Subgroups — C₆₇×#10056 #30689307

Order 17152.

646 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#494×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#476×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#2563	C₂	1	1	yes	maximal, characteristic
4	C₆₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#333×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₆₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₁₆×C₆₇	—	2	2	no	—
9	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
12	#494×C₆₇	—	2	2	no	—
13	#494×C₆₇	—	2	2	no	—
14	#476×C₆₇	—	2	2	no	—
15	#476×C₆₇	—	2	2	no	—
16	C₂×#106×C₆₇	—	2	1	no	—
17	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
19	C₂×#102×C₆₇	—	2	1	no	—
20	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
21	#393×C₆₇	—	2	2	no	—
22	#390×C₆₇	—	2	1	no	—
23	#382×C₆₇	—	2	1	no	—
24	#380×C₆₇	—	2	2	no	—
25	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
26	#340×C₆₇	—	2	2	no	—
27	#333×C₆₇	—	2	2	no	—
28	D₄⋊C₈×C₆₇	—	2	2	no	—
29	C₂²×Q₈×C₆₇	—	2	1	no	—
30	C₂²×Q₈×C₆₇	D₄	1	2	yes	—
31	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
32	C₂³×C₄×C₆₇	—	2	1	no	—
33	C₂×Q₁₆×C₆₇	—	2	8	no	—
34	C₂×Q₁₆×C₆₇	—	4	8	no	—
35	C₂²×C₈×C₆₇	—	2	1	no	—
36	C₂²×C₈×C₆₇	—	2	1	no	—
37	C₂²×C₈×C₆₇	—	2	1	no	—
38	C₄⋊Q₈×C₆₇	—	2	1	no	—
39	C₄⋊Q₈×C₆₇	—	2	1	no	—
40	C₄⋊Q₈×C₆₇	—	2	1	no	—
41	C₄⋊Q₈×C₆₇	—	2	1	no	—
42	C₄⋊Q₈×C₆₇	—	2	1	no	—
43	C₄⋊Q₈×C₆₇	—	2	1	no	—
44	C₄⋊Q₈×C₆₇	—	2	1	no	—
45	C₄⋊Q₈×C₆₇	D₄	1	2	yes	—
46	C₄×D₄×C₆₇	—	2	1	no	—
47	C₄×D₄×C₆₇	—	2	1	no	—
48	C₄×D₄×C₆₇	—	2	1	no	—
49	C₄×D₄×C₆₇	—	2	1	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
56	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
58	C₂×C₄²×C₆₇	—	2	1	no	—
59	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
60	#106×C₆₇	—	2	4	no	—
61	C₄⋊C₈×C₆₇	—	2	1	no	—
62	C₄⋊C₈×C₆₇	—	2	1	no	—
63	C₄⋊C₈×C₆₇	—	2	1	no	—
64	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
65	#102×C₆₇	—	2	4	no	—
66	C₄×C₈×C₆₇	—	2	1	no	—
67	C₄×C₈×C₆₇	D₄	1	2	yes	—
68	#95×C₆₇	—	2	4	no	—
69	#95×C₆₇	—	2	1	no	—
70	C₂⁴×C₆₇	—	2	1	no	—
71	C₂×Q₈×C₆₇	—	2	2	no	—
72	C₂×Q₈×C₆₇	—	2	2	no	—
73	C₂×Q₈×C₆₇	—	2	2	no	—
74	C₂×Q₈×C₆₇	—	4	4	no	—
75	C₂×Q₈×C₆₇	—	4	4	no	—
76	C₂×Q₈×C₆₇	—	4	1	no	—
77	C₂×D₄×C₆₇	—	2	1	no	—
78	C₂×D₄×C₆₇	—	2	1	no	—
79	C₂×D₄×C₆₇	—	2	1	no	—
80	C₂×D₄×C₆₇	—	2	1	no	—
81	C₂×D₄×C₆₇	—	2	1	no	—
82	C₂×D₄×C₆₇	Q₁₆	1	2	yes	complemented
83	C₂²×C₄×C₆₇	—	2	2	no	—
84	C₂²×C₄×C₆₇	—	2	2	no	—
85	C₂²×C₄×C₆₇	—	2	1	no	—
86	C₂²×C₄×C₆₇	—	4	1	no	—
87	C₂²×C₄×C₆₇	—	4	1	no	—
88	C₂²×C₄×C₆₇	—	4	1	no	—
89	C₂²×C₄×C₆₇	—	4	2	no	—
90	C₂²×C₄×C₆₇	—	4	2	no	—
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	Q₁₆×C₆₇	—	4	16	no	—
95	C₂×C₈×C₆₇	—	2	4	no	—
96	C₂×C₈×C₆₇	—	2	2	no	—
97	C₂×C₈×C₆₇	—	2	2	no	—
98	C₂×C₈×C₆₇	—	4	1	no	—
99	C₂×C₈×C₆₇	—	4	1	no	—
100	C₂×C₈×C₆₇	—	4	1	no	—
