Subgroups — #30754010

Order 17152.

460 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22561002	C₂	1	1	yes	maximal, characteristic
2	#22560074	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#14523965	C₂	1	1	yes	maximal, characteristic
4	C₂×#16863123	C₂	1	1	yes	maximal, characteristic
5	#22558048	C₂	1	1	yes	maximal, characteristic, complemented
6	C₆₇⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#334×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
9	C₂×#14523965	C₄	1	1	yes	characteristic
10	C₂×#14523965	C₄	1	1	yes	characteristic
11	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
12	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
13	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₈×Dic₆₇	—	2	1	no	—
16	C₄×C₄⋊Dic₆₇	C₂²	1	1	yes	characteristic
17	#16863159	C₄	1	1	yes	characteristic
18	#16863159	C₄	1	1	yes	characteristic
19	#16863150	—	2	1	no	—
20	#16863123	—	2	2	no	—
21	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
24	#334×C₆₇	—	2	2	no	—
25	C₂²×D₂₆₈	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₆₇	—	2	1	no	—
27	C₂²×C₆₇⋊C₈	—	2	1	no	—
28	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
29	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
30	C₄×D₂₆₈	—	2	1	no	—
31	C₄×D₂₆₈	—	2	1	no	—
32	C₄×D₂₆₈	—	2	1	no	—
33	C₄×D₂₆₈	—	2	1	no	—
34	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
37	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
38	C₂×C₄×Dic₆₇	—	2	1	no	—
39	#14523965	—	2	2	no	—
40	#14523965	C₈	1	4	yes	complemented
41	(C₂×D₆₇)⋊C₈	—	4	2	no	—
42	(C₂×D₆₇)⋊C₈	—	4	2	no	—
43	C₄×C₆₇⋊C₈	—	2	1	no	—
44	C₄×C₆₇⋊C₈	—	2	1	no	—
45	C₄×C₆₇⋊C₈	—	2	1	no	—
46	C₄×C₆₇⋊C₈	—	2	1	no	—
47	C₈×Dic₆₇	—	4	2	no	—
48	C₆₇⋊#95	—	2	1	no	—
49	C₂²×C₈×C₆₇	—	2	1	no	—
50	C₂²×C₈×C₆₇	—	2	1	no	—
51	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₆₇	—	2	1	no	—
55	C₄⋊C₈×C₆₇	—	2	1	no	—
56	C₄⋊C₈×C₆₇	—	2	1	no	—
57	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
58	C₄×C₈×C₆₇	—	2	1	no	—
59	C₄×C₈×C₆₇	—	2	1	no	—
60	C₂³×D₆₇	—	2	1	no	—
61	C₂×D₂₆₈	—	2	1	no	—
62	C₂×D₂₆₈	—	2	1	no	—
63	C₂×D₂₆₈	—	2	1	no	—
64	C₂×D₂₆₈	—	2	1	no	—
65	C₂×D₂₆₈	—	2	1	no	—
66	C₂×D₂₆₈	C₂×C₈	1	2	yes	—
67	C₂²×Dic₆₇	—	2	1	no	—
68	C₂²×Dic₆₇	—	2	1	no	—
69	C₂²×Dic₆₇	—	2	1	no	—
70	C₂×C₄×D₆₇	—	4	1	no	—
71	C₂×C₄×D₆₇	—	4	1	no	—
72	C₂×C₄×D₆₇	—	4	1	no	—
73	C₂×C₄×D₆₇	—	4	1	no	—
74	C₂×C₄×D₆₇	—	4	1	no	—
75	C₂×C₄×D₆₇	—	4	1	no	—
76	C₂×C₆₇⋊C₈	—	2	1	no	—
77	C₂×C₆₇⋊C₈	—	2	1	no	—
78	C₂×C₆₇⋊C₈	—	2	2	no	—
79	C₂×C₆₇⋊C₈	—	2	1	no	—
80	C₂×C₆₇⋊C₈	—	2	1	no	—
