Subgroups — C₃×#10589832 #13153299

Order 1728.

752 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₉×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#63508	C₂	1	4	yes	maximal, complemented
3	C₃×#63459	C₂	1	2	yes	maximal, complemented
4	C₃×#63455	C₂	1	2	yes	maximal
5	C₃×C₄⋊C₄×D₉	C₂	1	2	yes	maximal, complemented
6	C₃×#63452	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×D₃₆	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#5730	—	3	1	no	maximal
10	#10589832	C₃	1	1	yes	maximal, characteristic, direct product factor
11	C₂×C₃×Q₈×C₉	C₂²	1	2	yes	—
12	C₂×C₃×D₃₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×D₉	C₂²	1	2	yes	—
14	C₂×C₃×C₄×D₉	C₂²	1	4	yes	—
15	C₂×C₃×Dic₁₈	C₂²	1	1	yes	characteristic
16	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃×C₉×C₄⋊C₄	C₂²	1	2	yes	—
18	C₃×C₄²×C₉	C₂²	1	1	yes	characteristic
19	C₃×(C₂×D₉)⋊C₄	C₂²	1	2	yes	—
20	C₃×(C₂×D₉)⋊C₄	C₂²	1	4	yes	—
21	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
22	C₃×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
23	C₃×C₄⋊Dic₉	C₂²	1	4	yes	—
24	C₃×Dic₉⋊C₄	C₂²	1	2	yes	—
25	C₃×Dic₉⋊C₄	C₂²	1	4	yes	—
26	C₃×C₄×Dic₉	C₂²	1	2	yes	—
27	C₃²×C₄⋊Q₈	D₃	1	1	yes	characteristic
28	C₃×#946	—	3	4	no	—
29	C₃×#897	—	3	2	no	—
30	C₃×#893	—	3	2	no	—
31	C₃×D₃×C₄⋊C₄	—	3	2	no	—
32	C₃×#890	—	3	2	no	—
33	C₃×C₄×D₁₂	—	3	1	no	—
34	C₃×C₄×Dic₆	—	3	1	no	—
35	C₉×C₄⋊Q₈	—	2	1	no	—
36	C₉×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
37	#63508	C₂×C₃	1	4	yes	complemented
38	#63459	C₂×C₃	1	2	yes	complemented
39	#63455	C₂×C₃	1	2	yes	—
40	C₄⋊C₄×D₉	C₂×C₃	1	2	yes	complemented
41	#63452	C₂×C₃	1	2	yes	complemented
42	C₄×D₃₆	C₂×C₃	1	1	yes	characteristic
43	C₄×Dic₁₈	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₃×D₉	C₂³	1	2	yes	—
45	C₃×Q₈×C₉	—	4	2	no	—
46	C₂×C₃×C₄×C₉	C₂³	1	4	yes	—
47	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
49	C₂×C₃×C₄×C₉	C₂³	1	1	yes	characteristic
50	C₂×C₃×Dic₉	C₂³	1	2	yes	—
51	C₂×C₃×Dic₉	C₂³	1	2	yes	—
52	C₂×C₃×Dic₉	C₂³	1	2	yes	—
53	C₃×D₃₆	Q₈	1	4	yes	complemented
54	C₃×C₄×D₉	—	2	4	no	—
55	C₃×C₄×D₉	—	4	4	no	—
56	C₃×Dic₁₈	—	2	2	no	—
57	C₃×#554	—	9	1	no	—
58	#5730	—	3	1	no	—
59	C₂×C₃²×Q₈	C₂×D₃	1	2	yes	—
60	C₂×C₃×D₁₂	—	3	1	no	—
61	C₂×C₃×C₄×D₃	—	3	2	no	—
62	C₂×C₃×C₄×D₃	—	3	4	no	—
63	C₂×C₃×Dic₆	—	3	1	no	—
64	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
65	C₃²×C₄⋊C₄	C₂×D₃	1	2	yes	—
66	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic
