Subgroups — #30839616

Order 17152.

798 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569669	C₂	1	2	yes	maximal, complemented
2	C₂×C₈×D₂₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#22559643	C₂	1	4	yes	maximal, complemented
4	#22559595	C₂	1	2	yes	maximal, complemented
5	#22559561	C₂	1	2	yes	maximal, complemented
6	#22558968	C₂	1	1	yes	maximal, characteristic, complemented
7	#22558886	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14524068	—	2	2	no	—
10	C₂²×C₈×D₆₇	—	2	1	no	—
11	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
12	#16863608	—	2	4	no	—
13	#16863598	C₂²	1	4	yes	—
14	#16863588	C₂²	1	4	yes	—
15	C₈×D₂₆₈	—	2	1	no	—
16	C₈×D₂₆₈	—	2	1	no	—
17	C₈×D₂₆₈	C₂²	1	2	yes	—
18	C₈×D₂₆₈	C₂²	1	2	yes	—
19	#16863420	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
21	#16863397	—	2	2	no	—
22	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
23	#16863149	C₂²	1	2	yes	complemented
24	#16863149	C₂²	1	2	yes	complemented
25	#16863142	C₂²	1	4	yes	complemented
26	#16863140	C₂²	1	4	yes	complemented
27	#532×C₆₇	C₂²	1	2	yes	—
28	#500×C₆₇	C₂²	1	1	yes	characteristic, complemented
29	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#486×C₆₇	C₂²	1	2	yes	complemented
31	#466×C₆₇	—	2	1	no	—
32	#466×C₆₇	—	2	1	no	—
33	C₄×D₈×C₆₇	—	2	1	no	—
34	C₄×D₈×C₆₇	—	2	1	no	—
35	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×D₂₆₈	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₆₇	—	2	1	no	—
38	#14524068	—	4	8	no	—
39	C₂×#11761615	—	2	4	no	—
40	C₂×#11761613	—	2	4	no	—
41	C₂×#11761612	—	2	2	no	—
42	C₂²×C₆₇⋊C₈	—	2	1	no	—
43	C₂×C₈×D₆₇	—	2	2	no	—
44	C₂×C₈×D₆₇	—	2	2	no	—
45	C₂×C₈×D₆₇	—	4	4	no	—
46	C₄×D₂₆₈	—	2	1	no	—
47	C₄×D₂₆₈	—	2	1	no	—
48	C₄×D₂₆₈	D₄	1	2	yes	—
49	C₄×D₂₆₈	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₆₇	D₄	1	1	yes	characteristic
51	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
52	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
53	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
55	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
56	#14523967	—	2	4	no	—
57	#14523964	—	2	4	no	—
58	(C₂×D₆₇)⋊C₈	—	2	2	no	—
59	(C₂×D₆₇)⋊C₈	—	2	2	no	—
60	C₂×#41×C₆₇	—	2	2	no	—
61	C₂×D₈×C₆₇	—	2	1	no	—
62	C₂×D₈×C₆₇	—	2	1	no	—
63	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
64	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
65	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
66	#127×C₆₇	C₂³	1	2	yes	—
67	#124×C₆₇	—	2	2	no	—
68	#121×C₆₇	—	2	2	no	—
69	#121×C₆₇	—	2	2	no	—
70	C₄×D₄×C₆₇	—	2	2	no	—
71	C₄×D₄×C₆₇	—	2	2	no	—
72	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
73	#107×C₆₇	—	2	1	no	—
74	#107×C₆₇	—	2	1	no	—
75	#102×C₆₇	—	2	2	no	—
76	#102×C₆₇	—	2	2	no	—
77	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
78	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
79	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
80	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₂³×D₆₇	—	2	1	no	—
82	C₂×D₂₆₈	—	2	1	no	—
83	C₂×D₂₆₈	—	2	2	no	—
84	C₂×D₂₆₈	D₈	1	4	yes	complemented
85	C₂×D₂₆₈	C₂×D₄	1	2	yes	—