81	C₂×C₆₇⋊C₈	—	2	1	no	—
82	C₂×C₆₇⋊C₈	—	4	1	no	—
83	C₂×C₆₇⋊C₈	—	4	1	no	—
84	C₂×C₆₇⋊C₈	SD₁₆	1	2	yes	—
85	C₄⋊Dic₆₇	—	2	1	no	—
86	C₄⋊Dic₆₇	—	2	1	no	—
87	C₄⋊Dic₆₇	—	2	1	no	—
88	C₄⋊Dic₆₇	—	2	1	no	—
89	C₄⋊Dic₆₇	C₂×C₈	1	2	yes	—
90	C₄⋊Dic₆₇	M₁₆	1	2	yes	—
91	(C₂×D₆₇)⋊C₄	—	4	1	no	—
92	(C₂×D₆₇)⋊C₄	—	4	1	no	—
93	C₄×Dic₆₇	—	4	1	no	—
94	C₄×Dic₆₇	—	4	1	no	—
95	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
98	C₂×C₈×C₆₇	—	2	1	no	—
99	C₂×C₈×C₆₇	—	2	1	no	—
100	C₂×C₈×C₆₇	—	2	1	no	—
101	C₂×C₈×C₆₇	—	2	2	no	—
102	C₂×C₈×C₆₇	—	2	1	no	—
103	C₂×C₈×C₆₇	—	2	1	no	—
104	C₂×C₈×C₆₇	—	4	1	no	—
105	C₂×C₈×C₆₇	—	4	1	no	—
106	C₂×C₈×C₆₇	—	4	1	no	—
107	C₂×C₈×C₆₇	—	4	1	no	—
108	C₂×C₈×C₆₇	—	4	1	no	—
109	C₂×C₈×C₆₇	C₂×C₈	1	2	yes	—
110	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₆₇	#41	1	1	yes	characteristic
112	C₄²×C₆₇	#41	1	1	yes	characteristic
113	C₄²×C₆₇	#41	1	1	yes	characteristic
114	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
115	C₂²×D₆₇	—	2	2	no	—
116	C₂²×D₆₇	—	4	1	no	—
117	C₂²×D₆₇	—	4	1	no	—
118	C₂²×D₆₇	—	4	1	no	—
119	C₂²×D₆₇	—	4	1	no	—
120	C₂²×D₆₇	—	4	1	no	—
121	C₂²×D₆₇	—	4	1	no	—
122	C₂×C₄×C₆₇	—	2	1	no	—
123	C₂×C₄×C₆₇	—	2	1	no	—
124	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
125	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
126	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
127	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
128	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
129	C₂×C₄×C₆₇	#126	1	1	yes	characteristic
130	C₂×C₄×C₆₇	C₂²×C₈	1	1	yes	characteristic
131	C₂×C₄×C₆₇	C₂×M₁₆	1	1	yes	characteristic
132	C₂×C₄×C₆₇	#131	1	1	yes	characteristic
133	C₂×C₄×C₆₇	#131	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
135	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
136	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
137	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
138	C₂×Dic₆₇	—	2	2	no	—
139	C₂×Dic₆₇	—	2	2	no	—
140	C₂×Dic₆₇	—	4	1	no	—
141	C₂×Dic₆₇	—	4	1	no	—
142	C₂×Dic₆₇	—	4	1	no	—
143	C₂×Dic₆₇	—	4	1	no	—
144	C₂×Dic₆₇	—	4	1	no	—
145	C₂×Dic₆₇	—	4	1	no	—
146	C₂×Dic₆₇	—	4	1	no	—
147	D₂₆₈	—	2	2	no	—
148	D₂₆₈	—	2	2	no	—
149	D₂₆₈	—	4	1	no	—
150	D₂₆₈	—	4	1	no	—
151	C₄×D₆₇	—	8	1	no	—
152	C₄×D₆₇	—	8	1	no	—
153	C₄×D₆₇	—	8	1	no	—
154	C₄×D₆₇	—	8	1	no	—
155	C₈×C₆₇	—	2	2	no	—
156	C₈×C₆₇	—	4	1	no	—
157	C₈×C₆₇	—	4	2	no	—
158	C₈×C₆₇	—	8	1	no	—
159	C₆₇⋊C₈	—	2	2	no	—
160	C₆₇⋊C₈	—	4	2	no	—
161	C₆₇⋊C₈	—	4	1	no	—
162	C₂²×C₆₇	#388	1	1	yes	characteristic
163	C₂²×C₆₇	C₈×D₄	1	1	yes	characteristic
