Subgroups — C₃×#10596203 #13179483

Order 1728.

1544 conjugacy classes of subgroups.

The subgroup lattice has 356 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×#64156	C₂	1	2	yes	maximal
3	C₃×Q₈×C₃⋊Dic₃	C₂	1	2	yes	maximal, complemented
4	C₃×#64107	C₂	1	4	yes	maximal, complemented
5	C₃×#64106	C₂	1	2	yes	maximal, complemented
6	C₃×#64101	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
8	C₃×C₄×#634	C₂	1	1	yes	maximal, characteristic, complemented
9	#10596203	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₃×#5732	—	3	4	no	maximal
11	C₂×C₃³×Q₈	C₂²	1	2	yes	—
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	1	yes	characteristic
15	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
16	C₃³×C₄⋊C₄	C₂²	1	2	yes	—
17	C₃³×C₄²	C₂²	1	1	yes	characteristic
18	C₃×#3752	C₂²	1	2	yes	—
19	C₃×#3752	C₂²	1	4	yes	—
20	C₃×#3752	C₂²	1	4	yes	—
21	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
22	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	1	yes	characteristic
23	C₃×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	—
24	C₃×#3750	C₂²	1	2	yes	—
25	C₃×C₄×C₃⋊Dic₃	C₂²	1	2	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	#64156	C₂×C₃	1	2	yes	—
31	Q₈×C₃⋊Dic₃	C₂×C₃	1	2	yes	complemented
32	#64107	C₂×C₃	1	4	yes	complemented
33	#64106	C₂×C₃	1	2	yes	complemented
34	#64101	C₂×C₃	1	2	yes	complemented
35	C₄×C₄⋊(C₃⋊D₃)	C₂×C₃	1	1	yes	characteristic
36	C₄×#634	C₂×C₃	1	1	yes	characteristic, complemented
37	C₃×#947	—	3	8	no	—
38	C₃×Q₈×Dic₃	—	3	8	no	—
39	C₃×#898	—	3	16	no	—
40	C₃×#897	—	3	8	no	—
41	C₃×#892	—	3	8	no	—
42	C₃×C₄×D₁₂	—	3	4	no	—
43	C₃×C₄×Dic₆	—	3	4	no	—
44	C₂²×C₃×C₃⋊D₃	C₂³	1	2	yes	—
45	C₃³×Q₈	—	2	4	no	—
46	C₂×C₃³×C₄	C₂³	1	4	yes	—
47	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
48	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
49	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
50	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
51	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
52	C₂×C₃×C₃⋊Dic₃	C₂³	1	2	yes	—
53	C₃×C₄⋊(C₃⋊D₃)	—	2	2	no	—
54	C₃×C₄×C₃⋊D₃	—	2	4	no	—
55	C₃×#634	—	2	2	no	—
56	C₃×#556	—	9	1	no	—
57	#5732	—	3	4	no	—
58	C₂×C₃²×Q₈	—	2	8	no	—
59	C₂×C₃²×Q₈	C₂×D₃	1	8	yes	—
60	C₂×C₃²×Q₈	C₂²×C₃	1	2	yes	—
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	1	yes	characteristic
64	C₂×C₃×D₁₂	—	3	4	no	—
