Subgroups — C₃×#17963 #10636570

Order 768.

614 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3168	C₂	1	1	yes	maximal, characteristic
2	C₃×#2966	C₂	1	2	yes	maximal, complemented
3	C₃×#1594	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#1593	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#1592	C₂	1	2	yes	maximal, complemented
6	C₃×#1580	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1579	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
9	C₃×#1568	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#1494	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
12	#17963	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₃×#529	C₂²	1	2	yes	—
14	C₃×#499	C₄	1	1	yes	characteristic
15	C₃×#495	C₄	1	1	yes	characteristic
16	C₃×#488	C₄	1	2	yes	—
17	C₃×#467	C₄	1	1	yes	characteristic
18	C₃×#466	C₄	1	1	yes	characteristic
19	C₃×#465	C₄	1	2	yes	—
20	C₃×#446	C₂²	1	2	yes	—
21	C₃×C₈×Q₈	C₂²	1	2	yes	—
22	C₃×C₄×Q₁₆	C₂²	1	1	yes	characteristic
23	C₃×C₄×SD₁₆	C₂²	1	2	yes	—
24	C₃×C₄×D₈	C₂²	1	1	yes	characteristic
25	C₃×#436	C₂²	1	2	yes	—
26	C₃×#435	—	2	2	no	—
27	C₃×C₈×D₄	—	2	2	no	—
28	C₃×C₈×D₄	C₂²	1	2	yes	—
29	C₃×#433	—	2	2	no	—
30	C₃×#432	C₂²	1	2	yes	—
31	C₃×#405	—	2	2	no	—
32	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
35	C₃×#335	C₂²	1	2	yes	—
36	C₃×#334	C₂²	1	1	yes	characteristic
37	C₃×#334	C₂²	1	1	yes	characteristic
38	C₃×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₃×Q₈⋊C₈	C₂²	1	2	yes	—
40	C₃×D₄⋊C₈	C₂²	1	2	yes	—
41	C₃×D₄⋊C₈	C₂²	1	2	yes	—
42	C₃×#322	C₂²	1	1	yes	characteristic
43	C₃×#322	C₂²	1	1	yes	characteristic
44	C₃×#322	C₂²	1	1	yes	characteristic
45	C₃×#322	C₂²	1	1	yes	characteristic
46	#3168	C₂×C₃	1	1	yes	characteristic
47	#2966	C₂×C₃	1	2	yes	complemented
48	#1594	C₂×C₃	1	1	yes	characteristic, complemented
49	#1593	C₂×C₃	1	1	yes	characteristic, complemented
50	#1592	C₂×C₃	1	2	yes	complemented
51	#1580	C₂×C₃	1	1	yes	characteristic, complemented
52	#1579	C₂×C₃	1	1	yes	characteristic, complemented
53	SD₁₆⋊C₈	C₂×C₃	1	2	yes	complemented
54	#1568	C₂×C₃	1	1	yes	characteristic, complemented
55	#1494	C₂×C₃	1	2	yes	complemented
56	C₂×#322	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×C₃×Q₁₆	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×SD₁₆	C₂×C₄	1	2	yes	—
59	C₂×C₃×D₈	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×M₁₆	—	2	2	no	—
61	C₂²×C₃×C₈	—	2	1	no	—
62	C₂²×C₃×C₈	—	2	2	no	—
63	C₂²×C₃×C₈	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₃×C₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₃×C₈	D₄	1	2	yes	—
66	C₃×#126	—	2	2	no	—
67	C₃×#125	C₂×C₄	1	2	yes	—
68	C₃×#124	C₂×C₄	1	2	yes	—
69	C₃×#123	—	2	2	no	—
70	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₃×#121	C₂×C₄	1	2	yes	—
72	C₃×C₄×Q₈	C₂³	1	2	yes	—
73	C₃×C₄×D₄	—	2	2	no	—
74	C₃×C₄×D₄	C₂³	1	2	yes	—
75	C₃×#117	—	2	2	no	—
76	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
77	C₃×#107	C₂×C₄	1	1	yes	characteristic
78	C₃×#107	C₂×C₄	1	1	yes	characteristic
79	C₃×#106	C₂×C₄	1	2	yes	—
80	C₃×C₄⋊C₈	—	2	2	no	—
81	C₃×C₄⋊C₈	—	2	2	no	—
82	C₃×C₄⋊C₈	C₂³	1	2	yes	—
83	C₃×C₄⋊C₈	C₂³	1	2	yes	—
84	C₃×#103	C₂×C₄	1	2	yes	—
85	C₃×#103	C₂×C₄	1	2	yes	—