164	C₂²×C₆₇	#435	1	1	yes	characteristic
165	C₂²×C₆₇	C₄×SD₁₆	1	1	yes	characteristic
166	C₂²×C₆₇	#442	1	1	yes	characteristic
167	C₂²×C₆₇	#443	1	1	yes	characteristic
168	C₂²×C₆₇	#444	1	1	yes	characteristic
169	C₂×D₆₇	—	4	2	no	—
170	C₂×D₆₇	—	4	2	no	—
171	C₂×D₆₇	—	4	2	no	—
172	C₂×D₆₇	—	8	1	no	—
173	C₂×D₆₇	—	8	1	no	—
174	C₂×D₆₇	—	8	1	no	—
175	C₂×D₆₇	—	8	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	#431	1	1	yes	characteristic
179	C₄×C₆₇	#433	1	1	yes	characteristic
180	C₄×C₆₇	C₈×D₄	1	1	yes	characteristic
181	C₄×C₆₇	#436	1	1	yes	characteristic
182	C₄×C₆₇	#460	1	1	yes	characteristic
183	C₄×C₆₇	#463	1	1	yes	characteristic
184	C₄×C₆₇	#481	1	1	yes	characteristic
185	C₄×C₆₇	#482	1	1	yes	characteristic
186	Dic₆₇	—	4	2	no	—
187	Dic₆₇	—	4	2	no	—
188	Dic₆₇	—	8	1	no	—
189	#9542	—	67	1	no	maximal, Sylow
190	C₂×C₆₇	C₈×SD₁₆	1	1	yes	characteristic
191	C₂×C₆₇	#1580	1	1	yes	characteristic
192	C₂×C₆₇	#1583	1	1	yes	characteristic
193	C₂×C₆₇	#1586	1	1	yes	characteristic
194	C₂×C₆₇	#1923	1	1	yes	characteristic
195	C₂×C₆₇	#1926	1	1	yes	characteristic
196	C₂×C₆₇	#1929	1	1	yes	characteristic
197	D₆₇	—	8	2	no	—
198	#1954	—	67	1	no	—
199	C₈×C₄⋊C₄	—	67	1	no	—
200	C₄×#102	—	67	1	no	—
201	C₂×#334	D₆₇	1	1	yes	characteristic, complemented
202	C₂×D₄⋊C₈	—	67	1	no	—
203	#1279	—	67	1	no	—
204	#1273	—	67	1	no	—
205	C₆₇	#9542	1	1	yes	characteristic, complemented, Sylow
206	C₂×C₄×D₄	—	67	1	no	—
207	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
208	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
209	C₂×#102	—	67	1	no	—
210	C₂×#102	—	67	1	no	—
211	C₂×C₂²⋊C₈	—	134	1	no	—
212	C₂×C₂²⋊C₈	—	134	1	no	—
213	C₂×C₄×C₈	—	67	1	no	—
214	C₂×C₄×C₈	—	67	1	no	—
215	C₂×C₄×C₈	—	134	1	no	—
216	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
217	C₄×C₄⋊C₄	—	67	1	no	—
218	#340	—	67	1	no	—
219	#340	—	67	1	no	—
220	#336	—	134	1	no	—
221	#334	—	2	2	no	—
222	D₄⋊C₈	—	134	2	no	—
223	C₂²×D₄	—	67	1	no	—
224	C₂³×C₄	—	134	1	no	—
225	C₂²×C₈	—	2	1	no	—
226	C₂²×C₈	—	2	1	no	—
227	C₂²×C₈	—	67	1	no	—
228	C₂²×C₈	—	67	1	no	—
229	C₂²×C₈	—	134	1	no	—
230	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
231	C₂²×C₈	C₄×D₆₇	1	1	yes	characteristic
232	C₄×D₄	—	134	1	no	—
233	C₄×D₄	—	134	1	no	—
234	C₄×D₄	—	134	1	no	—
235	C₄×D₄	—	134	1	no	—
236	C₂×C₄⋊C₄	—	67	1	no	—
237	C₂×C₄⋊C₄	—	67	1	no	—
238	C₂×C₄⋊C₄	—	67	1	no	—
239	C₂×C₂²⋊C₄	—	134	1	no	—
240	C₂×C₄²	—	134	1	no	—
241	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
242	C₄⋊C₈	—	2	1	no	—
243	C₄⋊C₈	—	2	1	no	—
244	C₄⋊C₈	—	2	1	no	—
