Subgroups — #30869337

Order 17152.

714 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22570531	C₂	1	1	yes	maximal, characteristic
2	#22569143	C₂	1	1	yes	maximal, characteristic, complemented
3	#22561185	C₂	1	1	yes	maximal, characteristic, complemented
4	#22561038	C₂	1	1	yes	maximal, characteristic
5	#22560854	C₂	1	4	yes	maximal, complemented
6	#22560484	C₂	1	4	yes	maximal, complemented
7	#22560380	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559954	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic
10	#16863953	C₂²	1	1	yes	characteristic
11	#16863750	C₄	1	4	yes	complemented
12	#16863746	C₄	1	1	yes	characteristic, complemented
13	#16863746	C₄	1	1	yes	characteristic, complemented
14	#16863742	C₄	1	1	yes	characteristic, complemented
15	#16863742	C₄	1	1	yes	characteristic, complemented
16	#16863526	—	2	1	no	—
17	#16863526	—	2	1	no	—
18	C₈×Dic₁₃₄	—	2	1	no	—
19	C₈×Dic₁₃₄	—	2	1	no	—
20	C₂×#14523978	C₂²	1	4	yes	—
21	#16863422	C₂²	1	2	yes	—
22	#16863420	C₂²	1	1	yes	characteristic
23	C₂×#14523970	C₂²	1	4	yes	—
24	#16863392	C₂²	1	4	yes	—
25	#16863351	C₂²	1	2	yes	—
26	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
28	#16863157	C₂²	1	4	yes	—
29	#16863150	C₂²	1	2	yes	—
30	#16863150	C₂²	1	2	yes	—
31	C₂×#131×C₆₇	C₂²	1	2	yes	—
32	#532×C₆₇	C₂²	1	1	yes	characteristic
33	#436×C₆₇	—	2	1	no	—
34	#436×C₆₇	—	2	1	no	—
35	C₈×D₄×C₆₇	—	2	1	no	—
36	C₈×D₄×C₆₇	—	2	1	no	—
37	#423×C₆₇	C₂²	1	1	yes	characteristic
38	#408×C₆₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂×#11761612	C₂³	1	2	yes	—
41	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
42	#14524043	C₂×C₄	1	1	yes	characteristic
43	#14524043	C₂×C₄	1	1	yes	characteristic
44	#14524035	C₂×C₄	1	2	yes	—
45	#14524022	—	2	1	no	—
46	#14524022	—	2	1	no	—
47	C₄×Dic₁₃₄	—	2	1	no	—
48	C₄×Dic₁₃₄	—	2	1	no	—
49	#14524002	C₂³	1	2	yes	—
50	C₂×C₄×Dic₆₇	—	2	1	no	—
51	C₂×C₄×Dic₆₇	—	2	1	no	—
52	C₂×C₄×Dic₆₇	C₂³	1	2	yes	—
53	#14523978	—	4	4	no	—
54	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
56	Dic₆₇⋊C₈	—	2	2	no	—
57	Dic₆₇⋊C₈	—	2	2	no	—
58	#14523970	—	4	4	no	—
59	#14523967	C₂×C₄	1	4	yes	—
60	#14523967	C₂×C₄	1	4	yes	—
61	#14523964	C₂×C₄	1	4	yes	—
62	#14523964	C₂×C₄	1	4	yes	—
63	#14523953	—	2	2	no	—
64	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₄×C₆₇⋊C₈	C₂×C₄	1	2	yes	—
67	C₈×Dic₆₇	—	2	2	no	—
68	C₂×#41×C₆₇	C₂³	1	2	yes	—
69	#131×C₆₇	—	4	4	no	—
70	C₂×M₁₆×C₆₇	—	2	2	no	—
71	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
72	C₂²×C₈×C₆₇	—	2	2	no	—
73	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₄⋊Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
76	#127×C₆₇	C₂×C₄	1	1	yes	characteristic
77	#124×C₆₇	C₂×C₄	1	2	yes	—
