Subgroups — C₆₇×#33966 #30713217

Order 17152.

566 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3396	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2250	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2246	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2210	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2207	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2206	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2206	C₂	1	2	yes	maximal, complemented
9	C₆₇×#2183	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2177	C₂	1	2	yes	maximal, complemented
11	C₄×SD₃₂×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#559×C₆₇	—	2	1	no	—
13	#550×C₆₇	—	2	1	no	—
14	C₂×SD₃₂×C₆₇	C₂²	1	1	yes	characteristic
15	C₂×SD₃₂×C₆₇	C₂²	1	2	yes	—
16	C₂×D₁₆×C₆₇	C₂²	1	2	yes	—
17	C₂×D₁₆×C₆₇	C₂²	1	2	yes	—
18	C₂×D₁₆×C₆₇	C₂²	1	2	yes	—
19	#495×C₆₇	C₂²	1	2	yes	—
20	#493×C₆₇	C₂²	1	1	yes	characteristic
21	#493×C₆₇	C₂²	1	1	yes	characteristic
22	#493×C₆₇	C₂²	1	2	yes	—
23	#463×C₆₇	—	2	2	no	—
24	#460×C₆₇	—	2	1	no	—
25	#459×C₆₇	—	2	1	no	—
26	#459×C₆₇	—	2	2	no	—
27	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₄×D₈×C₆₇	C₂²	1	2	yes	—
31	C₄×D₈×C₆₇	C₂²	1	2	yes	—
32	#367×C₆₇	C₂²	1	1	yes	characteristic
33	C₄⋊C₁₆×C₆₇	C₂²	1	1	yes	characteristic
34	C₄⋊C₁₆×C₆₇	C₂²	1	2	yes	—
35	#358×C₆₇	C₂²	1	1	yes	characteristic
36	#357×C₆₇	C₂²	1	1	yes	characteristic
37	#357×C₆₇	C₂²	1	2	yes	—
38	#357×C₆₇	C₂²	1	2	yes	—
39	#346×C₆₇	C₂²	1	2	yes	—
40	C₄×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
41	C₂×#41×C₆₇	—	4	1	no	—
42	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
43	C₂×SD₁₆×C₆₇	—	2	2	no	—
44	C₂×D₈×C₆₇	—	2	2	no	—
45	C₂×D₈×C₆₇	—	2	1	no	—
46	C₂×D₈×C₆₇	—	2	1	no	—
47	C₂×D₈×C₆₇	C₂³	1	2	yes	—
48	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₆₇	C₂³	1	2	yes	—
50	#127×C₆₇	—	2	2	no	—
51	#127×C₆₇	—	2	1	no	—
52	#127×C₆₇	—	2	1	no	—
53	#124×C₆₇	—	2	2	no	—
54	#124×C₆₇	—	4	1	no	—
55	#123×C₆₇	—	4	2	no	—
56	#121×C₆₇	—	4	1	no	—
57	#121×C₆₇	—	4	2	no	—
58	C₄×Q₈×C₆₇	—	2	1	no	—
59	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
60	C₄×D₄×C₆₇	—	2	2	no	—
61	C₄×D₄×C₆₇	—	2	1	no	—
62	C₄×D₄×C₆₇	—	2	2	no	—
63	C₄×D₄×C₆₇	—	4	1	no	—
64	SD₃₂×C₆₇	—	2	2	no	—
65	SD₃₂×C₆₇	—	4	2	no	—
66	D₁₆×C₆₇	—	2	4	no	—
67	D₁₆×C₆₇	—	4	2	no	—
68	D₁₆×C₆₇	—	4	2	no	—
69	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
70	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
71	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
72	#107×C₆₇	C₂³	1	1	yes	characteristic
73	#107×C₆₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
75	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
76	#103×C₆₇	—	2	1	no	—
77	#102×C₆₇	—	2	2	no	—
78	#102×C₆₇	—	2	1	no	—
79	#102×C₆₇	—	2	2	no	—
80	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂³	1	2	yes	—
82	#41×C₆₇	—	8	4	no	—
83	C₂×Q₈×C₆₇	—	2	1	no	—
84	C₂×Q₈×C₆₇	D₈	1	1	yes	characteristic
85	C₂×D₄×C₆₇	—	2	2	no	—
86	C₂×D₄×C₆₇	—	2	2	no	—
87	C₂×D₄×C₆₇	—	2	1	no	—
88	C₂×D₄×C₆₇	—	4	1	no	—
89	C₂×D₄×C₆₇	—	4	2	no	—
90	C₂×D₄×C₆₇	—	4	1	no	—