245	C₄⋊C₈	C₂²⋊D₆₇	1	2	yes	—
246	#102	—	67	4	no	—
247	#102	—	134	2	no	—
248	C₂²⋊C₈	—	268	2	no	—
249	C₂²⋊C₈	—	268	2	no	—
250	C₄×C₈	—	2	1	no	—
251	C₄×C₈	—	2	1	no	—
252	C₄×C₈	—	268	2	no	—
253	C₄×C₈	—	134	1	no	—
254	C₄×C₈	—	134	1	no	—
255	C₄×C₈	—	134	1	no	—
256	C₄×C₈	—	134	1	no	—
257	#95	—	134	1	no	—
258	C₂⁴	—	134	1	no	—
259	C₂×D₄	—	67	2	no	—
260	C₂×D₄	—	134	1	no	—
261	C₂×D₄	—	134	1	no	—
262	C₂×D₄	—	134	1	no	—
263	C₂×D₄	—	134	1	no	—
264	C₂×D₄	—	134	1	no	—
265	C₂²×C₄	—	268	1	no	—
266	C₂²×C₄	—	268	1	no	—
267	C₂²×C₄	—	268	1	no	—
268	C₂²×C₄	—	268	1	no	—
269	C₂²×C₄	—	268	1	no	—
270	C₂²×C₄	—	268	1	no	—
271	C₂²×C₄	—	134	1	no	—
272	C₂²×C₄	—	134	1	no	—
273	C₂²×C₄	—	134	1	no	—
274	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
275	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
276	C₂²×C₄	#11761629	1	1	yes	characteristic
277	C₂×C₈	—	2	1	no	—
278	C₂×C₈	—	2	1	no	—
279	C₂×C₈	—	2	1	no	—
280	C₂×C₈	—	2	2	no	—
281	C₂×C₈	—	2	1	no	—
282	C₂×C₈	—	2	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	4	1	no	—
285	C₂×C₈	—	4	1	no	—
286	C₂×C₈	—	4	1	no	—
287	C₂×C₈	—	4	1	no	—
288	C₂×C₈	—	268	1	no	—
289	C₂×C₈	—	268	1	no	—
290	C₂×C₈	—	67	2	no	—
291	C₂×C₈	—	134	2	no	—
292	C₂×C₈	—	134	1	no	—
293	C₂×C₈	—	134	1	no	—
294	C₂×C₈	—	134	1	no	—
295	C₂×C₈	—	134	1	no	—
296	C₂×C₈	—	134	1	no	—
297	C₂×C₈	C₈×D₆₇	1	2	yes	—
298	C₄⋊C₄	—	67	2	no	—
299	C₄⋊C₄	—	67	2	no	—
300	C₄⋊C₄	—	134	1	no	—
301	C₄⋊C₄	—	134	1	no	—
302	C₄⋊C₄	—	134	1	no	—
303	C₄⋊C₄	—	134	1	no	—
304	C₂²⋊C₄	—	268	1	no	—
305	C₂²⋊C₄	—	268	1	no	—
306	C₄²	—	268	1	no	—
307	C₄²	—	268	1	no	—
308	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
309	C₄²	#11761627	1	1	yes	characteristic
310	C₄²	#11761628	1	1	yes	characteristic
311	C₄²	#11761629	1	1	yes	characteristic
312	C₂³	—	268	1	no	—
313	C₂³	—	268	1	no	—
314	C₂³	—	268	1	no	—
315	C₂³	—	268	1	no	—
316	C₂³	—	268	1	no	—
317	C₂³	—	268	1	no	—
318	C₂³	—	134	2	no	—
319	C₂³	#14524005	1	1	yes	characteristic
320	D₄	—	268	1	no	—
321	D₄	—	268	1	no	—
322	D₄	—	134	2	no	—
323	D₄	—	134	2	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	268	1	no	—
327	C₂×C₄	—	268	1	no	—
328	C₂×C₄	—	268	1	no	—
329	C₂×C₄	—	268	1	no	—
330	C₂×C₄	—	268	1	no	—
331	C₂×C₄	—	268	1	no	—
332	C₂×C₄	—	268	1	no	—
333	C₂×C₄	—	536	1	no	—
334	C₂×C₄	—	536	1	no	—
335	C₂×C₄	—	536	1	no	—
336	C₂×C₄	—	536	1	no	—
337	C₂×C₄	—	134	2	no	—
338	C₂×C₄	—	134	2	no	—
339	C₂×C₄	#14524001	1	1	yes	characteristic
340	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
341	C₂×C₄	#14524015	1	1	yes	characteristic
