Subgroups — C₆₇×#33179 #30712430

Order 17152.

1226 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#493×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#469×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₂×#466×C₆₇	C₂	1	2	yes	maximal, complemented
4	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2619	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1972	C₂	1	2	yes	maximal, complemented
7	C₆₇×#1970	C₂	1	2	yes	maximal, complemented
8	C₆₇×#1961	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
11	C₂²×D₈×C₆₇	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×#127×C₆₇	C₂²	1	2	yes	—
15	C₂×#121×C₆₇	C₂²	1	4	yes	—
16	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
17	#493×C₆₇	—	2	4	no	—
18	#469×C₆₇	—	2	8	no	—
19	#466×C₆₇	—	2	8	no	—
20	C₂×#107×C₆₇	C₂²	1	2	yes	—
21	C₂×#106×C₆₇	C₂²	1	2	yes	—
22	C₂×#102×C₆₇	C₂²	1	4	yes	—
23	C₂×#102×C₆₇	C₂²	1	4	yes	—
24	#405×C₆₇	—	2	4	no	—
25	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
29	#394×C₆₇	—	2	4	no	—
30	#392×C₆₇	—	2	4	no	—
31	#390×C₆₇	C₂²	1	4	yes	—
32	#382×C₆₇	C₂²	1	2	yes	—
33	C₂²×D₄×C₆₇	—	2	4	no	—
34	C₂²×D₄×C₆₇	—	2	4	no	—
35	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
36	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
37	C₂×D₈×C₆₇	—	2	4	no	—
38	C₂×D₈×C₆₇	—	2	4	no	—
39	C₂×D₈×C₆₇	—	2	4	no	—
40	C₂×D₈×C₆₇	—	2	4	no	—
41	C₂×D₈×C₆₇	—	2	4	no	—
42	C₂×D₈×C₆₇	—	2	4	no	—
43	C₂×M₁₆×C₆₇	—	2	2	no	—
44	C₂×M₁₆×C₆₇	—	2	2	no	—
45	C₂×M₁₆×C₆₇	D₄	1	4	yes	complemented
46	C₂²×C₈×C₆₇	—	2	2	no	—
47	C₂²×C₈×C₆₇	—	2	2	no	—
48	C₂²×C₈×C₆₇	D₄	1	4	yes	complemented
49	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
53	#127×C₆₇	—	2	4	no	—
54	#127×C₆₇	—	2	4	no	—
55	#121×C₆₇	—	2	8	no	—
56	#121×C₆₇	—	2	8	no	—
57	#117×C₆₇	—	2	2	no	—
58	#117×C₆₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₆₇	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
61	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
62	C₂×C₂²⋊C₄×C₆₇	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₆₇	D₄	1	2	yes	—
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
66	#107×C₆₇	—	2	4	no	—
67	#106×C₆₇	—	2	4	no	—
68	#102×C₆₇	—	2	8	no	—
69	#102×C₆₇	—	2	8	no	—
70	#97×C₆₇	—	2	2	no	—
71	#97×C₆₇	—	2	2	no	—
72	C₄×C₈×C₆₇	—	2	2	no	—
73	C₄×C₈×C₆₇	D₄	1	4	yes	complemented
74	#95×C₆₇	—	2	4	no	—
75	C₂⁴×C₆₇	—	2	4	no	—
76	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂×D₄×C₆₇	—	2	4	no	—
78	C₂×D₄×C₆₇	—	2	4	no	—
79	C₂×D₄×C₆₇	—	2	4	no	—
80	C₂×D₄×C₆₇	—	2	4	no	—
81	C₂×D₄×C₆₇	—	2	4	no	—
82	C₂×D₄×C₆₇	—	2	4	no	—
83	C₂×D₄×C₆₇	—	4	8	no	—
84	C₂×D₄×C₆₇	—	4	8	no	—
85	C₂×D₄×C₆₇	—	8	8	no	—
86	C₂×D₄×C₆₇	—	8	8	no	—
87	C₂²×C₄×C₆₇	—	2	1	no	—
88	C₂²×C₄×C₆₇	—	2	1	no	—
89	C₂²×C₄×C₆₇	—	2	1	no	—
90	C₂²×C₄×C₆₇	—	2	1	no	—
91	C₂²×C₄×C₆₇	—	2	4	no	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
98	D₈×C₆₇	—	4	8	no	—
99	D₈×C₆₇	—	4	8	no	—
100	M₁₆×C₆₇	—	2	8	no	—
101	C₂×C₈×C₆₇	—	2	1	no	—
102	C₂×C₈×C₆₇	—	2	1	no	—
103	C₂×C₈×C₆₇	—	2	1	no	—
104	C₂×C₈×C₆₇	—	2	1	no	—
105	C₂×C₈×C₆₇	—	2	8	no	—
