Subgroups — C₃×#79041 #11859467

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#907	C₂	1	2	yes	maximal, complemented
2	C₃×#5477	C₂	1	1	yes	maximal, characteristic
3	C₃²×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#5129	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#4838	C₂	1	4	yes	maximal, complemented
7	C₃×#4834	C₂	1	4	yes	maximal, complemented
8	C₃×#2931	—	3	1	no	maximal
9	#79041	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	C₂²	1	2	yes	—
11	C₂×C₃²×M₁₆	C₂²	1	2	yes	—
12	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
13	C₃×#930	C₄	1	4	yes	—
14	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₃×#907	—	2	8	no	—
17	C₂×C₃×ΓL(1,𝔽₂₅)	C₂²	1	4	yes	—
18	C₂×C₃×D₃×C₈	C₂²	1	4	yes	—
19	C₃×#875	C₄	1	2	yes	—
20	C₃×#874	C₄	1	1	yes	characteristic
21	C₃×C₄×D₁₂	C₂²	1	4	yes	—
22	C₃×#869	C₄	1	1	yes	characteristic
23	C₃²×C₄⋊C₈	C₂²	1	4	yes	—
24	C₃×(C₂×D₃)⋊C₈	C₂²	1	8	yes	—
25	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
26	C₃×C₄×C₃⋊C₈	C₂²	1	2	yes	—
27	C₂×C₃×#131	—	3	2	no	—
28	C₃×#532	—	3	1	no	—
29	C₂×#907	C₂×C₃	1	2	yes	complemented
30	#5477	C₂×C₃	1	1	yes	characteristic
31	C₃×#436	—	3	4	no	—
32	C₃×C₈×D₄	—	3	4	no	—
33	C₃×#423	—	2	1	no	—
34	C₃×#423	D₃	1	1	yes	characteristic, complemented
35	C₃×#423	C₂×C₃	1	1	yes	characteristic, complemented
36	C₃×#408	—	3	2	no	—
37	C₂×C₃×C₄×C₈	—	3	1	no	—
38	#5129	C₂×C₃	1	2	yes	complemented
39	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
40	#4838	C₂×C₃	1	4	yes	complemented
41	#4834	C₂×C₃	1	4	yes	complemented
42	C₂²×C₃²×C₄	C₂×C₄	1	2	yes	—
43	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
44	C₂×C₃×#67	C₂×C₄	1	4	yes	—
45	C₃×#235	—	2	4	no	—
46	C₃×#235	—	2	4	no	—
47	C₂×C₃×D₁₂	C₂×C₄	1	4	yes	—
48	C₂×C₃×D₁₂	C₂×C₄	1	2	yes	—
49	C₂×C₃×C₄×D₃	C₂³	1	4	yes	—
50	C₂×C₃×Dic₆	C₂×C₄	1	2	yes	—
51	C₃²×M₁₆	—	2	4	no	—
52	C₂×C₃²×C₈	C₂³	1	4	yes	—
53	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
54	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
55	C₃²×C₄²	C₂³	1	2	yes	—
56	C₃×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
57	C₃×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
58	C₂×C₃×C₃⋊C₈	—	2	2	no	—
59	C₂×C₃×C₃⋊C₈	D₄	1	4	yes	complemented
60	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
61	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₃⋊C₈	C₂³	1	1	yes	characteristic
63	C₃×ΓL(1,𝔽₂₅)	—	2	8	no	—
64	C₃×D₃×C₈	—	2	8	no	—
65	#2931	—	3	1	no	Sylow
66	C₂×C₃×#41	—	3	2	no	—
67	C₂×#235	C₂²×C₃	1	2	yes	—
68	C₃×#131	—	6	8	no	—
69	C₂×C₃×M₁₆	—	2	2	no	—