65	C₂×C₃×C₄×D₃	—	3	8	no	—
66	C₂×C₃×Dic₆	—	3	4	no	—
67	C₃²×C₄⋊C₄	—	2	8	no	—
68	C₃²×C₄⋊C₄	—	2	8	no	—
69	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
70	C₃²×C₄⋊C₄	C₂×D₃	1	8	yes	—
71	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
72	C₃²×C₄⋊C₄	C₂²×C₃	1	2	yes	—
73	C₃²×C₄²	—	2	4	no	—
74	C₃²×C₄²	C₂×D₃	1	4	yes	—
75	C₃²×C₄²	C₂²×C₃	1	1	yes	characteristic
76	#3752	C₂²×C₃	1	2	yes	—
77	#3752	C₂²×C₃	1	4	yes	—
78	#3752	C₂²×C₃	1	4	yes	—
79	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
80	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	1	yes	characteristic
81	C₄⋊(C₃⋊Dic₃)	C₂²×C₃	1	4	yes	—
82	#3750	C₂²×C₃	1	2	yes	—
83	C₄×C₃⋊Dic₃	C₂²×C₃	1	2	yes	—
84	C₄×C₃⋊Dic₃	C₂²×C₃	1	4	yes	—
85	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
86	C₃×(C₂×D₃)⋊C₄	—	3	16	no	—
87	C₃×(C₂×D₃)⋊C₄	—	3	8	no	—
88	C₃×C₄⋊Dic₃	—	3	4	no	—
89	C₃×C₄⋊Dic₃	—	3	16	no	—
90	C₃×C₄⋊Dic₃	—	3	4	no	—
91	C₃×Dic₃⋊C₄	—	3	8	no	—
92	C₃×C₄×Dic₃	—	3	16	no	—
93	C₃×C₄×Dic₃	—	3	8	no	—
94	C₂²×C₃³	C₂⁴	1	1	yes	characteristic
95	C₂×C₃×C₃⋊D₃	—	2	2	no	—
96	C₂×C₃×C₃⋊D₃	—	2	2	no	—
97	C₂×C₃×C₃⋊D₃	—	2	2	no	—
98	C₃³×C₄	—	2	4	no	—
99	C₃³×C₄	—	2	1	no	—
100	C₃³×C₄	#41	1	2	yes	—
101	C₃³×C₄	#41	1	2	yes	—
102	C₃×C₃⋊Dic₃	—	2	2	no	—
103	C₃×C₃⋊Dic₃	—	2	2	no	—
104	C₃×C₃⋊Dic₃	—	2	2	no	—
105	C₃×C₄⋊Q₈	—	2	4	no	—
106	C₃×C₄⋊Q₈	C₃×D₃	1	4	yes	complemented
107	C₃×C₄⋊Q₈	C₃⋊D₃	1	1	yes	characteristic, complemented
108	C₃×#126	—	9	4	no	—
109	C₃×#124	—	9	2	no	—
110	C₃×C₂²⋊Q₈	—	9	2	no	—
111	C₃×C₄×Q₈	—	9	2	no	—
112	C₃×C₄×Q₈	—	9	1	no	—
113	C₃×C₄×D₄	—	9	1	no	—
114	C₃×#117	—	9	2	no	—
115	#947	—	3	8	no	—
116	Q₈×Dic₃	—	3	8	no	—
117	#898	—	3	16	no	—
118	#897	—	3	8	no	—
119	#892	—	3	8	no	—
120	C₄×D₁₂	—	3	4	no	—
121	C₄×Dic₆	—	3	4	no	—
122	C₂²×C₃⋊D₃	C₂³×C₃	1	2	yes	—
123	C₂²×C₃×D₃	—	3	8	no	—
124	C₃²×Q₈	—	2	4	no	—
125	C₃²×Q₈	—	2	16	no	—
126	C₃²×Q₈	—	4	16	no	—
127	C₂×C₃²×C₄	—	2	4	no	—
128	C₂×C₃²×C₄	—	2	4	no	—
129	C₂×C₃²×C₄	—	2	4	no	—
130	C₂×C₃²×C₄	—	2	16	no	—
131	C₂×C₃²×C₄	C₂²×D₃	1	16	yes	—
132	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
133	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
134	C₂×C₃²×C₄	C₂²×D₃	1	4	yes	—
135	C₂×C₃²×C₄	C₂³×C₃	1	4	yes	—
136	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
137	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
138	C₂×C₃²×C₄	C₂³×C₃	1	1	yes	characteristic
