Subgroups — C₆₇×#20016 #30699267

Order 17152.

584 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3341	C₂	1	1	yes	maximal, characteristic
3	C₆₇×#3340	C₂	1	2	yes	maximal, complemented
4	C₆₇×#1707	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#1676	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇×#1671	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1669	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1646	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1638	C₂	1	2	yes	maximal, complemented
10	C₈×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#556×C₆₇	C₂²	1	2	yes	—
13	#555×C₆₇	C₂²	1	2	yes	—
14	#500×C₆₇	C₂²	1	1	yes	characteristic
15	#498×C₆₇	C₂²	1	2	yes	—
16	#495×C₆₇	—	2	1	no	—
17	#494×C₆₇	C₂²	1	1	yes	characteristic
18	#487×C₆₇	C₂²	1	2	yes	—
19	#485×C₆₇	—	2	2	no	—
20	#482×C₆₇	—	2	2	no	—
21	#482×C₆₇	—	2	2	no	—
22	#477×C₆₇	C₂²	1	2	yes	—
23	#476×C₆₇	C₂²	1	2	yes	—
24	#474×C₆₇	C₂²	1	2	yes	—
25	#466×C₆₇	—	2	1	no	—
26	#465×C₆₇	—	2	2	no	—
27	#464×C₆₇	—	2	2	no	—
28	#461×C₆₇	C₂²	1	2	yes	—
29	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₄×Q₁₆×C₆₇	—	2	1	no	—
31	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
32	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₈×D₄×C₆₇	C₂²	1	2	yes	—
34	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
35	#427×C₆₇	—	2	1	no	—
36	#427×C₆₇	—	2	2	no	—
37	#335×C₆₇	C₂²	1	1	yes	characteristic
38	#334×C₆₇	C₂²	1	1	yes	characteristic
39	#333×C₆₇	C₂²	1	2	yes	—
40	#332×C₆₇	C₂²	1	2	yes	—
41	Q₈⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
42	D₄⋊C₈×C₆₇	C₂²	1	2	yes	—
43	D₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×Q₁₆×C₆₇	—	2	1	no	—
46	C₂×Q₁₆×C₆₇	—	2	1	no	—
47	C₂×SD₁₆×C₆₇	—	2	2	no	—
48	C₂×SD₁₆×C₆₇	D₄	1	1	yes	characteristic
49	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₆₇	—	2	2	no	—
51	C₂²×C₈×C₆₇	—	2	1	no	—
52	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
54	#126×C₆₇	—	4	2	no	—
55	#124×C₆₇	—	2	2	no	—
56	#124×C₆₇	—	4	2	no	—
57	C₂²⋊Q₈×C₆₇	—	2	2	no	—
58	#121×C₆₇	—	2	2	no	—
59	#121×C₆₇	—	2	2	no	—
60	C₄×Q₈×C₆₇	—	2	2	no	—
61	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
62	C₄×D₄×C₆₇	C₂³	1	2	yes	—
63	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
64	#117×C₆₇	—	2	2	no	—
65	#117×C₆₇	—	2	2	no	—
66	#117×C₆₇	—	2	2	no	—
67	#107×C₆₇	—	2	1	no	—
68	#107×C₆₇	—	2	1	no	—
69	#107×C₆₇	—	2	2	no	—
70	#107×C₆₇	—	2	2	no	—
71	#107×C₆₇	D₄	1	1	yes	characteristic
72	#106×C₆₇	—	2	2	no	—
73	#106×C₆₇	—	2	2	no	—
74	#106×C₆₇	—	2	2	no	—
75	#106×C₆₇	D₄	1	1	yes	characteristic
76	C₄⋊C₈×C₆₇	—	2	1	no	—
77	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
79	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
80	#103×C₆₇	—	2	2	no	—
81	#103×C₆₇	—	2	2	no	—
82	#103×C₆₇	—	4	2	no	—
83	#103×C₆₇	D₄	1	1	yes	characteristic
84	#102×C₆₇	—	2	2	no	—
85	#102×C₆₇	—	2	2	no	—
86	#102×C₆₇	D₄	1	2	yes	—
87	#102×C₆₇	D₄	1	1	yes	characteristic
88	C₂²⋊C₈×C₆₇	—	2	1	no	—
89	C₂²⋊C₈×C₆₇	—	2	2	no	—
90	C₄×C₈×C₆₇	—	2	1	no	—
