Subgroups — #30748874

Order 17152.

542 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863461	C₂	1	1	yes	maximal, characteristic
2	#22560365	C₂	1	1	yes	maximal, characteristic, complemented
3	#22560210	C₂	1	1	yes	maximal, characteristic
4	#22560206	C₂	1	1	yes	maximal, characteristic
5	C₂×#16863146	C₂	1	1	yes	maximal, characteristic, complemented
6	#22558093	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₆₇	—	2	1	no	—
9	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
10	#16863461	—	2	2	no	—
11	#16863461	C₄	1	4	yes	complemented
12	C₂×#14523974	—	2	1	no	—
13	C₂×#14523974	—	2	1	no	—
14	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#14523965	—	2	1	no	—
16	C₂×#14523963	—	2	1	no	—
17	C₂×(C₂×D₆₇)⋊C₈	—	2	1	no	—
18	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
19	#16863266	C₂²	1	1	yes	characteristic
20	#16863159	—	2	1	no	—
21	#16863158	—	2	1	no	—
22	#16863146	—	2	2	no	—
23	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
25	#384×C₆₇	C₂²	1	1	yes	characteristic
26	C₂²×D₂₆₈	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₆₇	—	2	1	no	—
28	C₂²×C₆₇⋊C₈	—	2	1	no	—
29	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
30	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
31	C₂×C₈×D₆₇	—	2	4	no	—
32	C₂×C₈×D₆₇	—	4	2	no	—
33	C₂×C₈×D₆₇	—	4	2	no	—
34	C₄×D₂₆₈	—	2	1	no	—
35	C₄×D₂₆₈	—	2	1	no	—
36	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
37	C₄×D₂₆₈	Q₈	1	2	yes	—
38	C₂×C₄⋊Dic₆₇	—	2	1	no	—
39	C₂×C₄⋊Dic₆₇	—	2	1	no	—
40	C₂×C₄⋊Dic₆₇	—	2	1	no	—
41	C₂×C₄⋊Dic₆₇	D₄	1	1	yes	characteristic
42	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
43	#14523974	—	4	2	no	—
44	#14523974	—	4	2	no	—
45	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
46	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
47	#14523965	—	4	2	no	—
48	#14523963	—	4	2	no	—
49	(C₂×D₆₇)⋊C₈	—	2	4	no	—
50	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
51	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
52	C₂²×C₈×C₆₇	—	2	1	no	—
53	C₂²×C₈×C₆₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
57	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₆₇	—	2	1	no	—
59	C₄⋊C₈×C₆₇	—	2	1	no	—
60	C₄⋊C₈×C₆₇	—	2	1	no	—
61	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
62	C₂³×D₆₇	—	2	1	no	—
63	C₂×D₂₆₈	—	2	1	no	—
64	C₂×D₂₆₈	—	2	1	no	—
65	C₂×D₂₆₈	—	2	1	no	—
66	C₂×D₂₆₈	C₄⋊C₄	1	2	yes	—
67	C₂×D₂₆₈	SD₁₆	1	2	yes	—