106	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
107	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
110	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₆₇	#41	1	2	yes	—
113	C₂×C₈×C₆₇	#41	1	2	yes	—
114	C₄⋊C₄×C₆₇	—	2	4	no	—
115	C₄⋊C₄×C₆₇	—	2	4	no	—
116	C₄⋊C₄×C₆₇	—	2	4	no	—
117	C₂²⋊C₄×C₆₇	—	2	4	no	—
118	C₂²⋊C₄×C₆₇	—	4	8	no	—
119	C₂²⋊C₄×C₆₇	—	8	8	no	—
120	C₄²×C₆₇	—	2	1	no	—
121	C₄²×C₆₇	—	2	1	no	—
122	C₄²×C₆₇	C₂×D₄	1	2	yes	—
123	C₄²×C₆₇	#41	1	2	yes	—
124	C₂³×C₆₇	—	2	1	no	—
125	C₂³×C₆₇	—	2	1	no	—
126	C₂³×C₆₇	—	2	4	no	—
127	C₂³×C₆₇	—	4	4	no	—
128	C₂³×C₆₇	—	4	4	no	—
129	C₂³×C₆₇	—	4	4	no	—
130	C₂³×C₆₇	—	4	8	no	—
131	C₂³×C₆₇	—	4	8	no	—
132	C₂³×C₆₇	#127	1	2	yes	—
133	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
134	D₄×C₆₇	—	4	4	no	—
135	D₄×C₆₇	—	4	4	no	—
136	D₄×C₆₇	—	4	4	no	—
137	D₄×C₆₇	—	4	4	no	—
138	D₄×C₆₇	—	8	16	no	—
139	D₄×C₆₇	—	8	16	no	—
140	C₂×C₄×C₆₇	—	2	1	no	—
141	C₂×C₄×C₆₇	—	2	1	no	—
142	C₂×C₄×C₆₇	—	2	4	no	—
143	C₂×C₄×C₆₇	—	2	2	no	—
144	C₂×C₄×C₆₇	—	2	2	no	—
145	C₂×C₄×C₆₇	—	2	2	no	—
146	C₂×C₄×C₆₇	—	2	2	no	—
147	C₂×C₄×C₆₇	—	2	2	no	—
148	C₂×C₄×C₆₇	—	2	4	no	—
149	C₂×C₄×C₆₇	—	4	4	no	—
150	C₂×C₄×C₆₇	—	4	8	no	—
151	C₂×C₄×C₆₇	#121	1	4	yes	—
152	C₂×C₄×C₆₇	#127	1	2	yes	—
153	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
159	C₈×C₆₇	—	2	2	no	—
160	C₈×C₆₇	—	2	2	no	—
161	C₈×C₆₇	#121	1	4	yes	—
162	C₈×C₆₇	#121	1	4	yes	—
163	C₂²×C₆₇	—	2	2	no	—
164	C₂²×C₆₇	—	2	4	no	—
165	C₂²×C₆₇	—	4	2	no	—
166	C₂²×C₆₇	—	4	2	no	—
167	C₂²×C₆₇	—	8	4	no	—
168	C₂²×C₆₇	—	8	4	no	—
169	C₂²×C₆₇	—	8	4	no	—
170	C₂²×C₆₇	—	8	8	no	—
171	C₂²×C₆₇	—	8	8	no	—
172	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
173	C₂²×C₆₇	C₂×#127	1	1	yes	characteristic
174	C₂²×C₆₇	#532	1	1	yes	characteristic
175	C₂²×C₆₇	#576	1	4	yes	—
176	C₄×C₆₇	—	2	2	no	—
177	C₄×C₆₇	—	2	4	no	—
178	C₄×C₆₇	—	4	2	no	—
179	C₄×C₆₇	—	8	4	no	—
180	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
181	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
182	C₄×C₆₇	#532	1	1	yes	characteristic
183	C₄×C₆₇	#532	1	1	yes	characteristic
184	#33179	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂×C₆₇	—	4	2	no	—
186	C₂×C₆₇	—	16	4	no	—
187	C₂×C₆₇	#2856	1	1	yes	characteristic
188	C₂×C₆₇	#3058	1	2	yes	—
189	C₂×C₆₇	#3155	1	2	yes	—
190	C₂×C₆₇	#3176	1	2	yes	—
191	C₂×#493	C₂×C₆₇	1	1	yes	characteristic, complemented
192	C₂×#469	C₂×C₆₇	1	2	yes	complemented
193	C₂×#466	C₂×C₆₇	1	2	yes	complemented
194	C₂×#405	C₂×C₆₇	1	1	yes	characteristic, complemented
195	#2619	C₂×C₆₇	1	2	yes	complemented
196	#1972	C₂×C₆₇	1	2	yes	complemented
197	#1970	C₂×C₆₇	1	2	yes	complemented
198	#1961	C₂×C₆₇	1	2	yes	complemented
199	#1846	C₂×C₆₇	1	1	yes	characteristic, complemented
200	C₆₇	#33179	1	1	yes	characteristic, direct product factor, Sylow
201	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
202	C₂²×D₈	C₂²×C₆₇	1	2	yes	—
203	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
204	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