91	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₆₇	—	2	2	no	—
95	C₂×Q₈×C₆₇	—	2	2	no	—
96	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂×D₄×C₆₇	—	4	2	no	—
98	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
99	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₆₇	—	2	1	no	—
101	C₂²×C₄×C₆₇	—	2	2	no	—
102	Q₁₆×C₆₇	—	4	2	no	—
103	Q₁₆×C₆₇	—	8	1	no	—
104	SD₁₆×C₆₇	—	2	2	no	—
105	SD₁₆×C₆₇	—	8	2	no	—
106	D₈×C₆₇	—	2	2	no	—
107	C₂×C₈×C₆₇	—	2	1	no	—
108	C₂×C₈×C₆₇	—	2	2	no	—
109	C₂×C₈×C₆₇	—	2	1	no	—
110	C₂×C₈×C₆₇	—	2	1	no	—
111	C₂×C₈×C₆₇	—	4	4	no	—
112	C₂×C₈×C₆₇	—	4	2	no	—
113	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
117	C₄⋊C₄×C₆₇	—	2	1	no	—
118	C₄⋊C₄×C₆₇	—	2	2	no	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	2	2	no	—
122	C₄⋊C₄×C₆₇	—	4	2	no	—
123	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
124	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
126	C₂²⋊C₄×C₆₇	—	2	1	no	—
127	C₂²⋊C₄×C₆₇	—	2	2	no	—
128	C₂²⋊C₄×C₆₇	—	4	2	no	—
129	C₂²⋊C₄×C₆₇	—	4	2	no	—
130	C₂²⋊C₄×C₆₇	—	4	2	no	—
131	C₂²⋊C₄×C₆₇	—	4	2	no	—
132	C₄²×C₆₇	—	2	1	no	—
133	C₄²×C₆₇	—	4	2	no	—
134	C₄²×C₆₇	—	4	2	no	—
135	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
136	C₂³×C₆₇	—	2	2	no	—
137	C₂³×C₆₇	—	2	1	no	—
138	Q₈×C₆₇	—	2	1	no	—
139	Q₈×C₆₇	—	2	1	no	—
140	Q₈×C₆₇	—	4	2	no	—
141	Q₈×C₆₇	—	4	2	no	—
142	Q₈×C₆₇	—	8	2	no	—
143	D₄×C₆₇	—	2	2	no	—
144	D₄×C₆₇	—	2	1	no	—
145	D₄×C₆₇	—	2	2	no	—
146	D₄×C₆₇	—	2	1	no	—
147	D₄×C₆₇	—	16	2	no	—
148	C₂×C₄×C₆₇	—	2	1	no	—
149	C₂×C₄×C₆₇	—	2	1	no	—
150	C₂×C₄×C₆₇	—	2	1	no	—
151	C₂×C₄×C₆₇	—	2	2	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	—	4	1	no	—
154	C₂×C₄×C₆₇	—	4	1	no	—
155	C₂×C₄×C₆₇	—	4	2	no	—
156	C₂×C₄×C₆₇	—	4	2	no	—
157	C₂×C₄×C₆₇	—	4	2	no	—
158	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₆₇	—	2	1	no	—
162	C₈×C₆₇	—	2	1	no	—
163	C₈×C₆₇	—	4	1	no	—
164	C₈×C₆₇	—	4	2	no	—
165	C₈×C₆₇	—	4	1	no	—
166	C₈×C₆₇	—	4	1	no	—
167	C₈×C₆₇	#135	1	2	yes	—
168	C₈×C₆₇	#135	1	2	yes	—
169	C₂²×C₆₇	—	4	2	no	—
170	C₂²×C₆₇	—	4	1	no	—
171	C₂²×C₆₇	—	4	1	no	—
172	C₂²×C₆₇	—	4	2	no	—
173	C₂²×C₆₇	—	4	1	no	—
174	C₂²×C₆₇	—	4	2	no	—
175	C₂²×C₆₇	D₄²	1	1	yes	characteristic
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	4	2	no	—
178	C₄×C₆₇	—	4	1	no	—
179	C₄×C₆₇	—	4	1	no	—
180	C₄×C₆₇	—	4	1	no	—
181	C₄×C₆₇	—	8	2	no	—
182	C₄×C₆₇	—	8	2	no	—
183	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
184	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
185	C₄×C₆₇	#577	1	1	yes	characteristic
186	C₄×C₆₇	#578	1	1	yes	characteristic
187	#20016	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₆₇	—	8	2	no	—
189	C₂×C₆₇	—	8	1	no	—
190	C₂×C₆₇	#3283	1	1	yes	characteristic
191	C₂×C₆₇	#3284	1	1	yes	characteristic
192	C₂×C₆₇	#3290	1	1	yes	characteristic
193	#3393	C₂×C₆₇	1	1	yes	characteristic, complemented
194	#3341	C₂×C₆₇	1	1	yes	characteristic
195	#3340	C₂×C₆₇	1	2	yes	complemented
196	#1707	C₂×C₆₇	1	1	yes	characteristic, complemented
197	#1676	C₂×C₆₇	1	1	yes	characteristic, complemented
