Subgroups — C₆₇×#33585 #30712836

Order 17152.

748 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#509×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2210	C₂	1	4	yes	maximal, complemented
6	C₆₇×#2206	C₂	1	4	yes	maximal, complemented
7	C₆₇×#2151	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2140	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2138	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
11	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
12	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
13	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
14	#535×C₆₇	—	2	1	no	—
15	#518×C₆₇	—	2	1	no	—
16	#509×C₆₇	—	2	4	no	—
17	C₂×SD₃₂×C₆₇	C₂²	1	2	yes	complemented
18	C₂×D₁₆×C₆₇	—	2	4	no	—
19	C₂×D₁₆×C₆₇	C₂²	1	4	yes	—
20	C₂×D₁₆×C₆₇	C₂²	1	2	yes	complemented
21	C₂×M₃₂×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×C₁₆×C₆₇	C₂²	1	1	yes	characteristic
23	#496×C₆₇	—	2	2	no	—
24	#495×C₆₇	C₂²	1	2	yes	complemented
25	#493×C₆₇	C₂²	1	2	yes	complemented
26	#442×C₆₇	—	2	2	no	—
27	C₄×D₈×C₆₇	C₂²	1	4	yes	complemented
28	#427×C₆₇	C₂²	1	1	yes	characteristic
29	#418×C₆₇	—	2	1	no	—
30	#405×C₆₇	C₂²	1	1	yes	characteristic
31	C₄⋊C₁₆×C₆₇	C₂²	1	4	yes	complemented
32	#358×C₆₇	C₂²	1	2	yes	complemented
33	#357×C₆₇	C₂²	1	2	yes	complemented
34	#357×C₆₇	C₂²	1	4	yes	complemented
35	C₂×#41×C₆₇	—	2	1	no	—
36	C₂²×D₄×C₆₇	—	2	1	no	—
37	C₂²×D₄×C₆₇	—	2	1	no	—
38	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
39	#135×C₆₇	—	2	2	no	—
40	#135×C₆₇	—	2	2	no	—
41	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
42	C₂×SD₁₆×C₆₇	—	2	2	no	—
43	C₂×SD₁₆×C₆₇	—	2	1	no	—
44	C₂×D₈×C₆₇	—	2	1	no	—
45	C₂×D₈×C₆₇	—	2	2	no	—
46	C₂×D₈×C₆₇	—	2	2	no	—
47	C₂×D₈×C₆₇	—	2	1	no	—
48	C₂×D₈×C₆₇	—	2	2	no	—
49	C₂×D₈×C₆₇	—	2	2	no	—
50	C₂×D₈×C₆₇	D₄	1	4	yes	complemented
51	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
52	C₂×D₈×C₆₇	C₂³	1	2	yes	—
53	C₂×D₈×C₆₇	C₂³	1	2	yes	—
54	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
55	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
56	#127×C₆₇	—	2	2	no	—
57	#124×C₆₇	—	2	2	no	—
58	#121×C₆₇	—	4	2	no	—
59	#120×C₆₇	—	4	2	no	—
60	C₄×D₄×C₆₇	—	2	4	no	—
61	C₄×D₄×C₆₇	—	4	2	no	—
62	#117×C₆₇	—	2	1	no	—
63	#117×C₆₇	D₄	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
65	SD₃₂×C₆₇	—	2	4	no	—
66	D₁₆×C₆₇	—	2	8	no	—
67	D₁₆×C₆₇	—	2	4	no	—
68	M₃₂×C₆₇	—	2	2	no	—
69	C₂×C₁₆×C₆₇	—	2	2	no	—
70	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
