Subgroups — C₆₇×#33209 #30712460

Order 17152.

966 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#500×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2857	C₂	1	2	yes	maximal
4	C₆₇×#1990	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1942	C₂	1	4	yes	maximal, complemented
6	C₆₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1808	C₂	1	4	yes	maximal
8	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
9	C₂×C₄⋊Q₈×C₆₇	C₂²	1	2	yes	—
10	C₂×C₂²⋊Q₈×C₆₇	—	2	2	no	—
11	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
12	#500×C₆₇	—	2	4	no	—
13	C₂×#107×C₆₇	C₂²	1	4	yes	—
14	C₂×#107×C₆₇	C₂²	1	4	yes	—
15	C₂×C₄×C₈×C₆₇	—	2	4	no	—
16	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
18	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
19	#391×C₆₇	—	2	2	no	—
20	#389×C₆₇	—	2	2	no	—
21	#389×C₆₇	C₂²	1	4	yes	—
22	#384×C₆₇	C₂²	1	2	yes	—
23	#380×C₆₇	—	2	2	no	—
24	#380×C₆₇	C₂²	1	4	yes	—
25	#340×C₆₇	C₂²	1	8	yes	—
26	C₂²×Q₈×C₆₇	—	2	2	no	—
27	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
28	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
30	C₂²×C₈×C₆₇	—	2	4	no	—
31	C₂²×C₈×C₆₇	—	2	4	no	—
32	C₂²×C₈×C₆₇	Q₈	1	8	yes	complemented
33	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
34	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
35	C₄⋊Q₈×C₆₇	—	2	4	no	—
36	C₄⋊Q₈×C₆₇	—	2	4	no	—
37	C₂²⋊Q₈×C₆₇	—	4	8	no	—
38	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
40	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
43	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
44	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
45	C₂×C₄²×C₆₇	—	2	2	no	—
46	C₂×C₄²×C₆₇	—	2	2	no	—
47	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
48	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
49	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
51	#107×C₆₇	—	2	8	no	—
52	#107×C₆₇	—	2	8	no	—
53	C₄×C₈×C₆₇	—	2	4	no	—
54	C₄×C₈×C₆₇	—	2	2	no	—
55	C₄×C₈×C₆₇	D₄	1	4	yes	—
56	#95×C₆₇	—	2	4	no	—
57	#95×C₆₇	—	2	4	no	—
58	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
59	C₂×Q₈×C₆₇	—	4	4	no	—
60	C₂×Q₈×C₆₇	—	4	4	no	—
61	C₂×Q₈×C₆₇	—	4	4	no	—
62	C₂²×C₄×C₆₇	—	2	2	no	—
63	C₂²×C₄×C₆₇	—	2	2	no	—
64	C₂²×C₄×C₆₇	—	2	2	no	—
65	C₂²×C₄×C₆₇	—	2	2	no	—
66	C₂²×C₄×C₆₇	—	2	1	no	—
67	C₂²×C₄×C₆₇	—	2	1	no	—
68	C₂²×C₄×C₆₇	—	2	2	no	—
69	C₂²×C₄×C₆₇	—	2	4	no	—
70	C₂²×C₄×C₆₇	—	2	4	no	—
71	C₂²×C₄×C₆₇	D₈	1	4	yes	—
72	C₂²×C₄×C₆₇	Q₁₆	1	4	yes	—
73	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₂×Q₈	1	4	yes	—
79	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
80	C₂×C₈×C₆₇	—	2	2	no	—
81	C₂×C₈×C₆₇	—	2	2	no	—
82	C₂×C₈×C₆₇	—	2	16	no	—
83	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	—
84	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	—
85	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	—
86	C₂×C₈×C₆₇	#41	1	4	yes	—
87	C₄⋊C₄×C₆₇	—	2	4	no	—
88	C₄⋊C₄×C₆₇	—	2	8	no	—
89	C₄⋊C₄×C₆₇	—	2	4	no	—
90	C₄⋊C₄×C₆₇	—	4	4	no	—
91	C₄⋊C₄×C₆₇	—	4	4	no	—
92	C₄⋊C₄×C₆₇	—	4	8	no	—
93	C₄⋊C₄×C₆₇	—	4	4	no	—
94	C₂²⋊C₄×C₆₇	—	4	8	no	—
