Subgroups — C₃×D₄×C₃⋊(C₃⋊C₈) #13163048

Order 1728.

1180 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₃⋊(C₃⋊C₈)	C₂	1	2	yes	maximal, complemented
3	C₃×#63657	C₂	1	2	yes	maximal, complemented
4	C₃×C₄⋊(C₃⋊(C₃⋊C₈))	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₃⋊(C₃⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	D₄×C₃⋊(C₃⋊C₈)	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₃×D₄×C₃⋊C₈	—	3	4	no	maximal
8	C₂×C₃³×D₄	C₄	1	1	yes	characteristic
9	C₂²×C₃³×C₄	C₂²	1	2	yes	—
10	C₃³×C₄⋊C₄	C₄	1	1	yes	characteristic
11	C₃³×C₂²⋊C₄	C₄	1	2	yes	—
12	C₃³×C₄²	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₃⋊(C₃⋊C₈)	—	2	4	no	—
14	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	2	yes	—
15	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
17	C₃²×C₄×D₄	—	2	4	no	—
18	C₃²×C₄×D₄	D₃	1	4	yes	—
19	C₃²×C₄×D₄	C₂×C₃	1	1	yes	characteristic
20	C₂²×C₃⋊(C₃⋊C₈)	C₂×C₃	1	2	yes	complemented
21	C₂²×C₃×C₃⋊C₈	—	3	8	no	—
22	#63657	C₂×C₃	1	2	yes	complemented
23	C₄⋊(C₃⋊(C₃⋊C₈))	C₂×C₃	1	1	yes	characteristic, complemented
24	C₄×C₃⋊(C₃⋊C₈)	C₂×C₃	1	1	yes	characteristic, complemented
25	C₃×#830	—	3	8	no	—
26	C₃×C₄⋊(C₃⋊C₈)	—	3	4	no	—
27	C₃×C₄×C₃⋊C₈	—	3	4	no	—
28	C₂³×C₃³	C₂×C₄	1	2	yes	—
29	C₃³×D₄	C₈	1	4	yes	complemented
30	C₂×C₃³×C₄	—	2	2	no	—
31	C₂×C₃³×C₄	—	2	2	no	—
32	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
33	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
34	C₂×C₃³×C₄	C₂×C₄	1	1	yes	characteristic
35	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
36	C₃×C₃⋊(C₃⋊C₈)	—	2	2	no	—
37	C₃×C₃⋊(C₃⋊C₈)	—	2	1	no	—
38	C₃×C₃⋊(C₃⋊C₈)	D₄	1	2	yes	direct product factor
39	C₃×C₈×D₄	—	9	1	no	—
40	D₄×C₃⋊C₈	—	3	4	no	—
41	C₂×C₃²×D₄	—	2	4	no	—
42	C₂×C₃²×D₄	Dic₃	1	4	yes	—
43	C₂×C₃²×D₄	C₃×C₄	1	1	yes	characteristic
44	C₂²×C₃²×C₄	—	2	8	no	—
45	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
46	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
47	C₃²×C₄⋊C₄	—	2	4	no	—
48	C₃²×C₄⋊C₄	Dic₃	1	4	yes	—
49	C₃²×C₄⋊C₄	C₃×C₄	1	1	yes	characteristic
50	C₃²×C₂²⋊C₄	—	2	8	no	—
51	C₃²×C₂²⋊C₄	Dic₃	1	8	yes	—
52	C₃²×C₂²⋊C₄	C₃×C₄	1	2	yes	—
53	C₃²×C₄²	—	2	4	no	—
54	C₃²×C₄²	C₂×D₃	1	4	yes	—
55	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₃⋊(C₃⋊C₈)	—	2	4	no	—
57	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	2	yes	—
58	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
