Subgroups — C₃×#10592638 #13162977

Order 1728.

1980 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃³×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3752	C₂	1	4	yes	maximal, complemented
4	C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
5	#10592638	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₃×#4939	—	3	4	no	maximal
7	C₂³×C₃×C₃⋊D₃	C₂²	1	2	yes	—
8	C₂²×C₃³×C₄	C₂²	1	2	yes	—
9	C₂²×C₃³×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₃⋊Dic₃	C₂²	1	2	yes	—
11	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
12	C₂×C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
13	C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	1	4	yes	complemented
14	C₃³×C₄²	—	2	2	no	—
15	C₃×#3752	—	2	8	no	—
16	C₃×C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
17	C₂²×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic
18	C₂²×C₃×D₁₂	—	3	4	no	—
19	C₂×C₃²×C₄²	—	2	4	no	—
20	C₂×C₃²×C₄²	D₃	1	4	yes	complemented
21	C₂×C₃²×C₄²	C₂×C₃	1	1	yes	characteristic, complemented
22	C₂×#3752	C₂×C₃	1	4	yes	complemented
23	C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂×C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
25	C₂×C₃×C₄⋊Dic₃	—	3	4	no	—
26	C₂³×C₃³	C₂³	1	1	yes	characteristic
27	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
28	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
29	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
30	C₂²×C₃×C₃⋊D₃	—	2	4	no	—
31	C₂²×C₃×C₃⋊D₃	C₂×C₄	1	4	yes	—
32	C₂×C₃³×C₄	—	2	2	no	—
33	C₂×C₃³×C₄	—	2	2	no	—
34	C₂×C₃³×C₄	C₂×C₄	1	2	yes	—
35	C₂×C₃³×C₄	D₄	1	2	yes	—
36	C₂×C₃³×C₄	D₄	1	2	yes	—
37	C₂×C₃³×C₄	D₄	1	4	yes	complemented
38	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
39	C₂×C₃×C₃⋊Dic₃	—	2	4	no	—
40	C₃×C₄⋊(C₃⋊D₃)	—	2	8	no	—
41	C₃×#390	—	9	1	no	—
42	#4939	—	3	4	no	—
43	C₂³×C₃⋊D₃	C₂²×C₃	1	2	yes	—
44	C₂³×C₃×D₃	—	3	8	no	—
45	C₂²×C₃²×C₄	—	2	8	no	—
46	C₂²×C₃²×C₄	—	2	4	no	—
47	C₂²×C₃²×C₄	C₂×D₃	1	8	yes	—
48	C₂²×C₃²×C₄	C₂×D₃	1	4	yes	—
49	C₂²×C₃²×C₄	C₂²×C₃	1	2	yes	—
50	C₂²×C₃²×C₄	C₂²×C₃	1	1	yes	characteristic
51	C₂²×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
52	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
53	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
54	C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	1	4	yes	complemented
55	C₂²×C₃×Dic₃	—	3	8	no	—
56	C₂×C₃×D₁₂	—	3	16	no	—
57	C₂×C₃×D₁₂	—	6	8	no	—
58	C₂×C₃×D₁₂	—	6	8	no	—
59	C₃²×C₄²	—	2	16	no	—
60	C₃²×C₄²	—	2	8	no	—
61	C₃²×C₄²	—	2	2	no	—
62	#3752	—	2	8	no	—
