Subgroups — #13159512

Order 1728.

1132 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₄×#6289	C₂	1	1	yes	maximal, characteristic
3	C₂×#88785	C₂	1	1	yes	maximal, characteristic
4	C₃×#63641	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃²×Dic₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11722051	C₂	1	1	yes	maximal, characteristic, complemented
7	Dic₃⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃⋊D₃×C₄⋊C₈	—	3	1	no	maximal
9	#10590658	—	3	4	no	maximal
10	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
11	C₂×#6289	C₄	1	1	yes	characteristic
12	C₂×#6289	C₄	1	1	yes	characteristic
13	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
14	C₂×C₃⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic
15	C₈×C₃⋊(C₃⋊D₃)	—	2	2	no	—
16	C₃×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
18	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
19	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	Dic₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic
21	Dic₃×C₃⋊Dic₃	C₄	1	1	yes	characteristic
22	#88785	—	2	2	no	—
23	C₂×C₈×C₃⋊D₃	—	3	1	no	—
24	C₂×C₈×C₃⋊D₃	—	3	1	no	—
25	C₂×C₈×C₃⋊D₃	—	3	4	no	—
26	C₂×C₈×C₃⋊D₃	—	6	4	no	—
27	C₄²×C₃⋊D₃	—	3	1	no	—
28	C₄×#624	—	3	4	no	—
29	C₂×#3710	—	3	4	no	—
30	C₃²×C₄⋊C₈	—	3	1	no	—
31	#63641	—	3	1	no	—
32	#63641	D₃	1	1	yes	characteristic, complemented
33	C₄⋊(C₃⋊(C₃⋊C₈))	—	3	1	no	—
34	C₃×Dic₃⋊C₈	—	3	4	no	—
35	C₃×Dic₃⋊C₈	D₃	1	4	yes	complemented
36	Dic₃⋊(C₃⋊C₈)	—	3	4	no	—
37	Dic₃⋊(C₃⋊C₈)	—	3	4	no	—
38	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
40	C₂×C₃⋊(C₃⋊Dic₃)	C₂×C₄	1	1	yes	characteristic
41	C₄×C₃⋊(C₃⋊D₃)	D₄	1	2	yes	—
42	C₄×C₃⋊(C₃⋊D₃)	Q₈	1	2	yes	—
43	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₃×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃²×Dic₃	C₂×C₄	1	1	yes	characteristic
47	#6289	—	2	2	no	—
48	#6289	C₈	1	4	yes	complemented
49	C₃³×C₈	—	2	1	no	—
50	C₃⋊(C₃⋊(C₃⋊C₈))	—	2	1	no	—
51	C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
52	C₃²×C₃⋊C₈	—	2	1	no	—
53	D₃×C₄⋊C₈	—	9	4	no	—
54	D₃×C₄⋊C₈	—	9	1	no	—
55	C₂×C₄×C₃⋊D₃	—	3	1	no	—
56	C₂×C₄×C₃⋊D₃	—	3	4	no	—
57	C₂×C₄×C₃⋊D₃	—	3	1	no	—
58	C₂×C₄×C₃⋊D₃	—	3	1	no	—
59	C₂×C₄×C₃⋊D₃	—	6	4	no	—
60	C₂×#624	—	3	4	no	—
61	C₂×#624	—	3	4	no	—
62	C₂×C₃²×C₈	—	2	4	no	—
63	C₂×C₃²×C₈	—	3	1	no	—
64	C₂×C₃²×C₈	C₂×D₃	1	4	yes	—