70	C₂×C₃×M₁₆	—	3	4	no	—
71	C₂×C₃×M₁₆	C₂×D₃	1	2	yes	—
72	C₂×C₃×M₁₆	C₂²×C₃	1	2	yes	—
73	C₂²×C₃×C₈	—	3	1	no	—
74	C₂²×C₃×C₈	—	3	1	no	—
75	C₂²×C₃×C₈	—	3	4	no	—
76	C₃×C₄⋊Q₈	—	3	1	no	—
77	C₃×#127	—	3	1	no	—
78	C₃×#124	—	3	2	no	—
79	C₃×#121	—	3	4	no	—
80	C₃×C₄×D₄	—	3	4	no	—
81	C₂×C₃×C₄²	—	2	1	no	—
82	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
83	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
84	#930	C₃×C₄	1	4	yes	—
85	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
87	#907	—	2	8	no	—
88	C₂×ΓL(1,𝔽₂₅)	C₂²×C₃	1	4	yes	—
89	C₂×D₃×C₈	C₂²×C₃	1	4	yes	—
90	#875	C₃×C₄	1	2	yes	—
91	#874	C₃×C₄	1	1	yes	characteristic
92	C₄×D₁₂	C₂²×C₃	1	4	yes	—
93	#869	C₃×C₄	1	1	yes	characteristic
94	C₃×C₄⋊C₈	—	2	4	no	—
95	C₃×C₄⋊C₈	C₂×D₃	1	4	yes	—
96	C₃×C₄⋊C₈	C₂²×C₃	1	4	yes	—
97	C₃×C₂²⋊C₈	—	3	8	no	—
98	C₃×C₄×C₈	—	3	2	no	—
99	C₃×C₄×C₈	—	3	2	no	—
100	(C₂×D₃)⋊C₈	C₂²×C₃	1	8	yes	—
101	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
102	C₄×C₃⋊C₈	C₂²×C₃	1	2	yes	—
103	C₂³×C₃²	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₃×D₃	C₂²×C₄	1	4	yes	—
105	C₂×C₃²×C₄	—	2	4	no	—
106	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
107	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
109	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
110	C₂×C₃²×C₄	#41	1	2	yes	—
111	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
112	C₃×#67	—	2	8	no	—
113	C₂×C₃×Dic₃	C₂²×C₄	1	4	yes	—
114	C₃×D₁₂	—	2	4	no	—
115	C₃×D₁₂	—	2	8	no	—
116	C₃×C₄×D₃	—	2	4	no	—
117	C₃×C₄×D₃	—	2	4	no	—
118	C₃×Dic₆	—	2	4	no	—
119	C₃²×C₈	—	2	4	no	—
120	C₃×C₃⋊C₈	—	2	2	no	—
121	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
122	C₃×C₃⋊C₈	C₂×D₄	1	2	yes	—
123	C₂×#131	—	3	2	no	—
124	#532	—	3	1	no	—
125	#436	—	3	4	no	—
126	C₈×D₄	—	3	4	no	—
127	#423	C₃×D₃	1	1	yes	characteristic, complemented
128	#408	—	3	2	no	—
129	C₂×C₄×C₈	—	3	1	no	—
130	C₃×#41	—	6	4	no	—
131	C₃×#41	—	6	4	no	—
132	C₂×C₃×Q₈	—	3	2	no	—
133	C₂×C₃×D₄	—	3	4	no	—
134	C₂×C₃×D₄	—	3	4	no	—
135	C₂×C₃×D₄	—	3	2	no	—
136	C₂²×C₃×C₄	—	2	2	no	—
137	C₂²×C₃×C₄	—	2	1	no	—
138	C₂²×C₃×C₄	—	3	4	no	—
139	C₂²×C₃×C₄	C₄×D₃	1	2	yes	—
140	C₂²×C₃×C₄	C₂×C₃×C₄	1	2	yes	—
141	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
143	C₂×#67	C₂×C₃×C₄	1	4	yes	—
144	#235	—	2	4	no	—
145	#235	—	2	4	no	—
146	C₂×D₁₂	C₂×C₃×C₄	1	4	yes	—
147	C₂×D₁₂	C₂×C₃×C₄	1	2	yes	—
148	C₂×C₄×D₃	C₂³×C₃	1	4	yes	—
149	C₂×Dic₆	C₂×C₃×C₄	1	2	yes	—
150	C₃×M₁₆	—	2	4	no	—
151	C₃×M₁₆	—	2	4	no	—
152	C₃×M₁₆	—	4	4	no	—
153	C₃×M₁₆	—	6	8	no	—
154	C₂×C₃×C₈	—	2	4	no	—
