Subgroups — C₆₇×#21407 #30700658

Order 17152.

1154 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#97×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2283	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1993	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1960	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1892	C₂	1	4	yes	maximal
7	C₆₇×#1763	C₂	1	4	yes	maximal, complemented
8	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
9	#533×C₆₇	—	2	4	no	—
10	#533×C₆₇	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₆₇	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₆₇	—	2	1	no	—
17	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
18	C₂×#117×C₆₇	—	2	1	no	—
19	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
20	C₂×#103×C₆₇	C₂²	1	8	yes	—
21	C₂×#97×C₆₇	—	2	4	no	—
22	C₂×#97×C₆₇	C₂²	1	2	yes	—
23	C₂×#97×C₆₇	C₂²	1	2	yes	—
24	#383×C₆₇	—	2	1	no	—
25	#382×C₆₇	C₂²	1	2	yes	—
26	#381×C₆₇	—	2	1	no	—
27	#380×C₆₇	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
30	#376×C₆₇	—	2	1	no	—
31	#340×C₆₇	C₂²	1	8	yes	—
32	C₂²×Q₈×C₆₇	—	2	1	no	—
33	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₆₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
37	C₂²×C₈×C₆₇	—	2	4	no	—
38	C₂²×C₈×C₆₇	—	2	8	no	—
39	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₆₇	—	2	2	no	—
41	C₄⋊Q₈×C₆₇	—	2	2	no	—
42	C₄⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
43	C₄⋊Q₈×C₆₇	C₂×C₄	1	4	yes	—
44	#125×C₆₇	—	2	8	no	—
45	C₂²⋊Q₈×C₆₇	—	2	8	no	—
46	C₂²⋊Q₈×C₆₇	—	2	4	no	—
47	C₂²⋊Q₈×C₆₇	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₆₇	—	2	8	no	—
49	C₄×Q₈×C₆₇	—	2	4	no	—
50	C₄×Q₈×C₆₇	C₂×C₄	1	8	yes	—
51	#117×C₆₇	—	2	8	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
59	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
61	C₂×C₄²×C₆₇	—	2	2	no	—
62	C₂×C₄²×C₆₇	—	2	2	no	—
63	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	D₄	1	4	yes	—
67	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
69	#103×C₆₇	—	2	16	no	—
70	#97×C₆₇	—	2	4	no	—
71	#97×C₆₇	—	2	4	no	—
72	#95×C₆₇	—	2	2	no	—
73	#95×C₆₇	—	2	2	no	—
74	#95×C₆₇	—	2	2	no	—
75	#95×C₆₇	—	2	2	no	—
76	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₆₇	—	2	4	no	—
78	C₂×Q₈×C₆₇	—	2	2	no	—
79	C₂×Q₈×C₆₇	—	2	8	no	—
80	C₂×Q₈×C₆₇	—	4	4	no	—
81	C₂×Q₈×C₆₇	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₆₇	—	2	4	no	—
83	C₂²×C₄×C₆₇	—	2	4	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	—	4	2	no	—
88	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₆₇	C₂²⋊C₄	1	4	yes	—
90	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
98	C₂×C₈×C₆₇	—	2	16	no	—
99	C₂×C₈×C₆₇	—	2	4	no	—
100	C₂×C₈×C₆₇	—	2	4	no	—
101	C₂×C₈×C₆₇	#41	1	8	yes	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	4	no	—
104	C₄⋊C₄×C₆₇	—	2	4	no	—
105	C₄⋊C₄×C₆₇	—	2	8	no	—
106	C₄⋊C₄×C₆₇	—	2	8	no	—
107	C₄⋊C₄×C₆₇	—	2	2	no	—
108	C₄⋊C₄×C₆₇	—	2	8	no	—
109	C₄⋊C₄×C₆₇	C₂²×C₄	1	4	yes	—
110	C₂²⋊C₄×C₆₇	—	2	8	no	—
111	C₂²⋊C₄×C₆₇	—	4	4	no	—
112	C₄²×C₆₇	—	2	8	no	—
113	C₄²×C₆₇	—	4	4	no	—
114	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
115	C₄²×C₆₇	C₂²⋊C₄	1	4	yes	—
116	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
117	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₆₇	C₂×D₄	1	2	yes	—
119	C₄²×C₆₇	C₂×D₄	1	2	yes	—
120	C₂³×C₆₇	—	2	2	no	—
121	C₂³×C₆₇	—	2	2	no	—
122	C₂³×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
123	C₂³×C₆₇	#137	1	4	yes	—
124	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
