Subgroups — C₄²×D₃×C₃⋊D₃ #13175387

Order 1728.

3420 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₃×C₃⋊D₃	C₂	1	3	yes	maximal
2	C₄²×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₄²×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₄²×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#6289	C₂	1	3	yes	maximal, complemented
6	C₄×Dic₃×C₃⋊D₃	C₂	1	3	yes	maximal, complemented
7	C₄×D₃×C₃⋊Dic₃	C₂	1	3	yes	maximal, complemented
8	C₂×C₄²×C₃⋊D₃	—	3	1	no	maximal
9	C₄²×D₃²	—	3	4	no	maximal
10	C₂²×D₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	3	yes	—
12	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	3	yes	—
13	C₂×C₃²×C₄×D₃	C₂²	1	3	yes	—
14	C₂×#6289	C₂²	1	3	yes	—
15	C₂×Dic₃×C₃⋊D₃	C₂²	1	3	yes	—
16	C₂×D₃×C₃⋊Dic₃	C₂²	1	3	yes	—
17	C₄×D₃×C₃⋊D₃	C₄	1	24	yes	direct product factor
18	C₃³×C₄²	C₂²	1	1	yes	characteristic, complemented
19	C₄×C₃⋊(C₃⋊Dic₃)	C₂²	1	3	yes	complemented
20	C₃×C₄×C₃⋊Dic₃	C₂²	1	3	yes	complemented
21	C₃²×C₄×Dic₃	C₂²	1	3	yes	complemented
22	Dic₃×C₃⋊Dic₃	C₂²	1	6	yes	complemented
23	C₂²×C₄×C₃⋊D₃	—	3	3	no	—
24	C₂×C₄×D₃²	—	3	12	no	—
25	C₂×C₃²×C₄²	—	3	1	no	—
26	C₂×C₄×C₃⋊Dic₃	—	3	3	no	—
27	C₄²×C₃⋊D₃	—	3	3	no	—
28	C₄²×C₃⋊D₃	—	3	1	no	—
29	C₄²×C₃⋊D₃	—	3	3	no	—
30	C₄²×C₃⋊D₃	—	3	4	no	—
31	C₄²×C₃⋊D₃	—	6	4	no	—
32	C₄²×C₃⋊D₃	D₃	1	1	yes	characteristic, direct product factor
33	C₃×C₄²×D₃	—	3	4	no	—
34	C₃×C₄²×D₃	D₃	1	4	yes	complemented
35	C₄×#624	—	3	12	no	—
36	C₄×D₃×Dic₃	—	3	12	no	—
37	C₄×D₃×Dic₃	—	3	12	no	—
38	C₂²×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
39	C₂²×C₃×C₃⋊D₃	C₂³	1	1	yes	characteristic
40	C₂²×C₃²×D₃	C₂³	1	1	yes	characteristic
41	C₂×D₃×C₃⋊D₃	C₂×C₄	1	12	yes	—
42	C₂×C₃³×C₄	C₂³	1	3	yes	—
43	C₂×C₃⋊(C₃⋊Dic₃)	C₂³	1	3	yes	—
44	C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	1	12	yes	complemented
45	C₂×C₃×C₃⋊Dic₃	C₂³	1	3	yes	—
46	C₃×C₄×C₃⋊D₃	C₂×C₄	1	12	yes	complemented
47	C₂×C₃²×Dic₃	C₂³	1	3	yes	—
48	C₃²×C₄×D₃	C₂×C₄	1	12	yes	complemented
49	#6289	C₂×C₄	1	12	yes	complemented
50	Dic₃×C₃⋊D₃	C₂×C₄	1	12	yes	complemented