205	C₂×#127	C₂²×C₆₇	1	2	yes	—
206	C₂×#121	C₂²×C₆₇	1	4	yes	—
207	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
208	#493	—	2	4	no	—
209	#469	—	2	8	no	—
210	#466	—	2	8	no	—
211	C₂×#107	C₂²×C₆₇	1	2	yes	—
212	C₂×#106	C₂²×C₆₇	1	2	yes	—
213	C₂×#102	C₂²×C₆₇	1	4	yes	—
214	C₂×#102	C₂²×C₆₇	1	4	yes	—
215	#405	—	2	4	no	—
216	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
217	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic
218	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
219	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic
220	#394	—	2	4	no	—
221	#392	—	2	4	no	—
222	#390	C₂²×C₆₇	1	4	yes	—
223	#382	C₂²×C₆₇	1	2	yes	—
224	C₂²×D₄	—	2	4	no	—
225	C₂²×D₄	—	2	4	no	—
226	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
227	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
228	C₂×D₈	—	2	4	no	—
229	C₂×D₈	—	2	4	no	—
230	C₂×D₈	—	2	4	no	—
231	C₂×D₈	—	2	4	no	—
232	C₂×D₈	—	2	4	no	—
233	C₂×D₈	—	2	4	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	D₄×C₆₇	1	4	yes	complemented
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	D₄×C₆₇	1	4	yes	complemented
240	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
241	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
242	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
244	#127	—	2	4	no	—
245	#127	—	2	4	no	—
246	#121	—	2	8	no	—
247	#121	—	2	8	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	C₂×C₄⋊C₄	D₄×C₆₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
252	C₂×C₂²⋊C₄	—	2	4	no	—
253	C₂×C₂²⋊C₄	—	2	8	no	—
254	C₂×C₂²⋊C₄	D₄×C₆₇	1	2	yes	—
255	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
257	#107	—	2	4	no	—
258	#106	—	2	4	no	—
259	#102	—	2	8	no	—
260	#102	—	2	8	no	—
261	#97	—	2	2	no	—
262	#97	—	2	2	no	—
263	C₄×C₈	—	2	2	no	—
264	C₄×C₈	D₄×C₆₇	1	4	yes	complemented
265	#95	—	2	4	no	—
266	C₂⁴	—	2	4	no	—
267	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	2	4	no	—
270	C₂×D₄	—	2	4	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	4	no	—
273	C₂×D₄	—	2	4	no	—
274	C₂×D₄	—	4	8	no	—
275	C₂×D₄	—	4	8	no	—
276	C₂×D₄	—	8	8	no	—
277	C₂×D₄	—	8	8	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
284	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
285	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
287	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
288	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
289	D₈	—	4	8	no	—
290	D₈	—	4	8	no	—
291	M₁₆	—	2	8	no	—
292	C₂×C₈	—	2	1	no	—
293	C₂×C₈	—	2	1	no	—
294	C₂×C₈	—	2	1	no	—
295	C₂×C₈	—	2	1	no	—
296	C₂×C₈	—	2	8	no	—
297	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
298	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
299	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
300	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
301	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
302	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
303	C₂×C₈	#41×C₆₇	1	2	yes	—
304	C₂×C₈	#41×C₆₇	1	2	yes	—
