Subgroups — C₃×#10596055 #13179335

Order 1728.

1552 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#64155	C₂	1	2	yes	maximal, complemented
3	C₃×#64107	C₂	1	4	yes	maximal, complemented
4	C₃×#64101	C₂	1	2	yes	maximal, complemented
5	C₃×#64084	C₂	1	2	yes	maximal
6	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
7	C₃×#64078	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×#634	C₂	1	2	yes	maximal, complemented
9	#10596055	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5584	—	3	4	no	maximal
11	C₂×C₃³×Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₄×C₃⋊D₃	C₂²	1	2	yes	—
14	C₂×C₃×#634	C₂²	1	2	yes	—
15	C₃³×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃³×C₄²	C₂²	1	2	yes	—
18	C₃³×C₄²	C₂²	1	1	yes	characteristic
19	C₃×#3752	C₂²	1	2	yes	—
20	C₃×#3752	C₂²	1	4	yes	—
21	C₃×#3752	C₂²	1	4	yes	—
22	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
23	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
24	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
25	C₃×#3750	C₂²	1	4	yes	—
26	C₃×C₄×C₃⋊Dic₃	C₂²	1	4	yes	—
27	C₃²×C₄×Q₈	—	2	4	no	—
28	C₃²×C₄×Q₈	D₃	1	4	yes	complemented
29	C₃²×C₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
30	#64155	C₂×C₃	1	2	yes	complemented
31	#64107	C₂×C₃	1	4	yes	complemented
32	#64101	C₂×C₃	1	2	yes	complemented
33	#64084	C₂×C₃	1	2	yes	—
34	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic
35	#64078	C₂×C₃	1	1	yes	characteristic, complemented
36	C₄×#634	C₂×C₃	1	2	yes	complemented
37	C₃×#946	—	3	8	no	—
38	C₃×#898	—	3	16	no	—
39	C₃×#892	—	3	8	no	—
40	C₃×#875	—	3	8	no	—
41	C₃×C₄×D₁₂	—	3	4	no	—
42	C₃×#869	—	3	4	no	—
43	C₃×C₄×Dic₆	—	3	8	no	—
44	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
45	C₃³×Q₈	—	2	2	no	—
46	C₂×C₃³×C₄	C₂³	1	2	yes	—
47	C₂×C₃³×C₄	C₂³	1	2	yes	—
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	4	yes	—
53	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
54	C₃×C₄×C₃⋊D₃	—	2	4	no	—
55	C₃×#634	—	2	4	no	—
56	C₃×#556	—	9	1	no	—
57	#5584	—	3	4	no	—
58	C₂×C₃²×Q₈	—	2	4	no	—
59	C₂×C₃²×Q₈	C₂×D₃	1	4	yes	—
60	C₂×C₃²×Q₈	C₂²×C₃	1	1	yes	characteristic
61	C₂×C₄⋊(C₃⋊D₃)	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₄×C₃⋊D₃	C₂²×C₃	1	2	yes	—
63	C₂×#634	C₂²×C₃	1	2	yes	—
64	C₂×C₃×D₁₂	—	3	4	no	—
65	C₂×C₃×C₄×D₃	—	3	8	no	—
66	C₂×C₃×Dic₆	—	3	8	no	—
67	C₃²×C₄⋊C₄	—	2	4	no	—
68	C₃²×C₄⋊C₄	—	2	8	no	—
69	C₃²×C₄⋊C₄	C₂×D₃	1	4	yes	—
70	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
71	C₃²×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
72	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