155	C₂×C₃×C₈	—	3	4	no	—
156	C₂×C₃×C₈	—	3	1	no	—
157	C₂×C₃×C₈	—	3	1	no	—
158	C₂×C₃×C₈	—	3	2	no	—
159	C₂×C₃×C₈	—	6	8	no	—
160	C₂×C₃×C₈	—	6	2	no	—
161	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
162	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
163	C₃×C₄⋊C₄	—	3	4	no	—
164	C₃×C₂²⋊C₄	—	3	8	no	—
165	C₃×C₄²	—	2	1	no	—
166	C₃×C₄²	—	2	1	no	—
167	C₃×C₄²	—	2	2	no	—
168	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
169	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
170	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
171	C₃×C₄²	C₂×C₃×C₄	1	1	yes	characteristic
172	C₃×C₄²	C₂²×D₃	1	2	yes	—
173	C₃×C₄²	C₂³×C₃	1	2	yes	—
174	(C₂×D₃)⋊C₄	C₂×C₃×C₄	1	8	yes	—
175	C₄⋊Dic₃	C₂×C₃×C₄	1	4	yes	—
176	C₂×C₃⋊C₈	—	2	2	no	—
177	C₂×C₃⋊C₈	C₃×D₄	1	4	yes	complemented
178	C₂×C₃⋊C₈	C₂³×C₃	1	2	yes	—
179	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
180	C₂×C₃⋊C₈	C₂³×C₃	1	1	yes	characteristic
181	ΓL(1,𝔽₂₅)	—	2	8	no	—
182	D₃×C₈	—	2	8	no	—
183	C₂²×C₃²	—	2	2	no	—
184	C₂²×C₃²	C₄×D₄	1	2	yes	—
185	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₃×D₃	—	2	4	no	—
187	C₂×C₃×D₃	—	2	8	no	—
188	C₃²×C₄	—	2	2	no	—
189	C₃²×C₄	C₄×D₄	1	2	yes	—
190	C₃²×C₄	#131	1	4	yes	complemented
191	C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
192	C₃²×C₄	C₂×#41	1	1	yes	characteristic
193	C₃×Dic₃	—	2	4	no	—
194	C₂×#41	—	3	2	no	—
195	#131	—	6	8	no	—
196	C₂×M₁₆	—	3	4	no	—
197	C₂×M₁₆	C₂×C₃×D₃	1	2	yes	—
198	C₂²×C₈	—	3	1	no	—
199	C₂²×C₈	—	3	1	no	—
200	C₂²×C₈	—	3	4	no	—
201	C₄⋊Q₈	—	3	1	no	—
202	#127	—	3	1	no	—
203	#124	—	3	2	no	—
204	#121	—	3	4	no	—
205	C₄×D₄	—	3	4	no	—
206	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
207	C₄⋊C₈	C₂×C₃×D₃	1	4	yes	—
208	C₂²⋊C₈	—	3	8	no	—
209	C₄×C₈	—	3	2	no	—
210	C₄×C₈	—	3	2	no	—
211	C₂³×C₃	—	2	1	no	—
212	C₂³×C₃	—	3	4	no	—
213	C₂³×C₃	C₂×C₄×D₃	1	1	yes	characteristic
214	C₂³×C₃	C₂²×C₃×C₄	1	1	yes	characteristic
215	C₂²×D₃	C₂²×C₃×C₄	1	4	yes	—
216	C₃×Q₈	—	6	4	no	—
217	C₃×D₄	—	6	8	no	—
218	C₃×D₄	—	6	4	no	—
219	C₃×D₄	—	6	8	no	—
220	C₂×C₃×C₄	—	2	4	no	—
221	C₂×C₃×C₄	—	2	4	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	2	2	no	—
225	C₂×C₃×C₄	—	2	2	no	—
226	C₂×C₃×C₄	—	2	2	no	—
227	C₂×C₃×C₄	—	2	2	no	—
228	C₂×C₃×C₄	—	3	4	no	—
229	C₂×C₃×C₄	—	4	4	no	—
230	C₂×C₃×C₄	—	6	4	no	—
231	C₂×C₃×C₄	—	6	4	no	—
232	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
233	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
234	C₂×C₃×C₄	C₂×C₄×D₃	1	2	yes	—
235	C₂×C₃×C₄	D₃×D₄	1	2	yes	—
236	C₂×C₃×C₄	#239	1	2	yes	—
