Subgroups — C₃×#79039 #11858863

Order 1152.

847 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#872	C₂	1	1	yes	maximal, characteristic
2	C₃²×#423	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#5126	C₂	1	2	yes	maximal
4	C₃×Dic₃×M₁₆	C₂	1	2	yes	maximal, complemented
5	C₃×#4924	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4840	C₂	1	8	yes	maximal, complemented
7	C₃×#2921	—	3	1	no	maximal
8	#79039	C₃	1	1	yes	maximal, characteristic, direct product factor
9	C₂²×C₃×C₄×D₃	C₂²	1	1	yes	characteristic
10	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
11	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
12	C₂×C₃×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
13	C₂×C₃×Dic₃⋊C₄	C₄	1	2	yes	—
14	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×#208	C₂²	1	2	yes	—
16	C₃×#872	C₄	1	2	yes	—
17	C₃×#872	C₄	1	2	yes	—
18	C₃×#872	C₂²	1	4	yes	—
19	C₃²×C₄⋊C₈	C₂²	1	4	yes	complemented
20	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
21	C₃×#815	C₂²	1	4	yes	complemented
22	C₃×C₈×Dic₃	C₂²	1	4	yes	complemented
23	C₃×C₄⋊(C₃⋊C₈)	C₂²	1	4	yes	complemented
24	C₂×C₃×#117	—	3	1	no	—
25	C₂×#872	C₂×C₃	1	1	yes	characteristic
26	C₃×#433	—	3	8	no	—
27	C₃×#423	—	2	1	no	—
28	C₃×#423	—	3	1	no	—
29	C₃×#423	D₃	1	1	yes	characteristic, complemented
30	C₃×#423	C₂×C₃	1	1	yes	characteristic, complemented
31	C₃×#407	—	3	2	no	—
32	C₃×C₄×M₁₆	—	3	2	no	—
33	#5126	C₂×C₃	1	2	yes	—
34	Dic₃×M₁₆	C₂×C₃	1	2	yes	complemented
35	#4924	C₂×C₃	1	1	yes	characteristic, complemented
36	#4840	C₂×C₃	1	8	yes	complemented
37	C₂³×C₃×D₃	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂²×C₃×Dic₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₃×Dic₃	C₂×C₄	1	2	yes	—
42	C₂×C₃×C₄×D₃	—	2	2	no	—
43	C₂×C₃×C₄×D₃	—	2	2	no	—
44	C₂×C₃×C₄×D₃	C₂×C₄	1	2	yes	—
45	C₂×C₃×C₄×D₃	C₂³	1	2	yes	—
46	C₃²×M₁₆	—	2	4	no	—
47	C₂×C₃²×C₈	C₂³	1	4	yes	—
48	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
49	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
50	C₃²×C₄²	C₂³	1	2	yes	—
51	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
52	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
53	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
54	C₃×Dic₃⋊C₄	C₂×C₄	1	4	yes	—
55	C₃×C₄×Dic₃	C₂×C₄	1	2	yes	—
56	C₃×C₄×Dic₃	C₂³	1	2	yes	—
57	C₃×#208	—	2	4	no	—
58	C₂×C₃×C₃⋊C₈	C₂³	1	4	yes	—
59	#2921	—	3	1	no	Sylow
60	C₂³×C₃×C₄	—	3	1	no	—
61	C₂²×C₄×D₃	C₂²×C₃	1	1	yes	characteristic
62	C₂×C₃×M₁₆	—	2	2	no	—
63	C₂×C₃×M₁₆	—	3	2	no	—
64	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
65	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
66	C₃×#117	—	3	2	no	—
