Subgroups — C₃×#5632 #10595729

Order 576.

597 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×D₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#67	C₂	1	1	yes	maximal, characteristic
6	C₃×#897	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#896	C₂	1	2	yes	maximal, complemented
8	C₃×#888	C₂	1	2	yes	maximal, complemented
9	C₃×#887	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#67⋊C₄	C₂	1	2	yes	maximal
11	C₃×#878	C₂	1	2	yes	maximal, complemented
12	C₃×D₄×Q₈	—	3	1	no	maximal
13	#5632	C₃	1	1	yes	maximal, characteristic, direct product factor
14	C₂×C₃²×Q₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃²×C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×#67	C₂²	1	1	yes	characteristic
17	C₂²×C₃×Dic₃	C₂²	1	2	yes	—
18	C₃×D₃×Q₈	—	2	4	no	—
19	C₂×C₃×C₄×D₃	C₂²	1	2	yes	—
20	C₂×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₃×Dic₆	—	2	4	no	—
22	C₂×C₃×Dic₆	C₂²	1	2	yes	—
23	C₂×C₃×Dic₆	C₂²	1	2	yes	—
24	C₂×C₃×Dic₆	C₂²	1	1	yes	characteristic
25	C₂×C₃×Dic₆	C₂²	1	1	yes	characteristic
26	C₃²×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₃²×C₄⋊C₄	C₂²	1	2	yes	—
28	C₃²×C₂²⋊C₄	C₂²	1	2	yes	—
29	C₃×#217	C₂²	1	1	yes	characteristic
30	C₃×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
31	C₃×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
32	C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
33	C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
34	C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
35	C₃×Dic₃⋊C₄	C₂²	1	2	yes	—
36	C₃×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
37	C₃×C₄×Dic₃	C₂²	1	2	yes	—
38	C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
39	C₂²×C₃×Q₈	—	3	1	no	—
40	C₂²×C₃×Q₈	—	3	1	no	—
41	C₂×D₃×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×Dic₆	C₂×C₃	1	1	yes	characteristic, complemented
43	C₃×C₄⋊Q₈	—	3	1	no	—
44	C₃×C₄⋊Q₈	—	3	2	no	—
45	C₃×C₂²⋊Q₈	—	2	1	no	—
46	C₃×C₂²⋊Q₈	—	3	2	no	—
47	C₃×C₂²⋊Q₈	—	3	1	no	—
48	C₃×C₂²⋊Q₈	—	3	2	no	—
49	C₃×C₂²⋊Q₈	D₃	1	1	yes	characteristic, complemented
50	C₃×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
51	C₃×C₄×Q₈	—	3	1	no	—
52	C₃×C₄×D₄	—	3	1	no	—
53	C₃×C₄×D₄	—	3	2	no	—
54	#944	C₂×C₃	1	1	yes	characteristic, complemented
55	C₄×#67	C₂×C₃	1	1	yes	characteristic
56	#897	C₂×C₃	1	1	yes	characteristic, complemented
57	#896	C₂×C₃	1	2	yes	complemented
58	#888	C₂×C₃	1	2	yes	complemented
59	#887	C₂×C₃	1	1	yes	characteristic, complemented
60	#67⋊C₄	C₂×C₃	1	2	yes	—