125	Q₈×C₆₇	—	2	8	no	—
126	Q₈×C₆₇	—	4	8	no	—
127	Q₈×C₆₇	—	4	4	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	2	no	—
131	C₂×C₄×C₆₇	—	2	2	no	—
132	C₂×C₄×C₆₇	—	2	2	no	—
133	C₂×C₄×C₆₇	—	2	8	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	4	no	—
138	C₂×C₄×C₆₇	—	4	4	no	—
139	C₂×C₄×C₆₇	—	4	4	no	—
140	C₂×C₄×C₆₇	—	4	4	no	—
141	C₂×C₄×C₆₇	—	4	4	no	—
142	C₂×C₄×C₆₇	—	4	4	no	—
143	C₂×C₄×C₆₇	—	4	4	no	—
144	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
152	C₈×C₆₇	—	2	8	no	—
153	C₂²×C₆₇	—	2	2	no	—
154	C₂²×C₆₇	—	2	8	no	—
155	C₂²×C₆₇	—	2	2	no	—
156	C₂²×C₆₇	#419	1	4	yes	—
157	C₂²×C₆₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₆₇	#532	1	2	yes	—
159	C₂²×C₆₇	C₂×#137	1	2	yes	—
160	C₂²×C₆₇	#575	1	2	yes	—
161	C₄×C₆₇	—	2	2	no	—
162	C₄×C₆₇	—	2	2	no	—
163	C₄×C₆₇	—	2	2	no	—
164	C₄×C₆₇	—	2	2	no	—
165	C₄×C₆₇	—	2	2	no	—
166	C₄×C₆₇	—	4	4	no	—
167	C₄×C₆₇	—	4	4	no	—
168	C₄×C₆₇	—	8	4	no	—
169	C₄×C₆₇	C₄×#41	1	2	yes	—
170	C₄×C₆₇	#525	1	2	yes	—
171	#21407	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₆₇	—	2	4	no	—
173	C₂×C₆₇	#2297	1	1	yes	characteristic
174	C₂×C₆₇	C₂×#419	1	1	yes	characteristic
175	C₂×C₆₇	#2896	1	1	yes	characteristic
176	C₂×C₆₇	#3181	1	4	yes	—
177	C₂×#533	C₂×C₆₇	1	1	yes	characteristic
178	C₂²×#97	C₂×C₆₇	1	1	yes	characteristic
179	#2283	C₂×C₆₇	1	1	yes	characteristic
180	#1993	C₂×C₆₇	1	2	yes	complemented
181	#1960	C₂×C₆₇	1	2	yes	complemented
182	#1892	C₂×C₆₇	1	4	yes	—
183	#1763	C₂×C₆₇	1	4	yes	complemented
184	C₆₇	#21407	1	1	yes	characteristic, direct product factor, Sylow
185	C₂³×C₈	C₂²×C₆₇	1	2	yes	—
186	#533	—	2	4	no	—
187	#533	C₄×C₆₇	1	8	yes	complemented
188	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
189	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
190	C₂×#125	—	2	1	no	—
191	C₂×C₂²⋊Q₈	—	2	1	no	—
192	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	—
193	C₂×C₄×Q₈	—	2	1	no	—
194	C₂×C₄×Q₈	C₂²×C₆₇	1	2	yes	—
195	C₂×#117	—	2	1	no	—
196	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
197	C₂×#103	C₂²×C₆₇	1	8	yes	—
198	C₂×#97	—	2	4	no	—
199	C₂×#97	C₂²×C₆₇	1	2	yes	—
200	C₂×#97	C₂²×C₆₇	1	2	yes	—
201	#383	—	2	1	no	—
202	#382	C₂²×C₆₇	1	2	yes	—
203	#381	—	2	1	no	—
204	#380	C₂²×C₆₇	1	2	yes	—
205	C₄×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
206	C₄×C₂²⋊C₄	—	2	1	no	—
207	#376	—	2	1	no	—
208	#340	C₂²×C₆₇	1	8	yes	—
209	C₂²×Q₈	—	2	1	no	—
210	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
211	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
212	C₂³×C₄	D₄×C₆₇	1	1	yes	characteristic
213	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
214	C₂²×C₈	—	2	4	no	—
215	C₂²×C₈	—	2	8	no	—
216	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
217	C₄⋊Q₈	—	2	2	no	—
218	C₄⋊Q₈	—	2	2	no	—
219	C₄⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
220	C₄⋊Q₈	C₂×C₄×C₆₇	1	4	yes	—
221	#125	—	2	8	no	—
222	C₂²⋊Q₈	—	2	8	no	—
223	C₂²⋊Q₈	—	2	4	no	—
224	C₂²⋊Q₈	C₂×C₄×C₆₇	1	8	yes	—
225	C₄×Q₈	—	2	8	no	—
226	C₄×Q₈	—	2	4	no	—
227	C₄×Q₈	C₂×C₄×C₆₇	1	8	yes	—
228	#117	—	2	8	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	—	2	1	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
235	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
236	C₂×C₂²⋊C₄	—	2	2	no	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₄²	—	2	2	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	C₂×C₄×C₆₇	1	4	yes	—
241	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
242	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