59	C₂×C₃⋊(C₃⋊C₈)	C₂²×C₃	1	1	yes	characteristic
60	C₂×C₃×C₃⋊C₈	—	3	4	no	—
61	C₂×C₃×C₃⋊C₈	—	3	8	no	—
62	C₂×C₃×C₃⋊C₈	—	3	4	no	—
63	C₂×C₃×C₃⋊C₈	—	6	16	no	—
64	C₂²×C₃³	—	2	2	no	—
65	C₂²×C₃³	—	2	2	no	—
66	C₂²×C₃³	C₂×C₈	1	4	yes	complemented
67	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
68	C₃³×C₄	—	2	2	no	—
69	C₃³×C₄	—	2	1	no	—
70	C₃³×C₄	C₂×C₈	1	2	yes	complemented
71	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
72	C₃³×C₄	#41	1	1	yes	characteristic
73	C₂²×C₃×C₈	—	9	2	no	—
74	C₃×C₄×D₄	—	2	4	no	—
75	C₃×C₄×D₄	C₃×D₃	1	4	yes	—
76	C₃×C₄×D₄	C₃⋊D₃	1	1	yes	characteristic
77	C₂²×C₃⋊C₈	—	3	8	no	—
78	C₃×C₄⋊C₈	—	9	1	no	—
79	C₃×C₂²⋊C₈	—	9	2	no	—
80	C₃×C₄×C₈	—	9	1	no	—
81	#830	—	3	8	no	—
82	C₄⋊(C₃⋊C₈)	—	3	4	no	—
83	C₄×C₃⋊C₈	—	3	4	no	—
84	C₂³×C₃²	—	2	8	no	—
85	C₂³×C₃²	C₂×Dic₃	1	8	yes	—
86	C₂³×C₃²	C₂×C₃×C₄	1	2	yes	—
87	C₃²×D₄	—	2	16	no	—
88	C₃²×D₄	C₃⋊C₈	1	16	yes	complemented
89	C₃²×D₄	C₃×C₈	1	4	yes	complemented
90	C₂×C₃²×C₄	—	2	2	no	—
91	C₂×C₃²×C₄	—	2	2	no	—
92	C₂×C₃²×C₄	—	2	4	no	—
93	C₂×C₃²×C₄	—	2	4	no	—
94	C₂×C₃²×C₄	—	2	8	no	—
95	C₂×C₃²×C₄	—	2	4	no	—
96	C₂×C₃²×C₄	—	2	8	no	—
97	C₂×C₃²×C₄	—	2	8	no	—
98	C₂×C₃²×C₄	—	4	8	no	—
99	C₂×C₃²×C₄	—	4	8	no	—
100	C₂×C₃²×C₄	C₂×Dic₃	1	4	yes	—
101	C₂×C₃²×C₄	C₂×Dic₃	1	8	yes	—
102	C₂×C₃²×C₄	C₂×Dic₃	1	4	yes	—
103	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
104	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
105	C₂×C₃²×C₄	C₂×C₃×C₄	1	1	yes	characteristic
106	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
107	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
108	C₃⋊(C₃⋊C₈)	—	2	2	no	—
109	C₃⋊(C₃⋊C₈)	—	2	1	no	—
110	C₃⋊(C₃⋊C₈)	C₃×D₄	1	2	yes	direct product factor
111	C₃×C₃⋊C₈	—	3	8	no	—
112	C₃×C₃⋊C₈	—	6	8	no	—
113	C₃×C₃⋊C₈	—	6	4	no	—
114	C₈×D₄	—	9	1	no	Sylow
115	C₂×C₃³	—	2	4	no	—
116	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
117	C₂×C₃³	C₂²×C₈	1	1	yes	characteristic
118	C₂×C₃³	#131	1	1	yes	characteristic
119	C₂×C₃×D₄	—	2	4	no	—
120	C₂×C₃×D₄	C₃×Dic₃	1	4	yes	—
121	C₂×C₃×D₄	C₃⋊Dic₃	1	1	yes	characteristic
122	C₂²×C₃×C₄	—	2	8	no	—
123	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
124	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
125	C₂×C₃×C₈	—	9	1	no	—
126	C₂×C₃×C₈	—	9	1	no	—
127	C₂×C₃×C₈	—	9	2	no	—
128	C₂×C₃×C₈	—	18	4	no	—
129	C₃×C₄⋊C₄	—	2	4	no	—
130	C₃×C₄⋊C₄	C₃×Dic₃	1	4	yes	—
131	C₃×C₄⋊C₄	C₃⋊Dic₃	1	1	yes	characteristic