61	#878	C₂×C₃	1	2	yes	complemented
62	C₂³×C₃²	C₂³	1	1	yes	characteristic
63	C₂²×C₃×D₃	C₂³	1	1	yes	characteristic
64	C₃²×Q₈	—	2	2	no	—
65	C₂×C₃²×C₄	—	2	2	no	—
66	C₂×C₃²×C₄	C₂³	1	2	yes	—
67	C₂×C₃²×C₄	C₂³	1	2	yes	—
68	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
69	C₂×C₃²×C₄	C₂³	1	1	yes	characteristic
70	C₃×#67	Q₈	1	4	yes	complemented
71	C₂×C₃×Dic₃	—	2	4	no	—
72	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₃	C₂³	1	2	yes	—
74	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
75	C₂×C₃×Dic₃	C₂³	1	2	yes	—
76	C₂×C₃×Dic₃	C₂³	1	1	yes	characteristic
77	C₃×C₄×D₃	—	2	2	no	—
78	C₃×C₄×D₃	—	2	4	no	—
79	C₃×Dic₆	—	2	2	no	—
80	C₃×Dic₆	—	2	4	no	—
81	C₃×Dic₆	—	2	4	no	—
82	C₃×Dic₆	D₄	1	4	yes	complemented
83	D₄×Q₈	—	3	1	no	Sylow
84	C₂×C₃×Q₈	—	2	1	no	—
85	C₂×C₃×Q₈	—	3	1	no	—
86	C₂×C₃×Q₈	—	3	2	no	—
87	C₂×C₃×Q₈	—	3	2	no	—
88	C₂×C₃×Q₈	—	3	1	no	—
89	C₂×C₃×Q₈	—	6	4	no	—
90	C₂×C₃×Q₈	—	6	4	no	—
91	C₂×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
92	C₂×C₃×Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₃×D₄	—	3	1	no	—
94	C₂²×C₃×C₄	—	2	1	no	—
95	C₂²×C₃×C₄	—	3	2	no	—
96	C₂²×C₃×C₄	—	3	2	no	—
97	C₂²×C₃×C₄	—	3	1	no	—
98	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
99	C₂²×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
100	C₂×#67	C₂²×C₃	1	1	yes	characteristic
101	C₂²×Dic₃	C₂²×C₃	1	2	yes	—
102	D₃×Q₈	—	2	4	no	—
103	C₂×C₄×D₃	C₂²×C₃	1	2	yes	—
104	C₂×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
105	C₂×Dic₆	—	2	4	no	—
106	C₂×Dic₆	C₂²×C₃	1	2	yes	—
107	C₂×Dic₆	C₂²×C₃	1	2	yes	—
108	C₂×Dic₆	C₂²×C₃	1	1	yes	characteristic
109	C₂×Dic₆	C₂²×C₃	1	1	yes	characteristic
110	C₃×C₄⋊C₄	—	2	1	no	—
111	C₃×C₄⋊C₄	—	2	2	no	—
112	C₃×C₄⋊C₄	—	3	1	no	—
113	C₃×C₄⋊C₄	—	3	2	no	—
114	C₃×C₄⋊C₄	—	3	2	no	—
115	C₃×C₄⋊C₄	—	3	2	no	—
116	C₃×C₄⋊C₄	—	3	2	no	—
117	C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
118	C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
119	C₃×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
120	C₃×C₄⋊C₄	C₂²×C₃	1	2	yes	—
121	C₃×C₂²⋊C₄	—	2	2	no	—
122	C₃×C₂²⋊C₄	—	3	1	no	—
123	C₃×C₂²⋊C₄	—	3	1	no	—
124	C₃×C₂²⋊C₄	—	3	2	no	—
125	C₃×C₂²⋊C₄	C₂×D₃	1	2	yes	—
126	C₃×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
127	C₃×C₄²	—	3	2	no	—
128	C₃×C₄²	—	3	1	no	—
129	#217	C₂²×C₃	1	1	yes	characteristic
130	(C₂×D₃)⋊C₄	C₂²×C₃	1	2	yes	—
131	(C₂×D₃)⋊C₄	C₂²×C₃	1	1	yes	characteristic
132	C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
133	Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
