Subgroups — C₆₇×#33584 #30712835

Order 17152.

722 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#510×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#509×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#495×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2211	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2210	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2150	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2141	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2140	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₆₇	—	2	1	no	—
13	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₆₇	—	2	1	no	—
15	C₄×#41×C₆₇	—	2	1	no	—
16	#510×C₆₇	—	2	4	no	—
17	#509×C₆₇	—	2	4	no	—
18	C₂×Q₃₂×C₆₇	C₂²	1	2	yes	complemented
19	C₂×SD₃₂×C₆₇	C₂²	1	2	yes	—
20	C₂×SD₃₂×C₆₇	C₂²	1	2	yes	complemented
21	C₂×D₁₆×C₆₇	C₂²	1	2	yes	—
22	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
24	#495×C₆₇	—	2	2	no	—
25	#495×C₆₇	C₂²	1	4	yes	—
26	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
27	C₄×SD₁₆×C₆₇	—	2	2	no	—
28	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
29	#427×C₆₇	C₂²	1	1	yes	characteristic
30	#416×C₆₇	—	2	1	no	—
31	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
32	C₄⋊C₁₆×C₆₇	C₂²	1	4	yes	complemented
33	#358×C₆₇	C₂²	1	4	yes	complemented
34	#357×C₆₇	C₂²	1	4	yes	—
35	C₂×#41×C₆₇	—	2	1	no	—
36	C₂²×Q₈×C₆₇	—	2	1	no	—
37	C₂²×D₄×C₆₇	—	2	1	no	—
38	#135×C₆₇	—	2	2	no	—
39	#135×C₆₇	D₄	1	4	yes	—
40	C₂×Q₁₆×C₆₇	—	2	2	no	—
41	C₂×Q₁₆×C₆₇	—	2	1	no	—
42	C₂×Q₁₆×C₆₇	—	2	2	no	—
43	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
44	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
45	C₂×SD₁₆×C₆₇	—	2	1	no	—
46	C₂×SD₁₆×C₆₇	—	2	4	no	—
47	C₂×SD₁₆×C₆₇	—	4	4	no	—
48	C₂×D₈×C₆₇	—	2	2	no	—
49	C₂×D₈×C₆₇	—	2	1	no	—
50	C₂×D₈×C₆₇	—	2	2	no	—
51	C₂×D₈×C₆₇	C₂³	1	2	yes	—
52	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
54	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
55	#124×C₆₇	—	2	4	no	—
56	#124×C₆₇	—	4	1	no	—
57	#124×C₆₇	—	4	1	no	—
58	C₄×Q₈×C₆₇	—	2	2	no	—
59	C₄×D₄×C₆₇	—	2	2	no	—
60	C₄×D₄×C₆₇	—	4	2	no	—
61	#117×C₆₇	—	2	1	no	—
62	#117×C₆₇	—	4	1	no	—
63	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
64	C₂×C₄²×C₆₇	—	4	1	no	—
65	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
66	Q₃₂×C₆₇	—	2	4	no	—
67	SD₃₂×C₆₇	—	2	4	no	—
68	SD₃₂×C₆₇	—	2	4	no	—
69	D₁₆×C₆₇	—	2	4	no	—
70	M₃₂×C₆₇	—	2	2	no	—
71	M₃₂×C₆₇	—	2	2	no	—
72	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
73	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
74	#107×C₆₇	C₂³	1	2	yes	—
75	#106×C₆₇	—	2	1	no	—
76	#103×C₆₇	—	2	2	no	—
77	#102×C₆₇	—	2	2	no	—
78	C₄×C₈×C₆₇	D₄	1	2	yes	—
79	C₄×C₈×C₆₇	C₂³	1	2	yes	—
80	C₂⁴×C₆₇	—	4	1	no	—
81	#41×C₆₇	—	2	4	no	—
82	#41×C₆₇	—	4	2	no	—
83	C₂×Q₈×C₆₇	—	2	1	no	—
84	C₂×Q₈×C₆₇	—	2	2	no	—
85	C₂×Q₈×C₆₇	—	4	1	no	—
86	C₂×Q₈×C₆₇	—	4	2	no	—
87	C₂×Q₈×C₆₇	—	4	2	no	—
88	C₂×D₄×C₆₇	—	2	1	no	—
89	C₂×D₄×C₆₇	—	2	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	2	no	—
94	C₂²×C₄×C₆₇	—	4	1	no	—
95	C₂²×C₄×C₆₇	—	4	1	no	—
96	C₂²×C₄×C₆₇	—	4	2	no	—
