Subgroups — C₃×#10589868 #13153458

Order 1728.

804 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#63713	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₉×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#63505	C₂	1	2	yes	maximal, complemented
4	C₃×#63481	C₂	1	2	yes	maximal, complemented
5	C₃×#63480	C₂	1	4	yes	maximal, complemented
6	C₃×Q₁₆×D₉	C₂	1	2	yes	maximal, complemented
7	C₃×#63467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#63464	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5766	—	3	1	no	maximal
10	#10589868	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₃×#3701	—	2	2	no	—
13	C₃×#3701	C₂²	1	4	yes	—
14	C₃×Q₈×D₉	—	2	2	no	—
15	C₃×Q₈×D₉	C₂²	1	4	yes	—
16	C₃×#3697	—	2	4	no	—
17	C₃×#3697	C₂²	1	1	yes	characteristic
18	C₃×#3697	C₂²	1	2	yes	—
19	C₃×C₉×Q₁₆	C₂²	1	2	yes	—
20	C₃×C₉×Q₁₆	C₂²	1	2	yes	—
21	C₂×C₃×C₈×C₉	C₂²	1	1	yes	characteristic
22	C₃×#3675	C₂²	1	4	yes	—
23	C₃×#3674	C₂²	1	4	yes	—
24	C₃×#3667	C₂²	1	1	yes	characteristic
25	C₃×D₇₂	C₂²	1	1	yes	characteristic
26	C₃×#3664	C₂²	1	2	yes	—
27	C₃×#3663	C₂²	1	2	yes	—
28	C₃×C₈×D₉	C₂²	1	2	yes	—
29	C₃×Dic₃₆	C₂²	1	1	yes	characteristic
30	C₃×#1007	—	3	2	no	—
31	C₂×C₃²×Q₁₆	D₃	1	1	yes	characteristic
32	C₃×#942	—	3	2	no	—
33	C₃×#919	—	3	2	no	—
34	C₃×#918	—	3	4	no	—
35	C₃×D₃×Q₁₆	—	3	2	no	—
36	C₃×#904	—	3	1	no	—
37	C₃×#901	—	3	1	no	—
38	#63713	C₂×C₃	1	2	yes	complemented
39	C₂×C₉×Q₁₆	—	2	1	no	—
40	C₂×C₉×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
41	#63505	C₂×C₃	1	2	yes	complemented
42	#63481	C₂×C₃	1	2	yes	complemented
43	#63480	C₂×C₃	1	4	yes	complemented
44	Q₁₆×D₉	C₂×C₃	1	2	yes	complemented
45	#63467	C₂×C₃	1	1	yes	characteristic, complemented
46	#63464	C₂×C₃	1	1	yes	characteristic, complemented
47	C₃×Q₈×C₉	—	2	2	no	—
48	C₃×Q₈×C₉	C₂³	1	4	yes	—
49	C₂×C₃×C₄×C₉	—	2	2	no	—
50	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
51	C₃×#611	—	2	2	no	—
52	C₃×#611	D₄	1	2	yes	—
53	C₃×D₃₆	—	2	4	no	—
54	C₃×D₃₆	D₄	1	1	yes	characteristic
55	C₃×D₃₆	C₂³	1	2	yes	—
56	C₃×C₄×D₉	—	2	4	no	—
57	C₃×C₄×D₉	—	2	2	no	—