134	Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
135	Dic₃⋊C₄	C₂²×C₃	1	2	yes	—
136	Dic₃⋊C₄	C₂²×C₃	1	1	yes	characteristic
137	C₄×Dic₃	C₂²×C₃	1	2	yes	—
138	C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
139	C₂²×C₃²	—	2	1	no	—
140	C₂²×C₃²	—	2	1	no	—
141	C₂²×C₃²	C₂×Q₈	1	2	yes	complemented
142	C₂²×C₃²	C₂⁴	1	1	yes	characteristic
143	C₂×C₃×D₃	—	2	1	no	—
144	C₂×C₃×D₃	—	2	1	no	—
145	C₂×C₃×D₃	C₂×Q₈	1	2	yes	complemented
146	C₃²×C₄	—	2	1	no	—
147	C₃²×C₄	—	2	2	no	—
148	C₃²×C₄	—	2	2	no	—
149	C₃²×C₄	C₂×D₄	1	2	yes	—
150	C₃×Dic₃	—	2	1	no	—
151	C₃×Dic₃	—	2	2	no	—
152	C₃×Dic₃	—	2	1	no	—
153	C₃×Dic₃	C₂×D₄	1	4	yes	—
154	C₃×Dic₃	C₂×Q₈	1	2	yes	complemented
155	C₂²×Q₈	—	3	1	no	—
156	C₂²×Q₈	—	3	1	no	—
157	C₄⋊Q₈	—	3	1	no	—
158	C₄⋊Q₈	—	3	2	no	—
159	C₂²⋊Q₈	—	3	2	no	—
160	C₂²⋊Q₈	—	3	1	no	—
161	C₂²⋊Q₈	—	3	2	no	—
162	C₂²⋊Q₈	C₃×D₃	1	1	yes	characteristic, complemented
163	C₄×Q₈	—	3	1	no	—
164	C₄×D₄	—	3	1	no	—
165	C₄×D₄	—	3	2	no	—
166	C₂³×C₃	—	2	1	no	—
167	C₂³×C₃	—	3	1	no	—
168	C₂³×C₃	C₂²×D₃	1	1	yes	characteristic
169	C₂³×C₃	C₂³×C₃	1	1	yes	characteristic
170	C₂²×D₃	C₂³×C₃	1	1	yes	characteristic
171	C₃×Q₈	—	2	2	no	—
172	C₃×Q₈	—	2	2	no	—
173	C₃×Q₈	—	3	4	no	—
174	C₃×Q₈	—	4	2	no	—
175	C₃×Q₈	—	6	4	no	—
176	C₃×Q₈	—	6	4	no	—
177	C₃×Q₈	—	6	2	no	—
178	C₃×D₄	—	3	4	no	—
179	C₂×C₃×C₄	—	2	2	no	—
180	C₂×C₃×C₄	—	2	2	no	—
181	C₂×C₃×C₄	—	2	1	no	—
182	C₂×C₃×C₄	—	2	2	no	—
183	C₂×C₃×C₄	—	2	2	no	—
184	C₂×C₃×C₄	—	2	1	no	—
185	C₂×C₃×C₄	—	3	1	no	—
186	C₂×C₃×C₄	—	3	2	no	—
187	C₂×C₃×C₄	—	3	1	no	—
188	C₂×C₃×C₄	—	3	2	no	—
189	C₂×C₃×C₄	—	3	1	no	—
190	C₂×C₃×C₄	—	4	2	no	—
191	C₂×C₃×C₄	—	6	4	no	—
192	C₂×C₃×C₄	—	6	4	no	—
193	C₂×C₃×C₄	—	6	2	no	—
194	C₂×C₃×C₄	C₂²×D₃	1	2	yes	—
195	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
196	C₂×C₃×C₄	C₂²×D₃	1	2	yes	—
197	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
198	C₂×C₃×C₄	C₂³×C₃	1	2	yes	—
199	C₂×C₃×C₄	C₂³×C₃	1	2	yes	—
200	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
202	#67	C₃×Q₈	1	4	yes	complemented
203	C₂×Dic₃	—	2	4	no	—
204	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
205	C₂×Dic₃	C₂³×C₃	1	2	yes	—
206	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
207	C₂×Dic₃	C₂³×C₃	1	2	yes	—
208	C₂×Dic₃	C₂³×C₃	1	1	yes	characteristic
209	C₄×D₃	—	2	2	no	—
210	C₄×D₃	—	2	4	no	—
211	Dic₆	—	2	2	no	—
212	Dic₆	—	2	4	no	—
213	Dic₆	—	2	4	no	—
214	Dic₆	C₃×D₄	1	4	yes	complemented
215	C₂×C₃²	—	2	2	no	—
216	C₂×C₃²	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₃²	C₂²×Q₈	1	1	yes	characteristic