101	C₂×C₈×C₆₇	—	4	2	no	—
102	C₄⋊C₄×C₆₇	—	2	2	no	—
103	C₄⋊C₄×C₆₇	—	2	1	no	—
104	C₄⋊C₄×C₆₇	—	2	2	no	—
105	C₄⋊C₄×C₆₇	—	2	1	no	—
106	C₄⋊C₄×C₆₇	—	2	2	no	—
107	C₄⋊C₄×C₆₇	—	2	2	no	—
108	C₄⋊C₄×C₆₇	—	4	1	no	—
109	C₄⋊C₄×C₆₇	—	4	1	no	—
110	C₄⋊C₄×C₆₇	—	4	1	no	—
111	C₄⋊C₄×C₆₇	—	4	1	no	—
112	C₄⋊C₄×C₆₇	—	4	1	no	—
113	C₄⋊C₄×C₆₇	—	4	1	no	—
114	C₂²⋊C₄×C₆₇	—	4	1	no	—
115	C₂²⋊C₄×C₆₇	—	4	1	no	—
116	C₂²⋊C₄×C₆₇	—	8	4	no	—
117	C₄²×C₆₇	—	4	1	no	—
118	C₄²×C₆₇	—	4	1	no	—
119	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₆₇	#41	1	1	yes	characteristic
123	C₂³×C₆₇	—	2	2	no	—
124	C₂³×C₆₇	—	4	1	no	—
125	C₂³×C₆₇	—	4	2	no	—
126	C₂³×C₆₇	—	4	1	no	—
127	C₂³×C₆₇	—	4	2	no	—
128	C₂³×C₆₇	#120	1	1	yes	characteristic
129	Q₈×C₆₇	—	4	4	no	—
130	Q₈×C₆₇	—	4	4	no	—
131	Q₈×C₆₇	—	8	2	no	—
132	Q₈×C₆₇	—	8	2	no	—
133	D₄×C₆₇	—	2	2	no	—
134	D₄×C₆₇	—	2	2	no	—
135	D₄×C₆₇	—	4	1	no	—
136	D₄×C₆₇	—	4	1	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	4	1	no	—
139	C₂×C₄×C₆₇	—	4	2	no	—
140	C₂×C₄×C₆₇	—	4	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	4	no	—
146	C₂×C₄×C₆₇	—	8	2	no	—
147	C₂×C₄×C₆₇	—	8	2	no	—
148	C₂×C₄×C₆₇	—	8	1	no	—
149	C₂×C₄×C₆₇	—	8	1	no	—
150	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
151	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
152	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
155	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×Q₁₆	1	1	yes	characteristic
157	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
158	C₂×C₄×C₆₇	#135	1	2	yes	—
159	C₂×C₄×C₆₇	#137	1	1	yes	characteristic
160	C₂×C₄×C₆₇	#137	1	1	yes	characteristic
161	C₂×C₄×C₆₇	#137	1	2	yes	—
162	C₈×C₆₇	—	2	4	no	—
163	C₈×C₆₇	—	4	2	no	—
164	C₈×C₆₇	—	8	1	no	—
165	C₂²×C₆₇	—	4	4	no	—
166	C₂²×C₆₇	—	4	2	no	—
167	C₂²×C₆₇	—	8	2	no	—
168	C₂²×C₆₇	—	8	1	no	—
169	C₂²×C₆₇	—	8	1	no	—
170	C₂²×C₆₇	#392	1	1	yes	characteristic
171	C₂²×C₆₇	#451	1	1	yes	characteristic
172	C₂²×C₆₇	#452	1	2	yes	—
173	C₂²×C₆₇	#452	1	1	yes	characteristic
174	C₂²×C₆₇	#453	1	2	yes	—
175	C₄×C₆₇	—	2	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	8	2	no	—
178	C₄×C₆₇	—	8	2	no	—
179	C₄×C₆₇	—	8	2	no	—
180	C₄×C₆₇	—	8	1	no	—
181	C₄×C₆₇	#451	1	1	yes	characteristic
182	C₄×C₆₇	#452	1	1	yes	characteristic
183	C₄×C₆₇	#464	1	2	yes	—
184	C₄×C₆₇	#467	1	1	yes	characteristic
185	C₄×C₆₇	#470	1	1	yes	characteristic
186	C₄×C₆₇	#495	1	1	yes	characteristic
187	C₄×C₆₇	#497	1	1	yes	characteristic
188	#10056	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂×C₆₇	—	8	2	no	—
190	C₂×C₆₇	#1632	1	2	yes	—
191	C₂×C₆₇	#1634	1	2	yes	—
192	C₂×C₆₇	#2001	1	1	yes	characteristic
193	C₂×C₆₇	#2002	1	1	yes	characteristic
194	C₂×C₆₇	#2015	1	1	yes	characteristic
195	C₂×#494	C₂×C₆₇	1	1	yes	characteristic, complemented
196	C₂×#476	C₂×C₆₇	1	1	yes	characteristic
197	#2563	C₂×C₆₇	1	1	yes	characteristic
