Subgroups — C₃×#10590771 #13157757

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×C₃²×D₂₄	C₂	1	1	yes	maximal, characteristic
2	C₃×Dic₃×D₁₂	C₂	1	2	yes	maximal, complemented
3	C₃×#63644	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃²×#815	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#63563	C₂	1	2	yes	maximal, complemented
6	C₃×#5152	—	3	1	no	maximal
7	C₃×#4711	—	3	1	no	maximal
8	#10590771	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂×C₃²×D₁₂	C₂²	1	2	yes	—
10	C₂×C₃×D₃×Dic₃	—	2	2	no	—
11	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
13	C₃²×C₄×Dic₃	C₂²	1	1	yes	characteristic
14	C₂×C₃²×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₃²×D₂₄	C₄	1	4	yes	complemented
16	C₃×(C₂×D₃)⋊Dic₃	—	2	2	no	—
17	C₂×C₃²×D₈	—	3	1	no	—
18	C₃×D₄×Dic₃	—	3	2	no	—
19	C₂×C₃×D₂₄	—	2	1	no	—
20	C₂×C₃×D₂₄	D₃	1	1	yes	characteristic
21	C₂×C₃×D₂₄	C₂×C₃	1	1	yes	characteristic
22	C₃×C₄×D₁₂	—	3	2	no	—
23	Dic₃×D₁₂	C₂×C₃	1	2	yes	complemented
24	C₃²×#97	—	3	1	no	—
25	#63644	C₂×C₃	1	1	yes	characteristic, complemented
26	C₃×#832	—	3	2	no	—
27	C₃×#821	—	3	2	no	—
28	C₃×#817	—	3	1	no	—
29	C₃×#817	—	3	1	no	—
30	C₃×#817	—	6	1	no	—
31	C₃×#815	—	2	1	no	—
32	C₃×#815	D₃	1	1	yes	characteristic, complemented
33	C₃×#815	C₂×C₃	1	1	yes	characteristic, complemented
34	#63563	C₂×C₃	1	2	yes	complemented
35	C₂²×C₃²×D₃	—	2	2	no	—
36	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
37	C₂×C₃×C₃⋊Dic₃	—	2	2	no	—
38	C₂×C₃²×Dic₃	D₄	1	2	yes	—
39	C₃²×D₁₂	—	2	2	no	—
40	C₃²×D₁₂	C₂×C₄	1	4	yes	complemented
41	C₃×D₃×Dic₃	—	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	#5152	—	3	1	no	—
46	#4711	—	3	1	no	—
47	C₂×C₃²×D₄	—	3	2	no	—
48	C₂²×C₃×Dic₃	—	6	2	no	—
49	C₂×C₃×D₁₂	—	2	2	no	—
50	C₂×C₃×D₁₂	C₂×D₃	1	2	yes	—
51	C₂×C₃×D₁₂	C₂²×C₃	1	2	yes	—
52	C₂×C₃×C₄×D₃	—	6	2	no	—
53	C₂×D₃×Dic₃	—	2	2	no	—
54	C₃²×D₈	—	3	4	no	—
55	C₂×C₃²×C₈	—	2	1	no	—
56	C₂×C₃²×C₈	—	2	1	no	—
57	C₂×C₃²×C₈	—	2	1	no	—
58	C₂×C₃²×C₈	—	3	1	no	—
59	C₂×C₃²×C₈	—	4	1	no	—
60	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
61	C₂×C₃²×C₈	C₂×D₃	1	1	yes	characteristic
62	C₂×C₃²×C₈	C₂²×C₃	1	1	yes	characteristic
63	C₃²×C₄²	—	3	1	no	—
64	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