95	C₄²×C₆₇	—	2	2	no	—
96	C₄²×C₆₇	—	2	2	no	—
97	C₄²×C₆₇	—	2	1	no	—
98	C₄²×C₆₇	—	2	1	no	—
99	C₄²×C₆₇	C₂×D₄	1	2	yes	—
100	C₄²×C₆₇	#41	1	2	yes	—
101	C₂³×C₆₇	—	2	1	no	—
102	C₂³×C₆₇	—	2	1	no	—
103	C₂³×C₆₇	—	2	1	no	—
104	C₂³×C₆₇	—	2	1	no	—
105	C₂³×C₆₇	C₄⋊Q₈	1	2	yes	—
106	C₂³×C₆₇	C₂×D₈	1	2	yes	—
107	C₂³×C₆₇	C₂×Q₁₆	1	2	yes	—
108	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
109	Q₈×C₆₇	—	8	8	no	—
110	C₂×C₄×C₆₇	—	2	1	no	—
111	C₂×C₄×C₆₇	—	2	1	no	—
112	C₂×C₄×C₆₇	—	2	1	no	—
113	C₂×C₄×C₆₇	—	2	1	no	—
114	C₂×C₄×C₆₇	—	2	1	no	—
115	C₂×C₄×C₆₇	—	2	1	no	—
116	C₂×C₄×C₆₇	—	2	4	no	—
117	C₂×C₄×C₆₇	—	2	4	no	—
118	C₂×C₄×C₆₇	—	2	8	no	—
119	C₂×C₄×C₆₇	—	2	8	no	—
120	C₂×C₄×C₆₇	—	4	4	no	—
121	C₂×C₄×C₆₇	—	4	4	no	—
122	C₂×C₄×C₆₇	—	4	4	no	—
123	C₂×C₄×C₆₇	—	4	4	no	—
124	C₂×C₄×C₆₇	—	4	4	no	—
125	C₂×C₄×C₆₇	—	4	4	no	—
126	C₂×C₄×C₆₇	#121	1	2	yes	—
127	C₂×C₄×C₆₇	#121	1	2	yes	—
128	C₂×C₄×C₆₇	C₄⋊Q₈	1	2	yes	—
129	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
130	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
131	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
132	C₂×C₄×C₆₇	C₂×Q₁₆	1	2	yes	—
133	C₂×C₄×C₆₇	#135	1	2	yes	—
134	C₂×C₄×C₆₇	#135	1	2	yes	—
135	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂²×Q₈	1	2	yes	—
137	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
138	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
139	C₈×C₆₇	—	2	4	no	—
140	C₈×C₆₇	C₂²⋊Q₈	1	8	yes	complemented
141	C₂²×C₆₇	—	2	2	no	—
142	C₂²×C₆₇	—	2	2	no	—
143	C₂²×C₆₇	—	2	2	no	—
144	C₂²×C₆₇	—	2	2	no	—
145	C₂²×C₆₇	—	2	2	no	—
146	C₂²×C₆₇	—	2	2	no	—
147	C₂²×C₆₇	#500	1	4	yes	complemented
148	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
149	C₂²×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
150	C₂²×C₆₇	#532	1	1	yes	characteristic
151	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
152	C₂²×C₆₇	C₂²×Q₁₆	1	1	yes	characteristic
153	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
154	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
155	C₄×C₆₇	—	2	2	no	—
156	C₄×C₆₇	—	2	2	no	—
157	C₄×C₆₇	—	2	2	no	—
158	C₄×C₆₇	—	8	4	no	—
159	C₄×C₆₇	—	8	4	no	—
160	C₄×C₆₇	#466	1	4	yes	—
161	C₄×C₆₇	#467	1	4	yes	—
162	C₄×C₆₇	C₂×C₂²⋊Q₈	1	2	yes	—
163	C₄×C₆₇	#533	1	2	yes	—
164	#33209	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂×C₆₇	—	2	4	no	—
166	C₂×C₆₇	#2857	1	1	yes	characteristic
167	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
168	C₂×C₆₇	C₂×#467	1	1	yes	characteristic
169	C₂×C₆₇	C₂×#500	1	1	yes	characteristic
170	C₂×C₆₇	#3160	1	1	yes	characteristic
171	C₂×C₆₇	#3169	1	1	yes	characteristic
172	C₂×C₆₇	#3170	1	1	yes	characteristic
173	C₂×#500	C₂×C₆₇	1	1	yes	characteristic, complemented
174	C₂²×C₄×C₈	C₂×C₆₇	1	1	yes	characteristic
175	#2857	C₂×C₆₇	1	2	yes	—
176	#1990	C₂×C₆₇	1	2	yes	complemented
177	#1942	C₂×C₆₇	1	4	yes	complemented
178	#1845	C₂×C₆₇	1	1	yes	characteristic, complemented
179	#1808	C₂×C₆₇	1	4	yes	—
180	C₆₇	#33209	1	1	yes	characteristic, direct product factor, Sylow
181	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
