Subgroups — C₃×#29201 #10647808

Order 768.

770 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×#2647	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#2328	C₂	1	1	yes	maximal, characteristic
3	C₃×#2067	C₂	1	2	yes	maximal, complemented
4	C₃×#2065	C₂	1	2	yes	maximal, complemented
5	C₃×#1961	C₂	1	1	yes	maximal, characteristic
6	C₃×#1957	C₂	1	1	yes	maximal, characteristic
7	C₃×#1864	C₂	1	2	yes	maximal, complemented
8	C₃×#1862	C₂	1	2	yes	maximal, complemented
9	C₃×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1836	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	#29201	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#127	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄×D₄	C₂²	1	2	yes	—
15	C₂×C₃×#107	C₂²	1	2	yes	—
16	C₂×C₃×#106	C₂²	1	2	yes	—
17	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×#102	C₂²	1	2	yes	—
20	C₂×C₃×#102	C₂²	1	2	yes	—
21	C₂×C₃×#102	C₂²	1	2	yes	—
22	C₂×C₃×#102	C₂²	1	2	yes	—
23	C₂×C₃×#97	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
25	C₃×#400	—	2	2	no	—
26	C₃×#398	—	2	2	no	—
27	C₃×#390	C₂²	1	2	yes	—
28	C₃×#389	C₂²	1	2	yes	—
29	C₃×#389	C₂²	1	2	yes	—
30	C₃×#386	—	2	2	no	—
31	C₃×#386	—	2	2	no	—
32	C₃×#384	C₂²	1	1	yes	characteristic
33	C₃×#382	C₂²	1	1	yes	characteristic
34	C₃×#382	C₂²	1	1	yes	characteristic
35	C₃×#376	C₂²	1	1	yes	characteristic
36	C₃×#340	C₂²	1	2	yes	—
37	C₃×#340	C₂²	1	2	yes	—
38	C₃×#336	C₂²	1	1	yes	characteristic
39	C₃×#336	C₂²	1	1	yes	characteristic
40	#2647	C₂×C₃	1	1	yes	characteristic, complemented
41	#2328	C₂×C₃	1	1	yes	characteristic
42	#2067	C₂×C₃	1	2	yes	complemented
43	#2065	C₂×C₃	1	2	yes	complemented
44	#1961	C₂×C₃	1	1	yes	characteristic
45	#1957	C₂×C₃	1	1	yes	characteristic
46	#1864	C₂×C₃	1	2	yes	complemented
47	#1862	C₂×C₃	1	2	yes	complemented
48	#1846	C₂×C₃	1	1	yes	characteristic, complemented
49	#1836	C₂×C₃	1	1	yes	characteristic, complemented
50	#1768	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂²×C₃×D₄	—	2	2	no	—
52	C₂²×C₃×D₄	C₂³	1	2	yes	—
53	C₂³×C₃×C₄	—	2	2	no	—
54	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₈	C₂³	1	1	yes	characteristic
58	C₃×#127	—	2	2	no	—
59	C₃×#127	Q₈	1	4	yes	—
60	C₃×C₄×D₄	—	4	2	no	—
61	C₃×C₄×D₄	—	4	2	no	—
62	C₂×C₃×C₄⋊C₄	—	2	2	no	—
63	C₂×C₃×C₄⋊C₄	—	2	2	no	—
64	C₂×C₃×C₄⋊C₄	—	2	2	no	—
65	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
66	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
67	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
68	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
69	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
70	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
74	C₃×#107	—	4	2	no	—
75	C₃×#106	—	4	2	no	—
76	C₃×C₄⋊C₈	—	2	2	no	—
77	C₃×C₄⋊C₈	—	2	2	no	—
78	C₃×#102	—	2	4	no	—
79	C₃×#102	—	2	4	no	—
80	C₃×#102	—	4	2	no	—
81	C₃×#102	—	4	2	no	—
82	C₃×#97	—	2	2	no	—
83	C₃×C₄×C₈	—	2	2	no	—
84	C₃×#95	—	2	2	no	—
85	C₃×#95	—	2	2	no	—
