Subgroups — C₃×#68745 #11789937

Order 1152.

515 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#5129	C₂	1	1	yes	maximal, characteristic
2	C₃×#5002	C₂	1	1	yes	maximal, characteristic
3	C₃×#4999	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#805	C₂	1	1	yes	maximal, characteristic
5	C₂×C₃×C₄×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃²×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#4558	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1937	—	3	1	no	maximal
9	#68745	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂×C₃×#235	C₂²	1	1	yes	characteristic
11	C₂×C₃²×M₁₆	C₂²	1	1	yes	characteristic
12	C₃²×#117	C₂²	1	1	yes	characteristic
13	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
14	C₂×C₃×#208	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₃×(C₂×D₃)⋊C₈	—	2	2	no	—
18	C₃×#810	C₄	1	2	yes	complemented
19	C₃×#809	C₄	1	2	yes	complemented
20	C₃×#805	—	2	2	no	—
21	C₃×C₄⋊(C₃⋊C₈)	—	2	2	no	—
22	C₃×C₄×C₃⋊C₈	—	2	2	no	—
23	C₃×#424	—	3	1	no	—
24	C₂×C₃×#104	—	3	1	no	—
25	C₃×#416	—	3	1	no	—
26	C₃×#408	—	3	1	no	—
27	C₂×C₃×C₄×C₈	—	3	1	no	—
28	#5129	C₂×C₃	1	1	yes	characteristic
29	#5002	C₂×C₃	1	1	yes	characteristic
30	#4999	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#805	C₂×C₃	1	1	yes	characteristic
32	C₂×C₄×C₃⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
33	C₃×#341	—	3	1	no	—
34	C₃×#339	—	2	1	no	—
35	C₃×#339	D₃	1	1	yes	characteristic, complemented
36	C₃×#339	C₂×C₃	1	1	yes	characteristic, complemented
37	#4558	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂²×C₃²×C₄	—	2	1	no	—
39	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
40	C₂×C₃×#67	—	2	1	no	—
41	C₃×#235	—	2	1	no	—
42	C₃×#235	—	2	1	no	—
43	C₃×#235	—	2	1	no	—
44	C₃×#235	—	2	1	no	—
45	C₂×C₃×D₁₂	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃×C₄×D₃	—	2	1	no	—
47	C₂×C₃×Dic₆	C₂×C₄	1	1	yes	characteristic
48	C₃²×M₁₆	—	2	1	no	—
49	C₃²×M₁₆	—	2	1	no	—
50	C₂×C₃²×C₈	—	2	1	no	—
51	C₃²×C₄⋊C₄	C₂×C₄	1	2	yes	—
52	C₃²×C₂²⋊C₄	—	2	1	no	—
53	C₃²×C₄²	—	2	1	no	—
54	C₃²×C₄²	—	2	1	no	—
55	C₃²×C₄²	D₄	1	2	yes	—
56	C₃×#208	—	2	1	no	—
57	C₃×#208	—	2	1	no	—
58	C₂×C₃×C₃⋊C₈	—	2	1	no	—
59	C₂×C₃×C₃⋊C₈	—	2	1	no	—
60	C₂×C₃×C₃⋊C₈	—	2	1	no	—
61	C₂×C₃×C₃⋊C₈	—	2	1	no	—
62	C₂×C₃×C₃⋊C₈	—	2	1	no	—
63	C₂×C₃×C₃⋊C₈	C₂×C₄	1	2	yes	—
64	C₂×C₃×C₃⋊C₈	D₄	1	2	yes	—
65	#1937	—	3	1	no	Sylow
66	C₂×C₃×#41	—	3	1	no	—
67	C₂×#235	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₃×M₁₆	—	2	1	no	—
69	C₂×C₃×M₁₆	—	3	1	no	—
70	C₂×C₃×M₁₆	C₂×D₃	1	1	yes	characteristic
71	C₂×C₃×M₁₆	C₂²×C₃	1	1	yes	characteristic
72	C₂²×C₃×C₈	—	3	1	no	—
73	C₂²×C₃×C₈	—	3	1	no	—
74	C₃×#117	—	2	1	no	—
75	C₃×#117	C₂×D₃	1	1	yes	characteristic
76	C₃×#117	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₃×C₄²	—	2	1	no	—
78	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃×C₄²	C₂²×C₃	1	1	yes	characteristic
80	C₂×#208	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
82	C₂²×C₃⋊C₈	C₂²×C₃	1	1	yes	characteristic
83	C₃×C₄⋊C₈	—	6	2	no	—
