Subgroups — #135×C₃⋊(C₃⋊D₃) #13179892

Order 1728.

3724 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
2	C₃³×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	#11723991	C₂	1	2	yes	maximal, complemented
4	#11723960	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₁₆×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
6	#11723957	C₂	1	2	yes	maximal, complemented
7	SD₁₆×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
8	#11723953	C₂	1	1	yes	maximal, characteristic, complemented
9	D₈×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
10	#11723945	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₈×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃⋊D₃×#135	—	3	13	no	maximal
13	C₃³×#41	C₂²	1	2	yes	complemented
14	#89080	C₂²	1	2	yes	complemented
15	Q₈×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	—
16	#89078	—	2	2	no	—
17	#89078	C₂²	1	2	yes	complemented
18	D₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
19	D₄×C₃⋊(C₃⋊D₃)	C₂²	1	2	yes	—
20	#89076	—	2	2	no	—
21	#89076	C₂²	1	2	yes	complemented
22	C₂×C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
23	C₂×C₄×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
24	C₃³×Q₁₆	C₂²	1	1	yes	characteristic, complemented
25	C₃³×SD₁₆	C₂²	1	2	yes	complemented
26	C₃³×D₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃³×C₈	C₂²	1	1	yes	characteristic, complemented
28	#88863	C₂²	1	2	yes	complemented
29	#88862	C₂²	1	2	yes	complemented
30	#88861	C₂²	1	2	yes	complemented
31	#88860	C₂²	1	2	yes	complemented
32	C₂×C₃⋊(C₃⋊(C₃⋊C₈))	C₂²	1	1	yes	characteristic, complemented
33	#88853	C₂²	1	1	yes	characteristic, complemented
34	#88852	C₂²	1	1	yes	characteristic, complemented
35	#88851	C₂²	1	2	yes	complemented
36	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
37	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic
38	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
39	C₈×C₃⋊(C₃⋊D₃)	C₂²	1	1	yes	characteristic, complemented
40	#41×C₃⋊D₃	—	3	26	no	—
41	C₃²×#135	D₃	1	13	yes	complemented
42	#64159	—	3	26	no	—
43	#64128	—	3	13	no	—
44	Q₁₆×C₃⋊D₃	—	3	13	no	—
45	#64125	—	3	26	no	—
46	SD₁₆×C₃⋊D₃	—	3	26	no	—
47	#64121	—	3	13	no	—
48	D₈×C₃⋊D₃	—	3	13	no	—
49	#64113	—	3	13	no	—
50	C₂×C₈×C₃⋊D₃	—	3	13	no	—
51	C₂²×C₃⋊(C₃⋊D₃)	—	2	2	no	—
52	C₂²×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
53	C₃³×Q₈	C₂³	1	2	yes	—
54	C₃³×D₄	—	2	2	no	—
55	C₃³×D₄	C₂³	1	2	yes	—
56	C₂×C₃³×C₄	—	2	2	no	—
57	C₂×C₃³×C₄	C₂³	1	1	yes	characteristic
58	#6312	—	2	2	no	—
59	#6312	—	2	2	no	—
60	#6312	—	2	2	no	—