63	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
64	C₃×(C₂×D₃)⋊C₄	—	6	32	no	—
65	C₃×C₄⋊Dic₃	—	6	8	no	—
66	C₂²×C₃³	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₃³	C₂×D₄	1	2	yes	—
70	C₂²×C₃³	#41	1	2	yes	—
71	C₂×C₃×C₃⋊D₃	—	2	4	no	—
72	C₂×C₃×C₃⋊D₃	—	2	8	no	—
73	C₂×C₃×C₃⋊D₃	—	4	4	no	—
74	C₂×C₃×C₃⋊D₃	—	4	2	no	—
75	C₂×C₃×C₃⋊D₃	—	4	2	no	—
76	C₃³×C₄	—	2	4	no	—
77	C₃³×C₄	C₂²⋊C₄	1	4	yes	complemented
78	C₃×C₃⋊Dic₃	—	4	2	no	—
79	C₂²×C₃×D₄	—	9	1	no	—
80	C₂²×D₁₂	—	3	4	no	—
81	C₂×C₃×C₄⋊C₄	—	9	1	no	—
82	C₂×C₃×C₂²⋊C₄	—	9	4	no	—
83	C₂×C₃×C₄²	—	2	4	no	—
84	C₂×C₃×C₄²	C₃×D₃	1	4	yes	complemented
85	C₂×C₃×C₄²	C₃⋊D₃	1	1	yes	characteristic, complemented
86	C₂×(C₂×D₃)⋊C₄	—	3	16	no	—
87	C₂×C₄⋊Dic₃	—	3	4	no	—
88	C₂³×C₃²	—	2	4	no	—
89	C₂³×C₃²	C₂²×D₃	1	4	yes	—
90	C₂³×C₃²	C₂³×C₃	1	1	yes	characteristic
91	C₂²×C₃⋊D₃	—	2	4	no	—
92	C₂²×C₃⋊D₃	—	2	2	no	—
93	C₂²×C₃⋊D₃	—	2	2	no	—
94	C₂²×C₃⋊D₃	—	2	4	no	—
95	C₂²×C₃⋊D₃	C₂×C₃×C₄	1	4	yes	—
96	C₂²×C₃×D₃	—	3	16	no	—
97	C₂²×C₃×D₃	—	6	16	no	—
98	C₂²×C₃×D₃	—	6	8	no	—
99	C₂²×C₃×D₃	—	6	16	no	—
100	C₂²×C₃×D₃	—	6	8	no	—
101	C₂×C₃²×C₄	—	2	16	no	—
102	C₂×C₃²×C₄	—	2	16	no	—
103	C₂×C₃²×C₄	—	2	8	no	—
104	C₂×C₃²×C₄	—	2	8	no	—
105	C₂×C₃²×C₄	—	2	2	no	—
106	C₂×C₃²×C₄	—	2	2	no	—
107	C₂×C₃²×C₄	—	2	8	no	—
108	C₂×C₃²×C₄	—	2	8	no	—
109	C₂×C₃²×C₄	—	2	16	no	—
110	C₂×C₃²×C₄	—	2	8	no	—
111	C₂×C₃²×C₄	C₄×D₃	1	8	yes	—
112	C₂×C₃²×C₄	D₁₂	1	8	yes	—
113	C₂×C₃²×C₄	D₁₂	1	16	yes	complemented
114	C₂×C₃²×C₄	#67	1	8	yes	—
115	C₂×C₃²×C₄	C₂×C₃×C₄	1	2	yes	—
116	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
117	C₂×C₃²×C₄	C₃×D₄	1	2	yes	—
118	C₂×C₃²×C₄	C₃×D₄	1	4	yes	complemented
119	C₂×C₃⋊Dic₃	—	2	2	no	—
120	C₂×C₃⋊Dic₃	—	2	4	no	—
121	C₄⋊(C₃⋊D₃)	—	2	8	no	—
122	C₂×C₃×Dic₃	—	6	8	no	—
123	C₂×C₃×Dic₃	—	6	16	no	—
124	C₃×D₁₂	—	6	32	no	—
125	#390	—	9	1	no	Sylow
126	C₂×C₃³	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂×C₃³	C₄×D₄	1	2	yes	—
128	C₂×C₃³	#121	1	2	yes	—
129	C₂×C₃³	#124	1	1	yes	characteristic
130	C₂×C₃³	#127	1	1	yes	characteristic
131	C₃×C₃⋊D₃	—	4	4	no	—
132	C₂⁴×C₃	—	9	2	no	—
133	C₂³×D₃	—	3	8	no	—
134	C₂×C₃×D₄	—	9	4	no	—
135	C₂×C₃×D₄	—	18	2	no	—
136	C₂×C₃×D₄	—	18	2	no	—
137	C₂²×C₃×C₄	—	2	8	no	—
138	C₂²×C₃×C₄	—	2	4	no	—
139	C₂²×C₃×C₄	—	9	2	no	—
140	C₂²×C₃×C₄	C₂×C₃×D₃	1	8	yes	—
141	C₂²×C₃×C₄	C₂×C₃×D₃	1	4	yes	—
142	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	2	yes	—
143	C₂²×C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
144	C₂²×Dic₃	—	3	8	no	—
145	C₂×D₁₂	—	3	16	no	—
146	C₂×D₁₂	—	6	8	no	—
147	C₂×D₁₂	—	6	8	no	—