73	C₃²×C₄²	—	2	8	no	—
74	C₃²×C₄²	—	2	4	no	—
75	C₃²×C₄²	C₂×D₃	1	8	yes	—
76	C₃²×C₄²	C₂×D₃	1	4	yes	—
77	C₃²×C₄²	C₂²×C₃	1	2	yes	—
78	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
79	#3752	C₂²×C₃	1	2	yes	—
80	#3752	C₂²×C₃	1	4	yes	—
81	#3752	C₂²×C₃	1	4	yes	—
82	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
83	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
84	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	2	yes	—
85	#3750	C₂²×C₃	1	4	yes	—
86	C₄×C₃⋊Dic₃	C₂²×C₃	1	4	yes	—
87	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
88	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
89	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
90	C₃×C₄⋊Dic₃	—	3	8	no	—
91	C₃×C₄⋊Dic₃	—	3	8	no	—
92	C₃×C₄⋊Dic₃	—	3	4	no	—
93	C₃×Dic₃⋊C₄	—	3	16	no	—
94	C₃×C₄×Dic₃	—	3	16	no	—
95	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
96	C₂×C₃×C₃⋊D₃	—	2	2	no	—
97	C₂×C₃×C₃⋊D₃	—	2	2	no	—
98	C₂×C₃×C₃⋊D₃	—	2	2	no	—
99	C₃³×C₄	—	2	2	no	—
100	C₃³×C₄	—	2	2	no	—
101	C₃³×C₄	—	2	1	no	—
102	C₃³×C₄	#41	1	2	yes	—
103	C₃³×C₄	#41	1	2	yes	—
104	C₃×C₃⋊Dic₃	—	2	4	no	—
105	C₃×C₃⋊Dic₃	—	2	2	no	—
106	C₃×C₄⋊Q₈	—	9	1	no	—
107	C₃×#126	—	9	4	no	—
108	C₃×#124	—	9	2	no	—
109	C₃×C₂²⋊Q₈	—	9	2	no	—
110	C₃×C₄×Q₈	—	2	4	no	—
111	C₃×C₄×Q₈	—	9	2	no	—
112	C₃×C₄×Q₈	C₃×D₃	1	4	yes	complemented
113	C₃×C₄×Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
114	C₃×C₄×D₄	—	9	1	no	—
115	C₃×#117	—	9	2	no	—
116	#946	—	3	8	no	—
117	#898	—	3	16	no	—
118	#892	—	3	8	no	—
119	#875	—	3	8	no	—
120	C₄×D₁₂	—	3	4	no	—
121	#869	—	3	4	no	—
122	C₄×Dic₆	—	3	8	no	—
123	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
124	C₂²×C₃×D₃	—	3	8	no	—
125	C₃²×Q₈	—	2	16	no	—
126	C₃²×Q₈	—	2	8	no	—
127	C₃²×Q₈	—	2	2	no	—
128	C₂×C₃²×C₄	—	2	4	no	—
129	C₂×C₃²×C₄	—	2	8	no	—
130	C₂×C₃²×C₄	—	2	4	no	—
131	C₂×C₃²×C₄	—	2	8	no	—
132	C₂×C₃²×C₄	—	2	4	no	—
133	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
134	C₂×C₃²×C₄	C₂²×D₃	1	8	yes	—
135	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
136	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
137	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
138	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
139	C₂×C₃²×C₄	C₂³×C₃	1	2	yes	—
140	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
141	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
144	C₂×C₃⋊Dic₃	C₂³×C₃	1	4	yes	—
145	C₄⋊(C₃⋊D₃)	—	2	2	no	—
146	C₄×C₃⋊D₃	—	2	4	no	—
147	#634	—	2	4	no	—
148	C₂×C₃×Dic₃	—	3	8	no	—
149	C₂×C₃×Dic₃	—	3	16	no	—
150	C₃×D₁₂	—	6	8	no	—