68	C₂×D₂₆₈	SD₁₆	1	2	yes	—
69	C₂²×Dic₆₇	—	2	1	no	—
70	C₂²×Dic₆₇	—	4	1	no	—
71	C₂×C₄×D₆₇	—	2	2	no	—
72	C₂×C₄×D₆₇	—	2	2	no	—
73	C₂×C₄×D₆₇	—	4	1	no	—
74	C₂×C₄×D₆₇	—	4	1	no	—
75	C₂×C₄×D₆₇	—	4	1	no	—
76	C₂×C₄×D₆₇	—	4	1	no	—
77	C₂×C₆₇⋊C₈	—	2	1	no	—
78	C₂×C₆₇⋊C₈	—	2	1	no	—
79	C₂×C₆₇⋊C₈	—	4	1	no	—
80	C₂×C₆₇⋊C₈	—	4	1	no	—
81	C₂×C₆₇⋊C₈	—	4	1	no	—
82	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	2	yes	—
83	C₂×C₆₇⋊C₈	C₂²⋊C₄	1	2	yes	—
84	C₂×C₆₇⋊C₈	D₈	1	2	yes	—
85	C₂×C₆₇⋊C₈	SD₁₆	1	2	yes	—
86	C₈×D₆₇	—	4	8	no	—
87	C₄⋊Dic₆₇	—	2	1	no	—
88	C₄⋊Dic₆₇	—	4	1	no	—
89	C₄⋊Dic₆₇	—	4	1	no	—
90	C₄⋊Dic₆₇	—	4	1	no	—
91	C₄⋊Dic₆₇	—	4	1	no	—
92	C₄⋊Dic₆₇	—	8	1	no	—
93	C₄⋊Dic₆₇	C₄⋊C₄	1	2	yes	—
94	(C₂×D₆₇)⋊C₄	—	2	2	no	—
95	(C₂×D₆₇)⋊C₄	—	2	2	no	—
96	C₂²×C₄×C₆₇	—	4	1	no	—
97	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	—	4	1	no	—
102	C₂×C₈×C₆₇	—	4	1	no	—
103	C₂×C₈×C₆₇	—	4	1	no	—
104	C₂×C₈×C₆₇	—	4	1	no	—
105	C₂×C₈×C₆₇	—	4	1	no	—
106	C₄⋊C₄×C₆₇	—	4	1	no	—
107	C₄⋊C₄×C₆₇	—	4	1	no	—
108	C₄⋊C₄×C₆₇	—	4	1	no	—
109	C₄⋊C₄×C₆₇	—	4	1	no	—
110	C₄⋊C₄×C₆₇	—	8	1	no	—
111	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
114	C₄²×C₆₇	#41	1	1	yes	characteristic
115	C₂³×C₆₇	#121	1	1	yes	characteristic
116	C₂²×D₆₇	—	2	2	no	—
117	C₂²×D₆₇	—	2	2	no	—
118	C₂²×D₆₇	—	2	2	no	—
119	C₂²×D₆₇	—	4	1	no	—
120	C₂²×D₆₇	—	4	1	no	—
121	C₂²×D₆₇	—	4	1	no	—
122	C₂²×D₆₇	—	4	1	no	—
123	C₂×C₄×C₆₇	—	2	1	no	—
124	C₂×C₄×C₆₇	—	2	1	no	—
125	C₂×C₄×C₆₇	—	8	1	no	—
126	C₂×C₄×C₆₇	—	8	1	no	—
127	C₂×C₄×C₆₇	—	8	1	no	—
128	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
131	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂×SD₁₆	1	1	yes	characteristic
138	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
139	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
140	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
141	C₂×C₄×C₆₇	#137	1	1	yes	characteristic
142	C₂×Dic₆₇	—	2	2	no	—
143	C₂×Dic₆₇	—	4	1	no	—
144	C₂×Dic₆₇	—	4	1	no	—
145	C₂×Dic₆₇	—	8	1	no	—
146	C₂×Dic₆₇	—	8	1	no	—
147	C₂×Dic₆₇	—	8	1	no	—
148	D₂₆₈	—	2	2	no	—
149	D₂₆₈	—	2	2	no	—
150	D₂₆₈	—	2	2	no	—
151	D₂₆₈	#106	1	4	yes	complemented
152	C₄×D₆₇	—	4	2	no	—
153	C₄×D₆₇	—	4	2	no	—
154	C₄×D₆₇	—	4	2	no	—
155	C₄×D₆₇	—	4	2	no	—
156	C₈×C₆₇	—	4	2	no	—
157	C₈×C₆₇	—	8	1	no	—
158	C₆₇⋊C₈	—	2	2	no	—
159	C₆₇⋊C₈	—	8	1	no	—
160	C₆₇⋊C₈	#102	1	4	yes	complemented
161	C₂²×C₆₇	#380	1	1	yes	characteristic
162	C₂²×C₆₇	#459	1	1	yes	characteristic