86	C₃×#102	C₂×C₄	1	2	yes	—
87	C₃×#102	C₂×C₄	1	2	yes	—
88	C₃×C₂²⋊C₈	—	2	2	no	—
89	C₃×C₂²⋊C₈	—	2	2	no	—
90	C₃×C₂²⋊C₈	—	2	2	no	—
91	C₃×#97	—	2	2	no	—
92	C₃×#97	—	2	2	no	—
93	C₃×C₄×C₈	—	2	2	no	—
94	C₃×C₄×C₈	—	2	1	no	—
95	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
96	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
97	C₃×C₄×C₈	D₄	1	2	yes	—
98	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
99	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
100	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
101	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
102	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
103	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
104	#529	C₂²×C₃	1	2	yes	—
105	#499	C₃×C₄	1	1	yes	characteristic
106	#495	C₃×C₄	1	1	yes	characteristic
107	#488	C₃×C₄	1	2	yes	—
108	#467	C₃×C₄	1	1	yes	characteristic
109	#466	C₃×C₄	1	1	yes	characteristic
110	#465	C₃×C₄	1	2	yes	—
111	#446	C₂²×C₃	1	2	yes	—
112	C₈×Q₈	C₂²×C₃	1	2	yes	—
113	C₄×Q₁₆	C₂²×C₃	1	1	yes	characteristic
114	C₄×SD₁₆	C₂²×C₃	1	2	yes	—
115	C₄×D₈	C₂²×C₃	1	1	yes	characteristic
116	#436	C₂²×C₃	1	2	yes	—
117	#435	—	2	2	no	—
118	C₈×D₄	—	2	2	no	—
119	C₈×D₄	C₂²×C₃	1	2	yes	—
120	#433	—	2	2	no	—
121	#432	C₂²×C₃	1	2	yes	—
122	#405	—	2	2	no	—
123	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
124	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
126	#335	C₂²×C₃	1	2	yes	—
127	#334	C₂²×C₃	1	1	yes	characteristic
128	#334	C₂²×C₃	1	1	yes	characteristic
129	Q₈⋊C₈	C₂²×C₃	1	2	yes	—
130	Q₈⋊C₈	C₂²×C₃	1	2	yes	—
131	D₄⋊C₈	C₂²×C₃	1	2	yes	—
132	D₄⋊C₈	C₂²×C₃	1	2	yes	—
133	#322	C₂²×C₃	1	1	yes	characteristic
134	#322	C₂²×C₃	1	1	yes	characteristic
135	#322	C₂²×C₃	1	1	yes	characteristic
136	#322	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
138	C₂×C₃×D₄	—	2	2	no	—
139	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
140	C₂²×C₃×C₄	—	2	2	no	—
141	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₃×C₄	#41	1	1	yes	characteristic
144	C₃×Q₁₆	—	2	2	no	—
145	C₃×SD₁₆	—	2	4	no	—
146	C₃×D₈	—	2	2	no	—
147	C₃×M₁₆	—	4	4	no	—
148	C₂×C₃×C₈	—	2	2	no	—
149	C₂×C₃×C₈	—	2	2	no	—
150	C₂×C₃×C₈	—	2	2	no	—
151	C₂×C₃×C₈	—	2	2	no	—
152	C₂×C₃×C₈	—	2	1	no	—
153	C₂×C₃×C₈	—	2	1	no	—
154	C₂×C₃×C₈	—	4	2	no	—
155	C₂×C₃×C₈	—	4	4	no	—
156	C₂×C₃×C₈	—	4	2	no	—
157	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₃×C₈	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₈	C₂×D₄	1	2	yes	—
163	C₃×C₄⋊C₄	—	2	2	no	—
164	C₃×C₄⋊C₄	—	2	2	no	—
165	C₃×C₄⋊C₄	—	2	2	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
168	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
169	C₃×C₂²⋊C₄	—	2	2	no	—
170	C₃×C₂²⋊C₄	—	2	2	no	—
171	C₃×C₂²⋊C₄	—	2	2	no	—
172	C₃×C₂²⋊C₄	—	2	2	no	—
173	C₃×C₂²⋊C₄	—	2	2	no	—
174	C₃×C₄²	—	2	2	no	—
175	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
176	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
177	C₃×C₄²	#41	1	1	yes	characteristic
178	C₃×C₄²	C₂⁴	1	1	yes	characteristic
179	C₂×Q₁₆	C₂×C₃×C₄	1	1	yes	characteristic
180	C₂×SD₁₆	C₂×C₃×C₄	1	2	yes	—
181	C₂×D₈	C₂×C₃×C₄	1	1	yes	characteristic
182	C₂×M₁₆	—	2	2	no	—
183	C₂²×C₈	—	2	1	no	—
184	C₂²×C₈	—	2	2	no	—