67	C₃×#117	—	3	2	no	—
68	C₃×#117	—	3	4	no	—
69	C₂×C₃×C₄⋊C₄	—	3	2	no	—
70	C₂×C₃×C₂²⋊C₄	—	3	2	no	—
71	C₂×C₃×C₄²	—	2	1	no	—
72	C₂×C₃×C₄²	—	3	1	no	—
73	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
74	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
75	C₂×(C₂×D₃)⋊C₄	C₃×C₄	1	2	yes	—
76	C₂×Dic₃⋊C₄	C₃×C₄	1	2	yes	—
77	C₂×C₄×Dic₃	C₂²×C₃	1	1	yes	characteristic
78	C₂×#208	C₂²×C₃	1	2	yes	—
79	#872	C₃×C₄	1	2	yes	—
80	#872	C₃×C₄	1	2	yes	—
81	#872	C₂²×C₃	1	4	yes	—
82	C₃×C₄⋊C₈	—	2	4	no	—
83	C₃×C₄⋊C₈	—	3	4	no	—
84	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	complemented
85	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	complemented
86	C₃×C₂²⋊C₈	—	3	8	no	—
87	C₃×#97	—	3	4	no	—
88	C₃×C₄×C₈	—	3	4	no	—
89	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	—
90	#815	C₂²×C₃	1	4	yes	complemented
91	C₈×Dic₃	C₂²×C₃	1	4	yes	complemented
92	C₄⋊(C₃⋊C₈)	C₂²×C₃	1	4	yes	complemented
93	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₃×D₃	—	2	2	no	—
95	C₂²×C₃×D₃	—	4	2	no	—
96	C₂²×C₃×D₃	C₂²×C₄	1	2	yes	—
97	C₂×C₃²×C₄	—	4	2	no	—
98	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
99	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
100	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	#41	1	2	yes	—
102	C₂×C₃²×C₄	#41	1	2	yes	—
103	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
104	C₂×C₃×Dic₃	—	2	2	no	—
105	C₂×C₃×Dic₃	—	4	2	no	—
106	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
107	C₂×C₃×Dic₃	C₂²×C₄	1	2	yes	—
108	C₃×C₄×D₃	—	2	4	no	—
109	C₃×C₄×D₃	—	2	2	no	—
110	C₃×C₄×D₃	—	2	2	no	—
111	C₃²×C₈	—	2	4	no	—
112	C₃×C₃⋊C₈	—	2	4	no	—
113	C₂×#117	—	3	1	no	—
114	#433	—	3	8	no	—
115	#423	—	3	1	no	—
116	#423	C₃×D₃	1	1	yes	characteristic, complemented
117	#407	—	3	2	no	—
118	C₄×M₁₆	—	3	2	no	—
119	C₂⁴×C₃	—	3	1	no	—
120	C₂³×D₃	C₂×C₃×C₄	1	1	yes	characteristic
121	C₂²×C₃×C₄	—	2	2	no	—
122	C₂²×C₃×C₄	—	2	1	no	—
123	C₂²×C₃×C₄	—	3	1	no	—
124	C₂²×C₃×C₄	—	3	2	no	—
125	C₂²×C₃×C₄	—	3	2	no	—
126	C₂²×C₃×C₄	—	3	2	no	—
127	C₂²×C₃×C₄	—	6	2	no	—
128	C₂²×C₃×C₄	—	6	2	no	—
129	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
130	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
131	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
132	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
133	C₂²×Dic₃	C₂×C₃×C₄	1	1	yes	characteristic
134	C₂²×Dic₃	C₂×C₃×C₄	1	2	yes	—
135	C₂×C₄×D₃	—	2	2	no	—
136	C₂×C₄×D₃	—	2	2	no	—
137	C₂×C₄×D₃	C₂×C₃×C₄	1	2	yes	—
138	C₂×C₄×D₃	C₂³×C₃	1	2	yes	—
139	C₃×M₁₆	—	2	4	no	—
140	C₃×M₁₆	—	2	4	no	—
141	C₃×M₁₆	—	4	4	no	—
142	C₃×M₁₆	—	6	4	no	—
143	C₂×C₃×C₈	—	2	4	no	—
144	C₂×C₃×C₈	—	3	4	no	—