148	C₃×C₄⋊C₄	—	18	2	no	—
149	C₃×C₂²⋊C₄	—	18	8	no	—
150	C₃×C₄²	—	2	16	no	—
151	C₃×C₄²	—	2	8	no	—
152	C₃×C₄²	—	2	2	no	—
153	(C₂×D₃)⋊C₄	—	6	32	no	—
154	C₄⋊Dic₃	—	6	8	no	—
155	C₂²×C₃²	—	2	4	no	—
156	C₂²×C₃²	—	2	4	no	—
157	C₂²×C₃²	—	2	8	no	—
158	C₂²×C₃²	—	2	8	no	—
159	C₂²×C₃²	—	2	4	no	—
160	C₂²×C₃²	C₂×C₄×D₃	1	4	yes	—
161	C₂²×C₃²	C₂×D₁₂	1	8	yes	—
162	C₂²×C₃²	C₂×D₁₂	1	4	yes	—
163	C₂²×C₃²	#235	1	8	yes	—
164	C₂²×C₃²	C₂×#67	1	4	yes	—
165	C₂²×C₃²	C₂²×C₃×C₄	1	1	yes	characteristic
166	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
167	C₂²×C₃²	C₂×C₃×D₄	1	2	yes	—
168	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
169	C₂²×C₃²	C₃×#41	1	2	yes	—
170	C₂×C₃⋊D₃	—	2	4	no	—
171	C₂×C₃⋊D₃	—	2	8	no	—
172	C₂×C₃⋊D₃	—	4	4	no	—
173	C₂×C₃⋊D₃	—	4	2	no	—
174	C₂×C₃⋊D₃	—	4	2	no	—
175	C₂×C₃×D₃	—	6	32	no	—
176	C₂×C₃×D₃	—	6	16	no	—
177	C₂×C₃×D₃	—	12	8	no	—
178	C₂×C₃×D₃	—	12	8	no	—
179	C₂×C₃×D₃	—	12	16	no	—
180	C₃²×C₄	—	2	32	no	—
181	C₃²×C₄	—	2	16	no	—
182	C₃²×C₄	—	2	4	no	—
183	C₃²×C₄	—	2	16	no	—
184	C₃²×C₄	(C₂×D₃)⋊C₄	1	16	yes	complemented
185	C₃²×C₄	C₃×C₂²⋊C₄	1	4	yes	complemented
186	C₃⋊Dic₃	—	4	2	no	—
187	C₃×Dic₃	—	12	8	no	—
188	C₂²×D₄	—	9	1	no	—
189	C₂×C₄⋊C₄	—	9	1	no	—
190	C₂×C₂²⋊C₄	—	9	4	no	—
191	C₂×C₄²	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
192	C₃³	#390	1	1	yes	characteristic, complemented, Sylow
193	C₂³×C₃	—	2	4	no	—
194	C₂³×C₃	—	9	4	no	—
195	C₂³×C₃	—	18	4	no	—
196	C₂³×C₃	—	18	2	no	—
197	C₂³×C₃	—	18	4	no	—
198	C₂³×C₃	—	18	2	no	—
199	C₂³×C₃	C₂²×C₃×D₃	1	4	yes	—
200	C₂³×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
201	C₂²×D₃	—	3	16	no	—
202	C₂²×D₃	—	6	16	no	—
203	C₂²×D₃	—	6	8	no	—
204	C₂²×D₃	—	6	16	no	—
205	C₂²×D₃	—	6	8	no	—
206	C₃×D₄	—	18	8	no	—
207	C₂×C₃×C₄	—	2	16	no	—
208	C₂×C₃×C₄	—	2	16	no	—
209	C₂×C₃×C₄	—	2	8	no	—
210	C₂×C₃×C₄	—	2	8	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	2	8	no	—
214	C₂×C₃×C₄	—	2	8	no	—
215	C₂×C₃×C₄	—	2	16	no	—
216	C₂×C₃×C₄	—	2	8	no	—
217	C₂×C₃×C₄	—	18	4	no	—
218	C₂×C₃×C₄	—	18	2	no	—
219	C₂×C₃×C₄	C₃×C₄×D₃	1	8	yes	—
220	C₂×C₃×C₄	C₃×D₁₂	1	8	yes	—
221	C₂×C₃×C₄	C₃×D₁₂	1	16	yes	complemented
222	C₂×C₃×C₄	C₃×#67	1	8	yes	—
223	C₂×C₃×C₄	C₄×C₃⋊D₃	1	2	yes	—
224	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
225	C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	1	4	yes	complemented
226	C₂×C₃×C₄	#638	1	2	yes	—
227	C₂×Dic₃	—	6	8	no	—
228	C₂×Dic₃	—	6	16	no	—
229	D₁₂	—	6	32	no	—
230	C₂×C₃²	—	2	4	no	—
231	C₂×C₃²	—	2	8	no	—
232	C₂×C₃²	—	2	8	no	—
233	C₂×C₃²	—	2	4	no	—
234	C₂×C₃²	—	2	4	no	—