86	C₂²×Dic₆₇	—	2	1	no	—
87	C₂×C₄×D₆₇	—	2	2	no	—
88	C₂×C₄×D₆₇	—	2	2	no	—
89	C₂×C₄×D₆₇	—	4	2	no	—
90	C₂×C₄×D₆₇	—	4	2	no	—
91	#11761615	—	4	8	no	—
92	#11761613	—	4	8	no	—
93	#11761612	—	4	4	no	—
94	C₂×C₆₇⋊C₈	—	2	2	no	—
95	C₂×C₆₇⋊C₈	—	2	4	no	—
96	C₂×C₆₇⋊C₈	—	4	2	no	—
97	C₈×D₆₇	—	4	4	no	—
98	C₈×D₆₇	—	4	4	no	—
99	C₄⋊Dic₆₇	—	2	1	no	—
100	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
101	(C₂×D₆₇)⋊C₄	—	2	2	no	—
102	(C₂×D₆₇)⋊C₄	—	2	2	no	—
103	#41×C₆₇	—	4	4	no	—
104	#41×C₆₇	—	4	4	no	—
105	C₂×Q₈×C₆₇	—	2	2	no	—
106	C₂×D₄×C₆₇	—	2	2	no	—
107	C₂×D₄×C₆₇	—	2	2	no	—
108	C₂×D₄×C₆₇	—	2	2	no	—
109	C₂×D₄×C₆₇	—	4	2	no	—
110	C₂²×C₄×C₆₇	—	4	2	no	—
111	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
114	D₈×C₆₇	—	4	2	no	—
115	D₈×C₆₇	—	4	2	no	—
116	C₂×C₈×C₆₇	—	2	2	no	—
117	C₂×C₈×C₆₇	—	4	1	no	—
118	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	—	2	2	no	—
124	C₂²⋊C₄×C₆₇	—	4	2	no	—
125	C₂²⋊C₄×C₆₇	—	4	2	no	—
126	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₆₇	#41	1	1	yes	characteristic
129	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
130	C₂³×C₆₇	—	4	2	no	—
131	C₂³×C₆₇	#121	1	1	yes	characteristic
132	C₂²×D₆₇	—	2	2	no	—
133	C₂²×D₆₇	—	2	4	no	—
134	C₂²×D₆₇	—	4	2	no	—
135	C₂²×D₆₇	—	4	2	no	—
136	Q₈×C₆₇	—	4	2	no	—
137	Q₈×C₆₇	—	4	2	no	—
138	D₄×C₆₇	—	4	2	no	—
139	D₄×C₆₇	—	4	2	no	—
140	D₄×C₆₇	—	4	2	no	—
141	D₄×C₆₇	—	4	2	no	—
142	D₄×C₆₇	—	8	2	no	—
143	D₄×C₆₇	—	8	4	no	—
144	C₂×C₄×C₆₇	—	2	1	no	—
145	C₂×C₄×C₆₇	—	2	1	no	—
146	C₂×C₄×C₆₇	—	4	1	no	—
147	C₂×C₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	—	8	4	no	—
149	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
151	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂×D₈	1	2	yes	—
153	C₂×C₄×C₆₇	#135	1	2	yes	—
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×Dic₆₇	—	2	2	no	—
158	C₂×Dic₆₇	—	4	2	no	—
159	D₂₆₈	—	2	2	no	—
160	D₂₆₈	—	2	4	no	—
161	D₂₆₈	C₂×D₈	1	4	yes	—
162	C₄×D₆₇	—	4	4	no	—
163	C₄×D₆₇	—	4	2	no	—
164	C₄×D₆₇	—	4	2	no	—
165	C₈×C₆₇	—	2	1	no	—
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	2	1	no	—
168	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	complemented
169	C₆₇⋊C₈	—	4	4	no	—
170	C₆₇⋊C₈	—	4	2	no	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	—	8	2	no	—
174	C₂²×C₆₇	—	8	2	no	—
175	C₂²×C₆₇	—	8	2	no	—
176	C₂²×C₆₇	#466	1	2	yes	—
177	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
178	C₂×D₆₇	—	2	4	no	—
179	C₂×D₆₇	—	4	8	no	—
180	C₂×D₆₇	—	4	2	no	—
181	C₂×D₆₇	—	4	2	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	8	2	no	—
186	C₄×C₆₇	#466	1	2	yes	—
187	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
188	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
189	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
190	C₄×C₆₇	#575	1	1	yes	characteristic
191	Dic₆₇	—	4	2	no	—
192	#19255	—	67	1	no	maximal, Sylow
193	C₂×C₆₇	—	2	2	no	—
194	C₂×C₆₇	—	16	2	no	—
195	C₂×C₆₇	#3036	1	1	yes	characteristic
196	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
197	C₂×C₆₇	#3067	1	1	yes	characteristic
198	D₆₇	—	4	4	no	—
199	#3169	D₆₇	1	1	yes	characteristic, complemented