71	C₂×C₁₆×C₆₇	C₂³	1	2	yes	—
72	#107×C₆₇	C₂³	1	2	yes	—
73	#106×C₆₇	—	2	1	no	—
74	#102×C₆₇	—	2	4	no	—
75	#97×C₆₇	D₄	1	2	yes	—
76	C₄×C₈×C₆₇	C₂³	1	2	yes	—
77	C₂⁴×C₆₇	—	4	1	no	—
78	C₂⁴×C₆₇	—	4	1	no	—
79	#41×C₆₇	—	4	2	no	—
80	#41×C₆₇	—	4	2	no	—
81	C₂×Q₈×C₆₇	—	2	1	no	—
82	C₂×D₄×C₆₇	—	2	4	no	—
83	C₂×D₄×C₆₇	—	2	2	no	—
84	C₂×D₄×C₆₇	—	2	2	no	—
85	C₂×D₄×C₆₇	—	2	1	no	—
86	C₂×D₄×C₆₇	—	4	1	no	—
87	C₂×D₄×C₆₇	—	4	2	no	—
88	C₂×D₄×C₆₇	—	4	1	no	—
89	C₂×D₄×C₆₇	—	4	1	no	—
90	C₂×D₄×C₆₇	—	4	4	no	—
91	C₂×D₄×C₆₇	—	4	2	no	—
92	C₂×D₄×C₆₇	—	4	2	no	—
93	C₂²×C₄×C₆₇	—	4	1	no	—
94	C₂²×C₄×C₆₇	—	4	4	no	—
95	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
96	Q₁₆×C₆₇	—	2	1	no	—
97	Q₁₆×C₆₇	—	2	1	no	—
98	SD₁₆×C₆₇	—	4	4	no	—
99	SD₁₆×C₆₇	—	4	2	no	—
100	D₈×C₆₇	—	2	4	no	—
101	D₈×C₆₇	—	2	2	no	—
102	D₈×C₆₇	—	2	1	no	—
103	D₈×C₆₇	—	2	2	no	—
104	D₈×C₆₇	—	2	2	no	—
105	D₈×C₆₇	—	2	1	no	—
106	D₈×C₆₇	—	4	4	no	—
107	D₈×C₆₇	—	4	2	no	—
108	D₈×C₆₇	C₂×D₄	1	4	yes	—
109	M₁₆×C₆₇	—	2	2	no	—
110	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₆₇	#41	1	2	yes	—
114	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
115	C₄⋊C₄×C₆₇	—	2	2	no	—
116	C₄⋊C₄×C₆₇	D₈	1	2	yes	—
117	C₂²⋊C₄×C₆₇	—	4	1	no	—
118	C₂²⋊C₄×C₆₇	—	4	4	no	—
119	C₂²⋊C₄×C₆₇	—	4	4	no	—
120	C₂²⋊C₄×C₆₇	D₈	1	2	yes	—
121	C₄²×C₆₇	—	4	1	no	—
122	C₄²×C₆₇	C₂×D₄	1	2	yes	—
123	C₁₆×C₆₇	—	2	2	no	—
124	C₁₆×C₆₇	—	2	2	no	—
125	C₂³×C₆₇	—	4	2	no	—
126	C₂³×C₆₇	—	4	4	no	—
127	C₂³×C₆₇	—	4	2	no	—
128	C₂³×C₆₇	—	4	1	no	—
129	C₂³×C₆₇	—	8	2	no	—
130	C₂³×C₆₇	—	16	2	no	—
131	C₂³×C₆₇	—	16	2	no	—
132	C₂³×C₆₇	C₂×D₈	1	1	yes	characteristic
133	Q₈×C₆₇	—	4	1	no	—
134	Q₈×C₆₇	—	4	1	no	—
135	D₄×C₆₇	—	2	4	no	—
136	D₄×C₆₇	—	4	2	no	—
137	D₄×C₆₇	—	4	1	no	—
138	D₄×C₆₇	—	4	2	no	—
139	D₄×C₆₇	—	4	1	no	—
140	D₄×C₆₇	—	4	2	no	—
141	D₄×C₆₇	—	4	4	no	—
142	D₄×C₆₇	—	8	2	no	—
143	D₄×C₆₇	—	8	2	no	—
144	D₄×C₆₇	—	16	4	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	—	4	1	no	—
147	C₂×C₄×C₆₇	—	8	2	no	—
148	C₂×C₄×C₆₇	—	16	4	no	—
149	C₂×C₄×C₆₇	#121	1	2	yes	—
150	C₂×C₄×C₆₇	C₂×D₈	1	4	yes	—
151	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
152	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
153	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
154	C₈×C₆₇	—	2	2	no	—
155	C₈×C₆₇	#121	1	2	yes	—
156	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
158	C₂²×C₆₇	—	2	2	no	—
159	C₂²×C₆₇	—	4	4	no	—
160	C₂²×C₆₇	—	8	4	no	—
161	C₂²×C₆₇	—	8	2	no	—
162	C₂²×C₆₇	—	8	4	no	—
