Subgroups — C₃×#10590768 #13157754

Order 1728.

702 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#3745	C₂	1	1	yes	maximal, characteristic
2	C₃×#63894	C₂	1	2	yes	maximal, complemented
3	C₃²×#817	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63564	C₂	1	2	yes	maximal, complemented
6	C₃×#4869	—	3	1	no	maximal
7	C₃×#4711	—	3	1	no	maximal
8	#10590768	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	2	yes	—
10	C₂×C₃×#624	—	2	2	no	—
11	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
12	C₃×#3745	C₄	1	4	yes	complemented
13	C₃²×C₄⋊Dic₃	C₂²	1	2	yes	—
14	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₃×#3722	—	2	2	no	—
17	C₂×#3745	C₂×C₃	1	1	yes	characteristic
18	C₂×C₃×D₂₄	—	3	1	no	—
19	C₂×C₃×D₂₄	—	3	1	no	—
20	C₂×C₃×D₂₄	—	6	1	no	—
21	C₃×#893	—	3	2	no	—
22	C₃×C₄×D₁₂	—	3	2	no	—
23	#63894	C₂×C₃	1	2	yes	complemented
24	C₃²×#106	—	3	1	no	—
25	C₃²×#97	—	3	1	no	—
26	C₃×#821	—	3	2	no	—
27	C₃×#817	—	2	1	no	—
28	C₃×#817	D₃	1	1	yes	characteristic, complemented
29	C₃×#817	C₂×C₃	1	1	yes	characteristic, complemented
30	C₃×#815	—	2	1	no	—
31	C₃×#815	D₃	1	1	yes	characteristic, complemented
32	C₃×#815	C₂×C₃	1	1	yes	characteristic, complemented
33	C₃×#809	—	3	2	no	—
34	#63564	C₂×C₃	1	2	yes	complemented
35	C₂²×C₃×C₃⋊D₃	—	2	2	no	—
36	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
37	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
38	C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	1	4	yes	complemented
39	C₂×C₃²×Dic₃	—	2	2	no	—
40	C₂×C₃²×Dic₃	D₄	1	2	yes	—
41	C₃×#624	—	4	4	no	—
42	C₃³×C₈	C₂×C₄	1	2	yes	complemented
43	C₃²×C₃⋊C₈	—	2	1	no	—
44	C₃×#442	—	9	1	no	—
45	#4869	—	3	1	no	—
46	#4711	—	3	1	no	—
47	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	2	yes	—
48	C₂×C₃×D₁₂	—	3	2	no	—
49	C₂×C₃×D₁₂	—	3	2	no	—
50	C₂×C₃×D₁₂	—	6	2	no	—
51	C₂×C₃×C₄×D₃	—	6	2	no	—
52	C₂×C₃×C₄×D₃	—	6	2	no	—
53	C₂×#624	—	2	2	no	—
54	C₂×C₃²×C₈	—	2	1	no	—
55	C₂×C₃²×C₈	—	2	1	no	—
56	C₂×C₃²×C₈	—	2	1	no	—
57	C₂×C₃²×C₈	—	3	1	no	—
58	C₂×C₃²×C₈	—	4	1	no	—
59	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
60	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
62	C₃²×C₄⋊C₄	—	3	2	no	—
63	C₃²×C₄²	—	3	1	no	—
64	#3745	C₃×C₄	1	4	yes	complemented
65	C₃×(C₂×D₃)⋊C₄	—	6	2	no	—
66	C₃×(C₂×D₃)⋊C₄	—	6	2	no	—
67	C₃×C₄⋊Dic₃	—	2	2	no	—
68	C₃×C₄⋊Dic₃	C₂×D₃	1	2	yes	—
69	C₃×C₄⋊Dic₃	C₂²×C₃	1	2	yes	—
70	C₃×C₄×Dic₃	—	2	1	no	—
71	C₃×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
72	C₃×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
73	C₂×C₃×C₃⋊C₈	—	2	1	no	—
74	C₂×C₃×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