67	C₃×(C₂×D₃)⋊C₄	—	3	4	no	—
68	C₃×(C₂×D₃)⋊C₄	—	3	2	no	—
69	C₃×C₄⋊Dic₃	—	3	1	no	—
70	C₃×C₄⋊Dic₃	—	3	4	no	—
71	C₃×C₄⋊Dic₃	—	3	1	no	—
72	C₃×Dic₃⋊C₄	—	3	4	no	—
73	C₃×Dic₃⋊C₄	—	3	2	no	—
74	C₃×C₄×Dic₃	—	3	2	no	—
75	C₂×Q₈×C₉	—	2	2	no	—
76	C₂×Q₈×C₉	C₂²×C₃	1	2	yes	—
77	C₂×D₃₆	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₄×D₉	C₂²×C₃	1	2	yes	—
79	C₂×C₄×D₉	C₂²×C₃	1	4	yes	—
80	C₂×Dic₁₈	C₂²×C₃	1	1	yes	characteristic
81	C₉×C₄⋊C₄	—	2	2	no	—
82	C₉×C₄⋊C₄	—	2	2	no	—
83	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₉×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₄²×C₉	—	2	1	no	—
86	C₄²×C₉	C₂²×C₃	1	1	yes	characteristic
87	(C₂×D₉)⋊C₄	C₂²×C₃	1	2	yes	—
88	(C₂×D₉)⋊C₄	C₂²×C₃	1	4	yes	—
89	C₄⋊Dic₉	C₂²×C₃	1	4	yes	—
90	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
91	C₄⋊Dic₉	C₂²×C₃	1	1	yes	characteristic
92	Dic₉⋊C₄	C₂²×C₃	1	2	yes	—
93	Dic₉⋊C₄	C₂²×C₃	1	4	yes	—
94	C₄×Dic₉	C₂²×C₃	1	2	yes	—
95	C₂²×C₃×C₉	C₂⁴	1	1	yes	characteristic
96	C₂×C₃×D₉	—	2	2	no	—
97	C₂×C₃×D₉	—	2	2	no	—
98	C₂×C₃×D₉	C₂×Q₈	1	4	yes	—
99	C₃×C₄×C₉	—	2	1	no	—
100	C₃×C₄×C₉	—	2	4	no	—
101	C₃×C₄×C₉	C₂×Q₈	1	2	yes	—
102	C₃×C₄×C₉	#41	1	2	yes	—
103	C₃×Dic₉	—	2	2	no	—
104	C₃×Dic₉	—	2	2	no	—
105	C₃×Dic₉	—	2	2	no	—
106	C₃×C₄⋊Q₈	—	2	1	no	—
107	C₃×C₄⋊Q₈	D₉	1	1	yes	characteristic, complemented
108	C₃×C₄⋊Q₈	C₃×D₃	1	1	yes	characteristic
109	C₃×#125	—	9	2	no	—
110	C₃×C₂²⋊Q₈	—	9	4	no	—
111	C₃×C₂²⋊Q₈	—	9	2	no	—
112	C₃×C₄×Q₈	—	9	1	no	—
113	C₃×C₄×D₄	—	9	2	no	—
114	C₃×C₄×D₄	—	9	1	no	—
115	C₂×C₃×C₄⋊C₄	—	9	2	no	—
116	#946	—	3	4	no	—
117	#897	—	3	2	no	—
118	#893	—	3	2	no	—
119	D₃×C₄⋊C₄	—	3	2	no	—
120	#890	—	3	2	no	—
121	C₄×D₁₂	—	3	1	no	—
122	C₄×Dic₆	—	3	1	no	—
123	C₂²×C₃×D₃	—	3	2	no	—
124	C₃²×Q₈	—	4	2	no	—
125	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
126	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
127	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
128	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
129	C₂×C₃×Dic₃	—	3	2	no	—
130	C₂×C₃×Dic₃	—	3	2	no	—
131	C₂×C₃×Dic₃	—	3	2	no	—
132	C₃×D₁₂	—	3	4	no	—
133	C₃×C₄×D₃	—	6	4	no	—
134	C₃×C₄×D₃	—	12	4	no	—
135	C₃×Dic₆	—	6	2	no	—
136	C₂²×D₉	C₂³×C₃	1	2	yes	—
137	Q₈×C₉	—	4	2	no	—
138	Q₈×C₉	—	4	4	no	—
139	C₂×C₄×C₉	—	2	1	no	—
140	C₂×C₄×C₉	—	2	1	no	—
141	C₂×C₄×C₉	—	2	1	no	—
142	C₂×C₄×C₉	—	2	4	no	—
143	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
144	C₂×C₄×C₉	C₂³×C₃	1	4	yes	—