185	C₂²×C₈	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂²×C₈	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂²×C₈	C₃×D₄	1	2	yes	—
188	#126	—	2	2	no	—
189	#125	C₂×C₃×C₄	1	2	yes	—
190	#124	C₂×C₃×C₄	1	2	yes	—
191	#123	—	2	2	no	—
192	C₂²⋊Q₈	C₂×C₃×C₄	1	2	yes	—
193	#121	C₂×C₃×C₄	1	2	yes	—
194	C₄×Q₈	C₂³×C₃	1	2	yes	—
195	C₄×D₄	—	2	2	no	—
196	C₄×D₄	C₂³×C₃	1	2	yes	—
197	#117	—	2	2	no	—
198	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
199	#107	C₂×C₃×C₄	1	1	yes	characteristic
200	#107	C₂×C₃×C₄	1	1	yes	characteristic
201	#106	C₂×C₃×C₄	1	2	yes	—
202	C₄⋊C₈	—	2	2	no	—
203	C₄⋊C₈	—	2	2	no	—
204	C₄⋊C₈	C₂³×C₃	1	2	yes	—
205	C₄⋊C₈	C₂³×C₃	1	2	yes	—
206	#103	C₂×C₃×C₄	1	2	yes	—
207	#103	C₂×C₃×C₄	1	2	yes	—
208	#102	C₂×C₃×C₄	1	2	yes	—
209	#102	C₂×C₃×C₄	1	2	yes	—
210	C₂²⋊C₈	—	2	2	no	—
211	C₂²⋊C₈	—	2	2	no	—
212	C₂²⋊C₈	—	2	2	no	—
213	#97	—	2	2	no	—
214	#97	—	2	2	no	—
215	C₄×C₈	—	2	2	no	—
216	C₄×C₈	—	2	1	no	—
217	C₄×C₈	C₂×C₃×C₄	1	1	yes	characteristic
218	C₄×C₈	C₂×C₃×C₄	1	1	yes	characteristic
219	C₄×C₈	C₃×D₄	1	2	yes	—
220	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
221	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
222	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
223	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
224	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
225	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
226	C₂³×C₃	—	2	2	no	—
227	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
228	C₃×Q₈	—	2	2	no	—
229	C₃×Q₈	—	2	2	no	—
230	C₃×D₄	—	2	2	no	—
231	C₃×D₄	—	2	2	no	—
232	C₃×D₄	—	4	4	no	—
233	C₂×C₃×C₄	—	2	2	no	—
234	C₂×C₃×C₄	—	2	1	no	—
235	C₂×C₃×C₄	—	2	1	no	—
236	C₂×C₃×C₄	—	2	2	no	—
237	C₂×C₃×C₄	—	2	2	no	—
238	C₂×C₃×C₄	—	2	2	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	—	4	2	no	—
242	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
245	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
248	C₃×C₈	—	2	1	no	—
249	C₃×C₈	—	2	1	no	—
250	C₃×C₈	—	2	2	no	—
251	C₃×C₈	—	2	2	no	—
252	C₃×C₈	—	4	1	no	—
253	C₃×C₈	—	4	1	no	—
254	C₃×C₈	—	4	2	no	—
255	C₃×C₈	—	4	2	no	—
256	C₃×C₈	#131	1	2	yes	—
257	C₃×C₈	#131	1	2	yes	—
258	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
259	C₂×D₄	—	2	2	no	—
260	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
264	C₂²×C₄	C₃×#41	1	1	yes	characteristic
265	Q₁₆	—	2	2	no	—
266	SD₁₆	—	2	4	no	—
267	D₈	—	2	2	no	—
268	M₁₆	—	4	4	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	2	no	—
273	C₂×C₈	—	2	1	no	—
274	C₂×C₈	—	2	1	no	—
275	C₂×C₈	—	4	2	no	—
276	C₂×C₈	—	4	4	no	—
277	C₂×C₈	—	4	2	no	—
278	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
279	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
280	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
281	C₂×C₈	C₂²×C₃×C₄	1	1	yes	characteristic
282	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
283	C₂×C₈	C₂×C₃×D₄	1	2	yes	—
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	C₂²×C₃×C₄	1	2	yes	—
289	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
290	C₂²⋊C₄	—	2	2	no	—
291	C₂²⋊C₄	—	2	2	no	—
292	C₂²⋊C₄	—	2	2	no	—
293	C₂²⋊C₄	—	2	2	no	—
294	C₂²⋊C₄	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
