Subgroups — C₆₇×#33117 #30712368

Order 17152.

830 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#485×C₆₇	C₂	1	2	yes	maximal
2	C₆₇×#2621	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2274	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1981	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1949	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1928	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1927	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1872	C₂	1	2	yes	maximal
9	C₆₇×#1798	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
12	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
15	#485×C₆₇	—	2	8	no	—
16	C₂×#107×C₆₇	C₂²	1	2	yes	—
17	C₂×#106×C₆₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
19	C₂×#103×C₆₇	C₂²	1	2	yes	—
20	C₂×#103×C₆₇	C₂²	1	2	yes	—
21	C₂×#103×C₆₇	C₂²	1	2	yes	—
22	C₂×#103×C₆₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	—
24	#398×C₆₇	—	2	2	no	—
25	#397×C₆₇	—	2	2	no	—
26	#391×C₆₇	C₂²	1	2	yes	—
27	#382×C₆₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₆₇	—	2	2	no	—
29	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
30	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
31	C₄×C₂²⋊C₄×C₆₇	—	2	2	no	—
32	#340×C₆₇	C₂²	1	2	yes	—
33	#340×C₆₇	C₂²	1	2	yes	—
34	#336×C₆₇	C₂²	1	1	yes	characteristic
35	#336×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₆₇	—	2	1	no	—
38	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
39	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
40	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
41	C₄⋊Q₈×C₆₇	—	2	4	no	—
42	C₂²⋊Q₈×C₆₇	—	2	4	no	—
43	C₂²⋊Q₈×C₆₇	—	2	4	no	—
44	#117×C₆₇	—	2	2	no	—
45	#117×C₆₇	—	2	4	no	—
46	#117×C₆₇	D₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
48	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
53	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
54	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
55	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
56	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
58	C₂×C₄²×C₆₇	—	2	1	no	—
59	C₂×C₄²×C₆₇	—	2	2	no	—
60	C₂×C₄²×C₆₇	—	2	2	no	—
61	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
63	#107×C₆₇	—	2	4	no	—
64	#106×C₆₇	—	2	4	no	—
65	C₄⋊C₈×C₆₇	—	2	4	no	—
66	#103×C₆₇	—	2	4	no	—
67	#103×C₆₇	—	2	4	no	—
68	#103×C₆₇	—	2	4	no	—
69	#103×C₆₇	—	2	4	no	—
70	C₂²⋊C₈×C₆₇	—	2	4	no	—
71	#95×C₆₇	—	2	2	no	—
72	#95×C₆₇	—	2	2	no	—
73	#95×C₆₇	—	2	2	no	—
74	#95×C₆₇	—	2	4	no	—
75	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
76	C₂×Q₈×C₆₇	—	2	2	no	—
77	C₂×Q₈×C₆₇	—	2	2	no	—
78	C₂×Q₈×C₆₇	—	2	2	no	—
79	C₂×Q₈×C₆₇	—	2	2	no	—
80	C₂×Q₈×C₆₇	—	2	2	no	—
81	C₂×Q₈×C₆₇	—	2	2	no	—
82	C₂²×C₄×C₆₇	—	2	2	no	—
83	C₂²×C₄×C₆₇	—	2	2	no	—
84	C₂²×C₄×C₆₇	—	2	2	no	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	2	4	no	—
87	C₂²×C₄×C₆₇	—	2	2	no	—
88	C₂²×C₄×C₆₇	—	2	2	no	—
89	C₂²×C₄×C₆₇	—	8	2	no	—
90	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₇	#41	1	2	yes	—
95	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
96	C₂×C₈×C₆₇	—	2	2	no	—
97	C₂×C₈×C₆₇	—	2	2	no	—
98	C₂×C₈×C₆₇	—	2	2	no	—
99	C₂×C₈×C₆₇	—	2	2	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	—	2	2	no	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	4	no	—
104	C₄⋊C₄×C₆₇	—	2	2	no	—
105	C₄⋊C₄×C₆₇	—	2	2	no	—
106	C₄⋊C₄×C₆₇	—	2	2	no	—
107	C₄⋊C₄×C₆₇	—	2	2	no	—
108	C₄⋊C₄×C₆₇	—	4	4	no	—
109	C₄⋊C₄×C₆₇	—	4	4	no	—
110	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
111	C₄⋊C₄×C₆₇	#41	1	4	yes	—
112	C₂²⋊C₄×C₆₇	—	2	4	no	—
113	C₂²⋊C₄×C₆₇	—	2	4	no	—
114	C₂²⋊C₄×C₆₇	—	4	4	no	—
115	C₄²×C₆₇	—	2	4	no	—
116	C₄²×C₆₇	—	2	2	no	—
117	C₄²×C₆₇	—	8	2	no	—