145	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
146	C₂×C₄×C₉	C₂³×C₃	1	1	yes	characteristic
147	C₂×Dic₉	C₂³×C₃	1	2	yes	—
148	C₂×Dic₉	C₂³×C₃	1	2	yes	—
149	C₂×Dic₉	C₂³×C₃	1	2	yes	—
150	D₃₆	C₃×Q₈	1	4	yes	complemented
151	C₄×D₉	—	2	4	no	—
152	C₄×D₉	—	4	4	no	—
153	Dic₁₈	—	2	2	no	—
154	#554	—	9	1	no	Sylow
155	C₂×C₃×C₉	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₃×C₉	C₂×#41	1	1	yes	characteristic
157	C₂×C₃×C₉	H(5,𝔽₂)	1	1	yes	characteristic
158	C₃×D₉	—	2	4	no	—
159	C₂×C₃×Q₈	—	2	2	no	—
160	C₂×C₃×Q₈	—	9	1	no	—
161	C₂×C₃×Q₈	C₂×D₉	1	2	yes	—
162	C₂×C₃×Q₈	C₂×C₃×D₃	1	2	yes	—
163	C₂×C₃×D₄	—	9	1	no	—
164	C₂²×C₃×C₄	—	9	2	no	—
165	C₂²×C₃×C₄	—	9	4	no	—
166	C₂×D₁₂	—	3	1	no	—
167	C₂×C₄×D₃	—	3	2	no	—
168	C₂×C₄×D₃	—	3	4	no	—
169	C₂×Dic₆	—	3	1	no	—
170	C₃×C₄⋊C₄	—	2	2	no	—
171	C₃×C₄⋊C₄	—	2	2	no	—
172	C₃×C₄⋊C₄	—	9	4	no	—
173	C₃×C₄⋊C₄	—	9	2	no	—
174	C₃×C₄⋊C₄	—	9	1	no	—
175	C₃×C₄⋊C₄	—	9	1	no	—
176	C₃×C₄⋊C₄	—	9	4	no	—
177	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
178	C₃×C₄⋊C₄	C₂×D₉	1	2	yes	—
179	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
180	C₃×C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
181	C₃×C₂²⋊C₄	—	9	4	no	—
182	C₃×C₂²⋊C₄	—	9	2	no	—
183	C₃×C₄²	—	2	1	no	—
184	C₃×C₄²	—	9	2	no	—
185	C₃×C₄²	C₂×D₉	1	1	yes	characteristic
186	C₃×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
187	(C₂×D₃)⋊C₄	—	3	2	no	—
188	(C₂×D₃)⋊C₄	—	3	4	no	—
189	C₄⋊Dic₃	—	3	1	no	—
190	C₄⋊Dic₃	—	3	1	no	—
191	C₄⋊Dic₃	—	3	4	no	—
192	Dic₃⋊C₄	—	3	2	no	—
193	Dic₃⋊C₄	—	3	4	no	—
194	C₄×Dic₃	—	3	2	no	—
195	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
196	C₂×C₃×D₃	—	3	4	no	—
197	C₂×C₃×D₃	—	6	2	no	—
198	C₂×C₃×D₃	—	6	2	no	—
199	C₃²×C₄	—	2	1	no	—
200	C₃²×C₄	—	2	4	no	—
201	C₃²×C₄	D₃×Q₈	1	2	yes	—
202	C₃²×C₄	#239	1	2	yes	—
203	C₃×Dic₃	—	6	2	no	—
204	C₃×Dic₃	—	6	2	no	—
205	C₃×Dic₃	—	6	2	no	—
206	C₂²×C₉	—	2	1	no	—
207	C₂²×C₉	C₂⁴×C₃	1	1	yes	characteristic
208	C₂×D₉	—	2	2	no	—
209	C₂×D₉	—	2	2	no	—
210	C₂×D₉	C₂×C₃×Q₈	1	4	yes	—
211	C₄×C₉	—	2	2	no	—
212	C₄×C₉	—	2	4	no	—
213	C₄×C₉	—	2	1	no	—
214	C₄×C₉	—	2	2	no	—
215	C₄×C₉	—	2	2	no	—
216	C₄×C₉	—	4	4	no	—
217	C₄×C₉	C₂×C₃×Q₈	1	2	yes	—
218	C₄×C₉	C₃×#41	1	2	yes	—
219	Dic₉	—	2	2	no	—
220	Dic₉	—	2	2	no	—
221	Dic₉	—	2	2	no	—
222	C₄⋊Q₈	C₃×D₉	1	1	yes	characteristic, complemented
223	#125	—	9	2	no	—
224	C₂²⋊Q₈	—	9	4	no	—
225	C₂²⋊Q₈	—	9	2	no	—
226	C₄×Q₈	—	9	1	no	—
227	C₄×D₄	—	9	2	no	—