151	C₃×C₄×D₃	—	6	16	no	—
152	C₃×Dic₆	—	6	16	no	—
153	#556	—	9	1	no	Sylow
154	C₂×C₃³	C₂×#41	1	1	yes	characteristic
155	C₂×C₃³	C₂×#41	1	1	yes	characteristic
156	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
157	C₃×C₃⋊D₃	—	4	2	no	—
158	C₂×C₃×Q₈	—	2	4	no	—
159	C₂×C₃×Q₈	—	9	2	no	—
160	C₂×C₃×Q₈	C₂×C₃×D₃	1	4	yes	—
161	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	1	yes	characteristic
162	C₂×C₃×D₄	—	9	1	no	—
163	C₂²×C₃×C₄	—	9	2	no	—
164	C₂×D₁₂	—	3	4	no	—
165	C₂×C₄×D₃	—	3	8	no	—
166	C₂×Dic₆	—	3	8	no	—
167	C₃×C₄⋊C₄	—	2	4	no	—
168	C₃×C₄⋊C₄	—	2	8	no	—
169	C₃×C₄⋊C₄	—	9	4	no	—
170	C₃×C₄⋊C₄	—	9	2	no	—
171	C₃×C₄⋊C₄	—	9	1	no	—
172	C₃×C₄⋊C₄	—	9	2	no	—
173	C₃×C₄⋊C₄	C₂×C₃×D₃	1	4	yes	—
174	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
175	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
176	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
177	C₃×C₂²⋊C₄	—	9	4	no	—
178	C₃×C₂²⋊C₄	—	9	2	no	—
179	C₃×C₂²⋊C₄	—	9	4	no	—
180	C₃×C₄²	—	2	4	no	—
181	C₃×C₄²	—	2	8	no	—
182	C₃×C₄²	—	9	4	no	—
183	C₃×C₄²	C₂×C₃×D₃	1	8	yes	—
184	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
185	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
186	C₃×C₄²	C₂×C₃⋊D₃	1	2	yes	—
187	(C₂×D₃)⋊C₄	—	3	8	no	—
188	(C₂×D₃)⋊C₄	—	3	16	no	—
189	(C₂×D₃)⋊C₄	—	3	16	no	—
190	C₄⋊Dic₃	—	3	4	no	—
191	C₄⋊Dic₃	—	3	8	no	—
192	C₄⋊Dic₃	—	3	8	no	—
193	Dic₃⋊C₄	—	3	16	no	—
194	C₄×Dic₃	—	3	16	no	—
195	C₂²×C₃²	—	2	4	no	—
196	C₂²×C₃²	C₂³×D₃	1	4	yes	—
197	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
198	C₂×C₃⋊D₃	—	2	2	no	—
199	C₂×C₃⋊D₃	—	2	2	no	—
200	C₂×C₃⋊D₃	—	2	2	no	—
201	C₂×C₃×D₃	—	6	8	no	—
202	C₂×C₃×D₃	—	6	8	no	—
203	C₂×C₃×D₃	—	6	8	no	—
204	C₃²×C₄	—	2	16	no	—
205	C₃²×C₄	—	2	8	no	—
206	C₃²×C₄	—	2	2	no	—
207	C₃²×C₄	—	2	2	no	—
208	C₃²×C₄	—	2	1	no	—
209	C₃²×C₄	—	2	8	no	—
210	C₃²×C₄	—	2	8	no	—
211	C₃²×C₄	—	2	8	no	—
212	C₃²×C₄	—	2	4	no	—
213	C₃²×C₄	—	4	8	no	—
214	C₃²×C₄	—	4	4	no	—
215	C₃²×C₄	#235	1	8	yes	—
216	C₃²×C₄	#239	1	8	yes	—
217	C₃²×C₄	C₃×#41	1	2	yes	—
218	C₃²×C₄	C₃×#41	1	2	yes	—
219	C₃⋊Dic₃	—	2	4	no	—
220	C₃⋊Dic₃	—	2	2	no	—
221	C₃×Dic₃	—	6	8	no	—
222	C₃×Dic₃	—	6	16	no	—
223	C₄⋊Q₈	—	9	1	no	—
224	#126	—	9	4	no	—
225	#124	—	9	2	no	—
226	C₂²⋊Q₈	—	9	2	no	—
227	C₄×Q₈	—	9	2	no	—
228	C₄×Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
229	C₄×D₄	—	9	1	no	—
230	#117	—	9	2	no	—
231	C₃³	#556	1	1	yes	characteristic, complemented, Sylow
232	C₂³×C₃	—	9	2	no	—
233	C₂²×D₃	—	3	8	no	—
234	C₃×Q₈	—	2	16	no	—
235	C₃×Q₈	—	2	8	no	—
236	C₃×Q₈	—	2	2	no	—
237	C₃×Q₈	—	18	4	no	—
238	C₃×D₄	—	18	2	no	—
