Subgroups — C₃×#17960 #10636567

Order 768.

666 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#3167	C₂	1	1	yes	maximal, characteristic
2	C₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#2931	C₂	1	1	yes	maximal, characteristic
4	C₃×#1592	C₂	1	4	yes	maximal, complemented
5	C₃×SD₁₆⋊C₈	C₂	1	4	yes	maximal, complemented
6	C₃×#1567	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#1493	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#1492	C₂	1	1	yes	maximal, characteristic
9	C₂×C₃×#322	C₂	1	1	yes	maximal, characteristic, complemented
10	#17960	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₂×C₃×#131	—	2	1	no	—
12	C₃×#533	C₂²	1	1	yes	characteristic
13	C₃×#532	C₂²	1	1	yes	characteristic
14	C₃×#498	C₄	1	1	yes	characteristic
15	C₃×#492	C₄	1	1	yes	characteristic
16	C₃×#487	C₄	1	1	yes	characteristic
17	C₃×#486	C₄	1	1	yes	characteristic
18	C₃×#465	C₄	1	4	yes	—
19	C₃×#446	—	2	1	no	—
20	C₃×#446	C₂²	1	2	yes	—
21	C₃×C₈×Q₈	—	2	1	no	—
22	C₃×C₈×Q₈	C₂²	1	2	yes	—
23	C₃×C₄×SD₁₆	C₂²	1	4	yes	—
24	C₃×#436	—	2	1	no	—
25	C₃×#436	C₂²	1	2	yes	—
26	C₃×C₈×D₄	—	2	1	no	—
27	C₃×C₈×D₄	C₂²	1	2	yes	—
28	C₃×#424	—	2	1	no	—
29	C₃×#423	C₂²	1	1	yes	characteristic
30	C₃×#423	C₂²	1	1	yes	characteristic
31	C₃×#408	—	2	1	no	—
32	C₃×#405	—	2	1	no	—
33	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×C₈	C₂²	1	1	yes	characteristic
36	C₃×#335	C₂²	1	4	yes	—
37	C₃×Q₈⋊C₈	C₂²	1	4	yes	—
38	C₃×D₄⋊C₈	C₂²	1	4	yes	—
39	C₃×#322	C₂²	1	2	yes	—
40	C₃×#322	C₂²	1	2	yes	—
41	#3167	C₂×C₃	1	1	yes	characteristic
42	#2960	C₂×C₃	1	1	yes	characteristic, complemented
43	#2931	C₂×C₃	1	1	yes	characteristic
44	#1592	C₂×C₃	1	4	yes	complemented
45	SD₁₆⋊C₈	C₂×C₃	1	4	yes	complemented
46	#1567	C₂×C₃	1	1	yes	characteristic, complemented
47	#1493	C₂×C₃	1	1	yes	characteristic, complemented
48	#1492	C₂×C₃	1	1	yes	characteristic
49	C₂×#322	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×C₃×#41	—	2	1	no	—
51	C₂×C₃×SD₁₆	C₂×C₄	1	4	yes	—
52	C₃×#131	—	4	4	no	—
53	C₂×C₃×M₁₆	—	2	1	no	—
54	C₂×C₃×M₁₆	—	2	1	no	—
55	C₂×C₃×M₁₆	—	2	2	no	—
56	C₂²×C₃×C₈	—	2	1	no	—
57	C₂²×C₃×C₈	—	2	2	no	—
58	C₂²×C₃×C₈	C₂×C₄	1	2	yes	—
59	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
60	C₂²×C₃×C₈	D₄	1	1	yes	characteristic
61	C₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
62	C₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
63	C₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