86	C₃×#95	—	2	2	no	—
87	C₃×#95	—	2	2	no	—
88	C₃×#95	D₄	1	2	yes	—
89	C₃×#95	D₄	1	2	yes	—
90	C₂×#127	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₄×D₄	C₂²×C₃	1	2	yes	—
92	C₂×#107	C₂²×C₃	1	2	yes	—
93	C₂×#106	C₂²×C₃	1	2	yes	—
94	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
96	C₂×#102	C₂²×C₃	1	2	yes	—
97	C₂×#102	C₂²×C₃	1	2	yes	—
98	C₂×#102	C₂²×C₃	1	2	yes	—
99	C₂×#102	C₂²×C₃	1	2	yes	—
100	C₂×#97	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
102	#400	—	2	2	no	—
103	#398	—	2	2	no	—
104	#390	C₂²×C₃	1	2	yes	—
105	#389	C₂²×C₃	1	2	yes	—
106	#389	C₂²×C₃	1	2	yes	—
107	#386	—	2	2	no	—
108	#386	—	2	2	no	—
109	#384	C₂²×C₃	1	1	yes	characteristic
110	#382	C₂²×C₃	1	1	yes	characteristic
111	#382	C₂²×C₃	1	1	yes	characteristic
112	#376	C₂²×C₃	1	1	yes	characteristic
113	#340	C₂²×C₃	1	2	yes	—
114	#340	C₂²×C₃	1	2	yes	—
115	#336	C₂²×C₃	1	1	yes	characteristic
116	#336	C₂²×C₃	1	1	yes	characteristic
117	C₂⁴×C₃	—	2	2	no	—
118	C₂×C₃×D₄	—	2	8	no	—
119	C₂×C₃×D₄	—	2	2	no	—
120	C₂×C₃×D₄	—	2	2	no	—
121	C₂×C₃×D₄	—	2	2	no	—
122	C₂×C₃×D₄	—	2	2	no	—
123	C₂×C₃×D₄	—	2	2	no	—
124	C₂×C₃×D₄	—	8	2	no	—
125	C₂×C₃×D₄	—	8	2	no	—
126	C₂×C₃×D₄	C₂×Q₈	1	4	yes	—
127	C₂²×C₃×C₄	—	2	2	no	—
128	C₂²×C₃×C₄	—	2	2	no	—
129	C₂²×C₃×C₄	—	2	2	no	—
130	C₂²×C₃×C₄	—	4	4	no	—
131	C₂²×C₃×C₄	—	8	2	no	—
132	C₂²×C₃×C₄	—	8	2	no	—
133	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
135	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₃×C₄	C₂×D₄	1	2	yes	—
137	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
138	C₂×C₃×C₈	—	2	1	no	—
139	C₂×C₃×C₈	—	2	1	no	—
140	C₂×C₃×C₈	—	2	1	no	—
141	C₂×C₃×C₈	—	2	1	no	—
142	C₂×C₃×C₈	—	2	1	no	—
143	C₂×C₃×C₈	—	2	1	no	—
144	C₂×C₃×C₈	—	2	1	no	—
145	C₂×C₃×C₈	—	2	1	no	—
146	C₂×C₃×C₈	—	2	1	no	—
147	C₂×C₃×C₈	—	2	1	no	—
148	C₂×C₃×C₈	#41	1	2	yes	—
149	C₂×C₃×C₈	#41	1	2	yes	—
150	C₃×C₄⋊C₄	—	2	2	no	—
151	C₃×C₄⋊C₄	—	2	2	no	—
152	C₃×C₄⋊C₄	—	2	2	no	—
153	C₃×C₄⋊C₄	—	2	2	no	—
154	C₃×C₄⋊C₄	—	2	2	no	—
155	C₃×C₄⋊C₄	—	2	2	no	—
156	C₃×C₄⋊C₄	—	8	2	no	—
157	C₃×C₄⋊C₄	—	8	2	no	—
158	C₃×C₄⋊C₄	—	8	2	no	—
159	C₃×C₂²⋊C₄	—	4	4	no	—
160	C₃×C₂²⋊C₄	—	8	2	no	—
161	C₃×C₂²⋊C₄	—	8	2	no	—
162	C₃×C₄²	—	2	1	no	—
163	C₃×C₄²	—	2	1	no	—
164	C₃×C₄²	—	2	1	no	—
165	C₃×C₄²	—	2	1	no	—
166	C₃×C₄²	C₂×Q₈	1	2	yes	—
167	C₃×C₄²	#41	1	2	yes	—
168	C₂²×D₄	—	2	2	no	—
169	C₂²×D₄	C₂³×C₃	1	2	yes	—
170	C₂³×C₄	—	2	2	no	—
171	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
172	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
173	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
174	C₂²×C₈	C₂³×C₃	1	1	yes	characteristic
175	#127	—	2	2	no	—
176	#127	C₃×Q₈	1	4	yes	—
177	C₄×D₄	—	4	2	no	—
178	C₄×D₄	—	4	2	no	—
179	C₂×C₄⋊C₄	—	2	2	no	—
180	C₂×C₄⋊C₄	—	2	2	no	—
181	C₂×C₄⋊C₄	—	2	2	no	—
182	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
183	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
184	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
185	C₂×C₂²⋊C₄	—	2	2	no	—