342	C₂×C₄	#14524028	1	1	yes	characteristic
343	C₂×C₄	#14524032	1	1	yes	characteristic
344	C₂×C₄	#14524038	1	1	yes	characteristic
345	C₂×C₄	C₂×C₈×D₆₇	1	1	yes	characteristic
346	C₂×C₄	M₁₆×D₆₇	1	1	yes	characteristic
347	C₂×C₄	#14524049	1	1	yes	characteristic
348	C₂×C₄	#14524051	1	1	yes	characteristic
349	C₂×C₄	SD₁₆×D₆₇	1	1	yes	characteristic
350	C₂×C₄	#14524064	1	1	yes	characteristic
351	C₂×C₄	#14524070	1	1	yes	characteristic
352	C₂×C₄	#14524070	1	1	yes	characteristic
353	C₈	—	2	2	no	—
354	C₈	—	4	2	no	—
355	C₈	—	4	1	no	—
356	C₈	—	8	1	no	—
357	C₈	—	268	2	no	—
358	C₈	—	268	1	no	—
359	C₈	—	134	2	no	—
360	C₂²	—	268	2	no	—
361	C₂²	—	268	2	no	—
362	C₂²	—	268	2	no	—
363	C₂²	—	536	1	no	—
364	C₂²	—	536	1	no	—
365	C₂²	—	536	1	no	—
366	C₂²	—	536	1	no	—
367	C₂²	#16863286	1	1	yes	characteristic
368	C₂²	#16863461	1	1	yes	characteristic
369	C₂²	#16863466	1	1	yes	characteristic
370	C₂²	#16863483	1	1	yes	characteristic
371	C₂²	#16863507	1	1	yes	characteristic
372	C₂²	#16863512	1	1	yes	characteristic
373	C₂²	#16863517	1	1	yes	characteristic
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	268	2	no	—
377	C₄	—	268	2	no	—
378	C₄	—	536	1	no	—
379	C₄	#16863448	1	1	yes	characteristic
380	C₄	#16863456	1	1	yes	characteristic
381	C₄	C₈×C₂²⋊D₆₇	1	1	yes	characteristic
382	C₄	#16863472	1	1	yes	characteristic
383	C₄	#16863594	1	1	yes	characteristic
384	C₄	#16863613	1	1	yes	characteristic
385	C₄	#16863716	1	1	yes	characteristic
386	C₄	#16863722	1	1	yes	characteristic
387	C₂	—	536	2	no	—
388	C₂	#22559008	1	1	yes	characteristic
389	C₂	#22559032	1	1	yes	characteristic
390	C₂	#22559051	1	1	yes	characteristic
391	C₂	#22559072	1	1	yes	characteristic
392	C₂	#22560814	1	1	yes	characteristic
393	C₂	#22560835	1	1	yes	characteristic
394	C₂	#22560856	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₆₇
commutator	C₂×C₄×C₆₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₂×#334×C₆₇	C₂
socle	C₂³×C₆₇	C₄×D₄
prime radical	C₂²×D₂₆₈	C₂×C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₂×#334	D₆₇
hypocenter	C₆₇	#9542
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
2. #22560074	C₂	semidirect
5. #22558048	C₂	semidirect
6. C₆₇⋊#1273	C₂	semidirect
7. C₂×#334×C₆₇	C₂	semidirect
40. #14523965	C₈	semidirect
201. C₂×#334	D₆₇	semidirect
205. C₆₇	#9542	semidirect

Maximal subgroups

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

subgroup	index
#22561002	2
#22560074	2
C₄×#14523965	2
C₂×#16863123	2
#22558048	2
C₆₇⋊#1273	2
C₂×#334×C₆₇	2
#9542	67