51	D₃×C₃⋊Dic₃	C₂×C₄	1	12	yes	complemented
52	C₂×C₄²×D₃	—	9	4	no	—
53	C₂×C₄²×D₃	—	9	1	no	—
54	C₂³×C₃⋊D₃	—	3	1	no	—
55	C₂²×D₃²	—	3	4	no	—
56	C₂²×C₃²×C₄	—	3	3	no	—
57	C₂²×C₃⋊Dic₃	—	3	3	no	—
58	C₂×C₄×C₃⋊D₃	—	3	3	no	—
59	C₂×C₄×C₃⋊D₃	—	3	3	no	—
60	C₂×C₄×C₃⋊D₃	—	3	12	no	—
61	C₂×C₄×C₃⋊D₃	—	3	3	no	—
62	C₂×C₄×C₃⋊D₃	—	3	24	no	—
63	C₂×C₄×C₃⋊D₃	—	6	12	no	—
64	C₂×C₄×C₃⋊D₃	C₂×D₃	1	3	yes	—
65	C₂×C₃×C₄×D₃	—	3	12	no	—
66	C₂×C₃×C₄×D₃	C₂×D₃	1	12	yes	—
67	C₂×#624	—	3	12	no	—
68	C₂×D₃×Dic₃	—	3	12	no	—
69	C₂×D₃×Dic₃	—	3	12	no	—
70	C₄×D₃²	—	3	96	no	—
71	C₃²×C₄²	—	2	4	no	—
72	C₃²×C₄²	—	3	3	no	—
73	C₃²×C₄²	C₂×D₃	1	4	yes	complemented
74	C₃²×C₄²	C₂×D₃	1	1	yes	characteristic, complemented
75	C₄×C₃⋊Dic₃	—	3	3	no	—
76	C₄×C₃⋊Dic₃	—	3	12	no	—
77	C₄×C₃⋊Dic₃	—	3	6	no	—
78	C₄×C₃⋊Dic₃	—	6	12	no	—
79	C₄×C₃⋊Dic₃	C₂×D₃	1	3	yes	complemented
80	C₃×C₄×Dic₃	—	3	12	no	—
81	C₃×C₄×Dic₃	C₂×D₃	1	12	yes	complemented
82	Dic₃²	—	3	24	no	—
83	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
84	C₂×C₃⋊(C₃⋊D₃)	C₂²×C₄	1	6	yes	—
85	C₂×C₃×C₃⋊D₃	C₂²×C₄	1	6	yes	—
86	C₂×C₃²×D₃	C₂²×C₄	1	6	yes	—
87	D₃×C₃⋊D₃	C₄²	1	16	yes	direct product factor
88	C₃³×C₄	C₂²×C₄	1	6	yes	complemented
89	C₃⋊(C₃⋊Dic₃)	C₂²×C₄	1	6	yes	complemented
90	C₃×C₃⋊Dic₃	C₂²×C₄	1	6	yes	complemented
91	C₃²×Dic₃	C₂²×C₄	1	6	yes	complemented
92	C₂²×C₄×D₃	—	9	12	no	—
93	C₂²×C₄×D₃	—	9	3	no	—
94	C₂×C₃×C₄²	—	3	4	no	—
95	C₂×C₃×C₄²	—	9	1	no	—
96	C₂×C₄×Dic₃	—	9	12	no	—
97	C₂×C₄×Dic₃	—	9	3	no	—
98	C₄²×D₃	—	3	4	no	—
99	C₄²×D₃	—	9	12	no	—
100	C₄²×D₃	—	9	12	no	—
101	C₄²×D₃	—	9	3	no	—
102	C₄²×D₃	—	9	4	no	—
103	C₄²×D₃	—	9	1	no	—
104	C₄²×D₃	—	9	3	no	—
105	C₄²×D₃	—	18	4	no	—
106	C₄²×D₃	C₃⋊D₃	1	1	yes	characteristic, direct product factor
107	C₂³×C₃²	—	3	1	no	—
108	C₂²×C₃⋊D₃	—	3	1	no	—
109	C₂²×C₃⋊D₃	—	3	12	no	—
110	C₂²×C₃⋊D₃	—	3	4	no	—
111	C₂²×C₃⋊D₃	—	6	4	no	—
112	C₂²×C₃⋊D₃	C₂²×D₃	1	1	yes	characteristic
113	C₂²×C₃×D₃	—	3	4	no	—
114	C₂²×C₃×D₃	C₂²×D₃	1	4	yes	—
115	C₂×D₃²	—	3	48	no	—
116	C₂×C₃²×C₄	—	2	12	no	—
117	C₂×C₃²×C₄	—	3	3	no	—