65	C₃×#217	—	6	2	no	—
66	C₃×(C₂×D₃)⋊C₄	—	6	2	no	—
67	C₃×C₄⋊Dic₃	—	3	2	no	—
68	C₃×C₄⋊Dic₃	—	3	2	no	—
69	C₃×C₄⋊Dic₃	—	6	2	no	—
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	—	2	4	no	—
77	C₃×D₂₄	Dic₃	1	4	yes	complemented
78	C₃×D₂₄	C₃×C₄	1	4	yes	complemented
79	(C₂×D₃)⋊Dic₃	—	2	2	no	—
80	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
81	C₂×C₃²×D₃	—	2	4	no	—
82	C₂×C₃²×D₃	—	4	2	no	—
83	C₂×C₃²×D₃	—	4	2	no	—
84	C₃³×C₄	C₂²×C₄	1	1	yes	characteristic
85	C₃³×C₄	#41	1	1	yes	characteristic
86	C₃×C₃⋊Dic₃	—	4	2	no	—
87	C₃²×Dic₃	—	2	2	no	—
88	C₂×C₃×D₈	—	3	1	no	—
89	C₂×C₃×D₈	—	3	1	no	—
90	C₂×C₃×D₈	—	6	1	no	—
91	C₃×C₄×D₄	—	9	2	no	—
92	D₄×Dic₃	—	3	2	no	—
93	C₂×D₂₄	C₃×D₃	1	1	yes	characteristic
94	C₄×D₁₂	—	3	2	no	—
95	C₃×#106	—	9	1	no	—
96	C₃×#102	—	9	2	no	—
97	C₃×#97	—	3	1	no	—
98	C₃×#97	—	3	1	no	—
99	C₃×#97	—	6	1	no	—
100	#832	—	3	2	no	—
101	#821	—	3	2	no	—
102	#817	—	3	1	no	—
103	#817	—	3	1	no	—
104	#817	—	6	1	no	—
105	#815	C₃×D₃	1	1	yes	characteristic, complemented
106	C₂³×C₃²	—	6	2	no	—
107	C₂²×C₃×D₃	—	2	2	no	—
108	C₂²×C₃×D₃	—	2	2	no	—
109	C₂²×C₃×D₃	—	4	2	no	—
110	C₃²×D₄	—	3	4	no	—
111	C₃²×D₄	—	6	2	no	—
112	C₂×C₃²×C₄	—	2	1	no	—
113	C₂×C₃²×C₄	—	2	1	no	—
114	C₂×C₃²×C₄	—	2	1	no	—
115	C₂×C₃²×C₄	—	3	2	no	—
116	C₂×C₃²×C₄	—	4	1	no	—
117	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
118	C₂×C₃²×C₄	C₂²×D₃	1	1	yes	characteristic
119	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
120	C₂×C₃⋊Dic₃	—	2	2	no	—
121	C₂×C₃×Dic₃	—	2	2	no	—
122	C₂×C₃×Dic₃	—	6	2	no	—
123	C₂×C₃×Dic₃	—	6	2	no	—
124	C₂×C₃×Dic₃	—	12	2	no	—
125	C₂×C₃×Dic₃	—	12	4	no	—
126	C₂×C₃×Dic₃	D₁₂	1	2	yes	—
127	C₂×C₃×Dic₃	C₃×D₄	1	2	yes	—
128	C₃×D₁₂	—	2	2	no	—
129	C₃×D₁₂	—	2	2	no	—
130	C₃×D₁₂	—	2	4	no	—
131	C₃×D₁₂	—	4	2	no	—
132	C₃×D₁₂	C₂×Dic₃	1	4	yes	complemented
133	C₃×D₁₂	C₂×C₃×C₄	1	4	yes	complemented
134	C₃×C₄×D₃	—	12	4	no	—
135	D₃×Dic₃	—	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	C₂×Dic₃	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	C₃²×D₃	—	4	4	no	—
151	C₂×C₃×D₄	—	3	2	no	—
152	C₂×C₃×D₄	—	3	2	no	—
153	C₂×C₃×D₄	—	6	2	no	—
154	C₂²×C₃×C₄	—	18	2	no	—
155	C₂²×Dic₃	—	6	2	no	—
156	C₂×D₁₂	C₂×C₃×D₃	1	2	yes	—
157	C₂×C₄×D₃	—	6	2	no	—
158	C₃×D₈	—	3	4	no	—
159	C₃×D₈	—	3	4	no	—