97	C₂²×C₄×C₆₇	D₈	1	2	yes	—
98	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
99	Q₁₆×C₆₇	—	2	2	no	—
100	Q₁₆×C₆₇	—	2	1	no	—
101	Q₁₆×C₆₇	—	2	2	no	—
102	Q₁₆×C₆₇	—	4	2	no	—
103	Q₁₆×C₆₇	C₂×D₄	1	2	yes	—
104	SD₁₆×C₆₇	—	2	4	no	—
105	SD₁₆×C₆₇	—	4	8	no	—
106	D₈×C₆₇	—	2	2	no	—
107	D₈×C₆₇	—	2	1	no	—
108	D₈×C₆₇	—	2	2	no	—
109	D₈×C₆₇	—	4	2	no	—
110	D₈×C₆₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₆₇	—	2	2	no	—
112	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
114	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₆₇	#41	1	2	yes	—
116	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
117	C₄⋊C₄×C₆₇	—	2	2	no	—
118	C₄⋊C₄×C₆₇	—	4	2	no	—
119	C₂²⋊C₄×C₆₇	—	4	1	no	—
120	C₂²⋊C₄×C₆₇	—	4	4	no	—
121	C₂²⋊C₄×C₆₇	—	4	4	no	—
122	C₂²⋊C₄×C₆₇	—	4	2	no	—
123	C₄²×C₆₇	—	4	1	no	—
124	C₄²×C₆₇	—	4	2	no	—
125	C₄²×C₆₇	D₈	1	1	yes	characteristic
126	C₄²×C₆₇	D₈	1	1	yes	characteristic
127	C₄²×C₆₇	C₂×D₄	1	2	yes	—
128	C₁₆×C₆₇	—	2	2	no	—
129	C₁₆×C₆₇	—	2	2	no	—
130	C₂³×C₆₇	—	4	1	no	—
131	C₂³×C₆₇	—	4	2	no	—
132	C₂³×C₆₇	—	8	4	no	—
133	C₂³×C₆₇	—	8	2	no	—
134	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
135	Q₈×C₆₇	—	2	2	no	—
136	Q₈×C₆₇	—	4	1	no	—
137	Q₈×C₆₇	—	4	2	no	—
138	Q₈×C₆₇	—	4	2	no	—
139	Q₈×C₆₇	—	8	2	no	—
140	D₄×C₆₇	—	2	2	no	—
141	D₄×C₆₇	—	4	4	no	—
142	D₄×C₆₇	—	4	2	no	—
143	D₄×C₆₇	—	4	1	no	—
144	D₄×C₆₇	—	4	2	no	—
145	D₄×C₆₇	—	8	2	no	—
146	C₂×C₄×C₆₇	—	4	2	no	—
147	C₂×C₄×C₆₇	—	4	1	no	—
148	C₂×C₄×C₆₇	—	4	4	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	—	8	2	no	—
153	C₂×C₄×C₆₇	#121	1	2	yes	—
154	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
155	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
156	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	C₈×C₆₇	—	2	2	no	—
160	C₈×C₆₇	#121	1	2	yes	—
161	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
162	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
163	C₂²×C₆₇	—	2	2	no	—
164	C₂²×C₆₇	—	4	2	no	—
165	C₂²×C₆₇	—	8	2	no	—
166	C₂²×C₆₇	—	8	4	no	—
167	C₂²×C₆₇	—	8	2	no	—
168	C₂²×C₆₇	—	16	4	no	—
169	C₂²×C₆₇	#459	1	2	yes	—
170	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
171	C₄×C₆₇	—	2	2	no	—
172	C₄×C₆₇	—	2	2	no	—
173	C₄×C₆₇	—	4	2	no	—
174	C₄×C₆₇	—	8	2	no	—
175	C₄×C₆₇	—	8	2	no	—
176	C₄×C₆₇	#459	1	2	yes	—
177	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
178	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
179	#33584	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₆₇	—	2	2	no	—
181	C₂×C₆₇	—	8	2	no	—
182	C₂×C₆₇	—	16	2	no	—
183	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
184	C₂×C₆₇	#3414	1	2	yes	—
185	C₂×#510	C₂×C₆₇	1	1	yes	characteristic, complemented
186	C₂×#509	C₂×C₆₇	1	1	yes	characteristic
187	C₂×#495	C₂×C₆₇	1	1	yes	characteristic, complemented
188	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
189	#2211	C₂×C₆₇	1	4	yes	complemented
190	#2210	C₂×C₆₇	1	4	yes	complemented
191	#2150	C₂×C₆₇	1	1	yes	characteristic, complemented
192	#2141	C₂×C₆₇	1	1	yes	characteristic, complemented
193	#2140	C₂×C₆₇	1	1	yes	characteristic, complemented
194	C₆₇	#33584	1	1	yes	characteristic, direct product factor, Sylow