182	C₂×C₄⋊Q₈	C₂²×C₆₇	1	2	yes	—
183	C₂×C₂²⋊Q₈	—	2	2	no	—
184	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
185	#500	—	2	4	no	—
186	C₂×#107	C₂²×C₆₇	1	4	yes	—
187	C₂×#107	C₂²×C₆₇	1	4	yes	—
188	C₂×C₄×C₈	—	2	4	no	—
189	C₂×C₄×C₈	C₂²×C₆₇	1	2	yes	—
190	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
191	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
192	#391	—	2	2	no	—
193	#389	—	2	2	no	—
194	#389	C₂²×C₆₇	1	4	yes	—
195	#384	C₂²×C₆₇	1	2	yes	—
196	#380	—	2	2	no	—
197	#380	C₂²×C₆₇	1	4	yes	—
198	#340	C₂²×C₆₇	1	8	yes	—
199	C₂²×Q₈	—	2	2	no	—
200	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
201	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
202	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
203	C₂²×C₈	—	2	4	no	—
204	C₂²×C₈	—	2	4	no	—
205	C₂²×C₈	Q₈×C₆₇	1	8	yes	complemented
206	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
207	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
208	C₄⋊Q₈	—	2	4	no	—
209	C₄⋊Q₈	—	2	4	no	—
210	C₂²⋊Q₈	—	4	8	no	—
211	C₂×C₄⋊C₄	—	2	2	no	—
212	C₂×C₄⋊C₄	—	2	4	no	—
213	C₂×C₄⋊C₄	—	2	2	no	—
214	C₂×C₄⋊C₄	—	2	2	no	—
215	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
216	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
217	C₂×C₂²⋊C₄	—	2	4	no	—
218	C₂×C₄²	—	2	2	no	—
219	C₂×C₄²	—	2	2	no	—
220	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
221	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
222	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
223	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
224	#107	—	2	8	no	—
225	#107	—	2	8	no	—
226	C₄×C₈	—	2	4	no	—
227	C₄×C₈	—	2	2	no	—
228	C₄×C₈	D₄×C₆₇	1	4	yes	—
229	#95	—	2	4	no	—
230	#95	—	2	4	no	—
231	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
232	C₂×Q₈	—	4	4	no	—
233	C₂×Q₈	—	4	4	no	—
234	C₂×Q₈	—	4	4	no	—
235	C₂²×C₄	—	2	2	no	—
236	C₂²×C₄	—	2	2	no	—
237	C₂²×C₄	—	2	2	no	—
238	C₂²×C₄	—	2	2	no	—
239	C₂²×C₄	—	2	1	no	—
240	C₂²×C₄	—	2	1	no	—
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	4	no	—
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	D₈×C₆₇	1	4	yes	—
245	C₂²×C₄	Q₁₆×C₆₇	1	4	yes	—
246	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
247	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
248	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
249	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
250	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
251	C₂²×C₄	C₂×Q₈×C₆₇	1	4	yes	—
252	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
253	C₂×C₈	—	2	2	no	—
254	C₂×C₈	—	2	2	no	—
255	C₂×C₈	—	2	16	no	—
256	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	—
257	C₂×C₈	C₂×Q₈×C₆₇	1	4	yes	—
258	C₂×C₈	C₂×Q₈×C₆₇	1	4	yes	—
259	C₂×C₈	#41×C₆₇	1	4	yes	—
260	C₄⋊C₄	—	2	4	no	—
261	C₄⋊C₄	—	2	8	no	—
262	C₄⋊C₄	—	2	4	no	—
263	C₄⋊C₄	—	4	4	no	—
264	C₄⋊C₄	—	4	4	no	—
265	C₄⋊C₄	—	4	8	no	—
266	C₄⋊C₄	—	4	4	no	—
267	C₂²⋊C₄	—	4	8	no	—
268	C₄²	—	2	2	no	—
269	C₄²	—	2	2	no	—
270	C₄²	—	2	1	no	—
271	C₄²	—	2	1	no	—
272	C₄²	C₂×D₄×C₆₇	1	2	yes	—