200	#3036	—	67	2	no	—
201	C₂×C₈×D₄	—	67	1	no	—
202	#1681	—	67	4	no	—
203	#1673	—	67	2	no	—
204	#1667	—	67	2	no	—
205	#1567	—	67	1	no	—
206	#1547	—	67	2	no	—
207	C₆₇	#19255	1	1	yes	characteristic, complemented, Sylow
208	C₂×AGL(1,ℤ/8)	—	134	2	no	—
209	C₂³×C₈	—	134	1	no	—
210	#532	C₂×D₆₇	1	2	yes	—
211	C₂×C₄×D₄	—	67	1	no	—
212	#500	C₂×D₆₇	1	1	yes	characteristic, complemented
213	#493	C₂×D₆₇	1	1	yes	characteristic, complemented
214	#486	C₂×D₆₇	1	2	yes	complemented
215	#466	—	2	1	no	—
216	#466	—	2	1	no	—
217	#463	—	134	4	no	—
218	#461	—	67	4	no	—
219	#459	—	67	4	no	—
220	C₄×D₈	—	2	1	no	—
221	C₄×D₈	—	2	1	no	—
222	C₈×D₄	—	67	2	no	—
223	C₈×D₄	—	67	2	no	—
224	C₈×D₄	—	134	1	no	—
225	C₈×D₄	—	134	1	no	—
226	#423	—	67	2	no	—
227	C₂×C₄⋊C₈	—	67	1	no	—
228	#417	—	134	2	no	—
229	C₂×C₂²⋊C₈	—	134	1	no	—
230	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
231	#335	—	67	2	no	—
232	#335	—	67	2	no	—
233	#332	—	67	4	no	—
234	#331	—	67	4	no	—
235	C₂×#41	—	2	2	no	—
236	C₂²×D₄	—	67	1	no	—
237	C₂³×C₄	—	134	1	no	—
238	AGL(1,ℤ/8)	—	268	8	no	—
239	C₂×SD₁₆	—	134	4	no	—
240	C₂×D₈	—	2	1	no	—
241	C₂×D₈	—	2	1	no	—
242	C₂×D₈	—	134	4	no	—
243	C₂×M₁₆	—	134	2	no	—
244	C₂²×C₈	—	268	4	no	—
245	C₂²×C₈	—	134	1	no	—
246	C₂²×C₈	—	134	2	no	—
247	C₂²×C₈	—	134	2	no	—
248	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
249	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
250	C₄⋊Q₈	C₂²×D₆₇	1	2	yes	—
251	#127	C₂²×D₆₇	1	2	yes	—
252	#124	—	2	2	no	—
253	#121	—	2	2	no	—
254	#121	—	2	2	no	—
255	C₄×D₄	—	2	2	no	—
256	C₄×D₄	—	2	2	no	—
257	C₄×D₄	—	67	2	no	—
258	C₄×D₄	—	67	2	no	—
259	C₄×D₄	—	134	1	no	—
260	C₄×D₄	—	134	1	no	—
261	C₂×C₄⋊C₄	—	67	1	no	—
262	C₂×C₂²⋊C₄	—	134	1	no	—
263	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
264	#107	—	2	1	no	—
265	#107	—	2	1	no	—
266	C₄⋊C₈	—	67	2	no	—
267	C₄⋊C₈	—	67	4	no	—
268	C₄⋊C₈	—	134	2	no	—
269	C₄⋊C₈	—	134	1	no	—
270	#103	—	134	4	no	—
271	#102	—	2	2	no	—
272	#102	—	2	2	no	—
273	#102	—	134	4	no	—
274	C₂²⋊C₈	—	134	2	no	—
275	C₂²⋊C₈	—	134	2	no	—
276	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
277	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
278	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
279	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
280	C₂⁴	—	134	1	no	—
281	#41	—	4	4	no	—
282	#41	—	4	4	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	67	4	no	—
289	C₂×D₄	—	67	2	no	—
290	C₂×D₄	—	134	1	no	—
291	C₂×D₄	—	134	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	268	2	no	—
294	C₂²×C₄	—	268	2	no	—
295	C₂²×C₄	—	134	1	no	—
296	C₂²×C₄	—	134	2	no	—
297	C₂²×C₄	—	134	2	no	—
298	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
300	C₂²×C₄	#11761627	1	1	yes	characteristic
301	SD₁₆	—	268	8	no	—
302	D₈	—	4	2	no	—
303	D₈	—	4	2	no	—
304	D₈	—	268	8	no	—
305	M₁₆	—	268	4	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	268	4	no	—
309	C₂×C₈	—	268	2	no	—
310	C₂×C₈	—	268	4	no	—
311	C₂×C₈	—	134	4	no	—
312	C₂×C₈	—	134	2	no	—
313	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
314	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