118	C₄²×C₆₇	—	8	2	no	—
119	C₄²×C₆₇	#41	1	4	yes	—
120	C₂³×C₆₇	—	2	1	no	—
121	C₂³×C₆₇	—	2	1	no	—
122	C₂³×C₆₇	—	2	2	no	—
123	C₂³×C₆₇	—	2	2	no	—
124	C₂³×C₆₇	#121	1	2	yes	—
125	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
126	Q₈×C₆₇	—	4	2	no	—
127	Q₈×C₆₇	—	4	2	no	—
128	Q₈×C₆₇	—	4	2	no	—
129	Q₈×C₆₇	—	4	2	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	4	no	—
135	C₂×C₄×C₆₇	—	2	4	no	—
136	C₂×C₄×C₆₇	—	2	4	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	2	4	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	2	2	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	—	4	2	no	—
143	C₂×C₄×C₆₇	—	4	2	no	—
144	C₂×C₄×C₆₇	—	4	2	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	—	4	2	no	—
147	C₂×C₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	—	4	2	no	—
149	C₂×C₄×C₆₇	—	4	2	no	—
150	C₂×C₄×C₆₇	—	4	2	no	—
151	C₂×C₄×C₆₇	—	8	4	no	—
152	C₂×C₄×C₆₇	#121	1	2	yes	—
153	C₂×C₄×C₆₇	#123	1	4	yes	—
154	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
157	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
158	C₈×C₆₇	—	4	2	no	—
159	C₈×C₆₇	—	4	2	no	—
160	C₂²×C₆₇	—	2	2	no	—
161	C₂²×C₆₇	—	2	4	no	—
162	C₂²×C₆₇	—	4	2	no	—
163	C₂²×C₆₇	—	4	1	no	—
164	C₂²×C₆₇	—	4	1	no	—
165	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#123	1	1	yes	characteristic
167	C₂²×C₆₇	#525	1	1	yes	characteristic
168	C₂²×C₆₇	#577	1	2	yes	—
169	C₂²×C₆₇	#578	1	2	yes	—
170	C₄×C₆₇	—	2	4	no	—
171	C₄×C₆₇	—	2	2	no	—
172	C₄×C₆₇	—	4	2	no	—
173	C₄×C₆₇	—	4	4	no	—
174	C₄×C₆₇	—	4	4	no	—
175	C₄×C₆₇	—	8	2	no	—
176	C₄×C₆₇	—	8	2	no	—
177	C₄×C₆₇	#529	1	2	yes	—
178	C₄×C₆₇	#532	1	2	yes	—
179	#33117	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₆₇	—	4	2	no	—
181	C₂×C₆₇	#2854	1	1	yes	characteristic
182	C₂×C₆₇	#3046	1	2	yes	—
183	C₂×C₆₇	#3097	1	2	yes	—
184	C₂×C₆₇	#3123	1	1	yes	characteristic
185	C₂×C₆₇	#3127	1	1	yes	characteristic
186	C₂×#485	C₂×C₆₇	1	2	yes	—
187	#2621	C₂×C₆₇	1	1	yes	characteristic
188	#2274	C₂×C₆₇	1	1	yes	characteristic
189	#1981	C₂×C₆₇	1	2	yes	complemented
190	#1949	C₂×C₆₇	1	2	yes	complemented
191	#1928	C₂×C₆₇	1	2	yes	complemented
192	#1927	C₂×C₆₇	1	2	yes	complemented
193	#1872	C₂×C₆₇	1	2	yes	—
194	#1798	C₂×C₆₇	1	1	yes	characteristic
195	C₆₇	#33117	1	1	yes	characteristic, direct product factor, Sylow
196	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
197	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
198	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
199	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
200	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
201	#485	—	2	8	no	—
202	C₂×#107	C₂²×C₆₇	1	2	yes	—
203	C₂×#106	C₂²×C₆₇	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₆₇	1	2	yes	—
205	C₂×#103	C₂²×C₆₇	1	2	yes	—
206	C₂×#103	C₂²×C₆₇	1	2	yes	—
207	C₂×#103	C₂²×C₆₇	1	2	yes	—
208	C₂×#103	C₂²×C₆₇	1	2	yes	—
209	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	—
210	#398	—	2	2	no	—
211	#397	—	2	2	no	—
212	#391	C₂²×C₆₇	1	2	yes	—
213	#382	C₂²×C₆₇	1	1	yes	characteristic
214	C₄×C₄⋊C₄	—	2	2	no	—
215	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
216	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
217	C₄×C₂²⋊C₄	—	2	2	no	—
218	#340	C₂²×C₆₇	1	2	yes	—
219	#340	C₂²×C₆₇	1	2	yes	—
220	#336	C₂²×C₆₇	1	1	yes	characteristic
221	#336	C₂²×C₆₇	1	1	yes	characteristic
222	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
223	C₂³×C₄	—	2	1	no	—
224	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
225	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
226	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
227	C₄⋊Q₈	—	2	4	no	—
228	C₂²⋊Q₈	—	2	4	no	—
229	C₂²⋊Q₈	—	2	4	no	—