65	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
66	C₃²×C₄²	—	3	1	no	—
67	C₄×C₃⋊Dic₃	—	3	1	no	—
68	C₄×C₃⋊Dic₃	—	3	1	no	—
69	C₄×C₃⋊Dic₃	C₂×D₃	1	1	yes	characteristic
70	C₂×C₃⋊(C₃⋊C₈)	—	3	1	no	—
71	C₂×C₃⋊(C₃⋊C₈)	—	3	4	no	—
72	C₂×C₃⋊(C₃⋊C₈)	—	6	4	no	—
73	C₂×C₃⋊(C₃⋊C₈)	C₂×D₃	1	1	yes	characteristic
74	C₈×C₃⋊D₃	—	6	2	no	—
75	C₈×C₃⋊D₃	—	6	2	no	—
76	C₈×C₃⋊D₃	—	6	8	no	—
77	C₈×C₃⋊D₃	—	6	16	no	—
78	C₃×C₄×Dic₃	—	3	4	no	—
79	C₃×C₄×Dic₃	C₂×D₃	1	4	yes	—
80	C₂×C₃×C₃⋊C₈	—	3	4	no	—
81	C₂×C₃×C₃⋊C₈	C₂×D₃	1	4	yes	—
82	Dic₃²	—	3	4	no	—
83	Dic₃²	—	3	4	no	—
84	#3710	—	6	8	no	—
85	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃⋊(C₃⋊D₃)	C₄⋊C₄	1	2	yes	—
87	C₂×C₃⋊(C₃⋊D₃)	C₂×C₈	1	2	yes	—
88	C₂×C₃⋊(C₃⋊D₃)	M₁₆	1	2	yes	—
89	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
90	C₃³×C₄	C₂×Q₈	1	1	yes	characteristic
91	C₃⋊(C₃⋊Dic₃)	C₄⋊C₄	1	2	yes	—
92	C₃×C₃⋊Dic₃	—	2	1	no	—
93	C₃×C₃⋊Dic₃	C₂×C₈	1	2	yes	complemented
94	C₃²×Dic₃	—	2	1	no	—
95	C₃²×Dic₃	C₂×C₈	1	2	yes	complemented
96	C₂×D₃×C₈	—	9	4	no	—
97	C₂×D₃×C₈	—	9	4	no	—
98	C₂×D₃×C₈	—	9	1	no	—
99	C₂×D₃×C₈	—	9	1	no	—
100	C₂×D₃×C₈	—	18	4	no	—
101	C₄²×D₃	—	9	4	no	—
102	C₄²×D₃	—	9	1	no	—
103	C₃×C₄⋊C₈	—	3	4	no	—
104	C₃×C₄⋊C₈	—	9	1	no	—
105	Dic₃⋊C₈	—	3	4	no	—
106	Dic₃⋊C₈	—	9	4	no	—
107	Dic₃⋊C₈	—	9	1	no	—
108	Dic₃⋊C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
109	C₄⋊(C₃⋊C₈)	—	9	4	no	—
110	C₄⋊(C₃⋊C₈)	—	9	1	no	—
111	C₂²×C₃⋊D₃	—	3	1	no	—
112	C₂²×C₃⋊D₃	—	3	4	no	—
113	C₂²×C₃⋊D₃	—	6	4	no	—
114	C₂×C₃²×C₄	—	2	4	no	—
115	C₂×C₃²×C₄	—	3	1	no	—
116	C₂×C₃²×C₄	—	3	1	no	—
117	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
118	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
119	C₂×C₃⋊Dic₃	—	3	1	no	—
120	C₂×C₃⋊Dic₃	—	3	4	no	—
121	C₂×C₃⋊Dic₃	—	6	4	no	—
122	C₂×C₃⋊Dic₃	C₄×D₃	1	1	yes	characteristic
123	C₂×C₃⋊Dic₃	C₄×D₃	1	1	yes	characteristic
124	C₄×C₃⋊D₃	—	3	2	no	—
125	C₄×C₃⋊D₃	—	3	2	no	—
126	C₄×C₃⋊D₃	—	3	4	no	—
127	C₄×C₃⋊D₃	—	3	8	no	—
128	C₄×C₃⋊D₃	—	3	8	no	—
129	C₄×C₃⋊D₃	—	6	8	no	—
130	C₄×C₃⋊D₃	—	6	8	no	—
131	C₄×C₃⋊D₃	—	6	2	no	—
132	C₂×C₃×Dic₃	—	3	4	no	—
133	C₂×C₃×Dic₃	—	3	4	no	—
134	C₂×C₃×Dic₃	C₄×D₃	1	4	yes	—
135	C₂×C₃×Dic₃	C₄×D₃	1	4	yes	—
136	#624	—	3	16	no	—
137	#624	—	6	8	no	—
138	C₃²×C₈	—	2	8	no	—
139	C₃²×C₈	—	2	4	no	—
140	C₃²×C₈	—	2	1	no	—
141	C₃²×C₈	—	6	1	no	—
142	C₃⋊(C₃⋊C₈)	—	2	1	no	—