198	#1671	C₂×C₆₇	1	2	yes	complemented
199	#1669	C₂×C₆₇	1	1	yes	characteristic, complemented
200	#1646	C₂×C₆₇	1	2	yes	complemented
201	#1638	C₂×C₆₇	1	2	yes	complemented
202	C₈×SD₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
203	C₈×D₈	C₂×C₆₇	1	1	yes	characteristic, complemented
204	C₆₇	#20016	1	1	yes	characteristic, direct product factor, Sylow
205	#556	C₂²×C₆₇	1	2	yes	—
206	#555	C₂²×C₆₇	1	2	yes	—
207	#500	C₂²×C₆₇	1	1	yes	characteristic
208	#498	C₂²×C₆₇	1	2	yes	—
209	#495	—	2	1	no	—
210	#494	C₂²×C₆₇	1	1	yes	characteristic
211	#487	C₂²×C₆₇	1	2	yes	—
212	#485	—	2	2	no	—
213	#482	—	2	2	no	—
214	#482	—	2	2	no	—
215	#477	C₂²×C₆₇	1	2	yes	—
216	#476	C₂²×C₆₇	1	2	yes	—
217	#474	C₂²×C₆₇	1	2	yes	—
218	#466	—	2	1	no	—
219	#465	—	2	2	no	—
220	#464	—	2	2	no	—
221	#461	C₂²×C₆₇	1	2	yes	—
222	C₈×Q₈	C₂²×C₆₇	1	1	yes	characteristic
223	C₄×Q₁₆	—	2	1	no	—
224	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
225	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic
226	C₈×D₄	C₂²×C₆₇	1	2	yes	—
227	C₈×D₄	C₂²×C₆₇	1	1	yes	characteristic
228	#427	—	2	1	no	—
229	#427	—	2	2	no	—
230	#335	C₂²×C₆₇	1	1	yes	characteristic
231	#334	C₂²×C₆₇	1	1	yes	characteristic
232	#333	C₂²×C₆₇	1	2	yes	—
233	#332	C₂²×C₆₇	1	2	yes	—
234	Q₈⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
235	D₄⋊C₈	C₂²×C₆₇	1	2	yes	—
236	D₄⋊C₈	C₂²×C₆₇	1	1	yes	characteristic
237	C₈²	C₂²×C₆₇	1	1	yes	characteristic
238	C₂×Q₁₆	—	2	1	no	—
239	C₂×Q₁₆	—	2	1	no	—
240	C₂×SD₁₆	—	2	2	no	—
241	C₂×SD₁₆	D₄×C₆₇	1	1	yes	characteristic
242	C₂×D₈	D₄×C₆₇	1	1	yes	characteristic
243	C₂²×C₈	—	2	2	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
246	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
247	#126	—	4	2	no	—
248	#124	—	2	2	no	—
249	#124	—	4	2	no	—
250	C₂²⋊Q₈	—	2	2	no	—
251	#121	—	2	2	no	—
252	#121	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
255	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
256	C₄×D₄	C₂³×C₆₇	1	2	yes	—
257	#117	—	2	2	no	—
258	#117	—	2	2	no	—
259	#117	—	2	2	no	—
260	#107	—	2	1	no	—
261	#107	—	2	1	no	—
262	#107	—	2	2	no	—
263	#107	—	2	2	no	—
264	#107	D₄×C₆₇	1	1	yes	characteristic
265	#106	—	2	2	no	—
266	#106	—	2	2	no	—
267	#106	—	2	2	no	—
268	#106	D₄×C₆₇	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
271	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
272	C₄⋊C₈	C₂³×C₆₇	1	1	yes	characteristic
273	#103	—	2	2	no	—
274	#103	—	2	2	no	—
275	#103	—	4	2	no	—
276	#103	D₄×C₆₇	1	1	yes	characteristic
277	#102	—	2	2	no	—
278	#102	—	2	2	no	—
279	#102	D₄×C₆₇	1	2	yes	—
280	#102	D₄×C₆₇	1	1	yes	characteristic
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₄×C₈	—	2	1	no	—
284	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
285	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
286	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
292	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	2	no	—
295	Q₁₆	—	4	2	no	—
296	Q₁₆	—	8	1	no	—
297	SD₁₆	—	2	2	no	—
298	SD₁₆	—	8	2	no	—