163	C₂²×C₆₇	#461	1	1	yes	characteristic
164	C₂²×C₆₇	#465	1	1	yes	characteristic
165	C₂²×C₆₇	#465	1	1	yes	characteristic
166	C₂²×C₆₇	#471	1	1	yes	characteristic
167	C₂²×C₆₇	#471	1	1	yes	characteristic
168	C₂×D₆₇	—	2	4	no	—
169	C₂×D₆₇	—	4	2	no	—
170	C₂×D₆₇	—	4	2	no	—
171	C₂×D₆₇	—	4	2	no	—
172	C₂×D₆₇	—	4	2	no	—
173	C₂×D₆₇	—	4	2	no	—
174	C₂×D₆₇	—	4	2	no	—
175	C₄×C₆₇	—	2	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	16	1	no	—
178	C₄×C₆₇	C₂×#102	1	1	yes	characteristic
179	C₄×C₆₇	#417	1	1	yes	characteristic
180	C₄×C₆₇	C₂×#106	1	1	yes	characteristic
181	C₄×C₆₇	#427	1	1	yes	characteristic
182	C₄×C₆₇	#465	1	1	yes	characteristic
183	C₄×C₆₇	#465	1	1	yes	characteristic
184	C₄×C₆₇	#474	1	1	yes	characteristic
185	C₄×C₆₇	#476	1	1	yes	characteristic
186	Dic₆₇	—	4	2	no	—
187	Dic₆₇	—	16	1	no	—
188	#8642	—	67	1	no	maximal, Sylow
189	C₂×C₆₇	#1665	1	1	yes	characteristic
190	C₂×C₆₇	#1665	1	1	yes	characteristic
191	C₂×C₆₇	#1671	1	1	yes	characteristic
192	C₂×C₆₇	#1671	1	1	yes	characteristic
193	C₂×C₆₇	#1802	1	1	yes	characteristic
194	C₂×C₆₇	#1807	1	1	yes	characteristic
195	C₂×C₆₇	#1815	1	1	yes	characteristic
196	D₆₇	—	4	4	no	—
197	C₂×C₈×D₄	—	67	1	no	—
198	#1844	—	67	1	no	—
199	#1802	—	67	1	no	—
200	#1802	—	67	1	no	—
201	C₂×#334	—	67	1	no	—
202	#1296	—	67	1	no	—
203	#1296	D₆₇	1	1	yes	characteristic, complemented
204	C₆₇	#8642	1	1	yes	characteristic, complemented, Sylow
205	C₂³×C₈	—	134	1	no	—
206	C₂×C₄×D₄	—	67	1	no	—
207	C₈×D₄	—	67	4	no	—
208	C₈×D₄	—	134	2	no	—
209	C₂×#106	—	134	1	no	—
210	C₂×#106	—	134	1	no	—
211	C₂×C₄⋊C₈	—	67	1	no	—
212	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
213	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
214	C₂×#102	—	134	1	no	—
215	C₂×#102	—	134	1	no	—
216	C₂×C₂²⋊C₈	—	134	1	no	—
217	C₂×C₄×C₈	—	67	1	no	—
218	#384	—	67	1	no	—
219	#384	C₂×D₆₇	1	1	yes	characteristic
220	#340	—	134	1	no	—
221	#340	—	134	1	no	—
222	#334	—	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	—	268	2	no	—
228	C₂²×C₈	—	268	2	no	—
229	C₂²×C₈	—	67	1	no	—
230	C₂²×C₈	—	67	1	no	—
231	C₂²×C₈	—	134	4	no	—
232	C₂²×C₈	—	134	1	no	—
233	C₄×D₄	—	67	2	no	—
234	C₄×D₄	—	67	2	no	—
235	C₄×D₄	—	134	1	no	—
236	C₄×D₄	—	134	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	67	1	no	—
241	C₂×C₄⋊C₄	—	134	1	no	—
242	C₂×C₄⋊C₄	—	134	1	no	—
243	C₂×C₄⋊C₄	—	134	1	no	—
244	C₂×C₂²⋊C₄	—	134	1	no	—