218	C₂×C₃²	2₋¹⁺⁴	1	1	yes	characteristic
219	C₃×D₃	—	2	2	no	—
220	C₂×Q₈	—	3	1	no	—
221	C₂×Q₈	—	3	2	no	—
222	C₂×Q₈	—	3	2	no	—
223	C₂×Q₈	—	3	1	no	—
224	C₂×Q₈	—	6	4	no	—
225	C₂×Q₈	—	6	4	no	—
226	C₂×Q₈	C₂×C₃×D₃	1	1	yes	characteristic
227	C₂×D₄	—	3	1	no	—
228	C₂²×C₄	—	3	2	no	—
229	C₂²×C₄	—	3	2	no	—
230	C₂²×C₄	—	3	1	no	—
231	C₂²×C₄	C₂×C₃×D₃	1	1	yes	characteristic
232	C₄⋊C₄	—	3	1	no	—
233	C₄⋊C₄	—	3	2	no	—
234	C₄⋊C₄	—	3	2	no	—
235	C₄⋊C₄	—	3	2	no	—
236	C₄⋊C₄	—	3	2	no	—
237	C₄⋊C₄	C₂×C₃×D₃	1	1	yes	characteristic
238	C₄⋊C₄	C₂×C₃×D₃	1	2	yes	—
239	C₂²⋊C₄	—	3	1	no	—
240	C₂²⋊C₄	—	3	1	no	—
241	C₂²⋊C₄	—	3	2	no	—
242	C₂²⋊C₄	C₂×C₃×D₃	1	2	yes	—
243	C₄²	—	3	2	no	—
244	C₄²	—	3	1	no	—
245	C₂²×C₃	—	2	1	no	—
246	C₂²×C₃	—	2	1	no	—
247	C₂²×C₃	—	2	1	no	—
248	C₂²×C₃	—	2	1	no	—
249	C₂²×C₃	—	2	1	no	—
250	C₂²×C₃	—	2	2	no	—
251	C₂²×C₃	—	3	2	no	—
252	C₂²×C₃	—	4	1	no	—
253	C₂²×C₃	—	4	1	no	—
254	C₂²×C₃	—	6	1	no	—
255	C₂²×C₃	—	6	1	no	—
256	C₂²×C₃	D₃×Q₈	1	2	yes	complemented
257	C₂²×C₃	C₂×C₃×Q₈	1	2	yes	complemented
258	C₂²×C₃	C₂³×D₃	1	1	yes	characteristic
259	C₂²×C₃	C₂⁴×C₃	1	1	yes	characteristic
260	C₂×D₃	—	2	1	no	—
261	C₂×D₃	—	2	1	no	—
262	C₂×D₃	C₂×C₃×Q₈	1	2	yes	complemented
263	C₃×C₄	—	2	1	no	—
264	C₃×C₄	—	2	2	no	—
265	C₃×C₄	—	2	2	no	—
266	C₃×C₄	—	2	1	no	—
267	C₃×C₄	—	2	2	no	—
268	C₃×C₄	—	2	2	no	—
269	C₃×C₄	—	2	2	no	—
270	C₃×C₄	—	3	4	no	—
271	C₃×C₄	—	3	2	no	—
272	C₃×C₄	—	4	1	no	—
273	C₃×C₄	—	4	2	no	—
274	C₃×C₄	—	4	2	no	—
275	C₃×C₄	—	6	2	no	—
276	C₃×C₄	—	6	1	no	—
277	C₃×C₄	—	6	1	no	—
278	C₃×C₄	D₃×D₄	1	2	yes	—
279	C₃×C₄	C₂×C₃×D₄	1	2	yes	—
280	Dic₃	—	2	1	no	—
281	Dic₃	—	2	2	no	—
282	Dic₃	—	2	1	no	—
283	Dic₃	C₂×C₃×D₄	1	4	yes	—
284	Dic₃	C₂×C₃×Q₈	1	2	yes	complemented
285	C₃²	D₄×Q₈	1	1	yes	characteristic, complemented, Sylow
286	C₂³	—	3	1	no	—
287	C₂³	C₂²×C₃×D₃	1	1	yes	characteristic
288	Q₈	—	2	2	no	—
289	Q₈	—	3	4	no	—
290	Q₈	—	6	4	no	—
291	Q₈	—	6	4	no	—
292	Q₈	—	6	2	no	—
293	D₄	—	3	4	no	—
294	C₂×C₄	—	2	2	no	—
295	C₂×C₄	—	3	1	no	—
296	C₂×C₄	—	3	2	no	—
297	C₂×C₄	—	3	1	no	—
298	C₂×C₄	—	3	1	no	—
299	C₂×C₄	—	3	2	no	—
300	C₂×C₄	—	6	4	no	—
301	C₂×C₄	—	6	4	no	—
302	C₂×C₄	—	6	2	no	—
303	C₂×C₄	C₂²×C₃×D₃	1	2	yes	—
304	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
305	C₂×C₄	C₂²×C₃×D₃	1	2	yes	—
306	C₂×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
307	C₂×C₃	—	2	2	no	—
308	C₂×C₃	—	2	2	no	—
309	C₂×C₃	—	2	1	no	—
310	C₂×C₃	—	2	1	no	—
311	C₂×C₃	—	2	1	no	—
312	C₂×C₃	—	4	2	no	—
313	C₂×C₃	—	6	2	no	—