160	C₃×D₈	—	6	4	no	—
161	C₂×C₃×C₈	—	2	1	no	—
162	C₂×C₃×C₈	—	2	1	no	—
163	C₂×C₃×C₈	—	2	1	no	—
164	C₂×C₃×C₈	—	3	1	no	—
165	C₂×C₃×C₈	—	3	1	no	—
166	C₂×C₃×C₈	—	4	1	no	—
167	C₂×C₃×C₈	—	6	1	no	—
168	C₂×C₃×C₈	D₃²	1	1	yes	characteristic
169	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
170	C₂×C₃×C₈	C₂×C₃×D₃	1	1	yes	characteristic
171	C₃×C₄⋊C₄	—	9	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	#217	—	6	2	no	—
177	(C₂×D₃)⋊C₄	—	6	2	no	—
178	C₄⋊Dic₃	—	3	2	no	—
179	C₄⋊Dic₃	—	3	2	no	—
180	C₄⋊Dic₃	—	6	2	no	—
181	C₄×Dic₃	C₂×C₃×D₃	1	1	yes	characteristic
182	C₂×C₃⋊C₈	C₂×C₃×D₃	1	1	yes	characteristic
183	D₂₄	C₃×Dic₃	1	4	yes	complemented
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	—	6	4	no	—
189	C₂²×C₃²	—	12	2	no	—
190	C₂²×C₃²	—	12	2	no	—
191	C₂²×C₃²	C₂×D₁₂	1	1	yes	characteristic
192	C₂²×C₃²	D₃×D₄	1	1	yes	characteristic
193	C₂²×C₃²	C₂×C₃×D₄	1	1	yes	characteristic
194	C₂×C₃×D₃	—	2	4	no	—
195	C₂×C₃×D₃	—	2	4	no	—
196	C₂×C₃×D₃	—	4	4	no	—
197	C₂×C₃×D₃	—	4	2	no	—
198	C₂×C₃×D₃	—	4	2	no	—
199	C₂×C₃×D₃	—	4	2	no	—
200	C₂×C₃×D₃	—	4	2	no	—
201	C₂×C₃×D₃	—	8	2	no	—
202	C₂×C₃×D₃	—	8	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	C₂×C₄×D₃	1	1	yes	characteristic
213	C₃²×C₄	#235	1	1	yes	characteristic
214	C₃²×C₄	#237	1	1	yes	characteristic
215	C₃²×C₄	C₂²×Dic₃	1	1	yes	characteristic
216	C₃²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
217	C₃²×C₄	C₃×#41	1	1	yes	characteristic
218	C₃⋊Dic₃	—	4	2	no	—
219	C₃×Dic₃	—	2	2	no	—
220	C₃×Dic₃	—	2	2	no	—
221	C₃×Dic₃	—	4	2	no	—
222	C₃×Dic₃	—	12	2	no	—
223	C₃×Dic₃	—	12	2	no	—
224	C₃×Dic₃	—	24	2	no	—
225	C₂×D₈	—	3	1	no	—
226	C₄×D₄	—	9	2	no	—
227	#106	—	9	1	no	—
228	#102	—	9	2	no	—
229	#97	—	3	1	no	—
230	C₃³	#442	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₃	—	6	2	no	—
232	C₂³×C₃	—	6	2	no	—
233	C₂³×C₃	—	12	2	no	—
234	C₂²×D₃	—	2	2	no	—
235	C₃×D₄	—	3	4	no	—
236	C₃×D₄	—	3	4	no	—
237	C₃×D₄	—	6	4	no	—
238	C₃×D₄	—	6	2	no	—
239	C₃×D₄	—	6	2	no	—
240	C₃×D₄	—	12	2	no	—
241	C₂×C₃×C₄	—	2	1	no	—
242	C₂×C₃×C₄	—	2	1	no	—
243	C₂×C₃×C₄	—	2	1	no	—
244	C₂×C₃×C₄	—	3	2	no	—
245	C₂×C₃×C₄	—	3	2	no	—
246	C₂×C₃×C₄	—	4	1	no	—
247	C₂×C₃×C₄	—	6	2	no	—
248	C₂×C₃×C₄	—	18	2	no	—
249	C₂×C₃×C₄	—	36	4	no	—