243	C₂×C₄²	D₄×C₆₇	1	4	yes	—
244	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
246	#103	—	2	16	no	—
247	#97	—	2	4	no	—
248	#97	—	2	4	no	—
249	#95	—	2	2	no	—
250	#95	—	2	2	no	—
251	#95	—	2	2	no	—
252	#95	—	2	2	no	—
253	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
254	C₂×Q₈	—	2	4	no	—
255	C₂×Q₈	—	2	2	no	—
256	C₂×Q₈	—	2	8	no	—
257	C₂×Q₈	—	4	4	no	—
258	C₂×Q₈	C₂²×C₄×C₆₇	1	4	yes	—
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	2	no	—
265	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
266	C₂²×C₄	C₂²⋊C₄×C₆₇	1	4	yes	—
267	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
268	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
274	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
275	C₂×C₈	—	2	16	no	—
276	C₂×C₈	—	2	4	no	—
277	C₂×C₈	—	2	4	no	—
278	C₂×C₈	#41×C₆₇	1	8	yes	—
279	C₄⋊C₄	—	2	4	no	—
280	C₄⋊C₄	—	2	4	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	8	no	—
283	C₄⋊C₄	—	2	8	no	—
284	C₄⋊C₄	—	2	2	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	C₂²×C₄×C₆₇	1	4	yes	—
287	C₂²⋊C₄	—	2	8	no	—
288	C₂²⋊C₄	—	4	4	no	—
289	C₄²	—	2	8	no	—
290	C₄²	—	4	4	no	—
291	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
292	C₄²	C₂²⋊C₄×C₆₇	1	4	yes	—
293	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
294	C₄²	C₂²×C₄×C₆₇	1	2	yes	—
295	C₄²	C₂×D₄×C₆₇	1	2	yes	—
296	C₄²	C₂×D₄×C₆₇	1	2	yes	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
300	C₂³	#137×C₆₇	1	4	yes	—
301	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
302	Q₈	—	2	8	no	—
303	Q₈	—	4	8	no	—
304	Q₈	—	4	4	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	4	4	no	—
316	C₂×C₄	—	4	4	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
322	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
323	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
324	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
325	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	2	yes	—
326	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
327	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
328	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
329	C₈	—	2	8	no	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	2	no	—
332	C₂²	—	2	8	no	—
333	C₂²	#419×C₆₇	1	4	yes	—
334	C₂²	C₂²×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
335	C₂²	#532×C₆₇	1	2	yes	—
336	C₂²	C₂×#137×C₆₇	1	2	yes	—
337	C₂²	#575×C₆₇	1	2	yes	—
338	C₄	—	2	2	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	2	no	—
341	C₄	—	2	2	no	—
342	C₄	—	2	2	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	4	no	—
345	C₄	—	8	4	no	—
346	C₄	C₄×#41×C₆₇	1	2	yes	—
347	C₄	#525×C₆₇	1	2	yes	—
348	C₂	—	2	4	no	—
349	C₂	C₆₇×#2297	1	1	yes	characteristic
350	C₂	C₂×#419×C₆₇	1	1	yes	characteristic
351	C₂	C₆₇×#2896	1	1	yes	characteristic
352	C₂	C₆₇×#3181	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁴×C₆₇	C₂×D₄
LCS	G ▷ C₂×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
4. C₆₇×#1993	C₂	semidirect
5. C₆₇×#1960	C₂	semidirect
7. C₆₇×#1763	C₂	semidirect
10. #533×C₆₇	C₄	semidirect
171. #21407	C₆₇	direct (N × H)
180. #1993	C₂×C₆₇	semidirect
181. #1960	C₂×C₆₇	semidirect
183. #1763	C₂×C₆₇	semidirect
184. C₆₇	#21407	direct (N × H)
187. #533	C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₆₇	2
C₂²×#97×C₆₇	2
C₆₇×#2283	2
C₆₇×#1993	2
C₆₇×#1960	2
C₆₇×#1892	2
C₆₇×#1763	2
#21407	67

Subgroups — C67×#21407 #30700658

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#21407 #30700658