163	C₂²×C₆₇	—	8	1	no	—
164	C₂²×C₆₇	—	8	2	no	—
165	C₂²×C₆₇	—	16	4	no	—
166	C₂²×C₆₇	—	16	4	no	—
167	C₂²×C₆₇	#459	1	2	yes	—
168	C₂²×C₆₇	C₂²×D₈	1	1	yes	characteristic
169	C₄×C₆₇	—	2	4	no	—
170	C₄×C₆₇	—	8	2	no	—
171	C₄×C₆₇	—	8	1	no	—
172	C₄×C₆₇	#459	1	2	yes	—
173	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
174	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
175	#33585	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂×C₆₇	—	2	2	no	—
177	C₂×C₆₇	—	8	4	no	—
178	C₂×C₆₇	—	16	1	no	—
179	C₂×C₆₇	—	16	2	no	—
180	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
181	C₂×C₆₇	#3415	1	2	yes	—
182	C₂×#509	C₂×C₆₇	1	1	yes	characteristic, complemented
183	C₂²×D₁₆	C₂×C₆₇	1	1	yes	characteristic, complemented
184	#3155	C₂×C₆₇	1	1	yes	characteristic, complemented
185	#2948	C₂×C₆₇	1	1	yes	characteristic, complemented
186	#2210	C₂×C₆₇	1	4	yes	complemented
187	#2206	C₂×C₆₇	1	4	yes	complemented
188	#2151	C₂×C₆₇	1	1	yes	characteristic, complemented
189	#2140	C₂×C₆₇	1	1	yes	characteristic, complemented
190	#2138	C₂×C₆₇	1	1	yes	characteristic, complemented
191	C₆₇	#33585	1	1	yes	characteristic, direct product factor, Sylow
192	C₂×AGL(1,ℤ/8)	—	2	1	no	—
193	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
194	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
195	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
196	#535	—	2	1	no	—
197	#518	—	2	1	no	—
198	#509	—	2	4	no	—
199	C₂×SD₃₂	C₂²×C₆₇	1	2	yes	complemented
200	C₂×D₁₆	—	2	4	no	—
201	C₂×D₁₆	C₂²×C₆₇	1	4	yes	—
202	C₂×D₁₆	C₂²×C₆₇	1	2	yes	complemented
203	C₂×M₃₂	C₂²×C₆₇	1	1	yes	characteristic
204	C₂²×C₁₆	C₂²×C₆₇	1	1	yes	characteristic
205	#496	—	2	2	no	—
206	#495	C₂²×C₆₇	1	2	yes	complemented
207	#493	C₂²×C₆₇	1	2	yes	complemented
208	#442	—	2	2	no	—
209	C₄×D₈	C₂²×C₆₇	1	4	yes	complemented
210	#427	C₂²×C₆₇	1	1	yes	characteristic
211	#418	—	2	1	no	—
212	#405	C₂²×C₆₇	1	1	yes	characteristic
213	C₄⋊C₁₆	C₂²×C₆₇	1	4	yes	complemented
214	#358	C₂²×C₆₇	1	2	yes	complemented
215	#357	C₂²×C₆₇	1	2	yes	complemented
216	#357	C₂²×C₆₇	1	4	yes	complemented
217	C₂×#41	—	2	1	no	—
218	C₂²×D₄	—	2	1	no	—
219	C₂²×D₄	—	2	1	no	—
220	AGL(1,ℤ/8)	—	4	4	no	—
221	#135	—	2	2	no	—
222	#135	—	2	2	no	—
223	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
224	C₂×SD₁₆	—	2	1	no	—
225	C₂×SD₁₆	—	2	2	no	—
226	C₂×D₈	—	2	1	no	—
227	C₂×D₈	—	2	2	no	—
228	C₂×D₈	—	2	1	no	—
229	C₂×D₈	—	2	2	no	—
230	C₂×D₈	—	2	2	no	—
231	C₂×D₈	—	2	2	no	—