118	C₂×C₃²×C₄	—	3	12	no	—
119	C₂×C₃²×C₄	C₂²×D₃	1	12	yes	—
120	C₂×C₃²×C₄	C₂²×D₃	1	3	yes	—
121	C₂×C₃⋊Dic₃	—	3	3	no	—
122	C₂×C₃⋊Dic₃	—	3	12	no	—
123	C₂×C₃⋊Dic₃	—	3	12	no	—
124	C₂×C₃⋊Dic₃	—	6	12	no	—
125	C₂×C₃⋊Dic₃	C₂²×D₃	1	3	yes	—
126	C₄×C₃⋊D₃	—	3	12	no	—
127	C₄×C₃⋊D₃	—	3	12	no	—
128	C₄×C₃⋊D₃	—	3	12	no	—
129	C₄×C₃⋊D₃	—	3	48	no	—
130	C₄×C₃⋊D₃	—	6	48	no	—
131	C₄×C₃⋊D₃	C₄×D₃	1	12	yes	direct product factor
132	C₂×C₃×Dic₃	—	3	12	no	—
133	C₂×C₃×Dic₃	C₂²×D₃	1	12	yes	—
134	C₃×C₄×D₃	—	3	48	no	—
135	C₃×C₄×D₃	C₄×D₃	1	48	yes	complemented
136	#624	—	3	48	no	—
137	D₃×Dic₃	—	3	48	no	—
138	D₃×Dic₃	—	3	48	no	—
139	C₂²×C₄²	—	27	1	no	Sylow
140	C₂×C₃³	C₂³×C₄	1	3	yes	—
141	C₃⋊(C₃⋊D₃)	C₂×C₄²	1	4	yes	complemented
142	C₃×C₃⋊D₃	C₂×C₄²	1	4	yes	complemented
143	C₃²×D₃	C₂×C₄²	1	4	yes	complemented
144	C₂³×D₃	—	9	4	no	—
145	C₂³×D₃	—	9	1	no	—
146	C₂²×C₃×C₄	—	3	12	no	—
147	C₂²×C₃×C₄	—	9	3	no	—
148	C₂²×Dic₃	—	9	12	no	—
149	C₂²×Dic₃	—	9	3	no	—
150	C₂×C₄×D₃	—	3	12	no	—
151	C₂×C₄×D₃	—	9	96	no	—
152	C₂×C₄×D₃	—	9	12	no	—
153	C₂×C₄×D₃	—	9	12	no	—
154	C₂×C₄×D₃	—	9	3	no	—
155	C₂×C₄×D₃	—	9	12	no	—
156	C₂×C₄×D₃	—	9	3	no	—
157	C₂×C₄×D₃	—	9	3	no	—
158	C₂×C₄×D₃	—	9	24	no	—
159	C₂×C₄×D₃	—	18	12	no	—
160	C₂×C₄×D₃	C₂×C₃⋊D₃	1	3	yes	—
161	C₃×C₄²	—	2	4	no	—
162	C₃×C₄²	—	3	12	no	—
163	C₃×C₄²	—	9	3	no	—
164	C₃×C₄²	D₃²	1	4	yes	complemented
165	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic, complemented
166	C₄×Dic₃	—	3	12	no	—
167	C₄×Dic₃	—	9	24	no	—
168	C₄×Dic₃	—	9	12	no	—
169	C₄×Dic₃	—	9	3	no	—
170	C₄×Dic₃	—	9	6	no	—
171	C₄×Dic₃	—	18	12	no	—
172	C₄×Dic₃	C₂×C₃⋊D₃	1	3	yes	complemented
173	C₂²×C₃²	—	2	4	no	—
174	C₂²×C₃²	—	3	6	no	—
175	C₂²×C₃²	C₂³×D₃	1	4	yes	—
176	C₂²×C₃²	C₂³×D₃	1	1	yes	characteristic
177	C₂×C₃⋊D₃	—	3	6	no	—
178	C₂×C₃⋊D₃	—	3	16	no	—
179	C₂×C₃⋊D₃	—	3	24	no	—
180	C₂×C₃⋊D₃	—	6	24	no	—
181	C₂×C₃⋊D₃	C₂×C₄×D₃	1	6	yes	—
182	C₂×C₃×D₃	—	3	24	no	—
183	C₂×C₃×D₃	C₂×C₄×D₃	1	24	yes	—
184	D₃²	—	3	64	no	—
185	C₃²×C₄	—	2	24	no	—
186	C₃²×C₄	—	3	6	no	—
187	C₃²×C₄	C₂×C₄×D₃	1	24	yes	complemented