195	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
196	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic
197	C₂²×SD₁₆	—	2	1	no	—
198	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
199	C₂×#124	—	2	1	no	—
200	C₄×#41	—	2	1	no	—
201	#510	—	2	4	no	—
202	#509	—	2	4	no	—
203	C₂×Q₃₂	C₂²×C₆₇	1	2	yes	complemented
204	C₂×SD₃₂	C₂²×C₆₇	1	2	yes	—
205	C₂×SD₃₂	C₂²×C₆₇	1	2	yes	complemented
206	C₂×D₁₆	C₂²×C₆₇	1	2	yes	—
207	C₂×M₃₂	C₂²×C₆₇	1	1	yes	characteristic
208	C₂×M₃₂	C₂²×C₆₇	1	1	yes	characteristic
209	#495	—	2	2	no	—
210	#495	C₂²×C₆₇	1	4	yes	—
211	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
212	C₄×SD₁₆	—	2	2	no	—
213	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
214	#427	C₂²×C₆₇	1	1	yes	characteristic
215	#416	—	2	1	no	—
216	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
217	C₄⋊C₁₆	C₂²×C₆₇	1	4	yes	complemented
218	#358	C₂²×C₆₇	1	4	yes	complemented
219	#357	C₂²×C₆₇	1	4	yes	—
220	C₂×#41	—	2	1	no	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	#135	—	2	2	no	—
224	#135	D₄×C₆₇	1	4	yes	—
225	C₂×Q₁₆	—	2	2	no	—
226	C₂×Q₁₆	—	2	1	no	—
227	C₂×Q₁₆	—	2	2	no	—
228	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
229	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
230	C₂×SD₁₆	—	2	1	no	—
231	C₂×SD₁₆	—	2	4	no	—
232	C₂×SD₁₆	—	4	4	no	—
233	C₂×D₈	—	2	2	no	—
234	C₂×D₈	—	2	1	no	—
235	C₂×D₈	—	2	2	no	—
236	C₂×D₈	C₂³×C₆₇	1	2	yes	—
237	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
238	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
239	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
240	#124	—	2	4	no	—
241	#124	—	4	1	no	—
242	#124	—	4	1	no	—
243	C₄×Q₈	—	2	2	no	—
244	C₄×D₄	—	2	2	no	—
245	C₄×D₄	—	4	2	no	—
246	#117	—	2	1	no	—
247	#117	—	4	1	no	—
248	C₂×C₂²⋊C₄	—	4	2	no	—
249	C₂×C₄²	—	4	1	no	—
250	C₂×C₄²	D₄×C₆₇	1	1	yes	characteristic
251	Q₃₂	—	2	4	no	—
252	SD₃₂	—	2	4	no	—
253	SD₃₂	—	2	4	no	—
254	D₁₆	—	2	4	no	—
255	M₃₂	—	2	2	no	—
256	M₃₂	—	2	2	no	—
257	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
258	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
259	#107	C₂³×C₆₇	1	2	yes	—
260	#106	—	2	1	no	—
261	#103	—	2	2	no	—
262	#102	—	2	2	no	—
263	C₄×C₈	D₄×C₆₇	1	2	yes	—
264	C₄×C₈	C₂³×C₆₇	1	2	yes	—
265	C₂⁴	—	4	1	no	—
266	#41	—	2	4	no	—
267	#41	—	4	2	no	—
268	C₂×Q₈	—	2	1	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	—	4	1	no	—
271	C₂×Q₈	—	4	2	no	—
272	C₂×Q₈	—	4	2	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	2	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	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	4	1	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	D₈×C₆₇	1	2	yes	—
283	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
284	Q₁₆	—	2	2	no	—
285	Q₁₆	—	2	1	no	—
286	Q₁₆	—	2	2	no	—
287	Q₁₆	—	4	2	no	—
288	Q₁₆	C₂×D₄×C₆₇	1	2	yes	—
289	SD₁₆	—	2	4	no	—
290	SD₁₆	—	4	8	no	—
291	D₈	—	2	2	no	—
292	D₈	—	2	1	no	—
293	D₈	—	2	2	no	—
294	D₈	—	4	2	no	—
295	D₈	C₂×D₄×C₆₇	1	2	yes	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
298	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