58	C₃×C₄×D₉	—	2	4	no	—
59	C₃×C₄×D₉	C₂³	1	2	yes	—
60	C₃×Dic₁₈	—	2	4	no	—
61	C₃×Dic₁₈	D₄	1	1	yes	characteristic
62	C₃×Dic₁₈	C₂³	1	2	yes	—
63	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
64	C₃×C₈×C₉	C₂³	1	1	yes	characteristic
65	C₃×C₉⋊C₈	C₂³	1	2	yes	—
66	C₃×#578	—	9	1	no	—
67	#5766	—	3	1	no	—
68	C₂×C₃²×Q₈	C₂×D₃	1	2	yes	—
69	C₃×#239	—	3	4	no	—
70	C₃×#239	—	6	2	no	—
71	C₃×D₃×Q₈	—	3	4	no	—
72	C₃×D₃×Q₈	—	6	2	no	—
73	C₃×#235	—	3	1	no	—
74	C₃×#235	—	3	2	no	—
75	C₃×#235	—	6	4	no	—
76	C₃²×Q₁₆	C₂×D₃	1	2	yes	—
77	C₃²×Q₁₆	C₂×D₃	1	2	yes	—
78	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
79	C₃×#216	—	3	4	no	—
80	C₃×#215	—	3	4	no	—
81	C₃×#208	—	3	1	no	—
82	C₃×Dic₁₂	—	3	1	no	—
83	C₃×D₂₄	—	3	1	no	—
84	C₃×#204	—	3	2	no	—
85	C₃×ΓL(1,𝔽₂₅)	—	3	2	no	—
86	C₃×D₃×C₈	—	3	2	no	—
87	C₂×Q₈×C₉	—	2	2	no	—
88	C₂×Q₈×C₉	C₂²×C₃	1	2	yes	—
89	#3701	—	2	2	no	—
90	#3701	C₂²×C₃	1	4	yes	—
91	Q₈×D₉	—	2	2	no	—
92	Q₈×D₉	C₂²×C₃	1	4	yes	—
93	#3697	—	2	4	no	—
94	#3697	C₂²×C₃	1	1	yes	characteristic
95	#3697	C₂²×C₃	1	2	yes	—
96	C₉×Q₁₆	—	2	2	no	—
97	C₉×Q₁₆	—	2	2	no	—
98	C₉×Q₁₆	C₂²×C₃	1	2	yes	—
99	C₉×Q₁₆	C₂²×C₃	1	2	yes	—
100	C₂×C₈×C₉	—	2	1	no	—
101	C₂×C₈×C₉	C₂²×C₃	1	1	yes	characteristic
102	#3675	C₂²×C₃	1	4	yes	—
103	#3674	C₂²×C₃	1	4	yes	—
104	#3667	C₂²×C₃	1	1	yes	characteristic
105	D₇₂	C₂²×C₃	1	1	yes	characteristic
106	#3664	C₂²×C₃	1	2	yes	—
107	#3663	C₂²×C₃	1	2	yes	—
108	C₈×D₉	C₂²×C₃	1	2	yes	—
109	Dic₃₆	C₂²×C₃	1	1	yes	characteristic
110	C₂²×C₃×C₉	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×D₉	—	2	2	no	—
112	C₂×C₃×D₉	C₂×D₄	1	2	yes	—
113	C₃×C₄×C₉	—	2	4	no	—
114	C₃×C₄×C₉	C₂×D₄	1	1	yes	characteristic
115	C₃×C₄×C₉	C₂⁴	1	1	yes	characteristic
116	C₃×Dic₉	—	2	2	no	—
117	C₃×Dic₉	C₂×D₄	1	2	yes	—
118	C₃×2₋¹⁺⁴	—	9	2	no	—
119	#1007	—	3	2	no	—
120	C₃×#137	—	9	2	no	—
121	C₃×#137	—	9	4	no	—
122	C₃×#135	—	9	2	no	—
123	C₃×#135	—	9	1	no	—
124	C₂×C₃×Q₁₆	—	2	1	no	—
125	C₂×C₃×Q₁₆	—	9	2	no	—
126	C₂×C₃×Q₁₆	D₉	1	1	yes	characteristic, complemented
127	C₂×C₃×Q₁₆	C₃×D₃	1	1	yes	characteristic
128	C₃×#131	—	9	1	no	—
129	#942	—	3	2	no	—