64	C₃×#127	C₂×C₄	1	1	yes	characteristic
65	C₃×#125	—	2	1	no	—
66	C₃×#124	—	2	1	no	—
67	C₃×C₂²⋊Q₈	—	2	1	no	—
68	C₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
69	C₃×#121	—	2	1	no	—
70	C₃×#121	C₂×C₄	1	2	yes	—
71	C₃×C₄×Q₈	—	2	1	no	—
72	C₃×C₄×Q₈	C₂³	1	2	yes	—
73	C₃×C₄×D₄	—	2	1	no	—
74	C₃×C₄×D₄	C₂³	1	2	yes	—
75	C₃×#117	—	2	1	no	—
76	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
77	C₃×#106	C₂×C₄	1	4	yes	—
78	C₃×C₄⋊C₈	—	2	2	no	—
79	C₃×C₄⋊C₈	—	2	2	no	—
80	C₃×C₄⋊C₈	—	2	1	no	—
81	C₃×C₄⋊C₈	—	2	1	no	—
82	C₃×C₄⋊C₈	C₂³	1	2	yes	—
83	C₃×C₄⋊C₈	C₂³	1	2	yes	—
84	C₃×#103	C₂×C₄	1	4	yes	—
85	C₃×#102	C₂×C₄	1	4	yes	—
86	C₃×C₂²⋊C₈	—	2	2	no	—
87	C₃×C₂²⋊C₈	—	2	2	no	—
88	C₃×#97	—	2	2	no	—
89	C₃×C₄×C₈	—	2	2	no	—
90	C₃×C₄×C₈	—	2	1	no	—
91	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
92	C₃×C₄×C₈	C₂×C₄	1	1	yes	characteristic
93	C₃×C₄×C₈	D₄	1	1	yes	characteristic
94	C₃×C₄×C₈	D₄	1	1	yes	characteristic
95	C₃×C₄×C₈	C₂³	1	2	yes	—
96	C₃×C₄×C₈	C₂³	1	2	yes	—
97	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
98	C₃×C₄×C₈	C₂³	1	1	yes	characteristic
99	C₂×#131	—	2	1	no	—
100	#533	C₂²×C₃	1	1	yes	characteristic
101	#532	C₂²×C₃	1	1	yes	characteristic
102	#498	C₃×C₄	1	1	yes	characteristic
103	#492	C₃×C₄	1	1	yes	characteristic
104	#487	C₃×C₄	1	1	yes	characteristic
105	#486	C₃×C₄	1	1	yes	characteristic
106	#465	C₃×C₄	1	4	yes	—
107	#446	—	2	1	no	—
108	#446	C₂²×C₃	1	2	yes	—
109	C₈×Q₈	—	2	1	no	—
110	C₈×Q₈	C₂²×C₃	1	2	yes	—
111	C₄×SD₁₆	C₂²×C₃	1	4	yes	—
112	#436	—	2	1	no	—
113	#436	C₂²×C₃	1	2	yes	—
114	C₈×D₄	—	2	1	no	—
115	C₈×D₄	C₂²×C₃	1	2	yes	—
116	#424	—	2	1	no	—
117	#423	C₂²×C₃	1	1	yes	characteristic
118	#423	C₂²×C₃	1	1	yes	characteristic
119	#408	—	2	1	no	—
120	#405	—	2	1	no	—
121	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₄×C₈	C₂²×C₃	1	1	yes	characteristic
124	#335	C₂²×C₃	1	4	yes	—
125	Q₈⋊C₈	C₂²×C₃	1	4	yes	—
126	D₄⋊C₈	C₂²×C₃	1	4	yes	—
127	#322	C₂²×C₃	1	2	yes	—
128	#322	C₂²×C₃	1	2	yes	—
129	C₃×#41	—	4	2	no	—
130	C₃×#41	—	4	2	no	—
131	C₂×C₃×Q₈	—	2	1	no	—
132	C₂×C₃×Q₈	—	2	1	no	—
133	C₂×C₃×Q₈	C₂²×C₄	1	2	yes	—
134	C₂×C₃×D₄	—	2	2	no	—
135	C₂×C₃×D₄	—	2	1	no	—
136	C₂×C₃×D₄	—	2	1	no	—
137	C₂×C₃×D₄	C₂²×C₄	1	2	yes	—
138	C₂²×C₃×C₄	—	2	2	no	—
139	C₂²×C₃×C₄	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₃×C₄	#41	1	1	yes	characteristic
142	C₃×SD₁₆	—	2	8	no	—
143	C₃×M₁₆	—	4	4	no	—
144	C₃×M₁₆	—	4	2	no	—
145	C₃×M₁₆	—	4	2	no	—