228	C₄×D₄	—	9	1	no	—
229	C₂×C₄⋊C₄	—	9	2	no	—
230	C₃×C₉	#554	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₃	—	9	2	no	—
232	C₂²×D₃	—	3	2	no	—
233	C₃×Q₈	—	4	2	no	—
234	C₃×Q₈	—	4	2	no	—
235	C₃×Q₈	—	4	4	no	—
236	C₃×Q₈	—	18	2	no	—
237	C₃×D₄	—	9	4	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	2	1	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	9	2	no	—
243	C₂×C₃×C₄	—	9	2	no	—
244	C₂×C₃×C₄	—	9	2	no	—
245	C₂×C₃×C₄	—	18	4	no	—
246	C₂×C₃×C₄	—	36	4	no	—
247	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂²×D₉	1	4	yes	—
249	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×D₉	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
253	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
255	C₂×Dic₃	—	3	2	no	—
256	C₂×Dic₃	—	3	2	no	—
257	C₂×Dic₃	—	3	2	no	—
258	D₁₂	—	3	4	no	—
259	C₄×D₃	—	6	4	no	—
260	C₄×D₃	—	12	4	no	—
261	Dic₆	—	6	2	no	—
262	C₂×C₃²	#1004	1	1	yes	characteristic
263	C₂×C₃²	C₂×D₃×Q₈	1	1	yes	characteristic
264	C₂×C₃²	C₂×#239	1	1	yes	characteristic
265	C₃×D₃	—	6	4	no	—
266	C₂×C₉	—	2	1	no	—
267	C₂×C₉	—	2	1	no	—
268	C₂×C₉	—	2	1	no	—
269	C₂×C₉	C₂²×C₃×Q₈	1	1	yes	characteristic
270	C₂×C₉	C₂×C₃×#41	1	1	yes	characteristic
271	C₂×C₉	C₃×H(5,𝔽₂)	1	1	yes	characteristic
272	D₉	—	2	4	no	—
273	C₂×Q₈	—	9	1	no	—
274	C₂×Q₈	C₂×C₃×D₉	1	2	yes	—
275	C₂×D₄	—	9	1	no	—
276	C₂²×C₄	—	9	2	no	—
277	C₂²×C₄	—	9	4	no	—
278	C₄⋊C₄	—	9	1	no	—
279	C₄⋊C₄	—	9	4	no	—
280	C₄⋊C₄	—	9	1	no	—
281	C₄⋊C₄	—	9	2	no	—
282	C₄⋊C₄	—	9	4	no	—
283	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
284	C₄⋊C₄	C₂×C₃×D₉	1	2	yes	—
285	C₂²⋊C₄	—	9	4	no	—
286	C₂²⋊C₄	—	9	2	no	—
287	C₄²	—	9	2	no	—
288	C₄²	C₂×C₃×D₉	1	1	yes	characteristic
289	C₂²×C₃	—	2	1	no	—
290	C₂²×C₃	—	9	4	no	—
291	C₂²×C₃	—	18	2	no	—
292	C₂²×C₃	—	18	2	no	—
293	C₂²×C₃	C₂³×D₉	1	1	yes	characteristic
294	C₂²×C₃	C₂³×C₃×D₃	1	1	yes	characteristic
295	C₂×D₃	—	3	4	no	—
296	C₂×D₃	—	6	2	no	—
297	C₂×D₃	—	6	2	no	—
298	C₃×C₄	—	2	2	no	—
299	C₃×C₄	—	2	4	no	—
300	C₃×C₄	—	2	1	no	—
301	C₃×C₄	—	2	4	no	—
302	C₃×C₄	—	2	1	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	2	no	—
305	C₃×C₄	—	4	4	no	—
306	C₃×C₄	—	18	2	no	—
307	C₃×C₄	—	18	2	no	—
308	C₃×C₄	—	18	2	no	—
309	C₃×C₄	Q₈×D₉	1	2	yes	—
310	C₃×C₄	#3701	1	2	yes	—
311	C₃×C₄	C₃×D₃×Q₈	1	2	yes	—
312	C₃×C₄	C₃×#239	1	2	yes	—
313	Dic₃	—	6	2	no	—
314	Dic₃	—	6	2	no	—
315	Dic₃	—	6	2	no	—
316	C₃²	#5730	1	1	yes	characteristic
317	C₉	—	2	1	no	—