61	C₂×C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
62	C₂×C₃⋊(C₃⋊Dic₃)	D₄	1	1	yes	characteristic
63	C₄⋊(C₃⋊(C₃⋊D₃))	—	2	2	no	—
64	C₄⋊(C₃⋊(C₃⋊D₃))	C₂³	1	2	yes	—
65	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
66	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
67	C₄×C₃⋊(C₃⋊D₃)	—	2	2	no	—
68	C₄×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
69	C₄×C₃⋊(C₃⋊D₃)	D₄	1	1	yes	characteristic
70	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
71	C₄×C₃⋊(C₃⋊D₃)	C₂³	1	1	yes	characteristic
72	#6308	—	2	2	no	—
73	#6308	C₂³	1	2	yes	—
74	C₃³×C₈	C₂³	1	1	yes	characteristic
75	C₃³×C₈	C₂³	1	1	yes	characteristic
76	C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	1	1	yes	characteristic
77	C₃⋊(C₃⋊(C₃⋊C₈))	C₂³	1	1	yes	characteristic
78	D₃×#135	—	9	13	no	—
79	C₃²×#41	C₂×D₃	1	26	yes	complemented
80	#3832	—	3	26	no	—
81	Q₈×C₃⋊D₃	—	3	26	no	—
82	#3830	—	3	26	no	—
83	#3830	—	6	26	no	—
84	D₄×C₃⋊D₃	—	3	26	no	—
85	D₄×C₃⋊D₃	—	6	26	no	—
86	#3828	—	3	26	no	—
87	#3828	—	6	26	no	—
88	C₂×C₄×C₃⋊D₃	—	3	13	no	—
89	C₂×C₄×C₃⋊D₃	—	6	26	no	—
90	C₃²×Q₁₆	C₂×D₃	1	13	yes	complemented
91	C₃²×SD₁₆	C₂×D₃	1	26	yes	complemented
92	C₃²×D₈	C₂×D₃	1	13	yes	complemented
93	C₂×C₃²×C₈	C₂×D₃	1	13	yes	complemented
94	#3756	—	3	26	no	—
95	#3755	—	3	26	no	—
96	#3754	—	3	26	no	—
97	#3753	—	3	26	no	—
98	C₂×C₃⋊(C₃⋊C₈)	—	3	13	no	—
99	#3746	—	3	13	no	—
100	#3745	—	3	13	no	—
101	#3744	—	3	26	no	—
102	C₈×C₃⋊D₃	—	3	13	no	—
103	C₈×C₃⋊D₃	—	3	13	no	—
104	C₈×C₃⋊D₃	—	3	13	no	—
105	C₈×C₃⋊D₃	—	3	13	no	—
106	C₂²×C₃³	—	2	2	no	—
107	C₂²×C₃³	C₂×D₄	1	1	yes	characteristic
108	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
109	C₂×C₃⋊(C₃⋊D₃)	—	2	2	no	—
110	C₂×C₃⋊(C₃⋊D₃)	—	4	4	no	—
111	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃⋊(C₃⋊D₃)	C₂×D₄	1	1	yes	characteristic
113	C₃³×C₄	—	2	2	no	—
114	C₃³×C₄	C₂×D₄	1	1	yes	characteristic
115	C₃³×C₄	C₂⁴	1	1	yes	characteristic
116	C₃⋊(C₃⋊Dic₃)	—	2	2	no	—
117	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	1	yes	characteristic
118	C₃⋊(C₃⋊Dic₃)	C₂×D₄	1	1	yes	characteristic
119	D₃×#41	—	9	26	no	—
120	C₃×#135	C₃⋊D₃	1	13	yes	complemented
121	#950	—	9	26	no	—
122	#919	—	9	13	no	—
123	D₃×Q₁₆	—	9	13	no	—
124	#916	—	9	26	no	—
125	D₃×SD₁₆	—	9	26	no	—
126	#912	—	9	13	no	—
127	D₃×D₈	—	9	13	no	—
128	#904	—	9	13	no	—
129	C₂×D₃×C₈	—	9	13	no	—
130	C₂²×C₃⋊D₃	—	3	13	no	—
131	C₂²×C₃⋊D₃	—	6	26	no	—
132	C₃²×Q₈	C₂²×D₃	1	26	yes	—
133	C₃²×D₄	—	2	26	no	—
134	C₃²×D₄	C₂²×D₃	1	26	yes	—
135	C₂×C₃²×C₄	—	2	26	no	—
136	C₂×C₃²×C₄	C₂²×D₃	1	13	yes	—
137	#638	—	6	26	no	—
138	#638	—	6	26	no	—
139	#638	—	6	26	no	—
140	C₂×C₃⋊Dic₃	—	3	13	no	—