198	#1987	C₂×C₆₇	1	1	yes	characteristic, complemented
199	C₂×#333	C₂×C₆₇	1	1	yes	characteristic, complemented
200	C₂×D₄⋊C₈	C₂×C₆₇	1	1	yes	characteristic
201	#1279	C₂×C₆₇	1	1	yes	characteristic, complemented
202	C₆₇	#10056	1	1	yes	characteristic, direct product factor, Sylow
203	C₂²×Q₁₆	—	2	2	no	—
204	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
205	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
206	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
207	#494	—	2	2	no	—
208	#494	—	2	2	no	—
209	#476	—	2	2	no	—
210	#476	—	2	2	no	—
211	C₂×#106	—	2	1	no	—
212	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
214	C₂×#102	—	2	1	no	—
215	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
216	#393	—	2	2	no	—
217	#390	—	2	1	no	—
218	#382	—	2	1	no	—
219	#380	—	2	2	no	—
220	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
221	#340	—	2	2	no	—
222	#333	—	2	2	no	—
223	D₄⋊C₈	—	2	2	no	—
224	C₂²×Q₈	—	2	1	no	—
225	C₂²×Q₈	D₄×C₆₇	1	2	yes	—
226	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
227	C₂³×C₄	—	2	1	no	—
228	C₂×Q₁₆	—	2	8	no	—
229	C₂×Q₁₆	—	4	8	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₄⋊Q₈	—	2	1	no	—
234	C₄⋊Q₈	—	2	1	no	—
235	C₄⋊Q₈	—	2	1	no	—
236	C₄⋊Q₈	—	2	1	no	—
237	C₄⋊Q₈	—	2	1	no	—
238	C₄⋊Q₈	—	2	1	no	—
239	C₄⋊Q₈	—	2	1	no	—
240	C₄⋊Q₈	D₄×C₆₇	1	2	yes	—
241	C₄×D₄	—	2	1	no	—
242	C₄×D₄	—	2	1	no	—
243	C₄×D₄	—	2	1	no	—
244	C₄×D₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
250	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
251	C₂×C₂²⋊C₄	—	2	1	no	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
255	#106	—	2	4	no	—
256	C₄⋊C₈	—	2	1	no	—
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	D₄×C₆₇	1	2	yes	—
260	#102	—	2	4	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	D₄×C₆₇	1	2	yes	—
263	#95	—	2	4	no	—
264	#95	—	2	1	no	—
265	C₂⁴	—	2	1	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	2	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	4	4	no	—
270	C₂×Q₈	—	4	4	no	—
271	C₂×Q₈	—	4	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	Q₁₆×C₆₇	1	2	yes	complemented
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
289	Q₁₆	—	4	16	no	—
290	C₂×C₈	—	2	4	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	4	1	no	—
294	C₂×C₈	—	4	1	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	1	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	4	1	no	—
306	C₄⋊C₄	—	4	1	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₂²⋊C₄	—	4	1	no	—
310	C₂²⋊C₄	—	4	1	no	—
311	C₂²⋊C₄	—	8	4	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	1	no	—
314	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
315	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
316	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
317	C₄²	#41×C₆₇	1	1	yes	characteristic