235	C₂×C₃²	C₄×D₁₂	1	8	yes	—
236	C₂×C₃²	#874	1	4	yes	—
237	C₂×C₃²	#875	1	4	yes	—
238	C₂×C₃²	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
239	C₂×C₃²	#930	1	8	yes	—
240	C₂×C₃²	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₃²	C₃×C₄×D₄	1	2	yes	—
242	C₂×C₃²	C₃×#121	1	2	yes	—
243	C₂×C₃²	C₃×#124	1	1	yes	characteristic
244	C₂×C₃²	C₃×#127	1	1	yes	characteristic
245	C₃⋊D₃	—	4	4	no	—
246	C₃×D₃	—	12	16	no	—
247	C₂⁴	—	9	2	no	—
248	C₂×D₄	—	9	4	no	—
249	C₂×D₄	—	18	2	no	—
250	C₂×D₄	—	18	2	no	—
251	C₂²×C₄	—	9	2	no	—
252	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
253	C₂²×C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
254	C₄⋊C₄	—	18	2	no	—
255	C₂²⋊C₄	—	18	8	no	—
256	C₄²	—	2	2	no	—
257	C₂²×C₃	—	2	4	no	—
258	C₂²×C₃	—	2	8	no	—
259	C₂²×C₃	—	2	4	no	—
260	C₂²×C₃	—	2	8	no	—
261	C₂²×C₃	—	2	4	no	—
262	C₂²×C₃	—	18	8	no	—
263	C₂²×C₃	—	18	4	no	—
264	C₂²×C₃	—	36	2	no	—
265	C₂²×C₃	—	36	2	no	—
266	C₂²×C₃	—	36	4	no	—
267	C₂²×C₃	C₂×C₃×C₄×D₃	1	4	yes	—
268	C₂²×C₃	C₂×C₃×D₁₂	1	4	yes	—
269	C₂²×C₃	C₂×C₃×D₁₂	1	8	yes	—
270	C₂²×C₃	C₃×#235	1	8	yes	—
271	C₂²×C₃	C₂×C₃×#67	1	4	yes	—
272	C₂²×C₃	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
273	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
274	C₂²×C₃	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
275	C₂²×C₃	#3828	1	2	yes	—
276	C₂²×C₃	C₂×#638	1	1	yes	characteristic
277	C₂×D₃	—	6	16	no	—
278	C₂×D₃	—	6	32	no	—
279	C₂×D₃	—	12	16	no	—
280	C₂×D₃	—	12	8	no	—
281	C₂×D₃	—	12	8	no	—
282	C₃×C₄	—	2	32	no	—
283	C₃×C₄	—	2	16	no	—
284	C₃×C₄	—	2	4	no	—
285	C₃×C₄	—	2	16	no	—
286	C₃×C₄	—	36	2	no	—
287	C₃×C₄	C₃×(C₂×D₃)⋊C₄	1	16	yes	complemented
288	C₃×C₄	#3752	1	4	yes	complemented
289	Dic₃	—	12	8	no	—
290	C₃²	—	2	4	no	—
291	C₃²	#4939	1	4	yes	complemented
292	C₃²	C₃×#390	1	1	yes	characteristic, complemented
293	C₂³	—	9	4	no	—
294	C₂³	—	18	4	no	—
295	C₂³	—	18	2	no	—
296	C₂³	—	18	4	no	—
297	C₂³	—	18	2	no	—
298	C₂³	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
299	D₄	—	18	8	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	18	4	no	—
303	C₂×C₄	—	18	2	no	—
304	C₂×C₄	C₃×C₄×C₃⋊D₃	1	2	yes	—
305	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
306	C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	1	4	yes	complemented
307	C₂×C₄	C₃×#638	1	2	yes	—
308	C₂×C₃	—	2	8	no	—
309	C₂×C₃	—	2	4	no	—
310	C₂×C₃	—	2	4	no	—
311	C₂×C₃	—	2	4	no	—
312	C₂×C₃	—	2	8	no	—
313	C₂×C₃	—	36	4	no	—
314	C₂×C₃	C₃×C₄×D₁₂	1	8	yes	—
315	C₂×C₃	C₃×#874	1	4	yes	—
316	C₂×C₃	C₃×#875	1	4	yes	—
317	C₂×C₃	C₂×C₃×(C₂×D₃)⋊C₄	1	4	yes	—