141	C₂×C₃⋊Dic₃	—	6	26	no	—
142	C₄⋊(C₃⋊D₃)	—	3	26	no	—
143	C₄⋊(C₃⋊D₃)	—	6	26	no	—
144	C₄×C₃⋊D₃	—	3	13	no	—
145	C₄×C₃⋊D₃	—	3	13	no	—
146	C₄×C₃⋊D₃	—	3	13	no	—
147	C₄×C₃⋊D₃	—	3	13	no	—
148	C₄×C₃⋊D₃	—	6	26	no	—
149	C₄×C₃⋊D₃	—	6	26	no	—
150	C₄×C₃⋊D₃	—	6	26	no	—
151	#634	—	3	26	no	—
152	#634	—	6	26	no	—
153	C₃²×C₈	C₂²×D₃	1	13	yes	—
154	C₃²×C₈	C₂²×D₃	1	13	yes	—
155	C₃⋊(C₃⋊C₈)	—	3	13	no	—
156	C₃⋊(C₃⋊C₈)	—	3	13	no	—
157	C₂×#135	—	27	1	no	Sylow
158	C₂×C₃³	—	2	1	no	—
159	C₂×C₃³	—	4	2	no	—
160	C₂×C₃³	C₂²×D₄	1	1	yes	characteristic
161	C₃⋊(C₃⋊D₃)	—	2	1	no	—
162	C₃⋊(C₃⋊D₃)	—	4	2	no	—
163	C₃⋊(C₃⋊D₃)	#135	1	2	yes	direct product factor
164	C₃×#41	C₂×C₃⋊D₃	1	26	yes	complemented
165	#239	—	9	26	no	—
166	D₃×Q₈	—	9	26	no	—
167	#237	—	9	26	no	—
168	#237	—	18	26	no	—
169	D₃×D₄	—	9	26	no	—
170	D₃×D₄	—	18	26	no	—
171	#235	—	9	26	no	—
172	#235	—	18	26	no	—
173	C₂×C₄×D₃	—	9	13	no	—
174	C₂×C₄×D₃	—	18	26	no	—
175	C₃×Q₁₆	C₂×C₃⋊D₃	1	13	yes	complemented
176	C₃×SD₁₆	C₂×C₃⋊D₃	1	26	yes	complemented
177	C₃×D₈	C₂×C₃⋊D₃	1	13	yes	complemented
178	C₂×C₃×C₈	C₂×C₃⋊D₃	1	13	yes	complemented
179	#216	—	9	26	no	—
180	#215	—	9	26	no	—
181	#214	—	9	26	no	—
182	#213	—	9	26	no	—
183	C₂×C₃⋊C₈	—	9	13	no	—
184	Dic₁₂	—	9	13	no	—
185	D₂₄	—	9	13	no	—
186	#204	—	9	26	no	—
187	D₃×C₈	—	9	13	no	—
188	D₃×C₈	—	9	13	no	—
189	D₃×C₈	—	9	13	no	—
190	D₃×C₈	—	9	13	no	—
191	C₂²×C₃²	—	2	26	no	—
192	C₂²×C₃²	D₃×D₄	1	13	yes	—
193	C₂×C₃⋊D₃	—	3	13	no	—
194	C₂×C₃⋊D₃	—	3	13	no	—
195	C₂×C₃⋊D₃	—	6	26	no	—
196	C₂×C₃⋊D₃	—	6	26	no	—
197	C₂×C₃⋊D₃	—	12	52	no	—
198	C₃²×C₄	—	2	26	no	—
199	C₃²×C₄	D₃×D₄	1	13	yes	—
200	C₃²×C₄	C₂³×D₃	1	13	yes	—
201	C₃⋊Dic₃	—	3	13	no	—
202	C₃⋊Dic₃	—	3	13	no	—
203	C₃⋊Dic₃	—	6	26	no	—
204	C₂×#41	—	27	2	no	—
205	#135	—	27	2	no	—
206	#135	—	27	1	no	—
207	#135	—	27	2	no	—
208	#135	—	27	1	no	—
209	#135	—	27	1	no	—
210	#135	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, direct product factor
211	C₂×Q₁₆	—	27	1	no	—
212	C₂×SD₁₆	—	27	2	no	—
213	C₂×D₈	—	27	1	no	—
214	C₂²×C₈	—	27	1	no	—
215	C₃³	C₂×#135	1	1	yes	characteristic, complemented, Sylow
216	C₂²×D₃	—	9	13	no	—
217	C₂²×D₃	—	18	26	no	—
218	C₃×Q₈	C₂²×C₃⋊D₃	1	26	yes	—
219	C₃×D₄	—	2	26	no	—
220	C₃×D₄	C₂²×C₃⋊D₃	1	26	yes	—
221	C₂×C₃×C₄	—	2	26	no	—
222	C₂×C₃×C₄	C₂²×C₃⋊D₃	1	13	yes	—
223	#67	—	18	26	no	—
224	#67	—	18	26	no	—
225	#67	—	18	26	no	—
226	C₂×Dic₃	—	9	13	no	—
227	C₂×Dic₃	—	18	26	no	—
228	D₁₂	—	9	26	no	—
229	D₁₂	—	18	26	no	—
230	C₄×D₃	—	9	13	no	—
231	C₄×D₃	—	9	13	no	—
232	C₄×D₃	—	9	13	no	—
233	C₄×D₃	—	9	13	no	—
234	C₄×D₃	—	18	26	no	—
235	C₄×D₃	—	18	26	no	—
236	C₄×D₃	—	18	26	no	—