75	C₂×C₃×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
76	C₃×D₂₄	—	3	4	no	—
77	C₃×D₂₄	—	3	4	no	—
78	C₃×D₂₄	—	6	4	no	—
79	#3722	—	2	2	no	—
80	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃×C₃⋊D₃	—	2	4	no	—
82	C₂×C₃×C₃⋊D₃	—	4	2	no	—
83	C₂×C₃×C₃⋊D₃	—	4	2	no	—
84	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
85	C₃³×C₄	#41	1	1	yes	characteristic
86	C₃²×Dic₃	—	2	2	no	—
87	C₃²×Dic₃	—	4	2	no	—
88	C₂×C₃×D₈	—	9	1	no	—
89	C₃×C₄×D₄	—	9	2	no	—
90	C₂×D₂₄	—	3	1	no	—
91	C₂×D₂₄	—	3	1	no	—
92	C₂×D₂₄	—	6	1	no	—
93	#893	—	3	2	no	—
94	C₄×D₁₂	—	3	2	no	—
95	C₃×#106	—	3	1	no	—
96	C₃×#106	—	3	1	no	—
97	C₃×#106	—	6	1	no	—
98	C₃×#102	—	9	2	no	—
99	C₃×#97	—	3	1	no	—
100	C₃×#97	—	3	1	no	—
101	C₃×#97	—	6	1	no	—
102	#821	—	3	2	no	—
103	#817	C₃×D₃	1	1	yes	characteristic, complemented
104	#815	C₃×D₃	1	1	yes	characteristic, complemented
105	#809	—	3	2	no	—
106	C₂²×C₃⋊D₃	—	2	2	no	—
107	C₂²×C₃×D₃	—	6	2	no	—
108	C₂²×C₃×D₃	—	6	2	no	—
109	C₂²×C₃×D₃	—	12	2	no	—
110	C₂×C₃²×C₄	—	2	1	no	—
111	C₂×C₃²×C₄	—	2	1	no	—
112	C₂×C₃²×C₄	—	2	1	no	—
113	C₂×C₃²×C₄	—	3	2	no	—
114	C₂×C₃²×C₄	—	4	1	no	—
115	C₂×C₃²×C₄	—	6	2	no	—
116	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
117	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
119	C₄⋊(C₃⋊D₃)	—	2	2	no	—
120	C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	1	4	yes	complemented
121	C₂×C₃×Dic₃	—	2	2	no	—
122	C₂×C₃×Dic₃	—	2	2	no	—
123	C₂×C₃×Dic₃	—	2	2	no	—
124	C₂×C₃×Dic₃	—	4	2	no	—
125	C₂×C₃×Dic₃	D₁₂	1	2	yes	—
126	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
127	C₃×D₁₂	—	3	4	no	—
128	C₃×D₁₂	—	3	4	no	—
129	C₃×D₁₂	—	6	4	no	—
130	C₃×D₁₂	—	6	2	no	—
131	C₃×D₁₂	—	6	2	no	—
132	C₃×D₁₂	—	12	2	no	—
133	C₃×C₄×D₃	—	12	4	no	—
134	C₃×C₄×D₃	—	12	4	no	—
135	#624	—	4	4	no	—
136	C₃²×C₈	—	2	2	no	—
137	C₃²×C₈	—	2	2	no	—
138	C₃²×C₈	—	2	2	no	—
139	C₃²×C₈	—	4	2	no	—
140	C₃²×C₈	—	6	1	no	—
141	C₃²×C₈	C₄×D₃	1	2	yes	complemented
142	C₃²×C₈	C₄×D₃	1	2	yes	complemented
143	C₃²×C₈	C₂×C₃×C₄	1	2	yes	complemented
144	C₃×C₃⋊C₈	—	2	2	no	—
145	C₃×C₃⋊C₈	—	2	1	no	—
146	C₃×C₃⋊C₈	—	2	1	no	—
147	#442	—	9	1	no	Sylow
148	C₂×C₃³	C₄×D₄	1	1	yes	characteristic
149	C₂×C₃³	AGL(1,ℤ/8)	1	2	yes	—
150	C₃×C₃⋊D₃	—	4	4	no	—
151	C₂×C₃×D₄	—	9	2	no	—
152	C₂²×C₃×C₄	—	18	2	no	—
153	C₂×D₁₂	—	3	2	no	—
154	C₂×D₁₂	—	3	2	no	—
155	C₂×D₁₂	—	6	2	no	—
156	C₂×C₄×D₃	—	6	2	no	—
157	C₂×C₄×D₃	—	6	2	no	—
158	C₃×D₈	—	9	4	no	—
159	C₂×C₃×C₈	—	2	1	no	—
160	C₂×C₃×C₈	—	2	1	no	—
161	C₂×C₃×C₈	—	2	1	no	—
162	C₂×C₃×C₈	—	3	1	no	—
163	C₂×C₃×C₈	—	3	1	no	—
164	C₂×C₃×C₈	—	4	1	no	—
165	C₂×C₃×C₈	—	6	1	no	—
166	C₂×C₃×C₈	D₃²	1	1	yes	characteristic
167	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