91	C₂×D₄×C₆₇	—	4	2	no	—
92	C₂×D₄×C₆₇	—	4	1	no	—
93	C₂×D₄×C₆₇	—	4	1	no	—
94	C₂²×C₄×C₆₇	—	4	2	no	—
95	C₂²×C₄×C₆₇	—	4	1	no	—
96	C₂²×C₄×C₆₇	—	4	2	no	—
97	Q₁₆×C₆₇	—	2	1	no	—
98	Q₁₆×C₆₇	—	2	1	no	—
99	SD₁₆×C₆₇	—	8	2	no	—
100	D₈×C₆₇	—	2	2	no	—
101	D₈×C₆₇	—	2	2	no	—
102	D₈×C₆₇	—	2	1	no	—
103	D₈×C₆₇	—	2	1	no	—
104	D₈×C₆₇	—	2	2	no	—
105	D₈×C₆₇	—	2	2	no	—
106	D₈×C₆₇	—	8	1	no	—
107	D₈×C₆₇	—	8	1	no	—
108	D₈×C₆₇	—	8	2	no	—
109	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
112	C₄⋊C₄×C₆₇	—	2	1	no	—
113	C₄⋊C₄×C₆₇	—	2	1	no	—
114	C₄⋊C₄×C₆₇	—	4	1	no	—
115	C₄⋊C₄×C₆₇	D₈	1	1	yes	characteristic
116	C₄⋊C₄×C₆₇	D₈	1	2	yes	—
117	C₂²⋊C₄×C₆₇	—	4	2	no	—
118	C₂²⋊C₄×C₆₇	—	4	1	no	—
119	C₂²⋊C₄×C₆₇	—	4	2	no	—
120	C₂²⋊C₄×C₆₇	—	4	2	no	—
121	C₂²⋊C₄×C₆₇	—	4	2	no	—
122	C₄²×C₆₇	—	4	1	no	—
123	C₄²×C₆₇	C₂×D₄	1	2	yes	—
124	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₁₆×C₆₇	—	2	1	no	—
126	C₁₆×C₆₇	—	2	2	no	—
127	C₁₆×C₆₇	#41	1	2	yes	complemented
128	C₂³×C₆₇	—	4	2	no	—
129	C₂³×C₆₇	—	4	2	no	—
130	C₂³×C₆₇	—	4	1	no	—
131	Q₈×C₆₇	—	2	2	no	—
132	Q₈×C₆₇	—	4	1	no	—
133	Q₈×C₆₇	—	4	1	no	—
134	D₄×C₆₇	—	4	2	no	—
135	D₄×C₆₇	—	4	2	no	—
136	D₄×C₆₇	—	4	1	no	—
137	D₄×C₆₇	—	4	2	no	—
138	D₄×C₆₇	—	4	1	no	—
139	D₄×C₆₇	—	4	2	no	—
140	D₄×C₆₇	—	8	4	no	—
141	D₄×C₆₇	—	8	2	no	—
142	D₄×C₆₇	—	8	2	no	—
143	D₄×C₆₇	—	16	2	no	—
144	D₄×C₆₇	—	16	1	no	—
145	D₄×C₆₇	—	16	1	no	—
146	C₂×C₄×C₆₇	—	4	1	no	—
147	C₂×C₄×C₆₇	—	4	1	no	—
148	C₂×C₄×C₆₇	—	4	1	no	—
149	C₂×C₄×C₆₇	—	8	4	no	—
150	C₂×C₄×C₆₇	—	8	2	no	—
151	C₂×C₄×C₆₇	—	16	2	no	—
152	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
154	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₆₇	—	2	1	no	—
158	C₈×C₆₇	—	2	2	no	—
159	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
160	C₈×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂²×C₆₇	—	8	2	no	—
162	C₂²×C₆₇	—	8	1	no	—
163	C₂²×C₆₇	—	8	2	no	—
164	C₂²×C₆₇	—	8	2	no	—
165	C₂²×C₆₇	—	8	1	no	—
166	C₂²×C₆₇	—	8	2	no	—
167	C₂²×C₆₇	—	8	2	no	—
168	C₂²×C₆₇	—	8	1	no	—
169	C₂²×C₆₇	—	8	2	no	—
170	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
171	C₄×C₆₇	—	2	2	no	—
172	C₄×C₆₇	—	2	2	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	8	1	no	—
175	C₄×C₆₇	—	8	1	no	—
176	C₄×C₆₇	—	8	1	no	—
177	C₄×C₆₇	#509	1	2	yes	—
178	C₄×C₆₇	#550	1	1	yes	characteristic
179	C₄×C₆₇	#576	1	1	yes	characteristic
180	#33966	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂×C₆₇	—	16	2	no	—
182	C₂×C₆₇	—	16	1	no	—
183	C₂×C₆₇	—	16	2	no	—
184	C₂×C₆₇	#3391	1	1	yes	characteristic
185	C₂×C₆₇	C₂×#509	1	1	yes	characteristic
186	C₂×C₆₇	#3415	1	1	yes	characteristic
187	#3396	C₂×C₆₇	1	1	yes	characteristic, complemented
188	#3391	C₂×C₆₇	1	1	yes	characteristic, complemented
189	#2250	C₂×C₆₇	1	2	yes	complemented
190	#2246	C₂×C₆₇	1	1	yes	characteristic, complemented
191	#2210	C₂×C₆₇	1	2	yes	complemented
192	#2207	C₂×C₆₇	1	1	yes	characteristic, complemented
193	#2206	C₂×C₆₇	1	2	yes	complemented
194	#2206	C₂×C₆₇	1	1	yes	characteristic, complemented
195	#2183	C₂×C₆₇	1	1	yes	characteristic, complemented
196	#2177	C₂×C₆₇	1	2	yes	complemented
