	2	no	—
199	C₃×Dic₃	—	6	8	no	—
200	C₃×Dic₃	—	12	8	no	—
201	C₂×#41	—	9	1	no	—
202	C₂×M₁₆	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
203	C₂×C₄⋊C₄	—	9	1	no	—
204	#103	—	9	2	no	—
205	#102	—	9	2	no	—
206	C₃³	#417	1	1	yes	characteristic, complemented, Sylow
207	C₂³×C₃	—	2	4	no	—
208	C₂³×C₃	—	18	1	no	—
209	C₂³×C₃	C₃×D₁₂	1	4	yes	—
210	C₂³×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
211	C₂²×D₃	—	6	4	no	—
212	C₃×Q₈	—	9	2	no	—
213	C₃×Q₈	—	18	1	no	—
214	C₃×D₄	—	9	2	no	—
215	C₃×D₄	—	18	4	no	—
216	C₃×D₄	—	18	1	no	—
217	C₂×C₃×C₄	—	2	8	no	—
218	C₂×C₃×C₄	—	2	4	no	—
219	C₂×C₃×C₄	—	2	8	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	18	1	no	—
222	C₂×C₃×C₄	—	18	4	no	—
223	C₂×C₃×C₄	—	18	2	no	—
224	C₂×C₃×C₄	—	36	2	no	—
225	C₂×C₃×C₄	C₃×C₄×D₃	1	8	yes	—
226	C₂×C₃×C₄	C₃×D₁₂	1	4	yes	—
227	C₂×C₃×C₄	C₃×#67	1	8	yes	—
228	C₂×C₃×C₄	C₄×C₃⋊D₃	1	2	yes	—
229	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
230	C₂×C₃×C₄	#638	1	2	yes	—
231	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
232	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
233	#67	—	6	16	no	—
234	C₂×Dic₃	—	6	4	no	—
235	C₂×Dic₃	—	6	8	no	—
236	C₂×Dic₃	—	12	8	no	—
237	D₁₂	—	3	8	no	—
238	D₁₂	—	6	4	no	—
239	C₄×D₃	—	6	16	no	—
240	Dic₆	—	3	8	no	—
241	Dic₆	—	6	4	no	—
242	C₃×C₈	—	2	16	no	—
243	C₃×C₈	—	2	8	no	—
244	C₃×C₈	—	2	2	no	—
245	C₂×C₃²	—	2	2	no	—
246	C₂×C₃²	—	2	4	no	—
247	C₂×C₃²	—	2	4	no	—
248	C₂×C₃²	—	2	4	no	—
249	C₂×C₃²	—	2	8	no	—
250	C₂×C₃²	—	4	8	no	—
251	C₂×C₃²	#908	1	4	yes	—
252	C₂×C₃²	#909	1	4	yes	—
253	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
254	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
255	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂×C₃²	C₃×#137	1	1	yes	characteristic
257	C₃⋊D₃	—	4	2	no	—
258	C₃×D₃	—	12	8	no	—
259	#41	—	9	4	no	—
260	#41	—	18	2	no	—
261	C₂×Q₈	—	9	1	no	—
262	C₂×D₄	—	9	1	no	—
263	C₂×D₄	—	18	1	no	—
264	C₂²×C₄	—	18	1	no	—
265	C₂²×C₄	—	18	1	no	—
266	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
267	M₁₆	—	2	2	no	—
268	C₂×C₈	C₂×C₃×C₃⋊D₃	1	2	yes	—
269	C₄⋊C₄	—	9	2	no	—
270	C₄⋊C₄	—	18	1	no	—
271	C₂²×C₃	—	2	4	no	—
272	C₂²×C₃	—	2	4	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	2	8	no	—
276	C₂²×C₃	—	2	4	no	—
277	C₂²×C₃	—	4	4	no	—
278	C₂²×C₃	—	4	4	no	—
279	C₂²×C₃	—	18	2	no	—
280	C₂²×C₃	—	36	1	no	—
281	C₂²×C₃	—	36	1	no	—
282	C₂²×C₃	C₃×(C₂×D₃)⋊C₄	1	8	yes	—
283	C₂²×C₃	#3752	1	2	yes	—
284	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
285	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
286	C₂×D₃	—	6	8	no	—
287	C₂×D₃	—	12	4	no	—
288	C₂×D₃	—	12	4	no	—
289	C₃×C₄	—	2	8	no	—
290	C₃×C₄	—	2	4	no	—
291	C₃×C₄	—	2	4	no	—
292	C₃×C₄	—	18	2	no	—
293	C₃×C₄	—	36	2	no	—
294	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	8	yes	—
295	C₃×C₄	#3752	1	2	yes	—
296	C₃×C₄	C₂×C₃×C₄×D₃	1	4	yes	—
297	C₃×C₄	C₂×C₃×#67	1	4	yes	—
298	C₃×C₄	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
299	C₃×C₄	C₂×#638	1	1	yes	characteristic
300	Dic₃	—	6	8	no	—
301	Dic₃	—	12	8	no	—
302	C₃²	—	2	4	no	—
303	C₃²	#5133	1	4	yes	complemented