145	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
146	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
147	C₃×C₄⋊C₄	—	3	4	no	—
148	C₃×C₄⋊C₄	—	3	4	no	—
149	C₃×C₂²⋊C₄	—	3	4	no	—
150	C₃×C₂²⋊C₄	—	3	4	no	—
151	C₃×C₄²	—	2	1	no	—
152	C₃×C₄²	—	2	1	no	—
153	C₃×C₄²	—	2	2	no	—
154	C₃×C₄²	—	3	2	no	—
155	C₃×C₄²	—	3	2	no	—
156	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
157	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
158	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
159	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
160	C₃×C₄²	C₂²×D₃	1	2	yes	—
161	C₃×C₄²	C₂³×C₃	1	2	yes	—
162	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
163	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	4	yes	—
164	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
165	Dic₃⋊C₄	C₂×C₃×C₄	1	4	yes	—
166	C₄×Dic₃	C₂×C₃×C₄	1	2	yes	—
167	C₄×Dic₃	C₂³×C₃	1	2	yes	—
168	#208	—	2	4	no	—
169	C₂×C₃⋊C₈	C₂³×C₃	1	4	yes	—
170	C₂²×C₃²	—	2	2	no	—
171	C₂²×C₃²	#117	1	2	yes	—
172	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
173	C₂×C₃×D₃	—	2	2	no	—
174	C₂×C₃×D₃	—	2	4	no	—
175	C₂×C₃×D₃	—	4	4	no	—
176	C₃²×C₄	—	2	2	no	—
177	C₃²×C₄	—	2	2	no	—
178	C₃²×C₄	#117	1	2	yes	—
179	C₃²×C₄	C₂×#41	1	1	yes	characteristic
180	C₃²×C₄	C₂×#41	1	1	yes	characteristic
181	C₃×Dic₃	—	2	2	no	—
182	C₃×Dic₃	—	2	4	no	—
183	C₂³×C₄	—	3	1	no	—
184	C₂×M₁₆	—	3	2	no	—
185	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
186	#117	—	3	2	no	—
187	#117	—	3	2	no	—
188	#117	—	3	4	no	—
189	C₂×C₄⋊C₄	—	3	2	no	—
190	C₂×C₂²⋊C₄	—	3	2	no	—
191	C₂×C₄²	—	3	1	no	—
192	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
193	C₄⋊C₈	—	3	4	no	—
194	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	complemented
195	C₂²⋊C₈	—	3	8	no	—
196	#97	—	3	4	no	—
197	C₄×C₈	—	3	4	no	—
198	C₂³×C₃	—	2	1	no	—
199	C₂³×C₃	—	3	2	no	—
200	C₂³×C₃	—	6	2	no	—
201	C₂³×C₃	—	12	2	no	—
202	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
203	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
204	C₂²×D₃	—	2	2	no	—
205	C₂²×D₃	—	4	2	no	—
206	C₂²×D₃	C₂²×C₃×C₄	1	2	yes	—
207	C₂×C₃×C₄	—	2	1	no	—
208	C₂×C₃×C₄	—	2	2	no	—
209	C₂×C₃×C₄	—	2	1	no	—
210	C₂×C₃×C₄	—	2	2	no	—
211	C₂×C₃×C₄	—	2	2	no	—
212	C₂×C₃×C₄	—	2	2	no	—
213	C₂×C₃×C₄	—	3	4	no	—
214	C₂×C₃×C₄	—	3	2	no	—
215	C₂×C₃×C₄	—	4	2	no	—
216	C₂×C₃×C₄	—	4	2	no	—
217	C₂×C₃×C₄	—	4	4	no	—
218	C₂×C₃×C₄	—	6	2	no	—
219	C₂×C₃×C₄	—	6	4	no	—
220	C₂×C₃×C₄	—	6	2	no	—
221	C₂×C₃×C₄	—	6	2	no	—
222	C₂×C₃×C₄	—	12	2	no	—
223	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
224	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