197	C₄×SD₃₂	C₂×C₆₇	1	1	yes	characteristic, complemented
198	C₆₇	#33966	1	1	yes	characteristic, direct product factor, Sylow
199	#559	—	2	1	no	—
200	#550	—	2	1	no	—
201	C₂×SD₃₂	C₂²×C₆₇	1	1	yes	characteristic
202	C₂×SD₃₂	C₂²×C₆₇	1	2	yes	—
203	C₂×D₁₆	C₂²×C₆₇	1	2	yes	—
204	C₂×D₁₆	C₂²×C₆₇	1	2	yes	—
205	C₂×D₁₆	C₂²×C₆₇	1	2	yes	—
206	#495	C₂²×C₆₇	1	2	yes	—
207	#493	C₂²×C₆₇	1	2	yes	—
208	#493	C₂²×C₆₇	1	1	yes	characteristic
209	#493	C₂²×C₆₇	1	1	yes	characteristic
210	#463	—	2	2	no	—
211	#460	—	2	1	no	—
212	#459	—	2	1	no	—
213	#459	—	2	2	no	—
214	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
215	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
216	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
217	C₄×D₈	C₂²×C₆₇	1	2	yes	—
218	C₄×D₈	C₂²×C₆₇	1	2	yes	—
219	#367	C₂²×C₆₇	1	1	yes	characteristic
220	C₄⋊C₁₆	C₂²×C₆₇	1	1	yes	characteristic
221	C₄⋊C₁₆	C₂²×C₆₇	1	2	yes	—
222	#358	C₂²×C₆₇	1	1	yes	characteristic
223	#357	C₂²×C₆₇	1	1	yes	characteristic
224	#357	C₂²×C₆₇	1	2	yes	—
225	#357	C₂²×C₆₇	1	2	yes	—
226	#346	C₂²×C₆₇	1	2	yes	—
227	C₄×C₁₆	C₂²×C₆₇	1	1	yes	characteristic
228	C₂×#41	—	4	1	no	—
229	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
230	C₂×SD₁₆	—	2	2	no	—
231	C₂×D₈	—	2	2	no	—
232	C₂×D₈	—	2	1	no	—
233	C₂×D₈	—	2	1	no	—
234	C₂×D₈	C₂³×C₆₇	1	2	yes	—
235	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
236	C₂×D₈	C₂³×C₆₇	1	2	yes	—
237	#127	—	2	2	no	—
238	#127	—	2	1	no	—
239	#127	—	2	1	no	—
240	#124	—	2	2	no	—
241	#124	—	4	1	no	—
242	#123	—	4	2	no	—
243	#121	—	4	1	no	—
244	#121	—	4	2	no	—
245	C₄×Q₈	—	2	1	no	—
246	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
247	C₄×D₄	—	2	2	no	—
248	C₄×D₄	—	2	1	no	—
249	C₄×D₄	—	2	2	no	—
250	C₄×D₄	—	4	1	no	—
251	SD₃₂	—	2	2	no	—
252	SD₃₂	—	4	2	no	—
253	D₁₆	—	2	4	no	—
254	D₁₆	—	4	2	no	—
255	D₁₆	—	4	2	no	—
256	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
257	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
258	C₂×C₁₆	C₂³×C₆₇	1	1	yes	characteristic
259	#107	C₂³×C₆₇	1	1	yes	characteristic
260	#107	C₂³×C₆₇	1	1	yes	characteristic
261	C₄⋊C₈	D₄×C₆₇	1	1	yes	characteristic
262	C₄⋊C₈	D₄×C₆₇	1	2	yes	—
263	#103	—	2	1	no	—
264	#102	—	2	2	no	—
265	#102	—	2	1	no	—
266	#102	—	2	2	no	—
267	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
268	C₄×C₈	C₂³×C₆₇	1	2	yes	—
269	#41	—	8	4	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	D₈×C₆₇	1	1	yes	characteristic
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	4	1	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	1	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	1	no	—
280	C₂×D₄	—	4	1	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	2	no	—
284	Q₁₆	—	2	1	no	—
285	Q₁₆	—	2	1	no	—
286	SD₁₆	—	8	2	no	—
287	D₈	—	2	2	no	—
288	D₈	—	2	2	no	—
289	D₈	—	2	1	no	—
290	D₈	—	2	1	no	—
291	D₈	—	2	2	no	—
292	D₈	—	2	2	no	—
293	D₈	—	8	1	no	—
294	D₈	—	8	1	no	—
295	D₈	—	8	2	no	—
296	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
297	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
298	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	D₈×C₆₇	1	1	yes	characteristic