130	#919	—	3	2	no	—
131	#918	—	3	4	no	—
132	D₃×Q₁₆	—	3	2	no	—
133	#904	—	3	1	no	—
134	#901	—	3	1	no	—
135	C₃²×Q₈	—	2	2	no	—
136	C₃²×Q₈	C₂²×D₃	1	4	yes	—
137	C₂×C₃²×C₄	—	2	2	no	—
138	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₃×#67	—	3	2	no	—
140	C₃×#67	—	6	2	no	—
141	C₃×D₁₂	—	3	1	no	—
142	C₃×D₁₂	—	3	2	no	—
143	C₃×D₁₂	—	6	4	no	—
144	C₃×C₄×D₃	—	3	2	no	—
145	C₃×C₄×D₃	—	6	4	no	—
146	C₃×C₄×D₃	—	6	4	no	—
147	C₃×C₄×D₃	—	6	2	no	—
148	C₃×Dic₆	—	3	1	no	—
149	C₃×Dic₆	—	3	2	no	—
150	C₃×Dic₆	—	6	4	no	—
151	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
152	C₃²×C₈	C₂²×D₃	1	1	yes	characteristic
153	C₃×C₃⋊C₈	—	3	2	no	—
154	Q₈×C₉	—	2	2	no	—
155	Q₈×C₉	—	2	4	no	—
156	Q₈×C₉	—	4	2	no	—
157	Q₈×C₉	C₂³×C₃	1	4	yes	—
158	C₂×C₄×C₉	—	2	2	no	—
159	C₂×C₄×C₉	—	2	1	no	—
160	C₂×C₄×C₉	—	4	2	no	—
161	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
162	#611	—	2	2	no	—
163	#611	C₃×D₄	1	2	yes	—
164	D₃₆	—	2	4	no	—
165	D₃₆	C₃×D₄	1	1	yes	characteristic
166	D₃₆	C₂³×C₃	1	2	yes	—
167	C₄×D₉	—	2	4	no	—
168	C₄×D₉	—	2	2	no	—
169	C₄×D₉	—	2	4	no	—
170	C₄×D₉	C₂³×C₃	1	2	yes	—
171	Dic₁₈	—	2	4	no	—
172	Dic₁₈	C₃×D₄	1	1	yes	characteristic
173	Dic₁₈	C₂³×C₃	1	2	yes	—
174	C₈×C₉	—	2	1	no	—
175	C₈×C₉	—	2	1	no	—
176	C₈×C₉	C₂³×C₃	1	1	yes	characteristic
177	C₈×C₉	C₂³×C₃	1	1	yes	characteristic
178	C₉⋊C₈	C₂³×C₃	1	2	yes	—
179	#578	—	9	1	no	Sylow
180	C₂×C₃×C₉	—	2	1	no	—
181	C₂×C₃×C₉	C₂²×D₄	1	1	yes	characteristic
182	C₃×D₉	—	2	2	no	—
183	C₃×D₉	—	4	2	no	—
184	C₃×#41	—	9	1	no	—
185	C₃×#41	—	9	4	no	—
186	C₃×#41	—	9	2	no	—
187	C₃×#41	—	18	4	no	—
188	C₃×#41	—	18	2	no	—
189	C₂×C₃×Q₈	—	2	2	no	—
190	C₂×C₃×Q₈	—	9	4	no	—
191	C₂×C₃×Q₈	—	18	2	no	—
192	C₂×C₃×Q₈	C₂×D₉	1	2	yes	—
193	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
194	#239	—	3	4	no	—
195	#239	—	6	2	no	—
196	D₃×Q₈	—	3	4	no	—
197	D₃×Q₈	—	6	2	no	—
198	#235	—	3	1	no	—
199	#235	—	3	2	no	—
200	#235	—	6	4	no	—
201	C₃×Q₁₆	—	2	2	no	—
202	C₃×Q₁₆	—	2	2	no	—
203	C₃×Q₁₆	—	9	4	no	—
204	C₃×Q₁₆	—	9	1	no	—
205	C₃×Q₁₆	C₂×D₉	1	2	yes	—
206	C₃×Q₁₆	C₂×D₉	1	2	yes	—
207	C₃×Q₁₆	C₂×C₃×D₃	1	2	yes	—