146	C₂×C₃×C₈	—	2	2	no	—
147	C₂×C₃×C₈	—	2	2	no	—
148	C₂×C₃×C₈	—	2	4	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	—	4	4	no	—
153	C₂×C₃×C₈	—	4	2	no	—
154	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
155	C₂×C₃×C₈	C₂²×C₄	1	2	yes	—
156	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₈	C₂×D₄	1	1	yes	characteristic
160	C₃×C₄⋊C₄	—	2	1	no	—
161	C₃×C₄⋊C₄	—	2	1	no	—
162	C₃×C₄⋊C₄	—	2	1	no	—
163	C₃×C₄⋊C₄	—	2	1	no	—
164	C₃×C₄⋊C₄	—	2	2	no	—
165	C₃×C₄⋊C₄	—	2	2	no	—
166	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
167	C₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
168	C₃×C₂²⋊C₄	—	2	2	no	—
169	C₃×C₂²⋊C₄	—	2	2	no	—
170	C₃×C₂²⋊C₄	—	2	2	no	—
171	C₃×C₄²	—	2	2	no	—
172	C₃×C₄²	C₂²×C₄	1	1	yes	characteristic
173	C₃×C₄²	C₂×D₄	1	1	yes	characteristic
174	C₃×C₄²	#41	1	1	yes	characteristic
175	C₃×C₄²	C₂⁴	1	1	yes	characteristic
176	C₂×#41	—	2	1	no	—
177	C₂×SD₁₆	C₂×C₃×C₄	1	4	yes	—
178	#131	—	4	4	no	—
179	C₂×M₁₆	—	2	1	no	—
180	C₂×M₁₆	—	2	1	no	—
181	C₂×M₁₆	—	2	2	no	—
182	C₂²×C₈	—	2	1	no	—
183	C₂²×C₈	—	2	2	no	—
184	C₂²×C₈	C₂×C₃×C₄	1	2	yes	—
185	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
186	C₂²×C₈	C₃×D₄	1	1	yes	characteristic
187	C₄⋊Q₈	C₂×C₃×C₄	1	1	yes	characteristic
188	C₄⋊Q₈	C₂×C₃×C₄	1	1	yes	characteristic
189	C₄⋊Q₈	C₂×C₃×C₄	1	1	yes	characteristic
190	#127	C₂×C₃×C₄	1	1	yes	characteristic
191	#125	—	2	1	no	—
192	#124	—	2	1	no	—
193	C₂²⋊Q₈	—	2	1	no	—
194	C₂²⋊Q₈	C₂×C₃×C₄	1	2	yes	—
195	#121	—	2	1	no	—
196	#121	C₂×C₃×C₄	1	2	yes	—
197	C₄×Q₈	—	2	1	no	—
198	C₄×Q₈	C₂³×C₃	1	2	yes	—
199	C₄×D₄	—	2	1	no	—
200	C₄×D₄	C₂³×C₃	1	2	yes	—
201	#117	—	2	1	no	—
202	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
203	#106	C₂×C₃×C₄	1	4	yes	—
204	C₄⋊C₈	—	2	2	no	—
205	C₄⋊C₈	—	2	2	no	—
206	C₄⋊C₈	—	2	1	no	—
207	C₄⋊C₈	—	2	1	no	—
208	C₄⋊C₈	C₂³×C₃	1	2	yes	—
209	C₄⋊C₈	C₂³×C₃	1	2	yes	—
210	#103	C₂×C₃×C₄	1	4	yes	—
211	#102	C₂×C₃×C₄	1	4	yes	—
212	C₂²⋊C₈	—	2	2	no	—
213	C₂²⋊C₈	—	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	1	yes	characteristic
220	C₄×C₈	C₃×D₄	1	1	yes	characteristic
221	C₄×C₈	C₂³×C₃	1	2	yes	—
222	C₄×C₈	C₂³×C₃	1	2	yes	—
223	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
224	C₄×C₈	C₂³×C₃	1	1	yes	characteristic
225	C₂³×C₃	—	2	2	no	—
226	C₂³×C₃	C₄×D₄	1	1	yes	characteristic
227	C₃×Q₈	—	2	4	no	—
228	C₃×Q₈	—	4	2	no	—
229	C₃×Q₈	—	4	2	no	—
230	C₃×D₄	—	2	4	no	—
231	C₃×D₄	—	4	4	no	—
232	C₃×D₄	—	4	2	no	—
233	C₃×D₄	—	4	2	no	—