132	C₃×C₂²⋊C₄	—	2	8	no	—
133	C₃×C₂²⋊C₄	C₃×Dic₃	1	8	yes	—
134	C₃×C₂²⋊C₄	C₃⋊Dic₃	1	2	yes	—
135	C₃×C₄²	—	2	4	no	—
136	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
137	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
138	C₂×C₃⋊C₈	—	3	4	no	—
139	C₂×C₃⋊C₈	—	3	4	no	—
140	C₂×C₃⋊C₈	—	3	8	no	—
141	C₂×C₃⋊C₈	—	6	16	no	—
142	C₂²×C₃²	—	2	2	no	—
143	C₂²×C₃²	—	2	2	no	—
144	C₂²×C₃²	—	2	16	no	—
145	C₂²×C₃²	—	2	4	no	—
146	C₂²×C₃²	—	2	8	no	—
147	C₂²×C₃²	—	2	8	no	—
148	C₂²×C₃²	—	4	8	no	—
149	C₂²×C₃²	—	4	8	no	—
150	C₂²×C₃²	C₂×C₃⋊C₈	1	16	yes	complemented
151	C₂²×C₃²	C₂×C₃×C₈	1	4	yes	complemented
152	C₂²×C₃²	C₂²×Dic₃	1	4	yes	—
153	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
154	C₃²×C₄	—	2	2	no	—
155	C₃²×C₄	—	2	1	no	—
156	C₃²×C₄	—	2	8	no	—
157	C₃²×C₄	—	2	4	no	—
158	C₃²×C₄	—	2	4	no	—
159	C₃²×C₄	—	2	8	no	—
160	C₃²×C₄	—	2	4	no	—
161	C₃²×C₄	—	4	4	no	—
162	C₃²×C₄	—	4	8	no	—
163	C₃²×C₄	C₂×C₃⋊C₈	1	8	yes	complemented
164	C₃²×C₄	C₂×C₃×C₈	1	2	yes	complemented
165	C₃²×C₄	D₃×D₄	1	4	yes	—
166	C₃²×C₄	#237	1	4	yes	—
167	C₃²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
168	C₃²×C₄	C₃×#41	1	1	yes	characteristic
169	C₂²×C₈	—	9	2	no	—
170	C₄×D₄	C₃×C₃⋊D₃	1	1	yes	characteristic
171	C₄⋊C₈	—	9	1	no	—
172	C₂²⋊C₈	—	9	2	no	—
173	C₄×C₈	—	9	1	no	—
174	C₃³	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
175	C₂³×C₃	—	2	8	no	—
176	C₂³×C₃	C₂×C₃×Dic₃	1	8	yes	—
177	C₂³×C₃	C₂×C₃⋊Dic₃	1	2	yes	—
178	C₃×D₄	—	2	16	no	—
179	C₃×D₄	C₃×C₃⋊C₈	1	16	yes	complemented
180	C₃×D₄	C₃⋊(C₃⋊C₈)	1	4	yes	direct product factor
181	C₂×C₃×C₄	—	2	8	no	—
182	C₂×C₃×C₄	—	2	8	no	—
183	C₂×C₃×C₄	—	2	2	no	—
184	C₂×C₃×C₄	—	2	2	no	—
185	C₂×C₃×C₄	—	2	4	no	—
186	C₂×C₃×C₄	—	2	4	no	—
187	C₂×C₃×C₄	—	2	8	no	—
188	C₂×C₃×C₄	—	2	4	no	—
189	C₂×C₃×C₄	—	4	8	no	—
190	C₂×C₃×C₄	—	4	8	no	—
191	C₂×C₃×C₄	C₂×C₃×Dic₃	1	4	yes	—
192	C₂×C₃×C₄	C₂×C₃×Dic₃	1	8	yes	—
193	C₂×C₃×C₄	C₂×C₃×Dic₃	1	4	yes	—
194	C₂×C₃×C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
195	C₂×C₃×C₄	C₂×C₃⋊Dic₃	1	2	yes	—
196	C₂×C₃×C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
197	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
198	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
199	C₃×C₈	—	9	2	no	—
200	C₃×C₈	—	18	2	no	—
201	C₃×C₈	—	18	1	no	—
202	C₃⋊C₈	—	3	8	no	—
203	C₃⋊C₈	—	6	8	no	—
204	C₃⋊C₈	—	6	4	no	—
205	C₂×C₃²	—	2	4	no	—