299	D₈	—	2	2	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	4	4	no	—
305	C₂×C₈	—	4	2	no	—
306	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
307	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
308	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
309	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
317	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
318	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
319	C₂²⋊C₄	—	2	1	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₂²⋊C₄	—	4	2	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	4	2	no	—
327	C₄²	—	4	2	no	—
328	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
329	C₂³	—	2	2	no	—
330	C₂³	—	2	1	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	2	1	no	—
333	Q₈	—	4	2	no	—
334	Q₈	—	4	2	no	—
335	Q₈	—	8	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	2	1	no	—
338	D₄	—	2	2	no	—
339	D₄	—	2	1	no	—
340	D₄	—	16	2	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
352	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
353	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
354	C₈	—	2	1	no	—
355	C₈	—	2	1	no	—
356	C₈	—	4	1	no	—
357	C₈	—	4	2	no	—
358	C₈	—	4	1	no	—
359	C₈	—	4	1	no	—
360	C₈	#135×C₆₇	1	2	yes	—
361	C₈	#135×C₆₇	1	2	yes	—
362	C₂²	—	4	2	no	—
363	C₂²	—	4	1	no	—
364	C₂²	—	4	1	no	—
365	C₂²	—	4	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	D₄²×C₆₇	1	1	yes	characteristic
369	C₄	—	2	1	no	—
370	C₄	—	4	2	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	4	1	no	—
374	C₄	—	8	2	no	—
375	C₄	—	8	2	no	—
376	C₄	C₂×#135×C₆₇	1	1	yes	characteristic
377	C₄	C₂×#135×C₆₇	1	1	yes	characteristic
378	C₄	#577×C₆₇	1	1	yes	characteristic
379	C₄	#578×C₆₇	1	1	yes	characteristic
380	C₂	—	8	2	no	—
381	C₂	—	8	1	no	—
382	C₂	C₆₇×#3283	1	1	yes	characteristic
383	C₂	C₆₇×#3284	1	1	yes	characteristic
384	C₂	C₆₇×#3290	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
prime radical	C₆₇×#3341	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3393	C₂	semidirect
3. C₆₇×#3340	C₂	semidirect
4. C₆₇×#1707	C₂	semidirect
5. C₆₇×#1676	C₂	semidirect
6. C₆₇×#1671	C₂	semidirect
7. C₆₇×#1669	C₂	semidirect
8. C₆₇×#1646	C₂	semidirect
9. C₆₇×#1638	C₂	semidirect
10. C₈×SD₁₆×C₆₇	C₂	semidirect
11. C₈×D₈×C₆₇	C₂	semidirect
187. #20016	C₆₇	direct (N × H)
193. #3393	C₂×C₆₇	semidirect
195. #3340	C₂×C₆₇	semidirect
196. #1707	C₂×C₆₇	semidirect
197. #1676	C₂×C₆₇	semidirect
198. #1671	C₂×C₆₇	semidirect
199. #1669	C₂×C₆₇	semidirect
200. #1646	C₂×C₆₇	semidirect
201. #1638	C₂×C₆₇	semidirect
202. C₈×SD₁₆	C₂×C₆₇	semidirect
203. C₈×D₈	C₂×C₆₇	semidirect
204. C₆₇	#20016	direct (N × H)

Maximal subgroups

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

subgroup	index
C₆₇×#3393	2
C₆₇×#3341	2
C₆₇×#3340	2
C₆₇×#1707	2
C₆₇×#1676	2
C₆₇×#1671	2
C₆₇×#1669	2
C₆₇×#1646	2
C₆₇×#1638	2
C₈×SD₁₆×C₆₇	2
C₈×D₈×C₆₇	2
#20016	67

Subgroups — C67×#20016 #30699267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#20016 #30699267