234	C₂×C₃×C₄	—	2	2	no	—
235	C₂×C₃×C₄	—	2	2	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	—	4	2	no	—
240	C₂×C₃×C₄	—	4	2	no	—
241	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
242	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
243	C₂×C₃×C₄	C₄×D₄	1	1	yes	characteristic
244	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
245	C₂×C₃×C₄	#137	1	2	yes	—
246	C₂×C₃×C₄	C₂³×C₄	1	1	yes	characteristic
247	C₂×C₃×C₄	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
249	C₃×C₈	—	2	2	no	—
250	C₃×C₈	—	2	1	no	—
251	C₃×C₈	—	2	1	no	—
252	C₃×C₈	—	2	1	no	—
253	C₃×C₈	—	2	1	no	—
254	C₃×C₈	—	4	2	no	—
255	C₃×C₈	—	4	2	no	—
256	C₃×C₈	—	4	2	no	—
257	C₃×C₈	#131	1	4	yes	complemented
258	#41	—	4	2	no	—
259	#41	—	4	2	no	—
260	C₂×Q₈	—	2	1	no	—
261	C₂×Q₈	—	2	1	no	—
262	C₂×Q₈	C₂²×C₃×C₄	1	2	yes	—
263	C₂×D₄	—	2	2	no	—
264	C₂×D₄	—	2	1	no	—
265	C₂×D₄	—	2	1	no	—
266	C₂×D₄	C₂²×C₃×C₄	1	2	yes	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	C₂²×C₃×C₄	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
270	C₂²×C₄	C₃×#41	1	1	yes	characteristic
271	SD₁₆	—	2	8	no	—
272	M₁₆	—	4	4	no	—
273	M₁₆	—	4	2	no	—
274	M₁₆	—	4	2	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	2	2	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	4	4	no	—
282	C₂×C₈	—	4	2	no	—
283	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
284	C₂×C₈	C₂²×C₃×C₄	1	2	yes	—
285	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
286	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×C₈	C₂×C₃×D₄	1	1	yes	characteristic
289	C₄⋊C₄	—	2	1	no	—
290	C₄⋊C₄	—	2	1	no	—
291	C₄⋊C₄	—	2	1	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
296	C₄⋊C₄	C₂²×C₃×C₄	1	2	yes	—
297	C₂²⋊C₄	—	2	2	no	—
298	C₂²⋊C₄	—	2	2	no	—
299	C₂²⋊C₄	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	C₂²×C₃×C₄	1	1	yes	characteristic
302	C₄²	C₂×C₃×D₄	1	1	yes	characteristic
303	C₄²	C₃×#41	1	1	yes	characteristic
304	C₄²	C₂⁴×C₃	1	1	yes	characteristic
305	C₂²×C₃	—	2	1	no	—
306	C₂²×C₃	—	2	1	no	—
307	C₂²×C₃	—	4	2	no	—
308	C₂²×C₃	—	4	2	no	—
309	C₂²×C₃	—	4	2	no	—
310	C₂²×C₃	#440	1	2	yes	—
311	C₂²×C₃	C₂×C₄×D₄	1	1	yes	characteristic
312	C₃×C₄	—	2	1	no	—
313	C₃×C₄	—	2	1	no	—
314	C₃×C₄	—	4	2	no	—
315	C₃×C₄	—	4	2	no	—
316	C₃×C₄	—	4	2	no	—
317	C₃×C₄	#440	1	2	yes	—
318	C₃×C₄	#444	1	2	yes	—
319	C₃×C₄	C₂×#131	1	2	yes	—
320	C₃×C₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