84	C₃×#104	—	6	2	no	—
85	C₃×#103	—	3	2	no	—
86	C₃×#102	—	3	2	no	—
87	C₃×C₂²⋊C₈	—	6	2	no	—
88	C₃×C₄×C₈	—	6	2	no	—
89	(C₂×D₃)⋊C₈	—	2	2	no	—
90	#810	C₃×C₄	1	2	yes	complemented
91	#809	C₃×C₄	1	2	yes	complemented
92	#805	—	2	2	no	—
93	C₄⋊(C₃⋊C₈)	—	2	2	no	—
94	C₄×C₃⋊C₈	—	2	2	no	—
95	C₂³×C₃²	#41	1	1	yes	characteristic
96	C₂²×C₃×D₃	—	2	1	no	—
97	C₂×C₃²×C₄	—	2	4	no	—
98	C₂×C₃²×C₄	—	2	2	no	—
99	C₂×C₃²×C₄	—	2	2	no	—
100	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃²×C₄	#41	1	1	yes	characteristic
104	C₂×C₃²×C₄	#41	1	1	yes	characteristic
105	C₂×C₃²×C₄	#41	1	1	yes	characteristic
106	C₃×#67	—	4	1	no	—
107	C₃×#67	—	4	1	no	—
108	C₂×C₃×Dic₃	—	2	1	no	—
109	C₃×D₁₂	—	2	1	no	—
110	C₃×D₁₂	—	2	1	no	—
111	C₃×C₄×D₃	—	4	1	no	—
112	C₃×C₄×D₃	—	4	1	no	—
113	C₃×Dic₆	—	2	1	no	—
114	C₃×Dic₆	—	2	1	no	—
115	C₃²×C₈	—	4	1	no	—
116	C₃×C₃⋊C₈	—	2	2	no	—
117	C₃×C₃⋊C₈	—	2	2	no	—
118	C₃×C₃⋊C₈	—	4	1	no	—
119	#424	—	3	1	no	—
120	C₂×#104	—	3	1	no	—
121	#416	—	3	1	no	—
122	#408	—	3	1	no	—
123	C₂×C₄×C₈	—	3	1	no	—
124	#341	—	3	1	no	—
125	#339	C₃×D₃	1	1	yes	characteristic, complemented
126	C₃×#41	—	6	1	no	—
127	C₃×#41	—	6	1	no	—
128	C₃×#41	—	6	1	no	—
129	C₃×#41	—	6	1	no	—
130	C₂×C₃×Q₈	—	3	1	no	—
131	C₂×C₃×D₄	—	3	1	no	—
132	C₂×C₃×D₄	—	6	1	no	—
133	C₂²×C₃×C₄	—	2	1	no	—
134	C₂²×C₃×C₄	—	2	1	no	—
135	C₂²×C₃×C₄	—	2	1	no	—
136	C₂²×C₃×C₄	—	4	1	no	—
137	C₂²×C₃×C₄	—	6	1	no	—
138	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
139	C₂²×C₃×C₄	C₂³×C₃	1	1	yes	characteristic
140	C₂×#67	—	2	1	no	—
141	#235	—	2	1	no	—
142	#235	—	2	1	no	—
143	#235	—	2	1	no	—
144	#235	—	2	1	no	—
145	C₂×D₁₂	C₂×C₃×C₄	1	1	yes	characteristic
146	C₂×C₄×D₃	—	2	1	no	—
147	C₂×Dic₆	C₂×C₃×C₄	1	1	yes	characteristic
148	C₃×M₁₆	—	2	2	no	—
149	C₃×M₁₆	—	2	1	no	—
150	C₃×M₁₆	—	2	1	no	—
151	C₃×M₁₆	—	2	1	no	—
152	C₃×M₁₆	—	2	1	no	—
153	C₃×M₁₆	—	4	1	no	—
154	C₃×M₁₆	—	6	1	no	—
155	C₃×M₁₆	—	6	1	no	—
156	C₂×C₃×C₈	—	2	1	no	—
157	C₂×C₃×C₈	—	2	1	no	—
158	C₂×C₃×C₈	—	3	2	no	—
159	C₂×C₃×C₈	—	3	2	no	—
160	C₂×C₃×C₈	—	4	1	no	—
161	C₂×C₃×C₈	—	6	1	no	—
162	C₂×C₃×C₈	—	6	1	no	—
163	C₂×C₃×C₈	—	6	1	no	—
164	C₂×C₃×C₈	—	6	1	no	—
165	C₂×C₃×C₈	—	6	1	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	C₄×D₃	1	2	yes	—
168	C₃×C₄⋊C₄	C₂×C₃×C₄	1	2	yes	—
169	C₃×C₂²⋊C₄	—	2	1	no	—
170	C₃×C₂²⋊C₄	—	2	1	no	—
171	C₃×C₂²⋊C₄	—	4	1	no	—
172	C₃×C₄²	—	2	1	no	—
173	C₃×C₄²	—	2	1	no	—
174	C₃×C₄²	—	2	1	no	—
175	C₃×C₄²	—	2	1	no	—
176	C₃×C₄²	—	2	2	no	—
177	C₃×C₄²	—	4	1	no	—
178	C₃×C₄²	—	4	1	no	—
179	C₃×C₄²	D₁₂	1	2	yes	—
180	C₃×C₄²	C₃×D₄	1	2	yes	—
181	#208	—	2	1	no	—
182	#208	—	2	1	no	—
183	C₂×C₃⋊C₈	—	2	1	no	—
184	C₂×C₃⋊C₈	—	2	1	no	—
185	C₂×C₃⋊C₈	—	2	1	no	—
186	C₂×C₃⋊C₈	—	2	1	no	—
187	C₂×C₃⋊C₈	—	2	1	no	—
188	C₂×C₃⋊C₈	C₂×C₃×C₄	1	2	yes	—
189	C₂×C₃⋊C₈	C₃×D₄	1	2	yes	—
190	C₂²×C₃²	—	2	2	no	—
191	C₂²×C₃²	C₄×D₄	1	1	yes	characteristic
192	C₂²×C₃²	#123	1	1	yes	characteristic
193	C₂²×C₃²	#126	1	1	yes	characteristic
194	C₂×C₃×D₃	—	4	1	no	—
195	C₂×C₃×D₃	—	4	2	no	—
196	C₃²×C₄	—	2	4	no	—
197	C₃²×C₄	—	4	2	no	—
198	C₃²×C₄	#117	1	1	yes	characteristic