318	C₂³	—	2	2	no	—
319	C₂³	—	4	2	no	—
320	C₂³	—	4	1	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	1	no	—
323	C₂³	#120×C₆₇	1	1	yes	characteristic
324	Q₈	—	4	4	no	—
325	Q₈	—	4	4	no	—
326	Q₈	—	8	2	no	—
327	Q₈	—	8	2	no	—
328	D₄	—	2	2	no	—
329	D₄	—	2	2	no	—
330	D₄	—	4	1	no	—
331	D₄	—	4	1	no	—
332	C₂×C₄	—	2	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	—	4	4	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	8	2	no	—
342	C₂×C₄	—	8	2	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	8	1	no	—
345	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
346	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
347	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
348	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
349	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
350	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
351	C₂×C₄	C₂×Q₁₆×C₆₇	1	1	yes	characteristic
352	C₂×C₄	#135×C₆₇	1	1	yes	characteristic
353	C₂×C₄	#135×C₆₇	1	2	yes	—
354	C₂×C₄	#137×C₆₇	1	1	yes	characteristic
355	C₂×C₄	#137×C₆₇	1	1	yes	characteristic
356	C₂×C₄	#137×C₆₇	1	2	yes	—
357	C₈	—	2	4	no	—
358	C₈	—	4	2	no	—
359	C₈	—	8	1	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	8	1	no	—
363	C₂²	—	8	1	no	—
364	C₂²	—	8	2	no	—
365	C₂²	#392×C₆₇	1	1	yes	characteristic
366	C₂²	#451×C₆₇	1	1	yes	characteristic
367	C₂²	#452×C₆₇	1	1	yes	characteristic
368	C₂²	#452×C₆₇	1	2	yes	—
369	C₂²	#453×C₆₇	1	2	yes	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	8	2	no	—
373	C₄	—	8	2	no	—
374	C₄	—	8	1	no	—
375	C₄	—	8	2	no	—
376	C₄	#451×C₆₇	1	1	yes	characteristic
377	C₄	#452×C₆₇	1	1	yes	characteristic
378	C₄	#464×C₆₇	1	2	yes	—
379	C₄	#467×C₆₇	1	1	yes	characteristic
380	C₄	#470×C₆₇	1	1	yes	characteristic
381	C₄	#495×C₆₇	1	1	yes	characteristic
382	C₄	#497×C₆₇	1	1	yes	characteristic
383	C₂	—	8	2	no	—
384	C₂	C₆₇×#1632	1	2	yes	—
385	C₂	C₆₇×#1634	1	2	yes	—
386	C₂	C₆₇×#2001	1	1	yes	characteristic
387	C₂	C₆₇×#2002	1	1	yes	characteristic
388	C₂	C₆₇×#2015	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	#120
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₆₇
prime radical	C₂²×D₄×C₆₇	D₄
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#494×C₆₇	C₂	semidirect
4. C₆₇×#1987	C₂	semidirect
5. C₂×#333×C₆₇	C₂	semidirect
7. C₆₇×#1279	C₂	semidirect
82. C₂×D₄×C₆₇	Q₁₆	semidirect
188. #10056	C₆₇	direct (N × H)
195. C₂×#494	C₂×C₆₇	semidirect
198. #1987	C₂×C₆₇	semidirect
199. C₂×#333	C₂×C₆₇	semidirect
201. #1279	C₂×C₆₇	semidirect
202. C₆₇	#10056	direct (N × H)
277. C₂×D₄	Q₁₆×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#494×C₆₇	2
C₂×#476×C₆₇	2
C₆₇×#2563	2
C₆₇×#1987	2
C₂×#333×C₆₇	2
C₂×D₄⋊C₈×C₆₇	2
C₆₇×#1279	2
#10056	67

Subgroups — C67×#10056 #30689307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#10056 #30689307