299	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
300	C₂×C₈	#41×C₆₇	1	2	yes	—
301	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	1	no	—
305	C₂²⋊C₄	—	4	4	no	—
306	C₂²⋊C₄	—	4	4	no	—
307	C₂²⋊C₄	—	4	2	no	—
308	C₄²	—	4	1	no	—
309	C₄²	—	4	2	no	—
310	C₄²	D₈×C₆₇	1	1	yes	characteristic
311	C₄²	D₈×C₆₇	1	1	yes	characteristic
312	C₄²	C₂×D₄×C₆₇	1	2	yes	—
313	C₁₆	—	2	2	no	—
314	C₁₆	—	2	2	no	—
315	C₂³	—	4	1	no	—
316	C₂³	—	4	2	no	—
317	C₂³	—	8	4	no	—
318	C₂³	—	8	2	no	—
319	C₂³	C₂×D₈×C₆₇	1	1	yes	characteristic
320	Q₈	—	2	2	no	—
321	Q₈	—	4	1	no	—
322	Q₈	—	4	2	no	—
323	Q₈	—	4	2	no	—
324	Q₈	—	8	2	no	—
325	D₄	—	2	2	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	2	no	—
328	D₄	—	4	1	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	2	no	—
331	C₂×C₄	—	4	2	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	8	4	no	—
337	C₂×C₄	—	8	2	no	—
338	C₂×C₄	#121×C₆₇	1	2	yes	—
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	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
343	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
344	C₈	—	2	2	no	—
345	C₈	#121×C₆₇	1	2	yes	—
346	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
347	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
348	C₂²	—	2	2	no	—
349	C₂²	—	4	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	—	8	2	no	—
352	C₂²	—	8	4	no	—
353	C₂²	—	16	4	no	—
354	C₂²	#459×C₆₇	1	2	yes	—
355	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	4	2	no	—
359	C₄	—	8	2	no	—
360	C₄	—	8	2	no	—
361	C₄	#459×C₆₇	1	2	yes	—
362	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
363	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	8	2	no	—
366	C₂	—	16	2	no	—
367	C₂	C₂×#459×C₆₇	1	1	yes	characteristic
368	C₂	C₆₇×#3414	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
prime radical	C₂×#509×C₆₇	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₂×C₄²×C₆₇ ◁ C₂×C₄×C₈×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#510×C₆₇	C₂	semidirect
3. C₂×#495×C₆₇	C₂	semidirect
4. C₄×#135×C₆₇	C₂	semidirect
5. C₆₇×#2211	C₂	semidirect
6. C₆₇×#2210	C₂	semidirect
7. C₆₇×#2150	C₂	semidirect
8. C₆₇×#2141	C₂	semidirect
9. C₆₇×#2140	C₂	semidirect
18. C₂×Q₃₂×C₆₇	C₂²	semidirect
20. C₂×SD₃₂×C₆₇	C₂²	semidirect
26. C₄×Q₁₆×C₆₇	C₂²	semidirect
28. C₄×D₈×C₆₇	C₂²	semidirect
32. C₄⋊C₁₆×C₆₇	C₂²	semidirect
33. #358×C₆₇	C₂²	semidirect
179. #33584	C₆₇	direct (N × H)
185. C₂×#510	C₂×C₆₇	semidirect
187. C₂×#495	C₂×C₆₇	semidirect
188. C₄×#135	C₂×C₆₇	semidirect
189. #2211	C₂×C₆₇	semidirect
190. #2210	C₂×C₆₇	semidirect
191. #2150	C₂×C₆₇	semidirect
192. #2141	C₂×C₆₇	semidirect
193. #2140	C₂×C₆₇	semidirect
194. C₆₇	#33584	direct (N × H)
203. C₂×Q₃₂	C₂²×C₆₇	semidirect
205. C₂×SD₃₂	C₂²×C₆₇	semidirect
211. C₄×Q₁₆	C₂²×C₆₇	semidirect
213. C₄×D₈	C₂²×C₆₇	semidirect
217. C₄⋊C₁₆	C₂²×C₆₇	semidirect
218. #358	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#510×C₆₇	2
C₂×#509×C₆₇	2
C₂×#495×C₆₇	2
C₄×#135×C₆₇	2
C₆₇×#2211	2
C₆₇×#2210	2
C₆₇×#2150	2
C₆₇×#2141	2
C₆₇×#2140	2
#33584	67

Subgroups — C67×#33584 #30712835

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33584 #30712835