199	C₃²×C₄	C₄×D₄	1	1	yes	characteristic
200	C₃²×C₄	#121	1	1	yes	characteristic
201	C₃²×C₄	#124	1	1	yes	characteristic
202	C₃×Dic₃	—	4	1	no	—
203	C₂×#41	—	3	1	no	—
204	C₂×M₁₆	—	3	1	no	—
205	C₂×M₁₆	C₂×C₃×D₃	1	1	yes	characteristic
206	C₂²×C₈	—	3	1	no	—
207	C₂²×C₈	—	3	1	no	—
208	#117	C₂×C₃×D₃	1	1	yes	characteristic
209	C₂×C₄²	C₂×C₃×D₃	1	1	yes	characteristic
210	C₄⋊C₈	—	6	2	no	—
211	#104	—	6	2	no	—
212	#103	—	3	2	no	—
213	#102	—	3	2	no	—
214	C₂²⋊C₈	—	6	2	no	—
215	C₄×C₈	—	6	2	no	—
216	C₂³×C₃	—	2	1	no	—
217	C₂³×C₃	—	6	1	no	—
218	C₂³×C₃	#237	1	1	yes	characteristic
219	C₂³×C₃	C₃×#41	1	1	yes	characteristic
220	C₂²×D₃	—	2	1	no	—
221	C₃×Q₈	—	6	1	no	—
222	C₃×Q₈	—	6	1	no	—
223	C₃×D₄	—	6	1	no	—
224	C₃×D₄	—	6	1	no	—
225	C₃×D₄	—	12	1	no	—
226	C₃×D₄	—	12	1	no	—
227	C₂×C₃×C₄	—	2	4	no	—
228	C₂×C₃×C₄	—	2	4	no	—
229	C₂×C₃×C₄	—	2	2	no	—
230	C₂×C₃×C₄	—	2	2	no	—
231	C₂×C₃×C₄	—	2	2	no	—
232	C₂×C₃×C₄	—	2	2	no	—
233	C₂×C₃×C₄	—	2	1	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	1	no	—
237	C₂×C₃×C₄	—	2	1	no	—
238	C₂×C₃×C₄	—	2	1	no	—
239	C₂×C₃×C₄	—	4	2	no	—
240	C₂×C₃×C₄	—	4	4	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	—	6	1	no	—
243	C₂×C₃×C₄	—	12	1	no	—
244	C₂×C₃×C₄	—	12	1	no	—
245	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
247	C₂×C₃×C₄	#235	1	1	yes	characteristic
248	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
249	C₂×C₃×C₄	#237	1	1	yes	characteristic
250	C₂×C₃×C₄	#239	1	1	yes	characteristic
251	C₂×C₃×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
252	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂×C₃×C₄	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
255	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
256	C₂×C₃×C₄	C₃×#41	1	1	yes	characteristic
257	#67	—	4	1	no	—
258	#67	—	4	1	no	—
259	C₂×Dic₃	—	2	1	no	—
260	D₁₂	—	2	1	no	—
261	D₁₂	—	2	1	no	—
262	C₄×D₃	—	4	1	no	—
263	C₄×D₃	—	4	1	no	—
264	Dic₆	—	2	1	no	—
265	Dic₆	—	2	1	no	—
266	C₃×C₈	—	4	2	no	—
267	C₃×C₈	—	4	1	no	—
268	C₃×C₈	—	4	1	no	—
269	C₃×C₈	—	6	2	no	—
270	C₃×C₈	—	6	2	no	—
271	C₃×C₈	—	12	1	no	—
272	C₃⋊C₈	—	2	2	no	—
273	C₃⋊C₈	—	2	2	no	—
274	C₃⋊C₈	—	4	1	no	—
275	C₂×C₃²	—	2	1	no	—
276	C₂×C₃²	—	2	1	no	—
277	C₂×C₃²	#388	1	1	yes	characteristic
278	C₂×C₃²	#443	1	2	yes	—
279	C₃×D₃	—	8	1	no	—
280	#41	—	6	1	no	—
281	#41	—	6	1	no	—
282	#41	—	6	1	no	—
283	#41	—	6	1	no	—
284	C₂×Q₈	—	3	1	no	—
285	C₂×D₄	—	3	1	no	—
286	C₂×D₄	—	6	1	no	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	6	1	no	—
289	C₂²×C₄	C₂²×C₃×D₃	1	1	yes	characteristic
290	M₁₆	—	2	1	no	—
291	M₁₆	—	2	1	no	—
292	M₁₆	—	6	1	no	—
293	M₁₆	—	6	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	3	2	no	—
296	C₂×C₈	—	3	2	no	—
297	C₂×C₈	—	6	1	no	—
298	C₂×C₈	—	6	1	no	—
299	C₂×C₈	—	6	1	no	—
300	C₂×C₈	—	6	1	no	—
301	C₂×C₈	—	6	1	no	—
302	C₄⋊C₄	C₃×C₄×D₃	1	2	yes	—
303	C₂²⋊C₄	—	2	1	no	—
304	C₄²	—	2	1	no	—
305	C₄²	—	2	1	no	—
306	C₄²	C₃×D₁₂	1	2	yes	—
307	C₂²×C₃	—	2	2	no	—
308	C₂²×C₃	—	2	2	no	—
309	C₂²×C₃	—	2	1	no	—
310	C₂²×C₃	—	2	1	no	—