321	C₃×C₄	C₂×#137	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	C₃×C₄×D₄	1	1	yes	characteristic
324	Q₈	—	2	4	no	—
325	Q₈	—	4	2	no	—
326	Q₈	—	4	2	no	—
327	D₄	—	2	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	4	2	no	—
330	D₄	—	4	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
339	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
340	C₂×C₄	C₃×C₄×D₄	1	1	yes	characteristic
341	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
342	C₂×C₄	C₃×#137	1	2	yes	—
343	C₂×C₄	C₂³×C₃×C₄	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₃×D₄	1	1	yes	characteristic
345	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
346	C₈	—	2	2	no	—
347	C₈	—	2	1	no	—
348	C₈	—	2	1	no	—
349	C₈	—	2	1	no	—
350	C₈	—	2	1	no	—
351	C₈	—	4	2	no	—
352	C₈	—	4	2	no	—
353	C₈	—	4	2	no	—
354	C₈	C₃×#131	1	4	yes	complemented
355	C₂×C₃	—	2	2	no	—
356	C₂×C₃	—	8	2	no	—
357	C₂×C₃	#2931	1	1	yes	characteristic
358	C₂×C₃	C₂×#440	1	1	yes	characteristic
359	C₂×C₃	C₂×#444	1	1	yes	characteristic
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	4	2	no	—
365	C₂²	C₃×#440	1	2	yes	—
366	C₂²	C₂×C₃×C₄×D₄	1	1	yes	characteristic
367	C₄	—	2	1	no	—
368	C₄	—	2	1	no	—
369	C₄	—	4	2	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	2	no	—
372	C₄	C₃×#440	1	2	yes	—
373	C₄	C₃×#444	1	2	yes	—
374	C₄	C₂×C₃×#131	1	2	yes	—
375	C₄	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
376	C₄	C₂×C₃×#137	1	1	yes	characteristic
377	C₃	#17960	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	2	2	no	—
379	C₂	—	8	2	no	—
380	C₂	C₃×#2931	1	1	yes	characteristic
381	C₂	C₂×C₃×#440	1	1	yes	characteristic
382	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×#532	C₂²
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×#2960	C₂	semidirect
4. C₃×#1592	C₂	semidirect
5. C₃×SD₁₆⋊C₈	C₂	semidirect
6. C₃×#1567	C₂	semidirect
7. C₃×#1493	C₂	semidirect
9. C₂×C₃×#322	C₂	semidirect
10. #17960	C₃	direct (N × H)
42. #2960	C₂×C₃	semidirect
44. #1592	C₂×C₃	semidirect
45. SD₁₆⋊C₈	C₂×C₃	semidirect
46. #1567	C₂×C₃	semidirect
47. #1493	C₂×C₃	semidirect
49. C₂×#322	C₂×C₃	semidirect
257. C₃×C₈	#131	semidirect
354. C₈	C₃×#131	semidirect
377. C₃	#17960	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×#3167	2
C₃×#2960	2
C₃×#2931	2
C₃×#1592	2
C₃×SD₁₆⋊C₈	2
C₃×#1567	2
C₃×#1493	2
C₃×#1492	2
C₂×C₃×#322	2
#17960	3

Subgroups — C3×#17960 #10636567

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#17960 #10636567