225	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
226	C₂×C₃×C₄	#237	1	2	yes	—
227	C₂×C₃×C₄	#239	1	2	yes	—
228	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
229	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
230	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
231	C₂×C₃×C₄	C₃×#41	1	2	yes	—
232	C₂×C₃×C₄	C₃×#41	1	2	yes	—
233	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
235	C₂×Dic₃	—	2	2	no	—
236	C₂×Dic₃	—	4	2	no	—
237	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
238	C₂×Dic₃	C₂²×C₃×C₄	1	2	yes	—
239	C₄×D₃	—	2	4	no	—
240	C₄×D₃	—	2	2	no	—
241	C₄×D₃	—	2	2	no	—
242	C₃×C₈	—	2	4	no	—
243	C₃×C₈	—	2	4	no	—
244	C₃×C₈	—	4	4	no	—
245	C₃×C₈	—	6	4	no	—
246	C₃⋊C₈	—	2	4	no	—
247	C₂×C₃²	—	2	2	no	—
248	C₂×C₃²	C₂×#117	1	1	yes	characteristic
249	C₂×C₃²	#568	1	2	yes	—
250	C₃×D₃	—	4	2	no	—
251	C₂⁴	—	3	1	no	—
252	C₂²×C₄	—	3	1	no	—
253	C₂²×C₄	—	3	2	no	—
254	C₂²×C₄	—	3	2	no	—
255	C₂²×C₄	—	3	2	no	—
256	C₂²×C₄	—	6	2	no	—
257	C₂²×C₄	—	6	2	no	—
258	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
259	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
260	M₁₆	—	2	4	no	—
261	M₁₆	—	6	4	no	—
262	C₂×C₈	—	3	4	no	—
263	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
264	C₄⋊C₄	—	3	4	no	—
265	C₄⋊C₄	—	3	4	no	—
266	C₂²⋊C₄	—	3	4	no	—
267	C₂²⋊C₄	—	3	4	no	—
268	C₄²	—	3	2	no	—
269	C₄²	—	3	2	no	—
270	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
271	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
272	C₄²	C₂²×C₃×D₃	1	2	yes	—
273	C₂²×C₃	—	2	2	no	—
274	C₂²×C₃	—	2	2	no	—
275	C₂²×C₃	—	2	2	no	—
276	C₂²×C₃	—	2	1	no	—
277	C₂²×C₃	—	4	2	no	—
278	C₂²×C₃	—	6	4	no	—
279	C₂²×C₃	—	6	2	no	—
280	C₂²×C₃	—	12	4	no	—
281	C₂²×C₃	#892	1	2	yes	—
282	C₂²×C₃	C₃×#117	1	2	yes	—
283	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
284	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
285	C₂×D₃	—	2	4	no	—
286	C₂×D₃	—	2	2	no	—
287	C₂×D₃	—	4	4	no	—
288	C₃×C₄	—	2	4	no	—
289	C₃×C₄	—	2	2	no	—
290	C₃×C₄	—	2	2	no	—
291	C₃×C₄	—	2	2	no	—
292	C₃×C₄	—	2	2	no	—
293	C₃×C₄	—	2	2	no	—
294	C₃×C₄	—	2	1	no	—
295	C₃×C₄	—	2	1	no	—
296	C₃×C₄	—	4	2	no	—
297	C₃×C₄	—	6	4	no	—
298	C₃×C₄	—	6	2	no	—
299	C₃×C₄	#892	1	2	yes	—
300	C₃×C₄	C₃×#117	1	2	yes	—
301	C₃×C₄	C₂×#237	1	1	yes	characteristic
302	C₃×C₄	C₂×#239	1	1	yes	characteristic
303	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
304	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
305	Dic₃	—	2	4	no	—
306	Dic₃	—	2	2	no	—
307	C₃²	#2921	1	1	yes	characteristic, complemented, Sylow
308	C₂³	—	3	2	no	—
309	C₂³	—	6	2	no	—
310	C₂³	—	12	2	no	—
311	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