311	C₂²×C₃	—	2	1	no	—
312	C₂²×C₃	—	4	2	no	—
313	C₂²×C₃	—	12	1	no	—
314	C₂²×C₃	—	12	2	no	—
315	C₂²×C₃	#67⋊C₄	1	1	yes	characteristic
316	C₂²×C₃	#886	1	1	yes	characteristic
317	C₂²×C₃	#898	1	1	yes	characteristic
318	C₂²×C₃	C₃×C₄×D₄	1	1	yes	characteristic
319	C₂²×C₃	C₃×#123	1	1	yes	characteristic
320	C₂²×C₃	C₃×#126	1	1	yes	characteristic
321	C₂×D₃	—	4	1	no	—
322	C₂×D₃	—	4	2	no	—
323	C₃×C₄	—	2	4	no	—
324	C₃×C₄	—	2	4	no	—
325	C₃×C₄	—	2	1	no	—
326	C₃×C₄	—	2	1	no	—
327	C₃×C₄	—	2	1	no	—
328	C₃×C₄	—	2	1	no	—
329	C₃×C₄	—	4	4	no	—
330	C₃×C₄	—	4	2	no	—
331	C₃×C₄	—	4	2	no	—
332	C₃×C₄	—	8	2	no	—
333	C₃×C₄	—	12	1	no	—
334	C₃×C₄	C₄×D₁₂	1	1	yes	characteristic
335	C₃×C₄	#885	1	1	yes	characteristic
336	C₃×C₄	#892	1	1	yes	characteristic
337	C₃×C₄	#895	1	1	yes	characteristic
338	C₃×C₄	C₃×#117	1	1	yes	characteristic
339	C₃×C₄	C₃×C₄×D₄	1	1	yes	characteristic
340	C₃×C₄	C₃×#121	1	1	yes	characteristic
341	C₃×C₄	C₃×#124	1	1	yes	characteristic
342	Dic₃	—	4	1	no	—
343	C₃²	#1937	1	1	yes	characteristic, complemented, Sylow
344	C₂³	—	6	1	no	—
345	C₂³	C₃×#237	1	1	yes	characteristic
346	Q₈	—	6	1	no	—
347	Q₈	—	6	1	no	—
348	D₄	—	6	1	no	—
349	D₄	—	6	1	no	—
350	D₄	—	12	1	no	—
351	D₄	—	12	1	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	6	1	no	—
356	C₂×C₄	—	12	1	no	—
357	C₂×C₄	—	12	1	no	—
358	C₂×C₄	C₂×C₃×C₄×D₃	1	1	yes	characteristic
359	C₂×C₄	C₂×C₃×D₁₂	1	1	yes	characteristic
360	C₂×C₄	C₃×#235	1	1	yes	characteristic
361	C₂×C₄	C₃×D₃×D₄	1	1	yes	characteristic
362	C₂×C₄	C₃×#237	1	1	yes	characteristic
363	C₂×C₄	C₃×#239	1	1	yes	characteristic
364	C₈	—	4	1	no	—
365	C₈	—	6	2	no	—
366	C₈	—	6	2	no	—
367	C₈	—	12	1	no	—
368	C₂×C₃	—	2	1	no	—
369	C₂×C₃	—	2	1	no	—
370	C₂×C₃	—	2	1	no	—
371	C₂×C₃	—	2	1	no	—
372	C₂×C₃	—	2	1	no	—
373	C₂×C₃	—	2	2	no	—
374	C₂×C₃	—	4	1	no	—
375	C₂×C₃	—	4	1	no	—
376	C₂×C₃	—	24	1	no	—
377	C₂×C₃	#4670	1	1	yes	characteristic
378	C₂×C₃	#4824	1	2	yes	—
379	C₂×C₃	C₃×#388	1	1	yes	characteristic
380	C₂×C₃	C₃×#443	1	2	yes	—
381	D₃	—	8	1	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	12	1	no	—
384	C₂²	—	12	2	no	—
385	C₂²	C₃×#67⋊C₄	1	1	yes	characteristic
386	C₂²	C₃×#886	1	1	yes	characteristic
387	C₂²	C₃×#898	1	1	yes	characteristic
388	C₄	—	2	4	no	—
389	C₄	—	4	2	no	—
390	C₄	—	12	1	no	—
391	C₄	C₃×C₄×D₁₂	1	1	yes	characteristic
392	C₄	C₃×#885	1	1	yes	characteristic
393	C₄	C₃×#892	1	1	yes	characteristic
394	C₄	C₃×#895	1	1	yes	characteristic
395	C₃	—	2	1	no	—
396	C₃	#68745	1	1	yes	characteristic, direct product factor
397	C₃	C₃×#1937	1	1	yes	characteristic, complemented
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	24	1	no	—
401	C₂	C₃×#4670	1	1	yes	characteristic
402	C₂	C₃×#4824	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₃×D₄
commutator	C₂×C₃×C₄	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₃
Fitting	C₃²×#339	C₂
socle	C₂²×C₃²	C₄×D₄
prime radical	C₂×C₃×#235	C₂²
cosocle	C₂²×C₃×C₄	C₂³×C₃
hypercenter	C₃×#339	D₃
hypocenter	C₃	C₃×#1937
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#339