318	C₉	C₃×#554	1	1	yes	characteristic, complemented
319	C₂³	—	9	2	no	—
320	Q₈	—	4	2	no	—
321	Q₈	—	18	2	no	—
322	D₄	—	9	4	no	—
323	C₂×C₄	—	9	2	no	—
324	C₂×C₄	—	9	2	no	—
325	C₂×C₄	—	9	2	no	—
326	C₂×C₄	—	18	4	no	—
327	C₂×C₄	—	36	4	no	—
328	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₃×D₉	1	4	yes	—
330	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₃×D₉	1	1	yes	characteristic
332	C₂×C₃	—	2	1	no	—
333	C₂×C₃	—	2	1	no	—
334	C₂×C₃	—	2	1	no	—
335	C₂×C₃	—	18	4	no	—
336	C₂×C₃	#63710	1	1	yes	characteristic
337	C₂×C₃	C₂×Q₈×D₉	1	1	yes	characteristic
338	C₂×C₃	C₂×#3701	1	1	yes	characteristic
339	C₂×C₃	C₃×#1004	1	1	yes	characteristic
340	C₂×C₃	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
341	C₂×C₃	C₂×C₃×#239	1	1	yes	characteristic
342	D₃	—	6	4	no	—
343	C₂²	—	9	4	no	—
344	C₂²	—	18	2	no	—
345	C₂²	—	18	2	no	—
346	C₂²	C₂³×C₃×D₉	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	2	1	no	—
349	C₄	—	18	2	no	—
350	C₄	—	18	2	no	—
351	C₄	—	18	2	no	—
352	C₄	C₃×Q₈×D₉	1	2	yes	—
353	C₄	C₃×#3701	1	2	yes	—
354	C₃	—	2	1	no	—
355	C₃	#10589832	1	1	yes	characteristic, direct product factor
356	C₃	C₃×#5730	1	1	yes	characteristic
357	C₂	—	18	4	no	—
358	C₂	C₃×#63710	1	1	yes	characteristic
359	C₂	C₂×C₃×Q₈×D₉	1	1	yes	characteristic
360	C₂	C₂×C₃×#3701	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁴×C₃
Frattini	C₂²×C₃	C₂³×C₃×D₃
Fitting	C₃×C₉×C₄⋊Q₈	C₂
socle	C₂²×C₃²	C₂³×D₃
prime radical	C₂×C₃×D₃₆	C₂²
hypercenter	C₃×C₄⋊Q₈	D₉
hypocenter	C₉	C₃×#554
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₃×C₉×C₄⋊Q₈	C₂	semidirect
2. C₃×#63508	C₂	semidirect
3. C₃×#63459	C₂	semidirect
5. C₃×C₄⋊C₄×D₉	C₂	semidirect
6. C₃×#63452	C₂	semidirect
8. C₃×C₄×Dic₁₈	C₂	semidirect
10. #10589832	C₃	direct (N × H)
36. C₉×C₄⋊Q₈	C₂×C₃	semidirect
37. #63508	C₂×C₃	semidirect
38. #63459	C₂×C₃	semidirect
40. C₄⋊C₄×D₉	C₂×C₃	semidirect
41. #63452	C₂×C₃	semidirect
43. C₄×Dic₁₈	C₂×C₃	semidirect
53. C₃×D₃₆	Q₈	semidirect
107. C₃×C₄⋊Q₈	D₉	semidirect
150. D₃₆	C₃×Q₈	semidirect
222. C₄⋊Q₈	C₃×D₉	semidirect
230. C₃×C₉	#554	semidirect
318. C₉	C₃×#554	semidirect
355. C₃	#10589832	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×C₉×C₄⋊Q₈	2
C₃×#63508	2
C₃×#63459	2
C₃×#63455	2
C₃×C₄⋊C₄×D₉	2
C₃×#63452	2
C₃×C₄×D₃₆	2
C₃×C₄×Dic₁₈	2
C₃×#5730	3
#10589832	3

Subgroups — C3×#10589832 #13153299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10589832 #13153299