250	C₂×C₃×C₄	C₂×D₃²	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
253	C₂×Dic₃	—	6	2	no	—
254	C₂×Dic₃	—	6	2	no	—
255	C₂×Dic₃	—	12	2	no	—
256	C₂×Dic₃	—	12	4	no	—
257	C₂×Dic₃	C₃×D₁₂	1	2	yes	—
258	D₁₂	—	2	2	no	—
259	D₁₂	C₂×C₃×Dic₃	1	4	yes	complemented
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	D₃×Dic₃	1	2	yes	complemented
269	C₃×C₈	C₃×C₄×D₃	1	2	yes	complemented
270	C₃×C₈	C₂×C₃×Dic₃	1	2	yes	complemented
271	C₃⋊C₈	—	2	1	no	—
272	C₂×C₃²	—	2	2	no	—
273	C₂×C₃²	—	2	2	no	—
274	C₂×C₃²	—	2	2	no	—
275	C₂×C₃²	—	2	1	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	—	12	4	no	—
281	C₂×C₃²	C₄×D₁₂	1	1	yes	characteristic
282	C₂×C₃²	#908	1	2	yes	—
283	C₂×C₃²	#911	1	2	yes	—
284	C₂×C₃²	D₄×Dic₃	1	1	yes	characteristic
285	C₂×C₃²	C₃×C₄×D₄	1	1	yes	characteristic
286	C₂×C₃²	C₃×AGL(1,ℤ/8)	1	2	yes	—
287	C₃×D₃	—	4	4	no	—
288	C₃×D₃	—	4	4	no	—
289	C₃×D₃	—	8	4	no	—
290	C₂×D₄	—	3	2	no	—
291	C₂²×C₄	—	18	2	no	—
292	D₈	—	3	4	no	—
293	C₂×C₈	—	3	1	no	—
294	C₂×C₈	C₃×D₃²	1	1	yes	characteristic
295	C₄⋊C₄	—	9	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	—	6	4	no	—
303	C₂²×C₃	—	6	4	no	—
304	C₂²×C₃	—	12	4	no	—
305	C₂²×C₃	—	12	2	no	—
306	C₂²×C₃	—	12	2	no	—
307	C₂²×C₃	—	12	2	no	—
308	C₂²×C₃	—	12	2	no	—
309	C₂²×C₃	—	24	2	no	—
310	C₂²×C₃	—	24	2	no	—
311	C₂²×C₃	D₃×D₁₂	1	1	yes	characteristic
312	C₂²×C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
313	C₂²×C₃	C₃×D₃×D₄	1	1	yes	characteristic
314	C₂×D₃	—	2	4	no	—
315	C₂×D₃	—	4	2	no	—
316	C₂×D₃	—	4	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	—	36	2	no	—
329	C₃×C₄	#3795	1	1	yes	characteristic
330	C₃×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
331	C₃×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
332	C₃×C₄	C₃×#235	1	1	yes	characteristic
333	C₃×C₄	C₃×#237	1	1	yes	characteristic
334	C₃×C₄	C₂²×C₃×Dic₃	1	1	yes	characteristic
335	Dic₃	—	2	2	no	—
336	Dic₃	—	12	2	no	—
337	Dic₃	—	12	2	no	—
338	Dic₃	—	24	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	#5152	1	1	yes	characteristic, complemented
345	C₃²	C₃×#442	1	1	yes	characteristic, complemented
346	C₂³	—	6	2	no	—
347	D₄	—	3	4	no	—
348	D₄	—	6	2	no	—
349	C₂×C₄	—	3	2	no	—