168	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
169	C₃×C₄⋊C₄	—	3	2	no	—
170	C₃×C₄⋊C₄	—	3	2	no	—
171	C₃×C₄⋊C₄	—	6	2	no	—
172	C₃×C₂²⋊C₄	—	18	2	no	—
173	C₃×C₄²	—	3	1	no	—
174	C₃×C₄²	—	3	1	no	—
175	C₃×C₄²	—	6	1	no	—
176	(C₂×D₃)⋊C₄	—	6	2	no	—
177	(C₂×D₃)⋊C₄	—	6	2	no	—
178	C₄⋊Dic₃	C₂×C₃×D₃	1	2	yes	—
179	C₄×Dic₃	C₂×C₃×D₃	1	1	yes	characteristic
180	C₂×C₃⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
181	D₂₄	—	3	4	no	—
182	D₂₄	—	3	4	no	—
183	D₂₄	—	6	4	no	—
184	C₂²×C₃²	—	2	1	no	—
185	C₂²×C₃²	—	2	1	no	—
186	C₂²×C₃²	—	2	1	no	—
187	C₂²×C₃²	—	4	1	no	—
188	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
189	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
190	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
191	C₂×C₃⋊D₃	—	2	4	no	—
192	C₂×C₃⋊D₃	—	4	2	no	—
193	C₂×C₃⋊D₃	—	4	2	no	—
194	C₂×C₃×D₃	—	6	4	no	—
195	C₂×C₃×D₃	—	6	4	no	—
196	C₂×C₃×D₃	—	12	4	no	—
197	C₂×C₃×D₃	—	12	2	no	—
198	C₂×C₃×D₃	—	12	2	no	—
199	C₂×C₃×D₃	—	12	2	no	—
200	C₂×C₃×D₃	—	12	2	no	—
201	C₂×C₃×D₃	—	24	2	no	—
202	C₂×C₃×D₃	—	24	2	no	—
203	C₃²×C₄	—	2	1	no	—
204	C₃²×C₄	—	2	1	no	—
205	C₃²×C₄	—	2	1	no	—
206	C₃²×C₄	—	2	1	no	—
207	C₃²×C₄	—	2	1	no	—
208	C₃²×C₄	—	2	1	no	—
209	C₃²×C₄	—	4	1	no	—
210	C₃²×C₄	—	4	1	no	—
211	C₃²×C₄	—	6	2	no	—
212	C₃²×C₄	—	12	2	no	—
213	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
214	C₃²×C₄	C₂×C₄×D₃	1	1	yes	characteristic
215	C₃²×C₄	#235	1	1	yes	characteristic
216	C₃²×C₄	#239	1	1	yes	characteristic
217	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
218	C₃²×C₄	C₃×#41	1	1	yes	characteristic
219	C₃×Dic₃	—	2	2	no	—
220	C₃×Dic₃	—	2	2	no	—
221	C₃×Dic₃	—	4	2	no	—
222	C₃×Dic₃	—	4	2	no	—
223	C₃×Dic₃	—	4	2	no	—
224	C₃×Dic₃	—	8	2	no	—
225	C₂×D₈	—	9	1	no	—
226	C₄×D₄	—	9	2	no	—
227	#106	—	3	1	no	—
228	#102	—	9	2	no	—
229	#97	—	3	1	no	—
230	C₃³	#442	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₃	—	18	2	no	—
232	C₂²×D₃	—	6	2	no	—
233	C₂²×D₃	—	6	2	no	—
234	C₂²×D₃	—	12	2	no	—
235	C₃×D₄	—	9	4	no	—
236	C₃×D₄	—	18	2	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	2	1	no	—
240	C₂×C₃×C₄	—	3	2	no	—
241	C₂×C₃×C₄	—	3	2	no	—
242	C₂×C₃×C₄	—	4	1	no	—
243	C₂×C₃×C₄	—	6	2	no	—
244	C₂×C₃×C₄	—	6	2	no	—
245	C₂×C₃×C₄	—	6	2	no	—
246	C₂×C₃×C₄	—	12	2	no	—
247	C₂×C₃×C₄	—	36	4	no	—
248	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
250	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
251	C₂×Dic₃	—	2	2	no	—
252	C₂×Dic₃	C₃×D₁₂	1	2	yes	—
253	D₁₂	—	3	4	no	—
254	D₁₂	—	3	4	no	—
255	D₁₂	—	6	4	no	—
256	D₁₂	—	6	2	no	—
257	D₁₂	—	6	2	no	—
258	D₁₂	—	12	2	no	—
259	C₄×D₃	—	12	4	no	—
260	C₄×D₃	—	12	4	no	—