318	C₂×C₃	C₃×#930	1	8	yes	—
319	C₂×C₃	C₄×C₄⋊(C₃⋊D₃)	1	2	yes	—
320	C₂×C₃	#64083	1	1	yes	characteristic
321	C₂×C₃	#64084	1	1	yes	characteristic
322	C₂×C₃	C₂×#3752	1	1	yes	characteristic
323	C₂×C₃	#64139	1	2	yes	—
324	D₃	—	12	16	no	—
325	C₂²	—	18	8	no	—
326	C₂²	—	18	4	no	—
327	C₂²	—	36	2	no	—
328	C₂²	—	36	2	no	—
329	C₂²	—	36	4	no	—
330	C₂²	C₂×C₃×C₄×C₃⋊D₃	1	1	yes	characteristic
331	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	2	yes	—
332	C₂²	C₂×C₃×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
333	C₂²	C₃×#3828	1	2	yes	—
334	C₂²	C₂×C₃×#638	1	1	yes	characteristic
335	C₄	—	2	4	no	—
336	C₄	—	36	2	no	—
337	C₄	C₃×#3752	1	4	yes	complemented
338	C₃	—	2	4	no	—
339	C₃	C₃×#4939	1	4	yes	complemented
340	C₃	#10592638	1	1	yes	characteristic, direct product factor
341	C₂	—	36	4	no	—
342	C₂	C₃×C₄×C₄⋊(C₃⋊D₃)	1	2	yes	—
343	C₂	C₃×#64083	1	1	yes	characteristic
344	C₂	C₃×#64084	1	1	yes	characteristic
345	C₂	C₂×C₃×#3752	1	1	yes	characteristic
346	C₂	C₃×#64139	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂²×C₃⋊D₃
commutator	C₂²×C₃²	C₂²×C₃×C₄
Frattini	C₂³	C₂²×C₃×C₃⋊D₃
Fitting	C₂×C₃³×C₄²	C₂
socle	C₂³×C₃³	C₂³
prime radical	C₂²×C₃×C₄⋊(C₃⋊D₃)	C₂
cosocle	C₂³×C₃²	C₂³×C₃
hypercenter	C₂×C₃×C₄²	C₃⋊D₃
hypocenter	C₃²	C₃×#390
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂×C₃³×C₄²	C₂	semidirect
3. C₂×C₃×#3752	C₂	semidirect
4. C₂×C₃×C₄⋊(C₃⋊Dic₃)	C₂	semidirect
5. #10592638	C₃	direct (N × H)
13. C₂×C₃×C₄⋊(C₃⋊D₃)	C₄	semidirect
20. C₂×C₃²×C₄²	D₃	semidirect
21. C₂×C₃²×C₄²	C₂×C₃	semidirect
22. C₂×#3752	C₂×C₃	semidirect
23. C₂×C₄⋊(C₃⋊Dic₃)	C₂×C₃	semidirect
37. C₂×C₃³×C₄	D₄	semidirect
54. C₂×C₄⋊(C₃⋊D₃)	C₃×C₄	semidirect
77. C₃³×C₄	C₂²⋊C₄	semidirect
84. C₂×C₃×C₄²	C₃×D₃	semidirect
85. C₂×C₃×C₄²	C₃⋊D₃	semidirect
113. C₂×C₃²×C₄	D₁₂	semidirect
118. C₂×C₃²×C₄	C₃×D₄	semidirect
184. C₃²×C₄	(C₂×D₃)⋊C₄	semidirect
185. C₃²×C₄	C₃×C₂²⋊C₄	semidirect
191. C₂×C₄²	C₃×C₃⋊D₃	semidirect
192. C₃³	#390	semidirect
221. C₂×C₃×C₄	C₃×D₁₂	semidirect
225. C₂×C₃×C₄	C₄⋊(C₃⋊D₃)	semidirect
287. C₃×C₄	C₃×(C₂×D₃)⋊C₄	semidirect
288. C₃×C₄	#3752	semidirect
291. C₃²	#4939	semidirect
292. C₃²	C₃×#390	semidirect
306. C₂×C₄	C₃×C₄⋊(C₃⋊D₃)	semidirect
337. C₄	C₃×#3752	semidirect
339. C₃	C₃×#4939	semidirect
340. C₃	#10592638	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄⋊(C₃⋊D₃)	2
C₂×C₃³×C₄²	2
C₂×C₃×#3752	2
C₂×C₃×C₄⋊(C₃⋊Dic₃)	2
#10592638	3
C₃×#4939	3

Subgroups — C3×#10592638 #13162977

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10592638 #13162977