237	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
238	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
239	C₂×C₃×C₄	C₂²×C₃×C₄	1	2	yes	—
240	C₂×C₃×C₄	C₂×C₃×D₄	1	2	yes	—
241	C₂×C₃×C₄	C₃×#41	1	2	yes	—
242	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂⁴×C₃	1	1	yes	characteristic
244	#67	—	2	8	no	—
245	C₂×Dic₃	C₂²×C₃×C₄	1	4	yes	—
246	D₁₂	—	2	4	no	—
247	D₁₂	—	2	8	no	—
248	C₄×D₃	—	2	4	no	—
249	C₄×D₃	—	2	4	no	—
250	Dic₆	—	2	4	no	—
251	C₃×C₈	—	2	4	no	—
252	C₃×C₈	—	2	4	no	—
253	C₃×C₈	—	3	2	no	—
254	C₃×C₈	—	3	2	no	—
255	C₃×C₈	—	4	4	no	—
256	C₃×C₈	—	6	2	no	—
257	C₃⋊C₈	—	2	2	no	—
258	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
259	C₃⋊C₈	C₂×C₃×D₄	1	2	yes	—
260	C₂×C₃²	—	2	2	no	—
261	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
262	C₂×C₃²	C₂×#131	1	2	yes	—
263	C₃×D₃	—	4	4	no	—
264	#41	—	6	4	no	—
265	#41	—	6	4	no	—
266	C₂×Q₈	—	3	2	no	—
267	C₂×D₄	—	3	4	no	—
268	C₂×D₄	—	3	4	no	—
269	C₂×D₄	—	3	2	no	—
270	C₂²×C₄	—	3	4	no	—
271	C₂²×C₄	C₃×C₄×D₃	1	2	yes	—
272	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
273	M₁₆	—	2	4	no	—
274	M₁₆	—	6	8	no	—
275	C₂×C₈	—	3	1	no	—
276	C₂×C₈	—	3	1	no	—
277	C₂×C₈	—	3	4	no	—
278	C₂×C₈	—	3	2	no	—
279	C₂×C₈	—	6	8	no	—
280	C₂×C₈	—	6	2	no	—
281	C₂×C₈	C₂²×C₃×D₃	1	4	yes	—
282	C₄⋊C₄	—	3	4	no	—
283	C₂²⋊C₄	—	3	8	no	—
284	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
285	C₄²	C₃×C₄×D₃	1	1	yes	characteristic
286	C₄²	C₂²×C₃×D₃	1	2	yes	—
287	C₂²×C₃	—	2	2	no	—
288	C₂²×C₃	—	2	2	no	—
289	C₂²×C₃	—	2	2	no	—
290	C₂²×C₃	—	2	1	no	—
291	C₂²×C₃	—	4	2	no	—
292	C₂²×C₃	—	6	8	no	—
293	C₂²×C₃	—	6	4	no	—
294	C₂²×C₃	#893	1	2	yes	—
295	C₂²×C₃	C₃×C₄×D₄	1	2	yes	—
296	C₂²×C₃	C₂²×C₄×D₃	1	1	yes	characteristic
297	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
298	C₂×D₃	—	2	8	no	—
299	C₂×D₃	—	2	4	no	—
300	C₃×C₄	—	2	2	no	—
301	C₃×C₄	—	2	2	no	—
302	C₃×C₄	—	2	2	no	—
303	C₃×C₄	—	2	4	no	—
304	C₃×C₄	—	2	1	no	—
305	C₃×C₄	—	2	1	no	—
306	C₃×C₄	—	4	2	no	—
307	C₃×C₄	—	6	4	no	—
308	C₃×C₄	#893	1	2	yes	—
309	C₃×C₄	#907	1	4	yes	complemented
310	C₃×C₄	C₃×C₄×D₄	1	2	yes	—
311	C₃×C₄	C₃×#131	1	4	yes	complemented
312	C₃×C₄	C₂×D₃×D₄	1	1	yes	characteristic
313	C₃×C₄	C₂×#239	1	1	yes	characteristic
314	C₃×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
315	C₃×C₄	C₂×C₃×#41	1	1	yes	characteristic
316	Dic₃	—	2	4	no	—
317	C₃²	#2931	1	1	yes	characteristic, complemented, Sylow
318	C₂³	—	3	4	no	—
319	C₂³	C₂×C₃×C₄×D₃	1	1	yes	characteristic
320	Q₈	—	6	4	no	—
321	D₄	—	6	8	no	—
322	D₄	—	6	4	no	—
323	D₄	—	6	8	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	3	4	no	—