232	C₂×D₈	D₄×C₆₇	1	4	yes	complemented
233	C₂×D₈	C₂³×C₆₇	1	2	yes	—
234	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
235	C₂×D₈	C₂³×C₆₇	1	2	yes	—
236	C₂×M₁₆	D₄×C₆₇	1	1	yes	characteristic
237	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
238	#127	—	2	2	no	—
239	#124	—	2	2	no	—
240	#121	—	4	2	no	—
241	#120	—	4	2	no	—
242	C₄×D₄	—	2	4	no	—
243	C₄×D₄	—	4	2	no	—
244	#117	—	2	1	no	—
245	#117	D₄×C₆₇	1	1	yes	characteristic
246	C₂×C₂²⋊C₄	—	4	2	no	—
247	SD₃₂	—	2	4	no	—
248	D₁₆	—	2	8	no	—
249	D₁₆	—	2	4	no	—
250	M₃₂	—	2	2	no	—
251	C₂×C₁₆	—	2	2	no	—
252	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
253	C₂×C₁₆	C₂³×C₆₇	1	2	yes	—
254	#107	C₂³×C₆₇	1	2	yes	—
255	#106	—	2	1	no	—
256	#102	—	2	4	no	—
257	#97	D₄×C₆₇	1	2	yes	—
258	C₄×C₈	C₂³×C₆₇	1	2	yes	—
259	C₂⁴	—	4	1	no	—
260	C₂⁴	—	4	1	no	—
261	#41	—	4	2	no	—
262	#41	—	4	2	no	—
263	C₂×Q₈	—	2	1	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	—	2	1	no	—
268	C₂×D₄	—	4	1	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	4	1	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂²×C₄	—	4	1	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
278	Q₁₆	—	2	1	no	—
279	Q₁₆	—	2	1	no	—
280	SD₁₆	—	4	4	no	—
281	SD₁₆	—	4	2	no	—
282	D₈	—	2	4	no	—
283	D₈	—	2	2	no	—
284	D₈	—	2	1	no	—
285	D₈	—	2	2	no	—
286	D₈	—	2	2	no	—
287	D₈	—	2	1	no	—
288	D₈	—	4	4	no	—
289	D₈	—	4	2	no	—
290	D₈	C₂×D₄×C₆₇	1	4	yes	—
291	M₁₆	—	2	2	no	—
292	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
293	C₂×C₈	C₂×D₄×C₆₇	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
295	C₂×C₈	#41×C₆₇	1	2	yes	—
296	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	D₈×C₆₇	1	2	yes	—
299	C₂²⋊C₄	—	4	1	no	—
300	C₂²⋊C₄	—	4	4	no	—
301	C₂²⋊C₄	—	4	4	no	—
302	C₂²⋊C₄	D₈×C₆₇	1	2	yes	—
303	C₄²	—	4	1	no	—
304	C₄²	C₂×D₄×C₆₇	1	2	yes	—
305	C₁₆	—	2	2	no	—
306	C₁₆	—	2	2	no	—
307	C₂³	—	4	2	no	—
308	C₂³	—	4	4	no	—
309	C₂³	—	4	2	no	—
310	C₂³	—	4	1	no	—
311	C₂³	—	8	2	no	—
312	C₂³	—	16	2	no	—
313	C₂³	—	16	2	no	—
314	C₂³	C₂×D₈×C₆₇	1	1	yes	characteristic
315	Q₈	—	4	1	no	—
316	Q₈	—	4	1	no	—
317	D₄	—	2	4	no	—
318	D₄	—	4	4	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	1	no	—
321	D₄	—	4	2	no	—
322	D₄	—	4	1	no	—
323	D₄	—	4	2	no	—
324	D₄	—	8	2	no	—
325	D₄	—	8	2	no	—
326	D₄	—	16	4	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	8	2	no	—
330	C₂×C₄	—	16	4	no	—
331	C₂×C₄	#121×C₆₇	1	2	yes	—
332	C₂×C₄	C₂×D₈×C₆₇	1	4	yes	—
333	C₂×C₄	C₂×D₈×C₆₇	1	1	yes	characteristic