245	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
246	#106	—	268	2	no	—
247	#106	—	268	2	no	—
248	C₄⋊C₈	—	2	1	no	—
249	C₄⋊C₈	—	2	1	no	—
250	C₄⋊C₈	—	2	1	no	—
251	C₄⋊C₈	—	134	1	no	—
252	C₄⋊C₈	—	134	1	no	—
253	C₄⋊C₈	C₄×D₆₇	1	2	yes	—
254	#102	—	268	2	no	—
255	#102	—	268	2	no	—
256	C₂²⋊C₈	—	134	4	no	—
257	C₄×C₈	—	67	2	no	—
258	C₄×C₈	—	67	2	no	—
259	C₂⁴	—	134	1	no	—
260	C₂×D₄	—	67	2	no	—
261	C₂×D₄	—	67	2	no	—
262	C₂×D₄	—	67	2	no	—
263	C₂×D₄	—	134	1	no	—
264	C₂×D₄	—	134	1	no	—
265	C₂×D₄	—	134	1	no	—
266	C₂²×C₄	—	4	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	—	268	1	no	—
272	C₂²×C₄	—	134	1	no	—
273	C₂²×C₄	—	134	2	no	—
274	C₂²×C₄	—	134	2	no	—
275	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
276	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
277	C₂²×C₄	#11761628	1	1	yes	characteristic
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	4	1	no	—
280	C₂×C₈	—	4	1	no	—
281	C₂×C₈	—	4	1	no	—
282	C₂×C₈	—	4	1	no	—
283	C₂×C₈	—	4	1	no	—
284	C₂×C₈	—	268	8	no	—
285	C₂×C₈	—	268	1	no	—
286	C₂×C₈	—	268	1	no	—
287	C₂×C₈	—	268	1	no	—
288	C₂×C₈	—	67	2	no	—
289	C₂×C₈	—	67	2	no	—
290	C₂×C₈	—	67	2	no	—
291	C₂×C₈	—	67	2	no	—
292	C₂×C₈	—	134	1	no	—
293	C₂×C₈	—	134	1	no	—
294	C₄⋊C₄	—	4	1	no	—
295	C₄⋊C₄	—	4	1	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	—	8	1	no	—
299	C₄⋊C₄	—	268	1	no	—
300	C₄⋊C₄	—	268	1	no	—
301	C₄⋊C₄	—	268	1	no	—
302	C₄⋊C₄	—	268	1	no	—
303	C₄⋊C₄	—	536	1	no	—
304	C₄⋊C₄	—	67	2	no	—
305	C₄⋊C₄	—	134	1	no	—
306	C₂²⋊C₄	—	134	2	no	—
307	C₂²⋊C₄	—	134	2	no	—
308	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
309	C₄²	D₄×D₆₇	1	1	yes	characteristic
310	C₄²	Q₈×D₆₇	1	1	yes	characteristic
311	C₄²	#11761628	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	—	134	2	no	—
317	C₂³	—	134	2	no	—
318	C₂³	—	134	2	no	—
319	C₂³	#14524016	1	1	yes	characteristic
320	D₄	—	67	4	no	—
321	D₄	—	134	2	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	—	8	1	no	—
327	C₂×C₄	—	8	1	no	—
328	C₂×C₄	—	8	1	no	—
329	C₂×C₄	—	268	1	no	—
330	C₂×C₄	—	268	1	no	—
331	C₂×C₄	—	268	2	no	—
332	C₂×C₄	—	268	2	no	—
333	C₂×C₄	—	268	2	no	—
334	C₂×C₄	—	268	2	no	—
335	C₂×C₄	—	536	1	no	—
336	C₂×C₄	—	536	1	no	—
337	C₂×C₄	—	536	1	no	—
338	C₂×C₄	—	134	2	no	—
339	C₂×C₄	C₂²⋊C₄×D₆₇	1	1	yes	characteristic
340	C₂×C₄	C₄⋊C₄×D₆₇	1	1	yes	characteristic
341	C₂×C₄	#14524000	1	1	yes	characteristic
342	C₂×C₄	#14524016	1	1	yes	characteristic