Complements

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

N	H ≅ G/N	type
3. C₃×#4999	C₂	semidirect
5. C₂×C₃×C₄×C₃⋊C₈	C₂	semidirect
6. C₃²×#339	C₂	semidirect
7. C₃×#4558	C₂	semidirect
9. #68745	C₃	direct (N × H)
18. C₃×#810	C₄	semidirect
19. C₃×#809	C₄	semidirect
30. #4999	C₂×C₃	semidirect
32. C₂×C₄×C₃⋊C₈	C₂×C₃	semidirect
35. C₃×#339	D₃	semidirect
36. C₃×#339	C₂×C₃	semidirect
37. #4558	C₂×C₃	semidirect
90. #810	C₃×C₄	semidirect
91. #809	C₃×C₄	semidirect
125. #339	C₃×D₃	semidirect
343. C₃²	#1937	semidirect
396. C₃	#68745	direct (N × H)
397. C₃	C₃×#1937	semidirect

Maximal subgroups

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

subgroup	index
C₃×#5129	2
C₃×#5002	2
C₃×#4999	2
C₂×C₃×#805	2
C₂×C₃×C₄×C₃⋊C₈	2
C₃²×#339	2
C₃×#4558	2
C₃×#1937	3
#68745	3

Subgroups — C3×#68745 #11789937

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#68745 #11789937