261	C₃×C₈	—	2	2	no	—
262	C₃×C₈	—	2	2	no	—
263	C₃×C₈	—	2	2	no	—
264	C₃×C₈	—	4	2	no	—
265	C₃×C₈	—	6	2	no	—
266	C₃×C₈	—	6	1	no	—
267	C₃×C₈	—	6	1	no	—
268	C₃×C₈	#624	1	2	yes	complemented
269	C₃×C₈	C₃×C₄×D₃	1	2	yes	complemented
270	C₃×C₈	C₃×C₄×D₃	1	2	yes	complemented
271	C₃⋊C₈	—	2	1	no	—
272	C₂×C₃²	—	2	1	no	—
273	C₂×C₃²	—	2	2	no	—
274	C₂×C₃²	—	2	2	no	—
275	C₂×C₃²	—	2	2	no	—
276	C₂×C₃²	—	2	1	no	—
277	C₂×C₃²	—	2	1	no	—
278	C₂×C₃²	—	4	1	no	—
279	C₂×C₃²	—	4	2	no	—
280	C₂×C₃²	C₄×D₁₂	1	1	yes	characteristic
281	C₂×C₃²	#893	1	1	yes	characteristic
282	C₂×C₃²	#908	1	2	yes	—
283	C₂×C₃²	#914	1	2	yes	—
284	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
285	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	2	yes	—
286	C₃⋊D₃	—	4	4	no	—
287	C₃×D₃	—	12	4	no	—
288	C₃×D₃	—	12	4	no	—
289	C₃×D₃	—	24	4	no	—
290	C₂×D₄	—	9	2	no	—
291	C₂²×C₄	—	18	2	no	—
292	D₈	—	9	4	no	—
293	C₂×C₈	—	3	1	no	—
294	C₂×C₈	C₃×D₃²	1	1	yes	characteristic
295	C₄⋊C₄	—	3	2	no	—
296	C₂²⋊C₄	—	18	2	no	—
297	C₄²	—	3	1	no	—
298	C₂²×C₃	—	2	1	no	—
299	C₂²×C₃	—	2	1	no	—
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	4	1	no	—
302	C₂²×C₃	—	18	4	no	—
303	C₂²×C₃	—	36	2	no	—
304	C₂²×C₃	—	36	2	no	—
305	C₂²×C₃	D₃×D₁₂	1	1	yes	characteristic
306	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
307	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
308	C₂×D₃	—	6	4	no	—
309	C₂×D₃	—	6	4	no	—
310	C₂×D₃	—	12	4	no	—
311	C₂×D₃	—	12	2	no	—
312	C₂×D₃	—	12	2	no	—
313	C₂×D₃	—	12	2	no	—
314	C₂×D₃	—	12	2	no	—
315	C₂×D₃	—	24	2	no	—
316	C₂×D₃	—	24	2	no	—
317	C₃×C₄	—	2	1	no	—
318	C₃×C₄	—	2	1	no	—
319	C₃×C₄	—	2	1	no	—
320	C₃×C₄	—	2	1	no	—
321	C₃×C₄	—	2	1	no	—
322	C₃×C₄	—	2	1	no	—
323	C₃×C₄	—	4	1	no	—
324	C₃×C₄	—	4	1	no	—
325	C₃×C₄	—	6	2	no	—
326	C₃×C₄	—	6	2	no	—
327	C₃×C₄	—	12	2	no	—
328	C₃×C₄	—	12	2	no	—
329	C₃×C₄	—	12	2	no	—
330	C₃×C₄	—	24	2	no	—
331	C₃×C₄	#3799	1	1	yes	characteristic
332	C₃×C₄	C₂×#624	1	1	yes	characteristic
333	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
334	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
335	C₃×C₄	C₃×#235	1	1	yes	characteristic
336	C₃×C₄	C₃×#239	1	1	yes	characteristic
337	Dic₃	—	2	2	no	—
338	Dic₃	—	4	2	no	—
339	C₃²	—	2	1	no	—
340	C₃²	—	2	1	no	—
341	C₃²	—	2	1	no	—
342	C₃²	—	4	1	no	—
343	C₃²	#4711	1	1	yes	characteristic, complemented
344	C₃²	#4869	1	1	yes	characteristic, complemented
345	C₃²	C₃×#442	1	1	yes	characteristic, complemented
346	C₂³	—	18	2	no	—
347	D₄	—	9	4	no	—
348	D₄	—	18	2	no	—
349	C₂×C₄	—	3	2	no	—
350	C₂×C₄	—	6	2	no	—
351	C₂×C₄	—	36	4	no	—
352	C₂×C₄	C₂×C₃×D₃²	1	1	yes	characteristic
353	C₈	—	6	1	no	—