186	C₂×C₂²⋊C₄	—	2	2	no	—
187	C₂×C₂²⋊C₄	—	2	2	no	—
188	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
191	#107	—	4	2	no	—
192	#106	—	4	2	no	—
193	C₄⋊C₈	—	2	2	no	—
194	C₄⋊C₈	—	2	2	no	—
195	#102	—	2	4	no	—
196	#102	—	2	4	no	—
197	#102	—	4	2	no	—
198	#102	—	4	2	no	—
199	#97	—	2	2	no	—
200	C₄×C₈	—	2	2	no	—
201	#95	—	2	2	no	—
202	#95	—	2	2	no	—
203	#95	—	2	2	no	—
204	#95	—	2	2	no	—
205	#95	C₃×D₄	1	2	yes	—
206	#95	C₃×D₄	1	2	yes	—
207	C₂³×C₃	—	2	4	no	—
208	C₂³×C₃	—	4	2	no	—
209	C₂³×C₃	—	4	2	no	—
210	C₂³×C₃	—	4	2	no	—
211	C₂³×C₃	—	4	2	no	—
212	C₂³×C₃	—	4	2	no	—
213	C₂³×C₃	—	4	2	no	—
214	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
215	C₃×D₄	—	2	4	no	—
216	C₃×D₄	—	2	4	no	—
217	C₃×D₄	—	4	2	no	—
218	C₃×D₄	—	4	2	no	—
219	C₃×D₄	—	8	8	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	2	2	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	—	2	2	no	—
229	C₂×C₃×C₄	—	4	2	no	—
230	C₂×C₃×C₄	—	4	2	no	—
231	C₂×C₃×C₄	—	4	2	no	—
232	C₂×C₃×C₄	—	4	2	no	—
233	C₂×C₃×C₄	—	4	2	no	—
234	C₂×C₃×C₄	—	4	2	no	—
235	C₂×C₃×C₄	—	4	2	no	—
236	C₂×C₃×C₄	—	4	2	no	—
237	C₂×C₃×C₄	—	4	2	no	—
238	C₂×C₃×C₄	—	8	8	no	—
239	C₂×C₃×C₄	C₂²⋊Q₈	1	4	yes	—
240	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
241	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
242	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
243	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
244	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₃×C₄	H(5,𝔽₂)	1	1	yes	characteristic
246	C₃×C₈	—	2	2	no	—
247	C₃×C₈	—	2	2	no	—
248	C₃×C₈	—	4	1	no	—
249	C₃×C₈	—	4	1	no	—
250	C₂⁴	—	2	2	no	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	2	no	—
253	C₂×D₄	—	2	2	no	—
254	C₂×D₄	—	2	2	no	—
255	C₂×D₄	—	2	2	no	—
256	C₂×D₄	—	2	2	no	—
257	C₂×D₄	—	8	2	no	—
258	C₂×D₄	—	8	2	no	—
259	C₂×D₄	C₂×C₃×Q₈	1	4	yes	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	—	8	2	no	—
265	C₂²×C₄	—	8	2	no	—
266	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
268	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₃×D₄	1	2	yes	—
270	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
271	C₂×C₈	—	2	1	no	—
272	C₂×C₈	—	2	1	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	2	1	no	—
276	C₂×C₈	—	2	1	no	—
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	1	no	—
281	C₂×C₈	C₃×#41	1	2	yes	—
282	C₂×C₈	C₃×#41	1	2	yes	—
283	C₄⋊C₄	—	2	2	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	2	no	—
288	C₄⋊C₄	—	2	2	no	—
289	C₄⋊C₄	—	8	2	no	—
290	C₄⋊C₄	—	8	2	no	—
291	C₄⋊C₄	—	8	2	no	—
292	C₂²⋊C₄	—	4	4	no	—
293	C₂²⋊C₄	—	8	2	no	—
294	C₂²⋊C₄	—	8	2	no	—
295	C₄²	—	2	1	no	—
296	C₄²	—	2	1	no	—
297	C₄²	—	2	1	no	—
298	C₄²	—	2	1	no	—
299	C₄²	C₂×C₃×Q₈	1	2	yes	—
300	C₄²	C₃×#41	1	2	yes	—
301	C₂²×C₃	—	4	4	no	—
302	C₂²×C₃	—	4	4	no	—
303	C₂²×C₃	—	4	4	no	—
304	C₂²×C₃	—	8	2	no	—
305	C₂²×C₃	—	8	2	no	—
306	C₂²×C₃	—	8	2	no	—
307	C₂²×C₃	—	8	2	no	—
308	C₂²×C₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