206	C₂×C₃²	—	2	4	no	—
207	C₂×C₃²	—	2	4	no	—
208	C₂×C₃²	—	2	4	no	—
209	C₂×C₃²	—	2	16	no	—
210	C₂×C₃²	—	4	16	no	—
211	C₂×C₃²	C₂²×C₃⋊C₈	1	4	yes	—
212	C₂×C₃²	D₄×Dic₃	1	4	yes	—
213	C₂×C₃²	#948	1	4	yes	—
214	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
215	C₂×C₃²	C₂²×C₃×C₈	1	1	yes	characteristic
216	C₂×C₃²	C₃×#131	1	1	yes	characteristic
217	C₂×D₄	C₃×C₃⋊Dic₃	1	1	yes	characteristic
218	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
219	C₂×C₈	—	9	1	no	—
220	C₂×C₈	—	9	1	no	—
221	C₂×C₈	—	9	2	no	—
222	C₂×C₈	—	18	4	no	—
223	C₄⋊C₄	C₃×C₃⋊Dic₃	1	1	yes	characteristic
224	C₂²⋊C₄	C₃×C₃⋊Dic₃	1	2	yes	—
225	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
226	C₂²×C₃	—	2	8	no	—
227	C₂²×C₃	—	2	8	no	—
228	C₂²×C₃	—	2	2	no	—
229	C₂²×C₃	—	2	2	no	—
230	C₂²×C₃	—	2	16	no	—
231	C₂²×C₃	—	2	4	no	—
232	C₂²×C₃	—	4	8	no	—
233	C₂²×C₃	—	4	8	no	—
234	C₂²×C₃	C₂×C₃×C₃⋊C₈	1	16	yes	complemented
235	C₂²×C₃	C₂×C₃⋊(C₃⋊C₈)	1	4	yes	complemented
236	C₂²×C₃	C₂²×C₃×Dic₃	1	4	yes	—
237	C₂²×C₃	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
238	C₃×C₄	—	2	8	no	—
239	C₃×C₄	—	2	4	no	—
240	C₃×C₄	—	2	2	no	—
241	C₃×C₄	—	2	1	no	—
242	C₃×C₄	—	2	8	no	—
243	C₃×C₄	—	2	4	no	—
244	C₃×C₄	—	2	4	no	—
245	C₃×C₄	—	4	8	no	—
246	C₃×C₄	—	4	4	no	—
247	C₃×C₄	C₂×C₃×C₃⋊C₈	1	8	yes	complemented
248	C₃×C₄	C₂×C₃⋊(C₃⋊C₈)	1	2	yes	complemented
249	C₃×C₄	C₃×D₃×D₄	1	4	yes	—
250	C₃×C₄	C₃×#237	1	4	yes	—
251	C₃×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
252	C₃×C₄	#3830	1	1	yes	characteristic
253	C₃²	—	2	4	no	—
254	C₃²	D₄×C₃⋊C₈	1	4	yes	complemented
255	C₃²	C₃×C₈×D₄	1	1	yes	characteristic, complemented
256	C₂³	C₂×C₃×C₃⋊Dic₃	1	2	yes	—
257	D₄	C₃×C₃⋊(C₃⋊C₈)	1	4	yes	direct product factor
258	C₂×C₄	—	2	2	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	C₂×C₃×C₃⋊Dic₃	1	1	yes	characteristic
261	C₂×C₄	C₂×C₃×C₃⋊Dic₃	1	2	yes	—
262	C₂×C₄	C₂×C₃×C₃⋊Dic₃	1	1	yes	characteristic
263	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
264	C₈	—	9	2	no	—
265	C₈	—	18	2	no	—
266	C₈	—	18	1	no	—
267	C₂×C₃	—	2	16	no	—
268	C₂×C₃	—	2	4	no	—
269	C₂×C₃	—	2	4	no	—
270	C₂×C₃	—	2	4	no	—
271	C₂×C₃	—	2	4	no	—
272	C₂×C₃	—	4	16	no	—
273	C₂×C₃	C₂²×C₃×C₃⋊C₈	1	4	yes	—
274	C₂×C₃	C₃×D₄×Dic₃	1	4	yes	—
275	C₂×C₃	C₃×#948	1	4	yes	—
276	C₂×C₃	C₂²×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
277	C₂×C₃	D₄×C₃⋊Dic₃	1	1	yes	characteristic
278	C₂×C₃	#64157	1	1	yes	characteristic