188	C₃²×C₄	C₂×C₄×D₃	1	6	yes	complemented
189	C₃⋊Dic₃	—	3	6	no	—
190	C₃⋊Dic₃	—	3	24	no	—
191	C₃⋊Dic₃	—	6	24	no	—
192	C₃⋊Dic₃	C₂×C₄×D₃	1	6	yes	complemented
193	C₃×Dic₃	—	3	24	no	—
194	C₃×Dic₃	C₂×C₄×D₃	1	24	yes	complemented
195	C₂³×C₄	—	27	3	no	—
196	C₂×C₄²	—	3	1	no	—
197	C₂×C₄²	—	9	1	no	—
198	C₂×C₄²	—	27	3	no	—
199	C₂×C₄²	—	27	3	no	—
200	C₂×C₄²	—	27	3	no	—
201	C₂×C₄²	—	27	1	no	—
202	C₃³	C₂²×C₄²	1	1	yes	characteristic, complemented, Sylow
203	C₂³×C₃	—	3	4	no	—
204	C₂³×C₃	—	9	1	no	—
205	C₂²×D₃	—	3	4	no	—
206	C₂²×D₃	—	9	48	no	—
207	C₂²×D₃	—	9	4	no	—
208	C₂²×D₃	—	9	1	no	—
209	C₂²×D₃	—	9	12	no	—
210	C₂²×D₃	—	18	4	no	—
211	C₂²×D₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
212	C₂×C₃×C₄	—	2	12	no	—
213	C₂×C₃×C₄	—	3	12	no	—
214	C₂×C₃×C₄	—	3	48	no	—
215	C₂×C₃×C₄	—	9	3	no	—
216	C₂×C₃×C₄	—	9	12	no	—
217	C₂×C₃×C₄	C₂×D₃²	1	12	yes	—
218	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	3	yes	—
219	C₂×Dic₃	—	3	12	no	—
220	C₂×Dic₃	—	9	48	no	—
221	C₂×Dic₃	—	9	12	no	—
222	C₂×Dic₃	—	9	3	no	—
223	C₂×Dic₃	—	9	12	no	—
224	C₂×Dic₃	—	18	12	no	—
225	C₂×Dic₃	C₂²×C₃⋊D₃	1	3	yes	—
226	C₄×D₃	—	3	48	no	—
227	C₄×D₃	—	9	48	no	—
228	C₄×D₃	—	9	48	no	—
229	C₄×D₃	—	9	12	no	—
230	C₄×D₃	—	9	48	no	—
231	C₄×D₃	—	9	12	no	—
232	C₄×D₃	—	9	12	no	—
233	C₄×D₃	—	18	48	no	—
234	C₄×D₃	C₄×C₃⋊D₃	1	12	yes	direct product factor
235	C₂×C₃²	—	2	12	no	—
236	C₂×C₃²	—	3	4	no	—
237	C₂×C₃²	C₂²×C₄×D₃	1	12	yes	—
238	C₂×C₃²	C₂²×C₄×D₃	1	3	yes	—
239	C₃⋊D₃	—	3	4	no	—
240	C₃⋊D₃	—	3	16	no	—
241	C₃⋊D₃	—	6	16	no	—
242	C₃⋊D₃	C₄²×D₃	1	4	yes	direct product factor
243	C₃×D₃	—	3	16	no	—
244	C₃×D₃	C₄²×D₃	1	16	yes	complemented
245	C₂⁴	—	27	1	no	—
246	C₂²×C₄	—	3	3	no	—
247	C₂²×C₄	—	9	3	no	—
248	C₂²×C₄	—	27	3	no	—
249	C₂²×C₄	—	27	24	no	—
250	C₂²×C₄	—	27	3	no	—
251	C₂²×C₄	—	27	3	no	—
252	C₂²×C₄	—	27	3	no	—
253	C₄²	—	3	3	no	—
254	C₄²	—	9	3	no	—
255	C₄²	—	27	6	no	—
256	C₄²	—	27	3	no	—
257	C₄²	D₃×C₃⋊D₃	1	1	yes	characteristic, direct product factor
258	C₂²×C₃	—	2	4	no	—
259	C₂²×C₃	—	3	24	no	—
260	C₂²×C₃	—	9	6	no	—