208	C₃×Q₁₆	C₂×C₃×D₃	1	2	yes	—
209	C₃×SD₁₆	—	9	4	no	—
210	C₃×SD₁₆	—	9	2	no	—
211	C₃×D₈	—	9	1	no	—
212	C₃×M₁₆	—	9	1	no	—
213	C₃×M₁₆	—	9	2	no	—
214	C₂×C₃×C₈	—	2	1	no	—
215	C₂×C₃×C₈	—	9	2	no	—
216	C₂×C₃×C₈	C₂×D₉	1	1	yes	characteristic
217	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
218	#216	—	3	4	no	—
219	#215	—	3	4	no	—
220	#208	—	3	1	no	—
221	Dic₁₂	—	3	1	no	—
222	D₂₄	—	3	1	no	—
223	#204	—	3	2	no	—
224	ΓL(1,𝔽₂₅)	—	3	2	no	—
225	D₃×C₈	—	3	2	no	—
226	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
227	C₂×C₃×D₃	—	3	2	no	—
228	C₂×C₃×D₃	—	6	2	no	—
229	C₃²×C₄	—	2	4	no	—
230	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
231	C₃²×C₄	C₂³×D₃	1	1	yes	characteristic
232	C₃×Dic₃	—	3	2	no	—
233	C₃×Dic₃	—	6	2	no	—
234	C₂²×C₉	—	2	1	no	—
235	C₂²×C₉	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂×D₉	—	2	2	no	—
237	C₂×D₉	C₂×C₃×D₄	1	2	yes	—
238	C₄×C₉	—	2	4	no	—
239	C₄×C₉	—	2	1	no	—
240	C₄×C₉	—	2	1	no	—
241	C₄×C₉	—	4	4	no	—
242	C₄×C₉	C₂×C₃×D₄	1	1	yes	characteristic
243	C₄×C₉	C₂⁴×C₃	1	1	yes	characteristic
244	Dic₉	—	2	2	no	—
245	Dic₉	C₂×C₃×D₄	1	2	yes	—
246	2₋¹⁺⁴	—	9	2	no	—
247	#137	—	9	2	no	—
248	#137	—	9	4	no	—
249	#135	—	9	2	no	—
250	#135	—	9	1	no	—
251	C₂×Q₁₆	—	9	2	no	—
252	C₂×Q₁₆	C₃×D₉	1	1	yes	characteristic, complemented
253	#131	—	9	1	no	—
254	C₃×C₉	#578	1	1	yes	characteristic, complemented, Sylow
255	C₃×Q₈	—	2	2	no	—
256	C₃×Q₈	—	2	2	no	—
257	C₃×Q₈	—	2	4	no	—
258	C₃×Q₈	—	4	2	no	—
259	C₃×Q₈	—	9	1	no	—
260	C₃×Q₈	—	9	2	no	—
261	C₃×Q₈	—	18	4	no	—
262	C₃×Q₈	C₂²×D₉	1	4	yes	—
263	C₃×Q₈	C₂²×C₃×D₃	1	4	yes	—
264	C₃×D₄	—	9	2	no	—
265	C₃×D₄	—	9	1	no	—
266	C₃×D₄	—	9	2	no	—
267	C₃×D₄	—	18	4	no	—
268	C₃×D₄	—	18	2	no	—
269	C₂×C₃×C₄	—	2	2	no	—
270	C₂×C₃×C₄	—	2	2	no	—
271	C₂×C₃×C₄	—	2	1	no	—
272	C₂×C₃×C₄	—	4	2	no	—
273	C₂×C₃×C₄	—	9	2	no	—
274	C₂×C₃×C₄	—	18	4	no	—
275	C₂×C₃×C₄	—	18	4	no	—
276	C₂×C₃×C₄	—	18	2	no	—
277	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
279	#67	—	3	2	no	—
280	#67	—	6	2	no	—
281	D₁₂	—	3	2	no	—
282	D₁₂	—	3	1	no	—
283	D₁₂	—	6	4	no	—
284	C₄×D₃	—	3	2	no	—