303	C₄⋊C₄	D₈×C₆₇	1	2	yes	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₂²⋊C₄	—	4	1	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₂²⋊C₄	—	4	2	no	—
309	C₄²	—	4	1	no	—
310	C₄²	C₂×D₄×C₆₇	1	2	yes	—
311	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
312	C₁₆	—	2	1	no	—
313	C₁₆	—	2	2	no	—
314	C₁₆	#41×C₆₇	1	2	yes	complemented
315	C₂³	—	4	2	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	4	1	no	—
318	Q₈	—	2	2	no	—
319	Q₈	—	4	1	no	—
320	Q₈	—	4	1	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	2	no	—
323	D₄	—	4	1	no	—
324	D₄	—	4	2	no	—
325	D₄	—	4	1	no	—
326	D₄	—	4	2	no	—
327	D₄	—	8	4	no	—
328	D₄	—	8	2	no	—
329	D₄	—	8	2	no	—
330	D₄	—	16	2	no	—
331	D₄	—	16	1	no	—
332	D₄	—	16	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	8	4	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	—	16	2	no	—
339	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
340	C₂×C₄	C₂×D₈×C₆₇	1	2	yes	—
341	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
342	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
343	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
344	C₈	—	2	1	no	—
345	C₈	—	2	2	no	—
346	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
347	C₈	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
348	C₂²	—	8	2	no	—
349	C₂²	—	8	1	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	1	no	—
353	C₂²	—	8	2	no	—
354	C₂²	—	8	2	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	2	no	—
357	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	2	no	—
360	C₄	—	2	1	no	—
361	C₄	—	8	1	no	—
362	C₄	—	8	1	no	—
363	C₄	—	8	1	no	—
364	C₄	#509×C₆₇	1	2	yes	—
365	C₄	#550×C₆₇	1	1	yes	characteristic
366	C₄	#576×C₆₇	1	1	yes	characteristic
367	C₂	—	16	2	no	—
368	C₂	—	16	1	no	—
369	C₂	—	16	2	no	—
370	C₂	C₆₇×#3391	1	1	yes	characteristic
371	C₂	C₂×#509×C₆₇	1	1	yes	characteristic
372	C₂	C₆₇×#3415	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×Q₈×C₆₇ ◁ C₈×Q₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3396	C₂	semidirect
2. C₆₇×#3391	C₂	semidirect
3. C₆₇×#2250	C₂	semidirect
4. C₆₇×#2246	C₂	semidirect
5. C₆₇×#2210	C₂	semidirect
6. C₆₇×#2207	C₂	semidirect
7. C₆₇×#2206	C₂	semidirect
8. C₆₇×#2206	C₂	semidirect
9. C₆₇×#2183	C₂	semidirect
10. C₆₇×#2177	C₂	semidirect
11. C₄×SD₃₂×C₆₇	C₂	semidirect
127. C₁₆×C₆₇	#41	semidirect
180. #33966	C₆₇	direct (N × H)
187. #3396	C₂×C₆₇	semidirect
188. #3391	C₂×C₆₇	semidirect
189. #2250	C₂×C₆₇	semidirect
190. #2246	C₂×C₆₇	semidirect
191. #2210	C₂×C₆₇	semidirect
192. #2207	C₂×C₆₇	semidirect
193. #2206	C₂×C₆₇	semidirect
194. #2206	C₂×C₆₇	semidirect
195. #2183	C₂×C₆₇	semidirect
196. #2177	C₂×C₆₇	semidirect
197. C₄×SD₃₂	C₂×C₆₇	semidirect
198. C₆₇	#33966	direct (N × H)
314. C₁₆	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3396	2
C₆₇×#3391	2
C₆₇×#2250	2
C₆₇×#2246	2
C₆₇×#2210	2
C₆₇×#2207	2
C₆₇×#2206	2
C₆₇×#2183	2
C₆₇×#2177	2
C₄×SD₃₂×C₆₇	2
#33966	67

Subgroups — C67×#33966 #30713217

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33966 #30713217