261	C₂²×C₃	C₂²×D₃²	1	4	yes	—
262	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
263	C₂×D₃	—	3	24	no	—
264	C₂×D₃	—	9	64	no	—
265	C₂×D₃	—	9	24	no	—
266	C₂×D₃	—	9	6	no	—
267	C₂×D₃	—	9	16	no	—
268	C₂×D₃	—	18	24	no	—
269	C₂×D₃	C₂×C₄×C₃⋊D₃	1	6	yes	—
270	C₃×C₄	—	2	24	no	—
271	C₃×C₄	—	3	24	no	—
272	C₃×C₄	—	9	6	no	—
273	C₃×C₄	C₄×D₃²	1	24	yes	complemented
274	C₃×C₄	C₂×C₄×C₃⋊D₃	1	6	yes	complemented
275	Dic₃	—	3	24	no	—
276	Dic₃	—	9	24	no	—
277	Dic₃	—	9	6	no	—
278	Dic₃	—	18	24	no	—
279	Dic₃	C₂×C₄×C₃⋊D₃	1	6	yes	complemented
280	C₃²	—	2	4	no	—
281	C₃²	C₂×C₄²×D₃	1	4	yes	complemented
282	C₃²	C₂×C₄²×D₃	1	1	yes	characteristic, complemented
283	C₂³	—	3	1	no	—
284	C₂³	—	9	1	no	—
285	C₂³	—	27	12	no	—
286	C₂³	—	27	1	no	—
287	C₂×C₄	—	3	3	no	—
288	C₂×C₄	—	3	12	no	—
289	C₂×C₄	—	9	3	no	—
290	C₂×C₄	—	9	12	no	—
291	C₂×C₄	—	27	12	no	—
292	C₂×C₄	—	27	12	no	—
293	C₂×C₄	—	27	12	no	—
294	C₂×C₄	—	27	3	no	—
295	C₂×C₄	—	27	12	no	—
296	C₂×C₄	C₂×D₃×C₃⋊D₃	1	3	yes	—
297	C₂×C₃	—	2	12	no	—
298	C₂×C₃	—	3	16	no	—
299	C₂×C₃	—	9	4	no	—
300	C₂×C₃	C₂×C₄×D₃²	1	12	yes	—
301	C₂×C₃	C₂²×C₄×C₃⋊D₃	1	3	yes	—
302	D₃	—	3	16	no	—
303	D₃	—	9	4	no	—
304	D₃	—	9	16	no	—
305	D₃	—	18	16	no	—
306	D₃	C₄²×C₃⋊D₃	1	4	yes	direct product factor
307	C₂²	—	3	6	no	—
308	C₂²	—	9	6	no	—
309	C₂²	—	27	16	no	—
310	C₂²	—	27	6	no	—
311	C₂²	C₂²×D₃×C₃⋊D₃	1	1	yes	characteristic
312	C₄	—	3	6	no	—
313	C₄	—	9	6	no	—
314	C₄	—	27	6	no	—
315	C₄	C₄×D₃×C₃⋊D₃	1	6	yes	direct product factor
316	C₃	—	2	4	no	—
317	C₃	C₄²×D₃²	1	4	yes	complemented
318	C₃	C₂×C₄²×C₃⋊D₃	1	1	yes	characteristic, complemented
319	C₂	—	3	4	no	—
320	C₂	—	9	4	no	—
321	C₂	—	27	4	no	—
322	C₂	C₂×C₄×D₃×C₃⋊D₃	1	3	yes	—

	subgroup	G/H
center, hypercenter	C₄²	D₃×C₃⋊D₃
commutator, hypocenter	C₃³	C₂²×C₄²
Frattini	C₂²	C₂²×D₃×C₃⋊D₃
Fitting	C₃³×C₄²	C₂²
socle, cosocle	C₂²×C₃³	C₂⁴
prime radical	C₂²×D₃×C₃⋊D₃	C₂²
LCS	G ▷ C₃³
UCS	C₁ ◁ C₄²

Complements

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

N	H ≅ G/N	type
2. C₄²×C₃⋊(C₃⋊D₃)	C₂	semidirect
3. C₃×C₄²×C₃⋊D₃	C₂	semidirect