314	C₂×C₃	C₂×D₃×D₄	1	1	yes	characteristic
315	C₂×C₃	C₂×D₃×Q₈	1	1	yes	characteristic
316	C₂×C₃	#1010	1	1	yes	characteristic
317	C₂×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
318	C₂×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
319	C₂×C₃	C₃×2₋¹⁺⁴	1	1	yes	characteristic
320	D₃	—	2	2	no	—
321	C₂²	—	2	1	no	—
322	C₂²	—	2	1	no	—
323	C₂²	—	3	2	no	—
324	C₂²	—	6	1	no	—
325	C₂²	—	6	1	no	—
326	C₂²	C₃×D₃×Q₈	1	2	yes	complemented
327	C₂²	C₂³×C₃×D₃	1	1	yes	characteristic
328	C₄	—	2	1	no	—
329	C₄	—	2	2	no	—
330	C₄	—	2	2	no	—
331	C₄	—	3	4	no	—
332	C₄	—	3	2	no	—
333	C₄	—	6	2	no	—
334	C₄	—	6	1	no	—
335	C₄	—	6	1	no	—
336	C₄	C₃×D₃×D₄	1	2	yes	—
337	C₃	—	2	1	no	—
338	C₃	#5632	1	1	yes	characteristic, direct product factor
339	C₃	C₃×D₄×Q₈	1	1	yes	characteristic, complemented
340	C₂	—	2	2	no	—
341	C₂	—	6	2	no	—
342	C₂	C₂×C₃×D₃×D₄	1	1	yes	characteristic
343	C₂	C₂×C₃×D₃×Q₈	1	1	yes	characteristic
344	C₂	C₃×#1010	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×D₃
Fitting	C₃²×C₂²⋊Q₈	C₂
socle	C₂²×C₃²	C₂⁴
prime radical	C₂×C₃×#67	C₂²
hypercenter	C₃×C₂²⋊Q₈	D₃
hypocenter	C₃	C₃×D₄×Q₈
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×D₃×Q₈	C₂	semidirect
2. C₂²×C₃×Dic₆	C₂	semidirect
3. C₃²×C₂²⋊Q₈	C₂	semidirect
4. C₃×#944	C₂	semidirect
6. C₃×#897	C₂	semidirect
7. C₃×#896	C₂	semidirect
8. C₃×#888	C₂	semidirect
9. C₃×#887	C₂	semidirect
11. C₃×#878	C₂	semidirect
13. #5632	C₃	direct (N × H)
41. C₂×D₃×Q₈	C₂×C₃	semidirect
42. C₂²×Dic₆	C₂×C₃	semidirect
49. C₃×C₂²⋊Q₈	D₃	semidirect
50. C₃×C₂²⋊Q₈	C₂×C₃	semidirect
54. #944	C₂×C₃	semidirect
56. #897	C₂×C₃	semidirect
57. #896	C₂×C₃	semidirect
58. #888	C₂×C₃	semidirect
59. #887	C₂×C₃	semidirect
61. #878	C₂×C₃	semidirect
70. C₃×#67	Q₈	semidirect
82. C₃×Dic₆	D₄	semidirect
141. C₂²×C₃²	C₂×Q₈	semidirect
145. C₂×C₃×D₃	C₂×Q₈	semidirect
154. C₃×Dic₃	C₂×Q₈	semidirect
162. C₂²⋊Q₈	C₃×D₃	semidirect
202. #67	C₃×Q₈	semidirect
214. Dic₆	C₃×D₄	semidirect
256. C₂²×C₃	D₃×Q₈	semidirect
257. C₂²×C₃	C₂×C₃×Q₈	semidirect
262. C₂×D₃	C₂×C₃×Q₈	semidirect
284. Dic₃	C₂×C₃×Q₈	semidirect
285. C₃²	D₄×Q₈	semidirect
326. C₂²	C₃×D₃×Q₈	semidirect
338. C₃	#5632	direct (N × H)
339. C₃	C₃×D₄×Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×D₃×Q₈	2
C₂²×C₃×Dic₆	2
C₃²×C₂²⋊Q₈	2
C₃×#944	2
C₃×C₄×#67	2
C₃×#897	2
C₃×#896	2
C₃×#888	2
C₃×#887	2
C₃×#67⋊C₄	2
C₃×#878	2
C₃×D₄×Q₈	3
#5632	3

Subgroups — C3×#5632 #10595729

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#5632 #10595729