304	C₃²	C₃×#417	1	1	yes	characteristic, complemented
305	C₂³	—	18	1	no	—
306	C₂³	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
307	Q₈	—	9	2	no	—
308	Q₈	—	18	1	no	—
309	D₄	—	9	2	no	—
310	D₄	—	18	4	no	—
311	D₄	—	18	1	no	—
312	C₂×C₄	—	18	1	no	—
313	C₂×C₄	—	18	4	no	—
314	C₂×C₄	—	18	2	no	—
315	C₂×C₄	—	36	2	no	—
316	C₂×C₄	C₃×C₄×C₃⋊D₃	1	2	yes	—
317	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
318	C₂×C₄	C₃×#638	1	2	yes	—
319	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
320	C₈	—	2	2	no	—
321	C₂×C₃	—	2	2	no	—
322	C₂×C₃	—	2	8	no	—
323	C₂×C₃	—	2	4	no	—
324	C₂×C₃	—	2	4	no	—
325	C₂×C₃	—	2	4	no	—
326	C₂×C₃	—	4	8	no	—
327	C₂×C₃	—	36	2	no	—
328	C₂×C₃	C₃×#908	1	4	yes	—
329	C₂×C₃	C₃×#909	1	4	yes	—
330	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
331	C₂×C₃	#64117	1	1	yes	characteristic
332	C₂×C₃	#64118	1	1	yes	characteristic
333	C₂×C₃	C₂×#3752	1	1	yes	characteristic
334	D₃	—	12	8	no	—
335	C₂²	—	2	1	no	—
336	C₂²	—	2	1	no	—
337	C₂²	—	18	2	no	—
338	C₂²	—	36	1	no	—
339	C₂²	—	36	1	no	—
340	C₂²	C₃×#3752	1	2	yes	—
341	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
342	C₄	—	18	2	no	—
343	C₄	—	36	2	no	—
344	C₄	C₃×#3752	1	2	yes	—
345	C₄	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
346	C₄	C₂×C₃×#638	1	1	yes	characteristic
347	C₃	—	2	4	no	—
348	C₃	C₃×#5133	1	4	yes	complemented
349	C₃	#10592832	1	1	yes	characteristic, direct product factor
350	C₂	—	2	2	no	—
351	C₂	—	36	2	no	—
352	C₂	C₃×#64117	1	1	yes	characteristic
353	C₂	C₃×#64118	1	1	yes	characteristic
354	C₂	C₂×C₃×#3752	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)
commutator	C₃²×C₄	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₂×C₃³×M₁₆	C₂
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃×#3828	C₂
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₃×M₁₆	C₃⋊D₃
hypocenter	C₃²	C₃×#417
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×M₁₆	C₂	semidirect
3. C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	semidirect
4. C₃×#63648	C₂	semidirect
5. C₃×#63643	C₂	semidirect
6. #10592832	C₃	direct (N × H)
12. C₃×#3828	C₄	semidirect
23. C₂×C₃²×M₁₆	D₃	semidirect
24. C₂×C₃²×M₁₆	C₂×C₃	semidirect
25. C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	semidirect
27. #63648	C₂×C₃	semidirect
28. #63643	C₂×C₃	semidirect
42. C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	semidirect
45. C₃×#634	C₂×C₄	semidirect
55. #3828	C₃×C₄	semidirect
91. C₂×C₃×M₁₆	C₃×D₃	semidirect
92. C₂×C₃×M₁₆	C₃⋊D₃	semidirect
121. C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	semidirect
124. #634	C₂×C₃×C₄	semidirect
202. C₂×M₁₆	C₃×C₃⋊D₃	semidirect
206. C₃³	#417	semidirect
303. C₃²	#5133	semidirect
304. C₃²	C₃×#417	semidirect
348. C₃	C₃×#5133	semidirect
349. C₃	#10592832	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#3828	2
C₂×C₃³×M₁₆	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
C₃×#63648	2
C₃×#63643	2
#10592832	3
C₃×#5133	3

Subgroups — C3×#10592832 #13163170

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10592832 #13163170