230	#117	—	2	2	no	—
231	#117	—	2	4	no	—
232	#117	D₄×C₆₇	1	4	yes	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
240	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
241	C₂×C₂²⋊C₄	—	2	1	no	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
244	C₂×C₄²	—	2	1	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
249	#107	—	2	4	no	—
250	#106	—	2	4	no	—
251	C₄⋊C₈	—	2	4	no	—
252	#103	—	2	4	no	—
253	#103	—	2	4	no	—
254	#103	—	2	4	no	—
255	#103	—	2	4	no	—
256	C₂²⋊C₈	—	2	4	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	#95	—	2	2	no	—
260	#95	—	2	4	no	—
261	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
262	C₂×Q₈	—	2	2	no	—
263	C₂×Q₈	—	2	2	no	—
264	C₂×Q₈	—	2	2	no	—
265	C₂×Q₈	—	2	2	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	8	2	no	—
276	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
279	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
280	C₂²×C₄	#41×C₆₇	1	2	yes	—
281	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
282	C₂×C₈	—	2	2	no	—
283	C₂×C₈	—	2	2	no	—
284	C₂×C₈	—	2	2	no	—
285	C₂×C₈	—	2	2	no	—
286	C₂×C₈	—	2	2	no	—
287	C₂×C₈	—	2	2	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	4	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	2	no	—
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	4	4	no	—
295	C₄⋊C₄	—	4	4	no	—
296	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
297	C₄⋊C₄	#41×C₆₇	1	4	yes	—
298	C₂²⋊C₄	—	2	4	no	—
299	C₂²⋊C₄	—	2	4	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₄²	—	2	4	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	8	2	no	—
304	C₄²	—	8	2	no	—
305	C₄²	#41×C₆₇	1	4	yes	—
306	C₂³	—	2	1	no	—
307	C₂³	—	2	1	no	—
308	C₂³	—	2	2	no	—
309	C₂³	—	2	2	no	—
310	C₂³	#121×C₆₇	1	2	yes	—
311	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	Q₈	—	4	2	no	—
315	Q₈	—	4	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	2	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	8	4	no	—
338	C₂×C₄	#121×C₆₇	1	2	yes	—
339	C₂×C₄	#123×C₆₇	1	4	yes	—
340	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
341	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
342	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
343	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
344	C₈	—	4	2	no	—
345	C₈	—	4	2	no	—
346	C₂²	—	2	4	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	4	2	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	4	1	no	—
351	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
352	C₂²	C₂×#123×C₆₇	1	1	yes	characteristic
353	C₂²	#525×C₆₇	1	1	yes	characteristic
354	C₂²	#577×C₆₇	1	2	yes	—
355	C₂²	#578×C₆₇	1	2	yes	—
356	C₄	—	2	4	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	4	no	—
359	C₄	—	4	2	no	—
360	C₄	—	4	4	no	—
361	C₄	—	8	2	no	—
362	C₄	—	8	2	no	—
363	C₄	#529×C₆₇	1	2	yes	—
364	C₄	#532×C₆₇	1	2	yes	—
365	C₂	—	4	2	no	—
366	C₂	C₆₇×#2854	1	1	yes	characteristic
367	C₂	C₆₇×#3046	1	2	yes	—
368	C₂	C₆₇×#3097	1	2	yes	—
369	C₂	C₆₇×#3123	1	1	yes	characteristic
370	C₂	C₆₇×#3127	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 ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₆₇×#1981	C₂	semidirect
5. C₆₇×#1949	C₂	semidirect
6. C₆₇×#1928	C₂	semidirect
7. C₆₇×#1927	C₂	semidirect
179. #33117	C₆₇	direct (N × H)
189. #1981	C₂×C₆₇	semidirect
190. #1949	C₂×C₆₇	semidirect
191. #1928	C₂×C₆₇	semidirect
192. #1927	C₂×C₆₇	semidirect
195. C₆₇	#33117	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#485×C₆₇	2
C₆₇×#2621	2
C₆₇×#2274	2
C₆₇×#1981	2
C₆₇×#1949	2
C₆₇×#1928	2
C₆₇×#1927	2
C₆₇×#1872	2
C₆₇×#1798	2
#33117	67

Subgroups — C67×#33117 #30712368

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33117 #30712368