237	Dic₆	—	9	26	no	—
238	Dic₆	—	18	26	no	—
239	C₃×C₈	C₂²×C₃⋊D₃	1	13	yes	—
240	C₃×C₈	C₂²×C₃⋊D₃	1	13	yes	—
241	C₃⋊C₈	—	9	13	no	—
242	C₃⋊C₈	—	9	13	no	—
243	C₂×C₃²	—	2	13	no	—
244	C₂×C₃²	—	4	26	no	—
245	C₂×C₃²	C₂×D₃×D₄	1	13	yes	—
246	C₃⋊D₃	—	3	26	no	—
247	C₃⋊D₃	—	6	13	no	—
248	C₃⋊D₃	—	12	26	no	—
249	#41	—	27	2	no	—
250	#41	—	27	2	no	—
251	#41	—	27	2	no	—
252	#41	—	54	2	no	—
253	#41	—	54	2	no	—
254	#41	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
255	C₂×Q₈	—	27	2	no	—
256	C₂×D₄	—	27	2	no	—
257	C₂×D₄	—	54	2	no	—
258	C₂²×C₄	—	27	1	no	—
259	C₂²×C₄	—	54	2	no	—
260	Q₁₆	—	27	2	no	—
261	Q₁₆	—	27	1	no	—
262	Q₁₆	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
263	SD₁₆	—	27	2	no	—
264	SD₁₆	—	27	2	no	—
265	SD₁₆	—	27	2	no	—
266	SD₁₆	C₂×C₃⋊(C₃⋊D₃)	1	2	yes	complemented
267	D₈	—	27	2	no	—
268	D₈	—	27	1	no	—
269	D₈	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
270	C₂×C₈	—	27	1	no	—
271	C₂×C₈	—	27	1	no	—
272	C₂×C₈	—	27	1	no	—
273	C₂×C₈	—	27	1	no	—
274	C₂×C₈	—	27	1	no	—
275	C₂×C₈	C₂×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
276	C₂²×C₃	—	2	26	no	—
277	C₂²×C₃	D₄×C₃⋊D₃	1	13	yes	—
278	C₂×D₃	—	9	13	no	—
279	C₂×D₃	—	9	13	no	—
280	C₂×D₃	—	18	26	no	—
281	C₂×D₃	—	18	26	no	—
282	C₂×D₃	—	36	52	no	—
283	C₃×C₄	—	2	26	no	—
284	C₃×C₄	D₄×C₃⋊D₃	1	13	yes	—
285	C₃×C₄	C₂³×C₃⋊D₃	1	13	yes	—
286	Dic₃	—	9	13	no	—
287	Dic₃	—	9	13	no	—
288	Dic₃	—	18	26	no	—
289	C₃²	D₃×#135	1	13	yes	complemented
290	C₂³	—	27	1	no	—
291	C₂³	—	54	2	no	—
292	Q₈	—	27	2	no	—
293	Q₈	—	54	2	no	—
294	Q₈	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
295	D₄	—	2	2	no	—
296	D₄	—	27	2	no	—
297	D₄	—	54	2	no	—
298	D₄	—	54	2	no	—
299	D₄	—	54	2	no	—
300	D₄	—	54	2	no	—
301	D₄	C₂²×C₃⋊(C₃⋊D₃)	1	2	yes	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	27	1	no	—
304	C₂×C₄	—	27	1	no	—
305	C₂×C₄	—	27	1	no	—
306	C₂×C₄	—	27	1	no	—
307	C₂×C₄	—	27	1	no	—
308	C₂×C₄	—	54	2	no	—
309	C₂×C₄	—	54	2	no	—
310	C₂×C₄	—	54	2	no	—
311	C₂×C₄	—	54	2	no	—
312	C₂×C₄	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
313	C₈	—	27	1	no	—
314	C₈	—	27	1	no	—
315	C₈	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
316	C₈	C₂²×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
317	C₂×C₃	—	2	13	no	—
318	C₂×C₃	—	4	26	no	—
319	C₂×C₃	C₂×D₄×C₃⋊D₃	1	13	yes	—
320	D₃	—	9	26	no	—
321	D₃	—	18	13	no	—
322	D₃	—	36	26	no	—
323	C₂²	—	2	2	no	—
324	C₂²	—	27	1	no	—
325	C₂²	—	27	1	no	—
326	C₂²	—	54	2	no	—
327	C₂²	—	54	2	no	—
328	C₂²	—	108	4	no	—
329	C₂²	D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
330	C₄	—	2	2	no	—
331	C₄	—	27	1	no	—
332	C₄	—	27	1	no	—