343	C₂×C₄	#14524021	1	1	yes	characteristic
344	C₂×C₄	#14524021	1	1	yes	characteristic
345	C₂×C₄	D₈×D₆₇	1	1	yes	characteristic
346	C₂×C₄	SD₁₆×D₆₇	1	1	yes	characteristic
347	C₂×C₄	SD₁₆×D₆₇	1	1	yes	characteristic
348	C₂×C₄	SD₁₆×D₆₇	1	1	yes	characteristic
349	C₂×C₄	#14524062	1	1	yes	characteristic
350	C₂×C₄	#14524066	1	1	yes	characteristic
351	C₂×C₄	#14524070	1	1	yes	characteristic
352	C₂×C₄	#14524075	1	1	yes	characteristic
353	C₈	—	4	2	no	—
354	C₈	—	8	1	no	—
355	C₈	—	536	1	no	—
356	C₈	—	67	4	no	—
357	C₈	—	134	2	no	—
358	C₂²	—	268	2	no	—
359	C₂²	—	268	2	no	—
360	C₂²	—	268	2	no	—
361	C₂²	—	268	2	no	—
362	C₂²	—	268	2	no	—
363	C₂²	—	268	2	no	—
364	C₂²	—	134	4	no	—
365	C₂²	#16863255	1	1	yes	characteristic
366	C₂²	#16863590	1	1	yes	characteristic
367	C₂²	#16863600	1	1	yes	characteristic
368	C₂²	#16863624	1	1	yes	characteristic
369	C₂²	#16863628	1	1	yes	characteristic
370	C₂²	#16863658	1	1	yes	characteristic
371	C₂²	#16863662	1	1	yes	characteristic
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	268	2	no	—
375	C₄	—	16	1	no	—
376	C₄	—	1072	1	no	—
377	C₄	#102×D₆₇	1	1	yes	characteristic
378	C₄	#16863396	1	1	yes	characteristic
379	C₄	#106×D₆₇	1	1	yes	characteristic
380	C₄	#16863433	1	1	yes	characteristic
381	C₄	#16863624	1	1	yes	characteristic
382	C₄	#16863628	1	1	yes	characteristic
383	C₄	#16863675	1	1	yes	characteristic
384	C₄	#16863685	1	1	yes	characteristic
385	C₂	—	268	4	no	—
386	C₂	#22559549	1	1	yes	characteristic
387	C₂	#22559553	1	1	yes	characteristic
388	C₂	#22559583	1	1	yes	characteristic
389	C₂	#22559587	1	1	yes	characteristic
390	C₂	#22560208	1	1	yes	characteristic
391	C₂	#22560233	1	1	yes	characteristic
392	C₂	#22560267	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14524016
commutator	C₄²×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₆₇×#1296	C₂
socle	C₂³×C₆₇	#121
prime radical	C₂²×D₂₆₈	D₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	#1296	D₆₇
hypocenter	C₆₇	#8642
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
2. #22560365	C₂	semidirect
5. C₂×#16863146	C₂	semidirect
6. #22558093	C₂	semidirect
7. C₆₇×#1296	C₂	semidirect
11. #16863461	C₄	semidirect
151. D₂₆₈	#106	semidirect
160. C₆₇⋊C₈	#102	semidirect
203. #1296	D₆₇	semidirect
204. C₆₇	#8642	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863461	2
#22560365	2
#22560210	2
#22560206	2
C₂×#16863146	2
#22558093	2
C₆₇×#1296	2
#8642	67