139	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
140	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
141	C₂×C₃⋊Dic₃	C₂³×C₃	1	2	yes	—
142	C₄⋊(C₃⋊D₃)	—	2	2	no	—
143	C₄×C₃⋊D₃	—	2	4	no	—
144	#634	—	2	2	no	—
145	C₂×C₃×Dic₃	—	3	8	no	—
146	C₂×C₃×Dic₃	—	3	8	no	—
147	C₂×C₃×Dic₃	—	3	8	no	—
148	C₃×D₁₂	—	6	8	no	—
149	C₃×C₄×D₃	—	6	16	no	—
150	C₃×Dic₆	—	6	8	no	—
151	#556	—	9	1	no	Sylow
152	C₂×C₃³	C₂×#41	1	1	yes	characteristic
153	C₂×C₃³	C₂×#41	1	1	yes	characteristic
154	C₂×C₃³	2₋¹⁺⁴	1	1	yes	characteristic
155	C₃×C₃⋊D₃	—	4	2	no	—
156	C₂×C₃×Q₈	—	2	8	no	—
157	C₂×C₃×Q₈	—	9	1	no	—
158	C₂×C₃×Q₈	C₂×C₃×D₃	1	8	yes	—
159	C₂×C₃×Q₈	C₂×C₃⋊D₃	1	2	yes	—
160	C₂×C₃×D₄	—	9	1	no	—
161	C₂²×C₃×C₄	—	9	2	no	—
162	C₂×D₁₂	—	3	4	no	—
163	C₂×C₄×D₃	—	3	8	no	—
164	C₂×Dic₆	—	3	4	no	—
165	C₃×C₄⋊C₄	—	2	8	no	—
166	C₃×C₄⋊C₄	—	2	8	no	—
167	C₃×C₄⋊C₄	—	9	2	no	—
168	C₃×C₄⋊C₄	—	9	1	no	—
169	C₃×C₄⋊C₄	—	9	1	no	—
170	C₃×C₄⋊C₄	—	9	4	no	—
171	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
172	C₃×C₄⋊C₄	C₂×C₃×D₃	1	8	yes	—
173	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
174	C₃×C₄⋊C₄	C₂×C₃⋊D₃	1	2	yes	—
175	C₃×C₂²⋊C₄	—	9	4	no	—
176	C₃×C₂²⋊C₄	—	9	2	no	—
177	C₃×C₂²⋊C₄	—	9	4	no	—
178	C₃×C₄²	—	2	4	no	—
179	C₃×C₄²	—	9	4	no	—
180	C₃×C₄²	—	9	2	no	—
181	C₃×C₄²	C₂×C₃×D₃	1	4	yes	—
182	C₃×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
183	(C₂×D₃)⋊C₄	—	3	8	no	—
184	(C₂×D₃)⋊C₄	—	3	16	no	—
185	(C₂×D₃)⋊C₄	—	3	16	no	—
186	C₄⋊Dic₃	—	3	4	no	—
187	C₄⋊Dic₃	—	3	4	no	—
188	C₄⋊Dic₃	—	3	16	no	—
189	Dic₃⋊C₄	—	3	8	no	—
190	C₄×Dic₃	—	3	8	no	—
191	C₄×Dic₃	—	3	16	no	—
192	C₂²×C₃²	—	2	4	no	—
193	C₂²×C₃²	C₂³×D₃	1	4	yes	—
194	C₂²×C₃²	C₂⁴×C₃	1	1	yes	characteristic
195	C₂×C₃⋊D₃	—	2	2	no	—
196	C₂×C₃⋊D₃	—	2	2	no	—
197	C₂×C₃⋊D₃	—	2	2	no	—
198	C₂×C₃×D₃	—	6	8	no	—
199	C₂×C₃×D₃	—	6	8	no	—
200	C₂×C₃×D₃	—	6	8	no	—
201	C₃²×C₄	—	2	8	no	—
202	C₃²×C₄	—	2	4	no	—
203	C₃²×C₄	—	2	4	no	—
204	C₃²×C₄	—	2	1	no	—
205	C₃²×C₄	—	2	8	no	—
206	C₃²×C₄	—	2	8	no	—
207	C₃²×C₄	—	2	16	no	—
208	C₃²×C₄	—	4	16	no	—
209	C₃²×C₄	#237	1	8	yes	—
210	C₃²×C₄	#239	1	8	yes	—
211	C₃²×C₄	C₃×#41	1	2	yes	—
212	C₃²×C₄	C₃×#41	1	2	yes	—
213	C₃⋊Dic₃	—	2	2	no	—
214	C₃⋊Dic₃	—	2	2	no	—
215	C₃⋊Dic₃	—	2	2	no	—
216	C₃×Dic₃	—	6	8	no	—
217	C₃×Dic₃	—	6	8	no	—
218	C₃×Dic₃	—	6	8	no	—
219	C₄⋊Q₈	C₃×C₃⋊D₃	1	1	yes	characteristic, complemented
220	#126	—	9	4	no	—
221	#124	—	9	2	no	—