312	C₂×C₄	—	3	4	no	—
313	C₂×C₄	—	3	2	no	—
314	C₂×C₄	—	4	2	no	—
315	C₂×C₄	—	6	2	no	—
316	C₂×C₄	—	6	4	no	—
317	C₂×C₄	—	6	2	no	—
318	C₂×C₄	—	6	2	no	—
319	C₂×C₄	—	12	2	no	—
320	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
321	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
322	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
323	C₂×C₄	C₃×#237	1	2	yes	—
324	C₂×C₄	C₃×#239	1	2	yes	—
325	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
326	C₈	—	2	4	no	—
327	C₈	—	6	4	no	—
328	C₂×C₃	—	2	2	no	—
329	C₂×C₃	—	2	2	no	—
330	C₂×C₃	—	2	2	no	—
331	C₂×C₃	—	2	1	no	—
332	C₂×C₃	—	4	2	no	—
333	C₂×C₃	—	12	2	no	—
334	C₂×C₃	C₂×#892	1	1	yes	characteristic
335	C₂×C₃	#5745	1	2	yes	—
336	C₂×C₃	C₂×C₃×#117	1	1	yes	characteristic
337	C₂×C₃	C₃×#568	1	2	yes	—
338	D₃	—	4	2	no	—
339	C₂²	—	2	2	no	—
340	C₂²	—	6	4	no	—
341	C₂²	—	6	2	no	—
342	C₂²	—	12	4	no	—
343	C₂²	C₃×#892	1	2	yes	—
344	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	6	4	no	—
348	C₄	—	6	2	no	—
349	C₄	C₃×#892	1	2	yes	—
350	C₄	C₂×C₃×#237	1	1	yes	characteristic
351	C₄	C₂×C₃×#239	1	1	yes	characteristic
352	C₃	—	2	1	no	—
353	C₃	#79039	1	1	yes	characteristic, direct product factor
354	C₃	C₃×#2921	1	1	yes	characteristic, complemented
355	C₂	—	2	2	no	—
356	C₂	—	12	2	no	—
357	C₂	C₂×C₃×#892	1	1	yes	characteristic
358	C₂	C₃×#5745	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₃
Fitting	C₃²×#423	C₂
socle	C₂²×C₃²	C₂³×C₄
prime radical	C₂³×C₃×D₃	C₂×C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#423	D₃
hypocenter	C₃	C₃×#2921
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₃×#423

Complements

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

N	H ≅ G/N	type
2. C₃²×#423	C₂	semidirect
4. C₃×Dic₃×M₁₆	C₂	semidirect
5. C₃×#4924	C₂	semidirect
6. C₃×#4840	C₂	semidirect
8. #79039	C₃	direct (N × H)
19. C₃²×C₄⋊C₈	C₂²	semidirect
21. C₃×#815	C₂²	semidirect
22. C₃×C₈×Dic₃	C₂²	semidirect
23. C₃×C₄⋊(C₃⋊C₈)	C₂²	semidirect
29. C₃×#423	D₃	semidirect
30. C₃×#423	C₂×C₃	semidirect
34. Dic₃×M₁₆	C₂×C₃	semidirect
35. #4924	C₂×C₃	semidirect
36. #4840	C₂×C₃	semidirect
84. C₃×C₄⋊C₈	C₂×D₃	semidirect
85. C₃×C₄⋊C₈	C₂²×C₃	semidirect
90. #815	C₂²×C₃	semidirect
91. C₈×Dic₃	C₂²×C₃	semidirect
92. C₄⋊(C₃⋊C₈)	C₂²×C₃	semidirect
116. #423	C₃×D₃	semidirect
194. C₄⋊C₈	C₂×C₃×D₃	semidirect
307. C₃²	#2921	semidirect
353. C₃	#79039	direct (N × H)
354. C₃	C₃×#2921	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#872	2
C₃²×#423	2
C₃×#5126	2
C₃×Dic₃×M₁₆	2
C₃×#4924	2
C₃×#4840	2
C₃×#2921	3
#79039	3

Subgroups — C3×#79039 #11858863

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79039 #11858863