315	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
316	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	67	2	no	—
320	C₄⋊C₄	—	134	1	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	134	2	no	—
324	C₂²⋊C₄	—	134	2	no	—
325	C₄²	D₄×D₆₇	1	1	yes	characteristic
326	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
327	C₄²	#11761627	1	1	yes	characteristic
328	C₄²	C₂³×D₆₇	1	1	yes	characteristic
329	C₂³	—	4	2	no	—
330	C₂³	—	268	2	no	—
331	C₂³	—	268	2	no	—
332	C₂³	—	134	4	no	—
333	C₂³	—	134	2	no	—
334	C₂³	#14524014	1	1	yes	characteristic
335	Q₈	—	4	2	no	—
336	Q₈	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	4	no	—
343	D₄	—	67	4	no	—
344	D₄	—	134	4	no	—
345	D₄	—	134	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	8	4	no	—
351	C₂×C₄	—	268	4	no	—
352	C₂×C₄	—	268	2	no	—
353	C₂×C₄	—	268	2	no	—
354	C₂×C₄	—	268	2	no	—
355	C₂×C₄	—	134	2	no	—
356	C₂×C₄	#14524014	1	1	yes	characteristic
357	C₂×C₄	#14524014	1	1	yes	characteristic
358	C₂×C₄	#14524014	1	1	yes	characteristic
359	C₂×C₄	D₈×D₆₇	1	2	yes	—
360	C₂×C₄	#14524062	1	2	yes	—
361	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
362	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
363	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	—	268	4	no	—
368	C₈	—	268	2	no	—
369	C₈	#14524068	1	2	yes	complemented
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	268	8	no	—
376	C₂²	—	268	2	no	—
377	C₂²	—	268	2	no	—
378	C₂²	—	134	4	no	—
379	C₂²	#16863629	1	2	yes	—
380	C₂²	C₂×#14524014	1	1	yes	characteristic
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	8	2	no	—
385	C₄	—	268	2	no	—
386	C₄	#16863629	1	2	yes	—
387	C₄	C₂×D₈×D₆₇	1	1	yes	characteristic
388	C₄	C₂×#14524062	1	1	yes	characteristic
389	C₄	C₂×#14524068	1	1	yes	characteristic
390	C₄	#16864194	1	1	yes	characteristic
391	C₂	—	2	2	no	—
392	C₂	—	268	4	no	—
393	C₂	—	16	2	no	—
394	C₂	#22569669	1	1	yes	characteristic
395	C₂	C₂×#16863629	1	1	yes	characteristic
396	C₂	#22569925	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524014
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#3169	C₂
socle	C₂²×C₆₇	C₂×#121
hypercenter	#3169	D₆₇
hypocenter	C₆₇	#19255
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #22569669	C₂	semidirect
2. C₂×C₈×D₂₆₈	C₂	semidirect
3. #22559643	C₂	semidirect
4. #22559595	C₂	semidirect
5. #22559561	C₂	semidirect
6. #22558968	C₂	semidirect
7. #22558886	C₂	semidirect
8. C₆₇×#3169	C₂	semidirect
23. #16863149	C₂²	semidirect
24. #16863149	C₂²	semidirect
25. #16863142	C₂²	semidirect
26. #16863140	C₂²	semidirect
28. #500×C₆₇	C₂²	semidirect
29. #493×C₆₇	C₂²	semidirect
30. #486×C₆₇	C₂²	semidirect
84. C₂×D₂₆₈	D₈	semidirect
168. C₈×C₆₇	AGL(1,ℤ/8)	semidirect
199. #3169	D₆₇	semidirect
207. C₆₇	#19255	semidirect
212. #500	C₂×D₆₇	semidirect
213. #493	C₂×D₆₇	semidirect
214. #486	C₂×D₆₇	semidirect
369. C₈	#14524068	semidirect

Maximal subgroups

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

subgroup	index
#22569669	2
C₂×C₈×D₂₆₈	2
#22559643	2
#22559595	2
#22559561	2
#22558968	2
#22558886	2
C₆₇×#3169	2
#19255	67