222	C₂²⋊Q₈	—	9	2	no	—
223	C₄×Q₈	—	9	2	no	—
224	C₄×Q₈	—	9	1	no	—
225	C₄×D₄	—	9	1	no	—
226	#117	—	9	2	no	—
227	C₃³	#556	1	1	yes	characteristic, complemented, Sylow
228	C₂³×C₃	—	9	2	no	—
229	C₂²×D₃	—	3	8	no	—
230	C₃×Q₈	—	2	16	no	—
231	C₃×Q₈	—	2	4	no	—
232	C₃×Q₈	—	4	16	no	—
233	C₃×Q₈	—	18	2	no	—
234	C₃×D₄	—	18	2	no	—
235	C₂×C₃×C₄	—	2	4	no	—
236	C₂×C₃×C₄	—	2	4	no	—
237	C₂×C₃×C₄	—	2	4	no	—
238	C₂×C₃×C₄	—	2	16	no	—
239	C₂×C₃×C₄	—	9	2	no	—
240	C₂×C₃×C₄	—	9	2	no	—
241	C₂×C₃×C₄	—	9	2	no	—
242	C₂×C₃×C₄	—	18	4	no	—
243	C₂×C₃×C₄	C₂²×C₃×D₃	1	16	yes	—
244	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
245	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
246	C₂×C₃×C₄	C₂²×C₃×D₃	1	4	yes	—
247	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	4	yes	—
248	C₂×C₃×C₄	C₂²×C₃⋊D₃	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	—	3	8	no	—
252	C₂×Dic₃	—	3	8	no	—
253	C₂×Dic₃	—	3	8	no	—
254	D₁₂	—	6	8	no	—
255	C₄×D₃	—	6	16	no	—
256	Dic₆	—	6	8	no	—
257	C₂×C₃²	—	2	4	no	—
258	C₂×C₃²	—	2	4	no	—
259	C₂×C₃²	—	2	4	no	—
260	C₂×C₃²	C₂×#237	1	4	yes	—
261	C₂×C₃²	C₂×#239	1	4	yes	—
262	C₂×C₃²	#1007	1	4	yes	—
263	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
264	C₂×C₃²	C₂×C₃×#41	1	1	yes	characteristic
265	C₂×C₃²	C₃×2₋¹⁺⁴	1	1	yes	characteristic
266	C₃⋊D₃	—	4	2	no	—
267	C₃×D₃	—	12	8	no	—
268	C₂×Q₈	—	9	1	no	—
269	C₂×Q₈	C₂×C₃×C₃⋊D₃	1	2	yes	—
270	C₂×D₄	—	9	1	no	—
271	C₂²×C₄	—	9	2	no	—
272	C₄⋊C₄	—	9	1	no	—
273	C₄⋊C₄	—	9	1	no	—
274	C₄⋊C₄	—	9	4	no	—
275	C₄⋊C₄	—	9	2	no	—
276	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
277	C₄⋊C₄	C₂×C₃×C₃⋊D₃	1	2	yes	—
278	C₂²⋊C₄	—	9	4	no	—
279	C₂²⋊C₄	—	9	2	no	—
280	C₂²⋊C₄	—	9	4	no	—
281	C₄²	—	9	4	no	—
282	C₄²	—	9	2	no	—
283	C₄²	C₂×C₃×C₃⋊D₃	1	1	yes	characteristic
284	C₂²×C₃	—	2	4	no	—
285	C₂²×C₃	—	18	2	no	—
286	C₂²×C₃	—	18	2	no	—
287	C₂²×C₃	—	18	2	no	—
288	C₂²×C₃	C₂³×C₃×D₃	1	4	yes	—
289	C₂²×C₃	C₂³×C₃⋊D₃	1	1	yes	characteristic
290	C₂×D₃	—	6	8	no	—
291	C₂×D₃	—	6	8	no	—
292	C₂×D₃	—	6	8	no	—
293	C₃×C₄	—	2	8	no	—
294	C₃×C₄	—	2	16	no	—
295	C₃×C₄	—	2	4	no	—
296	C₃×C₄	—	2	4	no	—
297	C₃×C₄	—	2	1	no	—
298	C₃×C₄	—	2	8	no	—
299	C₃×C₄	—	2	8	no	—
300	C₃×C₄	—	4	16	no	—
301	C₃×C₄	—	18	2	no	—
302	C₃×C₄	—	18	2	no	—
303	C₃×C₄	—	18	2	no	—
304	C₃×C₄	C₃×#237	1	8	yes	—
305	C₃×C₄	C₃×#239	1	8	yes	—
306	C₃×C₄	#3830	1	2	yes	—
307	C₃×C₄	#3832	1	2	yes	—