285	C₄×D₃	—	6	4	no	—
286	C₄×D₃	—	6	4	no	—
287	C₄×D₃	—	6	2	no	—
288	Dic₆	—	3	1	no	—
289	Dic₆	—	3	2	no	—
290	Dic₆	—	6	4	no	—
291	C₃×C₈	—	2	1	no	—
292	C₃×C₈	—	2	1	no	—
293	C₃×C₈	—	9	2	no	—
294	C₃×C₈	C₂²×D₉	1	1	yes	characteristic
295	C₃×C₈	C₂²×D₉	1	1	yes	characteristic
296	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
297	C₃×C₈	C₂²×C₃×D₃	1	1	yes	characteristic
298	C₃⋊C₈	—	3	2	no	—
299	C₂×C₃²	—	2	1	no	—
300	C₂×C₃²	C₂×D₃×D₄	1	1	yes	characteristic
301	C₃×D₃	—	6	2	no	—
302	C₃×D₃	—	12	2	no	—
303	C₂×C₉	—	2	2	no	—
304	C₂×C₉	—	2	1	no	—
305	C₂×C₉	—	2	1	no	—
306	C₂×C₉	C₂²×C₃×D₄	1	1	yes	characteristic
307	D₉	—	2	2	no	—
308	D₉	—	4	2	no	—
309	#41	—	9	1	no	—
310	#41	—	9	4	no	—
311	#41	—	9	2	no	—
312	#41	—	18	4	no	—
313	#41	—	18	2	no	—
314	C₂×Q₈	—	9	4	no	—
315	C₂×Q₈	—	18	2	no	—
316	C₂×Q₈	C₂×C₃×D₉	1	2	yes	—
317	Q₁₆	—	9	4	no	—
318	Q₁₆	—	9	1	no	—
319	Q₁₆	C₂×C₃×D₉	1	2	yes	—
320	Q₁₆	C₂×C₃×D₉	1	2	yes	—
321	SD₁₆	—	9	4	no	—
322	SD₁₆	—	9	2	no	—
323	D₈	—	9	1	no	—
324	M₁₆	—	9	1	no	—
325	M₁₆	—	9	2	no	—
326	C₂×C₈	—	9	2	no	—
327	C₂×C₈	C₂×C₃×D₉	1	1	yes	characteristic
328	C₂²×C₃	—	2	1	no	—
329	C₂²×C₃	—	9	2	no	—
330	C₂²×C₃	—	18	2	no	—
331	C₂²×C₃	D₄×D₉	1	1	yes	characteristic
332	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
333	C₂×D₃	—	3	2	no	—
334	C₂×D₃	—	6	2	no	—
335	C₃×C₄	—	2	4	no	—
336	C₃×C₄	—	2	4	no	—
337	C₃×C₄	—	2	1	no	—
338	C₃×C₄	—	2	1	no	—
339	C₃×C₄	—	4	4	no	—
340	C₃×C₄	—	9	2	no	—
341	C₃×C₄	—	18	2	no	—
342	C₃×C₄	D₄×D₉	1	1	yes	characteristic
343	C₃×C₄	C₂³×D₉	1	1	yes	characteristic
344	C₃×C₄	C₃×D₃×D₄	1	1	yes	characteristic
345	C₃×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
346	Dic₃	—	3	2	no	—
347	Dic₃	—	6	2	no	—
348	C₃²	#5766	1	1	yes	characteristic
349	C₉	—	2	1	no	—
350	C₉	C₃×#578	1	1	yes	characteristic, complemented
351	Q₈	—	2	2	no	—
352	Q₈	—	9	1	no	—
353	Q₈	—	9	2	no	—
354	Q₈	—	18	4	no	—
355	Q₈	C₂²×C₃×D₉	1	4	yes	—
356	D₄	—	9	2	no	—
357	D₄	—	9	2	no	—
358	D₄	—	9	1	no	—
359	D₄	—	18	4	no	—
360	D₄	—	18	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	9	2	no	—
363	C₂×C₄	—	18	4	no	—