334	C₂×C₄	AGL(1,ℤ/8)×C₆₇	1	2	yes	—
335	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
336	C₈	—	2	2	no	—
337	C₈	#121×C₆₇	1	2	yes	—
338	C₈	C₂²×D₄×C₆₇	1	1	yes	characteristic
339	C₈	C₂×#41×C₆₇	1	1	yes	characteristic
340	C₂²	—	2	2	no	—
341	C₂²	—	4	4	no	—
342	C₂²	—	8	4	no	—
343	C₂²	—	8	1	no	—
344	C₂²	—	8	2	no	—
345	C₂²	—	8	2	no	—
346	C₂²	—	8	4	no	—
347	C₂²	—	16	4	no	—
348	C₂²	—	16	4	no	—
349	C₂²	#459×C₆₇	1	2	yes	—
350	C₂²	C₂²×D₈×C₆₇	1	1	yes	characteristic
351	C₄	—	2	4	no	—
352	C₄	—	8	1	no	—
353	C₄	—	8	2	no	—
354	C₄	#459×C₆₇	1	2	yes	—
355	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
356	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	1	yes	characteristic
357	C₂	—	2	2	no	—
358	C₂	—	8	4	no	—
359	C₂	—	16	2	no	—
360	C₂	—	16	1	no	—
361	C₂	C₂×#459×C₆₇	1	1	yes	characteristic
362	C₂	C₆₇×#3415	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₆₇
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #117×C₆₇ ◁ #405×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#509×C₆₇	C₂	semidirect
2. C₂²×D₁₆×C₆₇	C₂	semidirect
3. C₆₇×#3155	C₂	semidirect
4. C₆₇×#2948	C₂	semidirect
5. C₆₇×#2210	C₂	semidirect
6. C₆₇×#2206	C₂	semidirect
7. C₆₇×#2151	C₂	semidirect
8. C₆₇×#2140	C₂	semidirect
9. C₆₇×#2138	C₂	semidirect
17. C₂×SD₃₂×C₆₇	C₂²	semidirect
20. C₂×D₁₆×C₆₇	C₂²	semidirect
24. #495×C₆₇	C₂²	semidirect
25. #493×C₆₇	C₂²	semidirect
27. C₄×D₈×C₆₇	C₂²	semidirect
31. C₄⋊C₁₆×C₆₇	C₂²	semidirect
32. #358×C₆₇	C₂²	semidirect
33. #357×C₆₇	C₂²	semidirect
34. #357×C₆₇	C₂²	semidirect
50. C₂×D₈×C₆₇	D₄	semidirect
175. #33585	C₆₇	direct (N × H)
182. C₂×#509	C₂×C₆₇	semidirect
183. C₂²×D₁₆	C₂×C₆₇	semidirect
184. #3155	C₂×C₆₇	semidirect
185. #2948	C₂×C₆₇	semidirect
186. #2210	C₂×C₆₇	semidirect
187. #2206	C₂×C₆₇	semidirect
188. #2151	C₂×C₆₇	semidirect
189. #2140	C₂×C₆₇	semidirect
190. #2138	C₂×C₆₇	semidirect
191. C₆₇	#33585	direct (N × H)
199. C₂×SD₃₂	C₂²×C₆₇	semidirect
202. C₂×D₁₆	C₂²×C₆₇	semidirect
206. #495	C₂²×C₆₇	semidirect
207. #493	C₂²×C₆₇	semidirect
209. C₄×D₈	C₂²×C₆₇	semidirect
213. C₄⋊C₁₆	C₂²×C₆₇	semidirect
214. #358	C₂²×C₆₇	semidirect
215. #357	C₂²×C₆₇	semidirect
216. #357	C₂²×C₆₇	semidirect
232. C₂×D₈	D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#509×C₆₇	2
C₂²×D₁₆×C₆₇	2
C₆₇×#3155	2
C₆₇×#2948	2
C₆₇×#2210	2
C₆₇×#2206	2
C₆₇×#2151	2
C₆₇×#2140	2
C₆₇×#2138	2
#33585	67

Subgroups — C67×#33585 #30712836

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33585 #30712836