308	Dic₃	—	6	8	no	—
309	Dic₃	—	6	8	no	—
310	Dic₃	—	6	8	no	—
311	C₃²	—	2	4	no	—
312	C₃²	#5732	1	4	yes	complemented
313	C₃²	C₃×#556	1	1	yes	characteristic, complemented
314	C₂³	—	9	2	no	—
315	Q₈	—	2	4	no	—
316	Q₈	—	18	2	no	—
317	D₄	—	18	2	no	—
318	C₂×C₄	—	9	2	no	—
319	C₂×C₄	—	9	2	no	—
320	C₂×C₄	—	9	2	no	—
321	C₂×C₄	—	18	4	no	—
322	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	4	yes	—
323	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
324	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
325	C₂×C₄	C₂²×C₃×C₃⋊D₃	1	1	yes	characteristic
326	C₂×C₃	—	2	4	no	—
327	C₂×C₃	—	2	4	no	—
328	C₂×C₃	—	2	4	no	—
329	C₂×C₃	—	36	2	no	—
330	C₂×C₃	C₂×C₃×#237	1	4	yes	—
331	C₂×C₃	C₂×C₃×#239	1	4	yes	—
332	C₂×C₃	C₃×#1007	1	4	yes	—
333	C₂×C₃	C₂×#3830	1	1	yes	characteristic
334	C₂×C₃	C₂×#3832	1	1	yes	characteristic
335	C₂×C₃	#64364	1	1	yes	characteristic
336	D₃	—	12	8	no	—
337	C₂²	—	18	2	no	—
338	C₂²	—	18	2	no	—
339	C₂²	—	18	2	no	—
340	C₂²	C₂³×C₃×C₃⋊D₃	1	1	yes	characteristic
341	C₄	—	2	4	no	—
342	C₄	—	2	1	no	—
343	C₄	—	18	2	no	—
344	C₄	—	18	2	no	—
345	C₄	—	18	2	no	—
346	C₄	C₃×#3830	1	2	yes	—
347	C₄	C₃×#3832	1	2	yes	—
348	C₃	—	2	4	no	—
349	C₃	C₃×#5732	1	4	yes	complemented
350	C₃	#10596203	1	1	yes	characteristic, direct product factor
351	C₂	—	36	2	no	—
352	C₂	C₂×C₃×#3830	1	1	yes	characteristic
353	C₂	C₂×C₃×#3832	1	1	yes	characteristic
354	C₂	C₃×#64364	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
3. C₃×Q₈×C₃⋊Dic₃	C₂	semidirect
4. C₃×#64107	C₂	semidirect
5. C₃×#64106	C₂	semidirect
6. C₃×#64101	C₂	semidirect
8. C₃×C₄×#634	C₂	semidirect
9. #10596203	C₃	direct (N × H)
28. C₃²×C₄⋊Q₈	D₃	semidirect
29. C₃²×C₄⋊Q₈	C₂×C₃	semidirect
31. Q₈×C₃⋊Dic₃	C₂×C₃	semidirect
32. #64107	C₂×C₃	semidirect
33. #64106	C₂×C₃	semidirect
34. #64101	C₂×C₃	semidirect
36. C₄×#634	C₂×C₃	semidirect
106. C₃×C₄⋊Q₈	C₃×D₃	semidirect
107. C₃×C₄⋊Q₈	C₃⋊D₃	semidirect
219. C₄⋊Q₈	C₃×C₃⋊D₃	semidirect
227. C₃³	#556	semidirect
312. C₃²	#5732	semidirect
313. C₃²	C₃×#556	semidirect
349. C₃	C₃×#5732	semidirect
350. C₃	#10596203	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×#64156	2
C₃×Q₈×C₃⋊Dic₃	2
C₃×#64107	2
C₃×#64106	2
C₃×#64101	2
C₃×C₄×C₄⋊(C₃⋊D₃)	2
C₃×C₄×#634	2
#10596203	3
C₃×#5732	3

Subgroups — C3×#10596203 #13179483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10596203 #13179483