333	C₄	—	54	2	no	—
334	C₄	D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
335	C₄	C₂³×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
336	C₃	C₃⋊D₃×#135	1	13	yes	complemented
337	C₂	—	2	1	no	—
338	C₂	—	4	2	no	—
339	C₂	—	27	2	no	—
340	C₂	—	54	1	no	—
341	C₂	—	108	2	no	—
342	C₂	C₂×D₄×C₃⋊(C₃⋊D₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×C₃⋊(C₃⋊D₃)
commutator, cosocle	C₃³×C₄	C₂⁴
Frattini	C₄	C₂³×C₃⋊(C₃⋊D₃)
Fitting	C₃³×#135	C₂
socle	C₂×C₃³	C₂²×D₄
hypercenter	#135	C₃⋊(C₃⋊D₃)
hypocenter	C₃³	C₂×#135
LCS	G ▷ C₃³×C₄ ▷ C₂×C₃³ ▷ C₃³
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #41×C₃⋊(C₃⋊D₃)	C₂	semidirect
2. C₃³×#135	C₂	semidirect
3. #11723991	C₂	semidirect
4. #11723960	C₂	semidirect
5. Q₁₆×C₃⋊(C₃⋊D₃)	C₂	semidirect
6. #11723957	C₂	semidirect
7. SD₁₆×C₃⋊(C₃⋊D₃)	C₂	semidirect
8. #11723953	C₂	semidirect
9. D₈×C₃⋊(C₃⋊D₃)	C₂	semidirect
10. #11723945	C₂	semidirect
11. C₂×C₈×C₃⋊(C₃⋊D₃)	C₂	semidirect
13. C₃³×#41	C₂²	semidirect
14. #89080	C₂²	semidirect
17. #89078	C₂²	semidirect
21. #89076	C₂²	semidirect
24. C₃³×Q₁₆	C₂²	semidirect
25. C₃³×SD₁₆	C₂²	semidirect
26. C₃³×D₈	C₂²	semidirect
27. C₂×C₃³×C₈	C₂²	semidirect
28. #88863	C₂²	semidirect
29. #88862	C₂²	semidirect
30. #88861	C₂²	semidirect
31. #88860	C₂²	semidirect
32. C₂×C₃⋊(C₃⋊(C₃⋊C₈))	C₂²	semidirect
33. #88853	C₂²	semidirect
34. #88852	C₂²	semidirect
35. #88851	C₂²	semidirect
38. C₈×C₃⋊(C₃⋊D₃)	C₂²	semidirect
39. C₈×C₃⋊(C₃⋊D₃)	C₂²	semidirect
41. C₃²×#135	D₃	semidirect
79. C₃²×#41	C₂×D₃	semidirect
90. C₃²×Q₁₆	C₂×D₃	semidirect
91. C₃²×SD₁₆	C₂×D₃	semidirect
92. C₃²×D₈	C₂×D₃	semidirect
93. C₂×C₃²×C₈	C₂×D₃	semidirect
120. C₃×#135	C₃⋊D₃	semidirect
163. C₃⋊(C₃⋊D₃)	#135	direct (N × H)
164. C₃×#41	C₂×C₃⋊D₃	semidirect
175. C₃×Q₁₆	C₂×C₃⋊D₃	semidirect
176. C₃×SD₁₆	C₂×C₃⋊D₃	semidirect
177. C₃×D₈	C₂×C₃⋊D₃	semidirect
178. C₂×C₃×C₈	C₂×C₃⋊D₃	semidirect
210. #135	C₃⋊(C₃⋊D₃)	direct (N × H)
215. C₃³	C₂×#135	semidirect
254. #41	C₂×C₃⋊(C₃⋊D₃)	semidirect
262. Q₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
266. SD₁₆	C₂×C₃⋊(C₃⋊D₃)	semidirect
269. D₈	C₂×C₃⋊(C₃⋊D₃)	semidirect
275. C₂×C₈	C₂×C₃⋊(C₃⋊D₃)	semidirect
289. C₃²	D₃×#135	semidirect
336. C₃	C₃⋊D₃×#135	semidirect

Maximal subgroups

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

subgroup	index
#41×C₃⋊(C₃⋊D₃)	2
C₃³×#135	2
#11723991	2
#11723960	2
Q₁₆×C₃⋊(C₃⋊D₃)	2
#11723957	2
SD₁₆×C₃⋊(C₃⋊D₃)	2
#11723953	2
D₈×C₃⋊(C₃⋊D₃)	2
#11723945	2
C₂×C₈×C₃⋊(C₃⋊D₃)	2
C₃⋊D₃×#135	3

Subgroups — #135×C3⋊(C3⋊D3) #13179892

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #135×C₃⋊(C₃⋊D₃) #13179892