297	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
298	C₄²	C₃×#41	1	1	yes	characteristic
299	C₄²	C₂⁴×C₃	1	1	yes	characteristic
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	4	2	no	—
303	C₂²×C₃	—	4	2	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	#444	1	2	yes	—
306	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
307	C₃×C₄	—	2	1	no	—
308	C₃×C₄	—	2	1	no	—
309	C₃×C₄	—	2	1	no	—
310	C₃×C₄	—	2	1	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	—	4	2	no	—
313	C₃×C₄	—	4	2	no	—
314	C₃×C₄	C₂×#131	1	1	yes	characteristic
315	C₃×C₄	C₂×#131	1	1	yes	characteristic
316	C₃×C₄	#575	1	2	yes	—
317	C₂³	—	2	2	no	—
318	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
319	Q₈	—	2	2	no	—
320	Q₈	—	2	2	no	—
321	D₄	—	2	2	no	—
322	D₄	—	2	2	no	—
323	D₄	—	4	4	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
334	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
335	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
336	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
338	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
339	C₈	—	2	1	no	—
340	C₈	—	2	1	no	—
341	C₈	—	2	2	no	—
342	C₈	—	2	2	no	—
343	C₈	—	4	1	no	—
344	C₈	—	4	1	no	—
345	C₈	—	4	2	no	—
346	C₈	—	4	2	no	—
347	C₈	C₃×#131	1	2	yes	—
348	C₈	C₃×#131	1	2	yes	—
349	C₂×C₃	—	2	2	no	—
350	C₂×C₃	—	8	2	no	—
351	C₂×C₃	#2931	1	1	yes	characteristic
352	C₂×C₃	#2943	1	1	yes	characteristic
353	C₂×C₃	C₂×#444	1	1	yes	characteristic
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₃×#444	1	2	yes	—
360	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
361	C₄	—	2	1	no	—
362	C₄	—	2	1	no	—
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	C₂×C₃×#131	1	1	yes	characteristic
369	C₄	C₂×C₃×#131	1	1	yes	characteristic
370	C₄	C₃×#575	1	2	yes	—
371	C₃	#17963	1	1	yes	characteristic, direct product factor, Sylow
372	C₂	—	2	2	no	—
373	C₂	—	8	2	no	—
374	C₂	C₃×#2931	1	1	yes	characteristic
375	C₂	C₃×#2943	1	1	yes	characteristic
376	C₂	C₂×C₃×#444	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²×D₄
commutator	C₂×C₄	C₂³×C₃×C₄
Frattini, cosocle	C₄²	C₂⁴×C₃
socle	C₂²×C₃	C₂×C₄×D₄
prime radical	C₃×#466	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂×C₃×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×#2966	C₂	semidirect
3. C₃×#1594	C₂	semidirect
4. C₃×#1593	C₂	semidirect
5. C₃×#1592	C₂	semidirect
6. C₃×#1580	C₂	semidirect
7. C₃×#1579	C₂	semidirect
8. C₃×SD₁₆⋊C₈	C₂	semidirect
9. C₃×#1568	C₂	semidirect
10. C₃×#1494	C₂	semidirect
11. C₂×C₃×#322	C₂	semidirect
12. #17963	C₃	direct (N × H)
47. #2966	C₂×C₃	semidirect
48. #1594	C₂×C₃	semidirect
49. #1593	C₂×C₃	semidirect
50. #1592	C₂×C₃	semidirect
51. #1580	C₂×C₃	semidirect
52. #1579	C₂×C₃	semidirect
53. SD₁₆⋊C₈	C₂×C₃	semidirect
54. #1568	C₂×C₃	semidirect
55. #1494	C₂×C₃	semidirect
56. C₂×#322	C₂×C₃	semidirect
371. C₃	#17963	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×#3168	2
C₃×#2966	2
C₃×#1594	2
C₃×#1593	2
C₃×#1592	2
C₃×#1580	2
C₃×#1579	2
C₃×SD₁₆⋊C₈	2
C₃×#1568	2
C₃×#1494	2
C₂×C₃×#322	2
#17963	3

Subgroups — C3×#17963 #10636570

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17963 #10636570