305	C₄⋊C₄	—	2	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	4	no	—
309	C₂²⋊C₄	—	4	8	no	—
310	C₂²⋊C₄	—	8	8	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	C₂×D₄×C₆₇	1	2	yes	—
314	C₄²	#41×C₆₇	1	2	yes	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	4	8	no	—
322	C₂³	—	4	8	no	—
323	C₂³	#127×C₆₇	1	2	yes	—
324	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
325	D₄	—	4	4	no	—
326	D₄	—	4	4	no	—
327	D₄	—	4	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	8	16	no	—
330	D₄	—	8	16	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	4	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	8	no	—
342	C₂×C₄	#121×C₆₇	1	4	yes	—
343	C₂×C₄	#127×C₆₇	1	2	yes	—
344	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
345	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
346	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
347	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
348	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
349	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	2	2	no	—
352	C₈	#121×C₆₇	1	4	yes	—
353	C₈	#121×C₆₇	1	4	yes	—
354	C₂²	—	2	2	no	—
355	C₂²	—	2	4	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	8	8	no	—
359	C₂²	—	8	4	no	—
360	C₂²	—	8	4	no	—
361	C₂²	—	8	4	no	—
362	C₂²	—	8	8	no	—
363	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
364	C₂²	C₂×#127×C₆₇	1	1	yes	characteristic
365	C₂²	#532×C₆₇	1	1	yes	characteristic
366	C₂²	#576×C₆₇	1	4	yes	—
367	C₄	—	2	4	no	—
368	C₄	—	2	2	no	—
369	C₄	—	4	2	no	—
370	C₄	—	8	4	no	—
371	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
372	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
373	C₄	#532×C₆₇	1	1	yes	characteristic
374	C₄	#532×C₆₇	1	1	yes	characteristic
375	C₂	—	4	2	no	—
376	C₂	—	16	4	no	—
377	C₂	C₆₇×#2856	1	1	yes	characteristic
378	C₂	C₆₇×#3058	1	2	yes	—
379	C₂	C₆₇×#3155	1	2	yes	—
380	C₂	C₆₇×#3176	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂×#117×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#493×C₆₇	C₂	semidirect
2. C₂×#469×C₆₇	C₂	semidirect
3. C₂×#466×C₆₇	C₂	semidirect
4. C₂×#405×C₆₇	C₂	semidirect
5. C₆₇×#2619	C₂	semidirect
6. C₆₇×#1972	C₂	semidirect
7. C₆₇×#1970	C₂	semidirect
8. C₆₇×#1961	C₂	semidirect
9. C₆₇×#1846	C₂	semidirect
45. C₂×M₁₆×C₆₇	D₄	semidirect
48. C₂²×C₈×C₆₇	D₄	semidirect
73. C₄×C₈×C₆₇	D₄	semidirect
184. #33179	C₆₇	direct (N × H)
191. C₂×#493	C₂×C₆₇	semidirect
192. C₂×#469	C₂×C₆₇	semidirect
193. C₂×#466	C₂×C₆₇	semidirect
194. C₂×#405	C₂×C₆₇	semidirect
195. #2619	C₂×C₆₇	semidirect
196. #1972	C₂×C₆₇	semidirect
197. #1970	C₂×C₆₇	semidirect
198. #1961	C₂×C₆₇	semidirect
199. #1846	C₂×C₆₇	semidirect
200. C₆₇	#33179	direct (N × H)
236. C₂×M₁₆	D₄×C₆₇	semidirect
239. C₂²×C₈	D₄×C₆₇	semidirect
264. C₄×C₈	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×#493×C₆₇	2
C₂×#469×C₆₇	2
C₂×#466×C₆₇	2
C₂×#405×C₆₇	2
C₆₇×#2619	2
C₆₇×#1972	2
C₆₇×#1970	2
C₆₇×#1961	2
C₆₇×#1846	2
#33179	67

Subgroups — C67×#33179 #30712430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#33179 #30712430