326	C₂×C₄	—	6	4	no	—
327	C₂×C₄	—	6	4	no	—
328	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
329	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
330	C₂×C₄	C₂×C₃×C₄×D₃	1	2	yes	—
331	C₂×C₄	C₃×D₃×D₄	1	2	yes	—
332	C₂×C₄	C₃×#239	1	2	yes	—
333	C₂×C₄	C₂³×C₃×D₃	1	1	yes	characteristic
334	C₈	—	2	4	no	—
335	C₈	—	3	2	no	—
336	C₈	—	3	2	no	—
337	C₈	—	6	2	no	—
338	C₂×C₃	—	2	2	no	—
339	C₂×C₃	—	2	2	no	—
340	C₂×C₃	—	2	2	no	—
341	C₂×C₃	—	2	1	no	—
342	C₂×C₃	—	4	2	no	—
343	C₂×C₃	—	12	4	no	—
344	C₂×C₃	C₂×#893	1	1	yes	characteristic
345	C₂×C₃	C₂×#907	1	2	yes	—
346	C₂×C₃	C₂×C₃×C₄×D₄	1	1	yes	characteristic
347	C₂×C₃	C₂×C₃×#131	1	2	yes	—
348	D₃	—	4	4	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	6	8	no	—
351	C₂²	—	6	4	no	—
352	C₂²	C₃×#893	1	2	yes	—
353	C₂²	C₂²×C₃×C₄×D₃	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	6	4	no	—
356	C₄	C₃×#893	1	2	yes	—
357	C₄	C₃×#907	1	4	yes	complemented
358	C₄	C₂×C₃×D₃×D₄	1	1	yes	characteristic
359	C₄	C₂×C₃×#239	1	1	yes	characteristic
360	C₃	—	2	1	no	—
361	C₃	#79041	1	1	yes	characteristic, direct product factor
362	C₃	C₃×#2931	1	1	yes	characteristic, complemented
363	C₂	—	2	2	no	—
364	C₂	—	12	4	no	—
365	C₂	C₂×C₃×#893	1	1	yes	characteristic
366	C₂	C₂×C₃×#907	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	C₃×#5477	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₃
hypercenter	C₃×#423	D₃
hypocenter	C₃	C₃×#2931
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
1. C₂×C₃×#907	C₂	semidirect
3. C₃²×#423	C₂	semidirect
4. C₃×#5129	C₂	semidirect
5. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
6. C₃×#4838	C₂	semidirect
7. C₃×#4834	C₂	semidirect
9. #79041	C₃	direct (N × H)
29. C₂×#907	C₂×C₃	semidirect
34. C₃×#423	D₃	semidirect
35. C₃×#423	C₂×C₃	semidirect
38. #5129	C₂×C₃	semidirect
39. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
40. #4838	C₂×C₃	semidirect
41. #4834	C₂×C₃	semidirect
59. C₂×C₃×C₃⋊C₈	D₄	semidirect
127. #423	C₃×D₃	semidirect
177. C₂×C₃⋊C₈	C₃×D₄	semidirect
190. C₃²×C₄	#131	semidirect
309. C₃×C₄	#907	semidirect
311. C₃×C₄	C₃×#131	semidirect
317. C₃²	#2931	semidirect
357. C₄	C₃×#907	semidirect
361. C₃	#79041	direct (N × H)
362. C₃	C₃×#2931	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#907	2
C₃×#5477	2
C₃²×#423	2
C₃×#5129	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃×#4838	2
C₃×#4834	2
C₃×#2931	3
#79041	3

Subgroups — C3×#79041 #11859467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#79041 #11859467