239	C₂×C₃×C₄	—	2	4	no	—
240	C₂×C₃×C₄	—	2	8	no	—
241	C₂×C₃×C₄	—	2	4	no	—
242	C₂×C₃×C₄	—	2	8	no	—
243	C₂×C₃×C₄	—	2	4	no	—
244	C₂×C₃×C₄	—	9	2	no	—
245	C₂×C₃×C₄	—	9	4	no	—
246	C₂×C₃×C₄	—	18	4	no	—
247	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
248	C₂×C₃×C₄	C₂²×C₃×D₃	1	8	yes	—
249	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
250	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
251	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
252	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
253	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
254	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	2	yes	—
255	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
256	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
257	C₂×Dic₃	—	3	8	no	—
258	C₂×Dic₃	—	3	16	no	—
259	D₁₂	—	6	8	no	—
260	C₄×D₃	—	6	16	no	—
261	Dic₆	—	6	16	no	—
262	C₂×C₃²	—	2	4	no	—
263	C₂×C₃²	—	2	4	no	—
264	C₂×C₃²	—	2	4	no	—
265	C₂×C₃²	C₂×#235	1	4	yes	—
266	C₂×C₃²	C₂×#239	1	4	yes	—
267	C₂×C₃²	#1010	1	4	yes	—
268	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
269	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
270	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
271	C₃⋊D₃	—	4	2	no	—
272	C₃×D₃	—	12	8	no	—
273	C₂×Q₈	—	9	2	no	—
274	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
275	C₂×D₄	—	9	1	no	—
276	C₂²×C₄	—	9	2	no	—
277	C₄⋊C₄	—	9	2	no	—
278	C₄⋊C₄	—	9	1	no	—
279	C₄⋊C₄	—	9	4	no	—
280	C₄⋊C₄	—	9	2	no	—
281	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
282	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
283	C₂²⋊C₄	—	9	4	no	—
284	C₂²⋊C₄	—	9	2	no	—
285	C₂²⋊C₄	—	9	4	no	—
286	C₄²	—	9	4	no	—
287	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
288	C₄²	C₂×C₃×C₃⋊D₃	1	2	yes	—
289	C₂²×C₃	—	2	4	no	—
290	C₂²×C₃	—	18	2	no	—
291	C₂²×C₃	—	18	2	no	—
292	C₂²×C₃	—	18	2	no	—
293	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
294	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
295	C₂×D₃	—	6	8	no	—
296	C₂×D₃	—	6	8	no	—
297	C₂×D₃	—	6	8	no	—
298	C₃×C₄	—	2	16	no	—
299	C₃×C₄	—	2	8	no	—
300	C₃×C₄	—	2	8	no	—
301	C₃×C₄	—	2	4	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	2	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	8	no	—
306	C₃×C₄	—	2	8	no	—
307	C₃×C₄	—	4	8	no	—
308	C₃×C₄	—	4	4	no	—
309	C₃×C₄	—	18	2	no	—
310	C₃×C₄	—	18	4	no	—
311	C₃×C₄	C₃×#235	1	8	yes	—
312	C₃×C₄	C₃×#239	1	8	yes	—
313	C₃×C₄	#3828	1	2	yes	—
314	C₃×C₄	#3832	1	2	yes	—
315	Dic₃	—	6	8	no	—
316	Dic₃	—	6	16	no	—
317	C₃²	—	2	4	no	—
318	C₃²	#5584	1	4	yes	complemented