350	C₂×C₄	—	18	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×D₃×Dic₃	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	—	12	4	no	—
364	C₂×C₃	—	12	4	no	—
365	C₂×C₃	—	24	4	no	—
366	C₂×C₃	#63795	1	2	yes	—
367	C₂×C₃	Dic₃×D₁₂	1	1	yes	characteristic
368	C₂×C₃	C₃×C₄×D₁₂	1	1	yes	characteristic
369	C₂×C₃	C₃×#908	1	2	yes	—
370	C₂×C₃	C₃×#911	1	2	yes	—
371	C₂×C₃	C₃×D₄×Dic₃	1	1	yes	characteristic
372	D₃	—	4	4	no	—
373	C₂²	—	6	4	no	—
374	C₂²	—	12	2	no	—
375	C₂²	—	12	2	no	—
376	C₂²	C₃×D₃×D₁₂	1	1	yes	characteristic
377	C₄	—	6	2	no	—
378	C₄	—	36	2	no	—
379	C₄	C₃×#3795	1	1	yes	characteristic
380	C₄	C₂×C₃×D₃×Dic₃	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	#10590771	1	1	yes	characteristic, direct product factor
386	C₃	C₃×#4711	1	1	yes	characteristic, complemented
387	C₃	C₃×#5152	1	1	yes	characteristic, complemented
388	C₂	—	12	4	no	—
389	C₂	C₃×#63795	1	2	yes	—
390	C₂	C₃×Dic₃×D₁₂	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×C₃²×D₂₄	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×Dic₃×D₁₂	C₂	semidirect
3. C₃×#63644	C₂	semidirect
4. C₃²×#815	C₂	semidirect
5. C₃×#63563	C₂	semidirect
8. #10590771	C₃	direct (N × H)
15. C₃²×D₂₄	C₄	semidirect
23. Dic₃×D₁₂	C₂×C₃	semidirect
25. #63644	C₂×C₃	semidirect
32. C₃×#815	D₃	semidirect
33. C₃×#815	C₂×C₃	semidirect
34. #63563	C₂×C₃	semidirect
40. C₃²×D₁₂	C₂×C₄	semidirect
42. C₃³×C₈	C₂×C₄	semidirect
77. C₃×D₂₄	Dic₃	semidirect
78. C₃×D₂₄	C₃×C₄	semidirect
105. #815	C₃×D₃	semidirect
132. C₃×D₁₂	C₂×Dic₃	semidirect
133. C₃×D₁₂	C₂×C₃×C₄	semidirect
141. C₃²×C₈	C₄×D₃	semidirect
142. C₃²×C₈	C₂×Dic₃	semidirect
143. C₃²×C₈	C₂×C₃×C₄	semidirect
183. D₂₄	C₃×Dic₃	semidirect
230. C₃³	#442	semidirect
259. D₁₂	C₂×C₃×Dic₃	semidirect
268. C₃×C₈	D₃×Dic₃	semidirect
269. C₃×C₈	C₃×C₄×D₃	semidirect
270. C₃×C₈	C₂×C₃×Dic₃	semidirect
343. C₃²	#4711	semidirect
344. C₃²	#5152	semidirect
345. C₃²	C₃×#442	semidirect
354. C₈	C₃×D₃×Dic₃	semidirect
385. C₃	#10590771	direct (N × H)
386. C₃	C₃×#4711	semidirect
387. C₃	C₃×#5152	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₂₄	2
C₃×Dic₃×D₁₂	2
C₃×#63644	2
C₃²×#815	2
C₃×#63563	2
C₃×#5152	3
C₃×#4711	3
#10590771	3

Subgroups — C3×#10590771 #13157757

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10590771 #13157757