354	C₈	C₃×#624	1	2	yes	complemented
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	2	2	no	—
357	C₂×C₃	—	2	2	no	—
358	C₂×C₃	—	2	1	no	—
359	C₂×C₃	—	2	1	no	—
360	C₂×C₃	—	2	1	no	—
361	C₂×C₃	—	4	2	no	—
362	C₂×C₃	—	4	1	no	—
363	C₂×C₃	—	36	4	no	—
364	C₂×C₃	#63794	1	2	yes	—
365	C₂×C₃	#63894	1	1	yes	characteristic
366	C₂×C₃	C₃×C₄×D₁₂	1	1	yes	characteristic
367	C₂×C₃	C₃×#893	1	1	yes	characteristic
368	C₂×C₃	C₃×#908	1	2	yes	—
369	C₂×C₃	C₃×#914	1	2	yes	—
370	D₃	—	12	4	no	—
371	D₃	—	12	4	no	—
372	D₃	—	24	4	no	—
373	C₂²	—	18	4	no	—
374	C₂²	—	36	2	no	—
375	C₂²	—	36	2	no	—
376	C₂²	C₃×D₃×D₁₂	1	1	yes	characteristic
377	C₄	—	6	2	no	—
378	C₄	—	12	2	no	—
379	C₄	C₃×#3799	1	1	yes	characteristic
380	C₄	C₂×C₃×#624	1	1	yes	characteristic
381	C₃	—	2	1	no	—
382	C₃	—	2	1	no	—
383	C₃	—	2	1	no	—
384	C₃	—	4	1	no	—
385	C₃	#10590768	1	1	yes	characteristic, direct product factor
386	C₃	C₃×#4711	1	1	yes	characteristic, complemented
387	C₃	C₃×#4869	1	1	yes	characteristic, complemented
388	C₂	—	36	4	no	—
389	C₂	C₃×#63794	1	2	yes	—
390	C₂	C₃×#63894	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₃×D₁₂
commutator	C₃²×C₄	C₂²×C₃×C₄
Frattini	C₂×C₄	C₂×C₃×D₃²
Fitting	C₂×C₃³×C₈	C₂²
socle	C₂²×C₃³	C₂×D₄
prime radical	C₂×C₃×#3745	C₂
cosocle	C₂×C₃²×C₄	C₂³×C₃
hypercenter	C₂×C₃×C₈	D₃²
hypocenter	C₃²	C₃×#442
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₈

Complements

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

N	H ≅ G/N	type
2. C₃×#63894	C₂	semidirect
3. C₃²×#817	C₂	semidirect
4. C₃²×#815	C₂	semidirect
5. C₃×#63564	C₂	semidirect
8. #10590768	C₃	direct (N × H)
12. C₃×#3745	C₄	semidirect
23. #63894	C₂×C₃	semidirect
28. C₃×#817	D₃	semidirect
29. C₃×#817	C₂×C₃	semidirect
31. C₃×#815	D₃	semidirect
32. C₃×#815	C₂×C₃	semidirect
34. #63564	C₂×C₃	semidirect
38. C₃×C₄⋊(C₃⋊D₃)	C₂×C₄	semidirect
42. C₃³×C₈	C₂×C₄	semidirect
64. #3745	C₃×C₄	semidirect
103. #817	C₃×D₃	semidirect
104. #815	C₃×D₃	semidirect
120. C₄⋊(C₃⋊D₃)	C₂×C₃×C₄	semidirect
141. C₃²×C₈	C₄×D₃	semidirect
142. C₃²×C₈	C₄×D₃	semidirect
143. C₃²×C₈	C₂×C₃×C₄	semidirect
230. C₃³	#442	semidirect
268. C₃×C₈	#624	semidirect
269. C₃×C₈	C₃×C₄×D₃	semidirect
270. C₃×C₈	C₃×C₄×D₃	semidirect
343. C₃²	#4711	semidirect
344. C₃²	#4869	semidirect
345. C₃²	C₃×#442	semidirect
354. C₈	C₃×#624	semidirect
385. C₃	#10590768	direct (N × H)
386. C₃	C₃×#4711	semidirect
387. C₃	C₃×#4869	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#3745	2
C₃×#63894	2
C₃²×#817	2
C₃²×#815	2
C₃×#63564	2
C₃×#4869	3
C₃×#4711	3
#10590768	3

Subgroups — C3×#10590768 #13157754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10590768 #13157754