143	C₃⋊(C₃⋊C₈)	—	6	8	no	—
144	C₃⋊(C₃⋊C₈)	—	6	4	no	—
145	C₃⋊(C₃⋊C₈)	—	6	1	no	—
146	C₃×C₃⋊C₈	—	2	4	no	—
147	C₃×C₃⋊C₈	—	6	4	no	—
148	C₂×C₄⋊C₈	—	27	1	no	Sylow
149	C₂×C₃³	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₃³	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₃³	C₂×M₁₆	1	1	yes	characteristic
152	C₃⋊(C₃⋊D₃)	C₄⋊C₈	1	4	yes	complemented
153	C₂×C₄×D₃	—	9	4	no	—
154	C₂×C₄×D₃	—	9	4	no	—
155	C₂×C₄×D₃	—	9	1	no	—
156	C₂×C₄×D₃	—	9	1	no	—
157	C₂×C₄×D₃	—	9	4	no	—
158	C₂×C₄×D₃	—	9	1	no	—
159	C₂×C₄×D₃	—	18	4	no	—
160	C₂×C₃×C₈	—	2	4	no	—
161	C₂×C₃×C₈	—	3	4	no	—
162	C₂×C₃×C₈	—	9	1	no	—
163	C₂×C₃×C₈	D₃²	1	4	yes	—
164	C₂×C₃×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
165	C₃×C₄²	—	3	4	no	—
166	C₃×C₄²	—	9	1	no	—
167	C₄×Dic₃	—	3	4	no	—
168	C₄×Dic₃	—	9	4	no	—
169	C₄×Dic₃	—	9	4	no	—
170	C₄×Dic₃	—	9	1	no	—
171	C₄×Dic₃	—	9	1	no	—
172	C₄×Dic₃	C₂×C₃⋊D₃	1	1	yes	characteristic
173	C₂×C₃⋊C₈	—	3	4	no	—
174	C₂×C₃⋊C₈	—	9	4	no	—
175	C₂×C₃⋊C₈	—	9	1	no	—
176	C₂×C₃⋊C₈	—	18	4	no	—
177	C₂×C₃⋊C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
178	D₃×C₈	—	18	2	no	—
179	D₃×C₈	—	18	8	no	—
180	D₃×C₈	—	18	8	no	—
181	D₃×C₈	—	18	2	no	—
182	D₃×C₈	—	18	16	no	—
183	C₂²×C₃²	—	2	4	no	—
184	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
185	C₂²×C₃²	C₂×C₄×D₃	1	1	yes	characteristic
186	C₂×C₃⋊D₃	—	3	2	no	—
187	C₂×C₃⋊D₃	—	3	2	no	—
188	C₂×C₃⋊D₃	—	3	2	no	—
189	C₂×C₃⋊D₃	—	3	8	no	—
190	C₂×C₃⋊D₃	—	3	8	no	—
191	C₂×C₃⋊D₃	—	3	8	no	—
192	C₂×C₃⋊D₃	—	6	8	no	—
193	C₂×C₃⋊D₃	—	6	8	no	—
194	C₂×C₃⋊D₃	—	6	8	no	—
195	C₃²×C₄	—	2	4	no	—
196	C₃²×C₄	—	2	4	no	—
197	C₃²×C₄	—	3	2	no	—
198	C₃²×C₄	—	6	1	no	—
199	C₃²×C₄	D₃×D₄	1	4	yes	—
200	C₃²×C₄	D₃×D₄	1	1	yes	characteristic
201	C₃²×C₄	D₃×Q₈	1	4	yes	—
202	C₃²×C₄	D₃×Q₈	1	1	yes	characteristic
203	C₃⋊Dic₃	—	2	1	no	—
204	C₃⋊Dic₃	—	3	2	no	—
205	C₃⋊Dic₃	—	3	8	no	—
206	C₃⋊Dic₃	—	6	8	no	—
207	C₃⋊Dic₃	D₃×C₈	1	2	yes	complemented
208	C₃×Dic₃	—	2	4	no	—
209	C₃×Dic₃	—	3	8	no	—
210	C₃×Dic₃	—	6	4	no	—
211	C₃×Dic₃	D₃×C₈	1	8	yes	complemented
212	C₂²×C₈	—	27	1	no	—
213	C₂²×C₈	—	27	1	no	—
214	C₂×C₄²	—	27	1	no	—
215	C₄⋊C₈	—	3	1	no	—
216	C₄⋊C₈	—	9	1	no	—
217	C₄⋊C₈	—	27	1	no	—
218	C₄⋊C₈	—	27	1	no	—
219	C₃³	C₂×C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
220	C₂²×D₃	—	9	4	no	—
221	C₂²×D₃	—	9	1	no	—
222	C₂²×D₃	—	18	4	no	—
223	C₂×C₃×C₄	—	2	4	no	—