273	C₄²	#41×C₆₇	1	2	yes	—
274	C₂³	—	2	1	no	—
275	C₂³	—	2	1	no	—
276	C₂³	—	2	1	no	—
277	C₂³	—	2	1	no	—
278	C₂³	C₄⋊Q₈×C₆₇	1	2	yes	—
279	C₂³	C₂×D₈×C₆₇	1	2	yes	—
280	C₂³	C₂×Q₁₆×C₆₇	1	2	yes	—
281	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
282	Q₈	—	8	8	no	—
283	C₂×C₄	—	2	1	no	—
284	C₂×C₄	—	2	1	no	—
285	C₂×C₄	—	2	1	no	—
286	C₂×C₄	—	2	1	no	—
287	C₂×C₄	—	2	1	no	—
288	C₂×C₄	—	2	1	no	—
289	C₂×C₄	—	2	8	no	—
290	C₂×C₄	—	2	8	no	—
291	C₂×C₄	—	2	4	no	—
292	C₂×C₄	—	2	4	no	—
293	C₂×C₄	—	4	4	no	—
294	C₂×C₄	—	4	4	no	—
295	C₂×C₄	—	4	4	no	—
296	C₂×C₄	—	4	4	no	—
297	C₂×C₄	—	4	4	no	—
298	C₂×C₄	—	4	4	no	—
299	C₂×C₄	#121×C₆₇	1	2	yes	—
300	C₂×C₄	#121×C₆₇	1	2	yes	—
301	C₂×C₄	C₄⋊Q₈×C₆₇	1	2	yes	—
302	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
303	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
304	C₂×C₄	C₂×Q₁₆×C₆₇	1	2	yes	—
305	C₂×C₄	C₂×Q₁₆×C₆₇	1	2	yes	—
306	C₂×C₄	#135×C₆₇	1	2	yes	—
307	C₂×C₄	#135×C₆₇	1	2	yes	—
308	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
309	C₂×C₄	C₂²×Q₈×C₆₇	1	2	yes	—
310	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
311	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
312	C₈	—	2	4	no	—
313	C₈	C₂²⋊Q₈×C₆₇	1	8	yes	complemented
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	2	2	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	2	no	—
320	C₂²	#500×C₆₇	1	4	yes	complemented
321	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
322	C₂²	C₂×C₄⋊Q₈×C₆₇	1	1	yes	characteristic
323	C₂²	#532×C₆₇	1	1	yes	characteristic
324	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
325	C₂²	C₂²×Q₁₆×C₆₇	1	1	yes	characteristic
326	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
327	C₂²	C₂×#135×C₆₇	1	1	yes	characteristic
328	C₄	—	2	2	no	—
329	C₄	—	2	2	no	—
330	C₄	—	2	2	no	—
331	C₄	—	8	4	no	—
332	C₄	—	8	4	no	—
333	C₄	#466×C₆₇	1	4	yes	—
334	C₄	#467×C₆₇	1	4	yes	—
335	C₄	C₂×C₂²⋊Q₈×C₆₇	1	2	yes	—
336	C₄	#533×C₆₇	1	2	yes	—
337	C₂	—	2	4	no	—
338	C₂	C₆₇×#2857	1	1	yes	characteristic
339	C₂	C₂×#466×C₆₇	1	1	yes	characteristic
340	C₂	C₂×#467×C₆₇	1	1	yes	characteristic
341	C₂	C₂×#500×C₆₇	1	1	yes	characteristic
342	C₂	C₆₇×#3160	1	1	yes	characteristic
343	C₂	C₆₇×#3169	1	1	yes	characteristic
344	C₂	C₆₇×#3170	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂²×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#500×C₆₇	C₂	semidirect
4. C₆₇×#1990	C₂	semidirect
5. C₆₇×#1942	C₂	semidirect
6. C₆₇×#1845	C₂	semidirect
32. C₂²×C₈×C₆₇	Q₈	semidirect
140. C₈×C₆₇	C₂²⋊Q₈	semidirect
147. C₂²×C₆₇	#500	semidirect
164. #33209	C₆₇	direct (N × H)
173. C₂×#500	C₂×C₆₇	semidirect
176. #1990	C₂×C₆₇	semidirect
177. #1942	C₂×C₆₇	semidirect
178. #1845	C₂×C₆₇	semidirect
180. C₆₇	#33209	direct (N × H)
205. C₂²×C₈	Q₈×C₆₇	semidirect
313. C₈	C₂²⋊Q₈×C₆₇	semidirect
320. C₂²	#500×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#500×C₆₇	2
C₂²×C₄×C₈×C₆₇	2
C₆₇×#2857	2
C₆₇×#1990	2
C₆₇×#1942	2
C₆₇×#1845	2
C₆₇×#1808	2
#33209	67

Subgroups — C67×#33209 #30712460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33209 #30712460