4. C₃²×C₄²×D₃	C₂	semidirect
5. C₄×#6289	C₂	semidirect
6. C₄×Dic₃×C₃⋊D₃	C₂	semidirect
7. C₄×D₃×C₃⋊Dic₃	C₂	semidirect
17. C₄×D₃×C₃⋊D₃	C₄	direct (N × H)
18. C₃³×C₄²	C₂²	semidirect
19. C₄×C₃⋊(C₃⋊Dic₃)	C₂²	semidirect
20. C₃×C₄×C₃⋊Dic₃	C₂²	semidirect
21. C₃²×C₄×Dic₃	C₂²	semidirect
22. Dic₃×C₃⋊Dic₃	C₂²	semidirect
32. C₄²×C₃⋊D₃	D₃	direct (N × H)
34. C₃×C₄²×D₃	D₃	semidirect
44. C₄×C₃⋊(C₃⋊D₃)	C₂×C₄	semidirect
46. C₃×C₄×C₃⋊D₃	C₂×C₄	semidirect
48. C₃²×C₄×D₃	C₂×C₄	semidirect
49. #6289	C₂×C₄	semidirect
50. Dic₃×C₃⋊D₃	C₂×C₄	semidirect
51. D₃×C₃⋊Dic₃	C₂×C₄	semidirect
73. C₃²×C₄²	C₂×D₃	semidirect
74. C₃²×C₄²	C₂×D₃	semidirect
79. C₄×C₃⋊Dic₃	C₂×D₃	semidirect
81. C₃×C₄×Dic₃	C₂×D₃	semidirect
87. D₃×C₃⋊D₃	C₄²	direct (N × H)
88. C₃³×C₄	C₂²×C₄	semidirect
89. C₃⋊(C₃⋊Dic₃)	C₂²×C₄	semidirect
90. C₃×C₃⋊Dic₃	C₂²×C₄	semidirect
91. C₃²×Dic₃	C₂²×C₄	semidirect
106. C₄²×D₃	C₃⋊D₃	direct (N × H)
131. C₄×C₃⋊D₃	C₄×D₃	direct (N × H)
135. C₃×C₄×D₃	C₄×D₃	semidirect
141. C₃⋊(C₃⋊D₃)	C₂×C₄²	semidirect
142. C₃×C₃⋊D₃	C₂×C₄²	semidirect
143. C₃²×D₃	C₂×C₄²	semidirect
164. C₃×C₄²	D₃²	semidirect
165. C₃×C₄²	C₂×C₃⋊D₃	semidirect
172. C₄×Dic₃	C₂×C₃⋊D₃	semidirect
187. C₃²×C₄	C₂×C₄×D₃	semidirect
188. C₃²×C₄	C₂×C₄×D₃	semidirect
192. C₃⋊Dic₃	C₂×C₄×D₃	semidirect
194. C₃×Dic₃	C₂×C₄×D₃	semidirect
202. C₃³	C₂²×C₄²	semidirect
234. C₄×D₃	C₄×C₃⋊D₃	direct (N × H)
242. C₃⋊D₃	C₄²×D₃	direct (N × H)
244. C₃×D₃	C₄²×D₃	semidirect
257. C₄²	D₃×C₃⋊D₃	direct (N × H)
273. C₃×C₄	C₄×D₃²	semidirect
274. C₃×C₄	C₂×C₄×C₃⋊D₃	semidirect
279. Dic₃	C₂×C₄×C₃⋊D₃	semidirect
281. C₃²	C₂×C₄²×D₃	semidirect
282. C₃²	C₂×C₄²×D₃	semidirect
306. D₃	C₄²×C₃⋊D₃	direct (N × H)
315. C₄	C₄×D₃×C₃⋊D₃	direct (N × H)
317. C₃	C₄²×D₃²	semidirect
318. C₃	C₂×C₄²×C₃⋊D₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₃×C₃⋊D₃	2
C₄²×C₃⋊(C₃⋊D₃)	2
C₃×C₄²×C₃⋊D₃	2
C₃²×C₄²×D₃	2
C₄×#6289	2
C₄×Dic₃×C₃⋊D₃	2
C₄×D₃×C₃⋊Dic₃	2
C₂×C₄²×C₃⋊D₃	3
C₄²×D₃²	3

Subgroups — C42×D3×C3⋊D3 #13175387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄²×D₃×C₃⋊D₃ #13175387