224	C₂×C₃×C₄	—	3	4	no	—
225	C₂×C₃×C₄	—	3	4	no	—
226	C₂×C₃×C₄	—	9	1	no	—
227	C₂×C₃×C₄	—	9	1	no	—
228	C₂×C₃×C₄	C₂×D₃²	1	4	yes	—
229	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
230	C₂×Dic₃	—	3	4	no	—
231	C₂×Dic₃	—	3	4	no	—
232	C₂×Dic₃	—	9	4	no	—
233	C₂×Dic₃	—	9	1	no	—
234	C₂×Dic₃	—	18	4	no	—
235	C₂×Dic₃	C₄×C₃⋊D₃	1	1	yes	characteristic
236	C₂×Dic₃	C₄×C₃⋊D₃	1	1	yes	characteristic
237	C₄×D₃	—	9	16	no	—
238	C₄×D₃	—	9	8	no	—
239	C₄×D₃	—	9	8	no	—
240	C₄×D₃	—	9	2	no	—
241	C₄×D₃	—	9	2	no	—
242	C₄×D₃	—	9	4	no	—
243	C₄×D₃	—	18	8	no	—
244	C₄×D₃	—	18	8	no	—
245	C₄×D₃	—	18	2	no	—
246	C₄×D₃	—	18	8	no	—
247	C₃×C₈	—	2	8	no	—
248	C₃×C₈	—	2	4	no	—
249	C₃×C₈	—	2	1	no	—
250	C₃×C₈	—	6	4	no	—
251	C₃×C₈	—	18	1	no	—
252	C₃⋊C₈	—	2	1	no	—
253	C₃⋊C₈	—	6	4	no	—
254	C₃⋊C₈	—	18	8	no	—
255	C₃⋊C₈	—	18	4	no	—
256	C₃⋊C₈	—	18	1	no	—
257	C₂×C₃²	—	2	4	no	—
258	C₂×C₃²	—	2	4	no	—
259	C₂×C₃²	—	2	4	no	—
260	C₂×C₃²	D₃×C₄⋊C₄	1	4	yes	—
261	C₂×C₃²	D₃×C₄⋊C₄	1	1	yes	characteristic
262	C₂×C₃²	C₂×D₃×C₈	1	4	yes	—
263	C₂×C₃²	C₂×D₃×C₈	1	1	yes	characteristic
264	C₂×C₃²	D₃×M₁₆	1	4	yes	—
265	C₂×C₃²	D₃×M₁₆	1	1	yes	characteristic
266	C₃⋊D₃	—	3	4	no	—
267	C₃⋊D₃	—	3	16	no	—
268	C₃⋊D₃	—	6	16	no	—
269	C₂²×C₄	—	27	1	no	—
270	C₂²×C₄	—	27	1	no	—
271	C₂²×C₄	—	27	1	no	—
272	C₂×C₈	—	3	1	no	—
273	C₂×C₈	—	9	1	no	—
274	C₂×C₈	—	27	1	no	—
275	C₂×C₈	—	54	2	no	—
276	C₂×C₈	—	54	2	no	—
277	C₂×C₈	D₃×C₃⋊D₃	1	1	yes	characteristic
278	C₄²	—	3	1	no	—
279	C₄²	—	9	1	no	—
280	C₄²	—	27	1	no	—
281	C₄²	—	27	1	no	—
282	C₂²×C₃	—	2	4	no	—
283	C₂²×C₃	C₄×D₃²	1	4	yes	—
284	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
285	C₂×D₃	—	9	8	no	—
286	C₂×D₃	—	9	8	no	—
287	C₂×D₃	—	9	2	no	—
288	C₂×D₃	—	9	2	no	—
289	C₂×D₃	—	9	2	no	—
290	C₂×D₃	—	9	8	no	—
291	C₂×D₃	—	18	8	no	—
292	C₂×D₃	—	18	8	no	—
293	C₂×D₃	—	18	8	no	—
294	C₃×C₄	—	2	4	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	3	8	no	—
297	C₃×C₄	—	6	4	no	—
298	C₃×C₄	—	9	2	no	—
299	C₃×C₄	—	18	1	no	—
300	C₃×C₄	#3797	1	4	yes	—
301	C₃×C₄	#3811	1	4	yes	—
302	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
303	C₃×C₄	Q₈×C₃⋊D₃	1	1	yes	characteristic
304	Dic₃	—	2	1	no	—
305	Dic₃	—	3	8	no	—
306	Dic₃	—	6	4	no	—
307	Dic₃	—	9	2	no	—
308	Dic₃	—	9	8	no	—
309	Dic₃	—	18	8	no	—
310	Dic₃	C₈×C₃⋊D₃	1	2	yes	complemented
311	C₃²	—	2	4	no	—
312	C₃²	D₃×C₄⋊C₈	1	4	yes	complemented