319	C₃²	C₃×#556	1	1	yes	characteristic, complemented
320	C₂³	—	9	2	no	—
321	Q₈	—	2	2	no	—
322	Q₈	—	18	4	no	—
323	D₄	—	18	2	no	—
324	C₂×C₄	—	9	2	no	—
325	C₂×C₄	—	9	4	no	—
326	C₂×C₄	—	18	4	no	—
327	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
328	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	2	yes	—
330	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
331	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
332	C₂×C₃	—	2	4	no	—
333	C₂×C₃	—	2	4	no	—
334	C₂×C₃	—	2	4	no	—
335	C₂×C₃	—	36	2	no	—
336	C₂×C₃	C₂×C₃×#235	1	4	yes	—
337	C₂×C₃	C₂×C₃×#239	1	4	yes	—
338	C₂×C₃	C₃×#1010	1	4	yes	—
339	C₂×C₃	C₂×#3828	1	1	yes	characteristic
340	C₂×C₃	C₂×#3832	1	1	yes	characteristic
341	C₂×C₃	#64367	1	1	yes	characteristic
342	D₃	—	12	8	no	—
343	C₂²	—	18	2	no	—
344	C₂²	—	18	2	no	—
345	C₂²	—	18	2	no	—
346	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
347	C₄	—	2	2	no	—
348	C₄	—	2	2	no	—
349	C₄	—	2	1	no	—
350	C₄	—	18	2	no	—
351	C₄	—	18	4	no	—
352	C₄	C₃×#3828	1	2	yes	—
353	C₄	C₃×#3832	1	2	yes	—
354	C₃	—	2	4	no	—
355	C₃	C₃×#5584	1	4	yes	complemented
356	C₃	#10596055	1	1	yes	characteristic, direct product factor
357	C₂	—	36	2	no	—
358	C₂	C₂×C₃×#3828	1	1	yes	characteristic
359	C₂	C₂×C₃×#3832	1	1	yes	characteristic
360	C₂	C₃×#64367	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂³×C₃⋊D₃
commutator, cosocle	C₂²×C₃²	C₂⁴×C₃
Frattini	C₂²	C₂³×C₃×C₃⋊D₃
Fitting	C₃³×C₄×Q₈	C₂
socle	C₂²×C₃³	C₂⁴
prime radical	C₂×C₃×C₄⋊(C₃⋊D₃)	C₂²
hypercenter	C₃×C₄×Q₈	C₃⋊D₃
hypocenter	C₃²	C₃×#556
LCS	G ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₃³×C₄×Q₈	C₂	semidirect
2. C₃×#64155	C₂	semidirect
3. C₃×#64107	C₂	semidirect
4. C₃×#64101	C₂	semidirect
7. C₃×#64078	C₂	semidirect
8. C₃×C₄×#634	C₂	semidirect
9. #10596055	C₃	direct (N × H)
28. C₃²×C₄×Q₈	D₃	semidirect
29. C₃²×C₄×Q₈	C₂×C₃	semidirect
30. #64155	C₂×C₃	semidirect
31. #64107	C₂×C₃	semidirect
32. #64101	C₂×C₃	semidirect
35. #64078	C₂×C₃	semidirect
36. C₄×#634	C₂×C₃	semidirect
112. C₃×C₄×Q₈	C₃×D₃	semidirect
113. C₃×C₄×Q₈	C₃⋊D₃	semidirect
228. C₄×Q₈	C₃×C₃⋊D₃	semidirect
231. C₃³	#556	semidirect
318. C₃²	#5584	semidirect
319. C₃²	C₃×#556	semidirect
355. C₃	C₃×#5584	semidirect
356. C₃	#10596055	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×Q₈	2
C₃×#64155	2
C₃×#64107	2
C₃×#64101	2
C₃×#64084	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×#64078	2
C₃×C₄×#634	2
#10596055	3
C₃×#5584	3

Subgroups — C3×#10596055 #13179335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596055 #13179335