364	C₂×C₄	—	18	4	no	—
365	C₂×C₄	—	18	2	no	—
366	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
367	C₈	—	9	2	no	—
368	C₈	C₂²×C₃×D₉	1	1	yes	characteristic
369	C₈	C₂²×C₃×D₉	1	1	yes	characteristic
370	C₂×C₃	—	2	2	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	1	no	—
374	C₂×C₃	—	18	2	no	—
375	C₂×C₃	—	36	2	no	—
376	C₂×C₃	C₂×D₄×D₉	1	1	yes	characteristic
377	C₂×C₃	C₂×C₃×D₃×D₄	1	1	yes	characteristic
378	D₃	—	6	2	no	—
379	D₃	—	12	2	no	—
380	C₂²	—	9	2	no	—
381	C₂²	—	18	2	no	—
382	C₂²	C₃×D₄×D₉	1	1	yes	characteristic
383	C₄	—	2	4	no	—
384	C₄	—	9	2	no	—
385	C₄	—	18	2	no	—
386	C₄	C₃×D₄×D₉	1	1	yes	characteristic
387	C₄	C₂³×C₃×D₉	1	1	yes	characteristic
388	C₃	—	2	1	no	—
389	C₃	#10589868	1	1	yes	characteristic, direct product factor
390	C₃	C₃×#5766	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	18	2	no	—
393	C₂	—	36	2	no	—
394	C₂	C₂×C₃×D₄×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂×D₄×D₉
commutator, cosocle	C₄×C₉	C₂⁴×C₃
Frattini	C₃×C₄	C₂³×C₃×D₃
Fitting	C₂×C₃×C₉×Q₁₆	C₂
socle	C₂×C₃²	C₂×D₃×D₄
hypercenter	C₂×C₃×Q₁₆	D₉
hypocenter	C₉	C₃×#578
LCS	G ▷ C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₃×#63713	C₂	semidirect
2. C₂×C₃×C₉×Q₁₆	C₂	semidirect
3. C₃×#63505	C₂	semidirect
4. C₃×#63481	C₂	semidirect
5. C₃×#63480	C₂	semidirect
6. C₃×Q₁₆×D₉	C₂	semidirect
7. C₃×#63467	C₂	semidirect
8. C₃×#63464	C₂	semidirect
10. #10589868	C₃	direct (N × H)
38. #63713	C₂×C₃	semidirect
40. C₂×C₉×Q₁₆	C₂×C₃	semidirect
41. #63505	C₂×C₃	semidirect
42. #63481	C₂×C₃	semidirect
43. #63480	C₂×C₃	semidirect
44. Q₁₆×D₉	C₂×C₃	semidirect
45. #63467	C₂×C₃	semidirect
46. #63464	C₂×C₃	semidirect
126. C₂×C₃×Q₁₆	D₉	semidirect
252. C₂×Q₁₆	C₃×D₉	semidirect
254. C₃×C₉	#578	semidirect
350. C₉	C₃×#578	semidirect
389. C₃	#10589868	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×#63713	2
C₂×C₃×C₉×Q₁₆	2
C₃×#63505	2
C₃×#63481	2
C₃×#63480	2
C₃×Q₁₆×D₉	2
C₃×#63467	2
C₃×#63464	2
C₃×#5766	3
#10589868	3

Subgroups — C3×#10589868 #13153458

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589868 #13153458