313	C₃²	D₃×C₄⋊C₈	1	1	yes	characteristic, complemented
314	C₂³	—	27	1	no	—
315	C₂×C₄	—	3	1	no	—
316	C₂×C₄	—	3	1	no	—
317	C₂×C₄	—	9	1	no	—
318	C₂×C₄	—	9	1	no	—
319	C₂×C₄	—	27	4	no	—
320	C₂×C₄	—	27	1	no	—
321	C₂×C₄	—	27	2	no	—
322	C₂×C₄	—	27	2	no	—
323	C₂×C₄	—	54	2	no	—
324	C₂×C₄	C₂×D₃×C₃⋊D₃	1	1	yes	characteristic
325	C₈	—	2	1	no	—
326	C₈	—	6	1	no	—
327	C₈	—	18	1	no	—
328	C₈	—	54	1	no	—
329	C₂×C₃	—	2	4	no	—
330	C₂×C₃	—	2	4	no	—
331	C₂×C₃	—	2	4	no	—
332	C₂×C₃	D₃²×C₈	1	4	yes	—
333	C₂×C₃	#63791	1	4	yes	—
334	C₂×C₃	#63883	1	4	yes	—
335	C₂×C₃	C₄⋊C₄×C₃⋊D₃	1	1	yes	characteristic
336	C₂×C₃	C₂×C₈×C₃⋊D₃	1	1	yes	characteristic
337	C₂×C₃	M₁₆×C₃⋊D₃	1	1	yes	characteristic
338	D₃	—	9	4	no	—
339	D₃	—	9	16	no	—
340	D₃	—	18	16	no	—
341	C₂²	—	27	2	no	—
342	C₂²	—	27	2	no	—
343	C₂²	—	27	2	no	—
344	C₂²	C₄×D₃×C₃⋊D₃	1	1	yes	characteristic
345	C₄	—	3	2	no	—
346	C₄	—	6	1	no	—
347	C₄	—	9	2	no	—
348	C₄	—	18	1	no	—
349	C₄	—	27	2	no	—
350	C₄	#89019	1	1	yes	characteristic
351	C₄	#89039	1	1	yes	characteristic
352	C₃	—	2	4	no	—
353	C₃	#10590658	1	4	yes	complemented
354	C₃	C₃⋊D₃×C₄⋊C₈	1	1	yes	characteristic, complemented
355	C₂	—	27	4	no	—
356	C₂	D₃×C₈×C₃⋊D₃	1	1	yes	characteristic
357	C₂	#11723312	1	1	yes	characteristic
358	C₂	#11723470	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×D₃×C₃⋊D₃
commutator	C₂×C₃³	C₂²×C₈
Fitting	C₂×C₃³×C₈	C₂²
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂²×C₃⋊(C₃⋊D₃)	C₂×C₄
cosocle	C₂×C₃³×C₄	C₂³
hypercenter	C₂×C₈	D₃×C₃⋊D₃
hypocenter	C₃³	C₂×C₄⋊C₈
LCS	G ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
4. C₃×#63641	C₂	semidirect
5. C₃²×Dic₃⋊C₈	C₂	semidirect
6. #11722051	C₂	semidirect
7. Dic₃⋊(C₃⋊(C₃⋊C₈))	C₂	semidirect
32. #63641	D₃	semidirect
35. C₃×Dic₃⋊C₈	D₃	semidirect
48. #6289	C₈	semidirect
93. C₃×C₃⋊Dic₃	C₂×C₈	semidirect
95. C₃²×Dic₃	C₂×C₈	semidirect
108. Dic₃⋊C₈	C₃⋊D₃	semidirect
152. C₃⋊(C₃⋊D₃)	C₄⋊C₈	semidirect
207. C₃⋊Dic₃	D₃×C₈	semidirect
211. C₃×Dic₃	D₃×C₈	semidirect
219. C₃³	C₂×C₄⋊C₈	semidirect
310. Dic₃	C₈×C₃⋊D₃	semidirect
312. C₃²	D₃×C₄⋊C₈	semidirect
313. C₃²	D₃×C₄⋊C₈	semidirect
353. C₃	#10590658	semidirect
354. C₃	C₃⋊D₃×C₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₃⋊(C₃⋊D₃)	2
C₄×#6289	2
C₂×#88785	2
C₃×#63641	2
C₃²×Dic₃⋊C₈	2
#11722051	2
Dic₃⋊(C₃⋊(C₃⋊C₈))	2
C₃⋊D₃×C₄⋊C₈	3
#10590658	3