309	C₂²×C₃	#532	1	1	yes	characteristic
310	C₂²×C₃	#535	1	1	yes	characteristic
311	C₂²×C₃	#576	1	2	yes	—
312	C₂²×C₃	#577	1	2	yes	—
313	C₃×C₄	—	2	4	no	—
314	C₃×C₄	—	4	1	no	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	—	8	2	no	—
318	C₃×C₄	—	8	2	no	—
319	C₃×C₄	—	8	2	no	—
320	C₃×C₄	#553	1	1	yes	characteristic
321	C₃×C₄	#553	1	1	yes	characteristic
322	C₃×C₄	#554	1	1	yes	characteristic
323	C₃×C₄	#554	1	1	yes	characteristic
324	C₂³	—	2	4	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
332	D₄	—	2	4	no	—
333	D₄	—	2	4	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	2	no	—
336	D₄	—	8	8	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	8	8	no	—
356	C₂×C₄	C₃×C₂²⋊Q₈	1	4	yes	—
357	C₂×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
358	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
359	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
360	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
361	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂×C₄	C₃×H(5,𝔽₂)	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	2	2	no	—
365	C₈	—	4	1	no	—
366	C₈	—	4	1	no	—
367	C₂×C₃	—	8	4	no	—
368	C₂×C₃	#2566	1	1	yes	characteristic
369	C₂×C₃	#3081	1	2	yes	—
370	C₂×C₃	#3174	1	1	yes	characteristic
371	C₂×C₃	#3176	1	1	yes	characteristic
372	C₂×C₃	#3224	1	2	yes	—
373	C₂²	—	4	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
381	C₂²	C₃×#532	1	1	yes	characteristic
382	C₂²	C₃×#535	1	1	yes	characteristic
383	C₂²	C₃×#576	1	2	yes	—
384	C₂²	C₃×#577	1	2	yes	—
385	C₄	—	2	4	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	2	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	C₃×#553	1	1	yes	characteristic
393	C₄	C₃×#553	1	1	yes	characteristic
394	C₄	C₃×#554	1	1	yes	characteristic
395	C₄	C₃×#554	1	1	yes	characteristic
396	C₃	#29201	1	1	yes	characteristic, direct product factor, Sylow
397	C₂	—	8	4	no	—
398	C₂	C₃×#2566	1	1	yes	characteristic
399	C₂	C₃×#3081	1	2	yes	—
400	C₂	C₃×#3174	1	1	yes	characteristic
401	C₂	C₃×#3176	1	1	yes	characteristic
402	C₂	C₃×#3224	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
prime radical	C₂×C₃×#127	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×#2647	C₂	semidirect
3. C₃×#2067	C₂	semidirect
4. C₃×#2065	C₂	semidirect
7. C₃×#1864	C₂	semidirect
8. C₃×#1862	C₂	semidirect
9. C₃×#1846	C₂	semidirect
10. C₃×#1836	C₂	semidirect
11. C₃×#1768	C₂	semidirect
12. #29201	C₃	direct (N × H)
40. #2647	C₂×C₃	semidirect
42. #2067	C₂×C₃	semidirect
43. #2065	C₂×C₃	semidirect
46. #1864	C₂×C₃	semidirect
47. #1862	C₂×C₃	semidirect
48. #1846	C₂×C₃	semidirect
49. #1836	C₂×C₃	semidirect
50. #1768	C₂×C₃	semidirect
396. C₃	#29201	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#2647	2
C₃×#2328	2
C₃×#2067	2
C₃×#2065	2
C₃×#1961	2
C₃×#1957	2
C₃×#1864	2
C₃×#1862	2
C₃×#1846	2
C₃×#1836	2
C₃×#1768	2
#29201	3

Subgroups — C3×#29201 #10647808

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#29201 #10647808