279	C₂²	—	2	2	no	—
280	C₂²	—	2	2	no	—
281	C₂²	C₂×C₃×C₃⋊(C₃⋊C₈)	1	4	yes	complemented
282	C₂²	C₂²×C₃×C₃⋊Dic₃	1	1	yes	characteristic
283	C₄	—	2	2	no	—
284	C₄	—	2	1	no	—
285	C₄	C₂×C₃×C₃⋊(C₃⋊C₈)	1	2	yes	complemented
286	C₄	C₃×D₄×C₃⋊D₃	1	1	yes	characteristic
287	C₄	C₃×#3830	1	1	yes	characteristic
288	C₃	—	2	4	no	—
289	C₃	C₃×D₄×C₃⋊C₈	1	4	yes	complemented
290	C₃	D₄×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic, direct product factor
291	C₂	—	2	4	no	—
292	C₂	C₂²×C₃×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
293	C₂	C₃×D₄×C₃⋊Dic₃	1	1	yes	characteristic
294	C₂	C₃×#64157	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×C₃⋊D₃
commutator	C₂×C₃²	C₂²×C₃×C₈
Frattini	C₂×C₄	C₂²×C₃×C₃⋊D₃
Fitting	C₃³×C₄×D₄	C₂
socle	C₂²×C₃³	C₂²×C₄
prime radical	C₂×C₃³×D₄	C₄
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₃×C₄×D₄	C₃⋊D₃
hypocenter	C₃²	C₃×C₈×D₄
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₃⋊(C₃⋊C₈)	C₂	semidirect
3. C₃×#63657	C₂	semidirect
4. C₃×C₄⋊(C₃⋊(C₃⋊C₈))	C₂	semidirect
5. C₃×C₄×C₃⋊(C₃⋊C₈)	C₂	semidirect
6. D₄×C₃⋊(C₃⋊C₈)	C₃	direct (N × H)
20. C₂²×C₃⋊(C₃⋊C₈)	C₂×C₃	semidirect
22. #63657	C₂×C₃	semidirect
23. C₄⋊(C₃⋊(C₃⋊C₈))	C₂×C₃	semidirect
24. C₄×C₃⋊(C₃⋊C₈)	C₂×C₃	semidirect
29. C₃³×D₄	C₈	semidirect
38. C₃×C₃⋊(C₃⋊C₈)	D₄	direct (N × H)
66. C₂²×C₃³	C₂×C₈	semidirect
70. C₃³×C₄	C₂×C₈	semidirect
88. C₃²×D₄	C₃⋊C₈	semidirect
89. C₃²×D₄	C₃×C₈	semidirect
110. C₃⋊(C₃⋊C₈)	C₃×D₄	direct (N × H)
150. C₂²×C₃²	C₂×C₃⋊C₈	semidirect
151. C₂²×C₃²	C₂×C₃×C₈	semidirect
163. C₃²×C₄	C₂×C₃⋊C₈	semidirect
164. C₃²×C₄	C₂×C₃×C₈	semidirect
174. C₃³	C₈×D₄	semidirect
179. C₃×D₄	C₃×C₃⋊C₈	semidirect
180. C₃×D₄	C₃⋊(C₃⋊C₈)	direct (N × H)
234. C₂²×C₃	C₂×C₃×C₃⋊C₈	semidirect
235. C₂²×C₃	C₂×C₃⋊(C₃⋊C₈)	semidirect
247. C₃×C₄	C₂×C₃×C₃⋊C₈	semidirect
248. C₃×C₄	C₂×C₃⋊(C₃⋊C₈)	semidirect
254. C₃²	D₄×C₃⋊C₈	semidirect
255. C₃²	C₃×C₈×D₄	semidirect
257. D₄	C₃×C₃⋊(C₃⋊C₈)	direct (N × H)
281. C₂²	C₂×C₃×C₃⋊(C₃⋊C₈)	semidirect
285. C₄	C₂×C₃×C₃⋊(C₃⋊C₈)	semidirect
289. C₃	C₃×D₄×C₃⋊C₈	semidirect
290. C₃	D₄×C₃⋊(C₃⋊C₈)	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃³×C₄×D₄	2
C₂²×C₃×C₃⋊(C₃⋊C₈)	2
C₃×#63657	2
C₃×C₄⋊(C₃⋊(C₃⋊C₈))	2
C₃×C₄×C₃⋊(C₃⋊C₈)	2
D₄×C₃⋊(C₃⋊C₈)	3
C₃×D₄×C₃⋊C₈	3

Subgroups — C3×D4×C3⋊(C3⋊C8) #13163048

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₄×C₃⋊(C₃⋊C₈) #13163048