78	#121×C₆₇	—	2	1	no	—
79	#121×C₆₇	—	2	1	no	—
80	C₄×D₄×C₆₇	—	2	1	no	—
81	C₄×D₄×C₆₇	—	2	1	no	—
82	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₆₇	—	2	1	no	—
84	C₄⋊C₈×C₆₇	—	2	1	no	—
85	C₂²⋊C₈×C₆₇	—	2	2	no	—
86	C₂²⋊C₈×C₆₇	—	2	2	no	—
87	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
88	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
89	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
90	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
91	C₂×Dic₁₃₄	—	2	1	no	—
92	C₂×Dic₁₃₄	—	2	1	no	—
93	C₂²×Dic₆₇	—	2	2	no	—
94	#11761612	—	2	4	no	—
95	C₂×C₆₇⋊C₈	—	2	2	no	—
96	C₂×C₆₇⋊C₈	—	2	2	no	—
97	C₂×C₆₇⋊C₈	—	2	2	no	—
98	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
99	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
100	C₄⋊Dic₆₇	—	2	1	no	—
101	C₄⋊Dic₆₇	—	2	1	no	—
102	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
103	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
104	Dic₆₇⋊C₄	—	2	2	no	—
105	Dic₆₇⋊C₄	—	2	2	no	—
106	C₂²⋊Dic₆₇	—	2	2	no	—
107	C₄×Dic₆₇	—	2	4	no	—
108	C₄×Dic₆₇	—	2	2	no	—
109	C₄×Dic₆₇	—	2	2	no	—
110	C₄×Dic₆₇	—	2	2	no	—
111	C₄×Dic₆₇	—	4	2	no	—
112	#41×C₆₇	—	2	4	no	—
113	#41×C₆₇	—	2	4	no	—
114	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
115	C₂×D₄×C₆₇	—	2	2	no	—
116	C₂×D₄×C₆₇	—	2	1	no	—
117	C₂×D₄×C₆₇	—	2	1	no	—
118	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₆₇	—	2	2	no	—
120	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
121	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
122	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
123	M₁₆×C₆₇	—	2	4	no	—
124	M₁₆×C₆₇	—	4	4	no	—
125	C₂×C₈×C₆₇	—	2	2	no	—
126	C₂×C₈×C₆₇	—	2	2	no	—
127	C₂×C₈×C₆₇	—	2	2	no	—
128	C₂×C₈×C₆₇	—	4	4	no	—
129	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
133	C₄⋊C₄×C₆₇	—	2	1	no	—
134	C₄⋊C₄×C₆₇	—	2	1	no	—
135	C₂²⋊C₄×C₆₇	—	2	2	no	—
136	C₂²⋊C₄×C₆₇	—	2	2	no	—
137	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂³×C₆₇	—	2	2	no	—
142	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
143	Q₈×C₆₇	—	2	4	no	—
144	D₄×C₆₇	—	2	4	no	—
145	D₄×C₆₇	—	4	4	no	—
146	D₄×C₆₇	—	4	2	no	—
147	D₄×C₆₇	—	4	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	2	2	no	—
151	C₂×C₄×C₆₇	—	4	2	no	—
152	C₂×C₄×C₆₇	—	4	2	no	—
153	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
160	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
161	C₂×Dic₆₇	—	2	4	no	—
162	C₂×Dic₆₇	—	2	2	no	—
163	C₂×Dic₆₇	—	2	2	no	—
164	C₂×Dic₆₇	—	4	2	no	—
165	C₂×Dic₆₇	—	4	2	no	—
166	Dic₁₃₄	—	4	2	no	—
167	Dic₁₃₄	—	4	2	no	—
168	C₈×C₆₇	—	2	1	no	—
169	C₈×C₆₇	—	2	1	no	—
170	C₈×C₆₇	—	2	1	no	—
171	C₈×C₆₇	—	2	1	no	—
172	C₈×C₆₇	—	4	2	no	—
173	C₆₇⋊C₈	—	2	2	no	—
174	C₆₇⋊C₈	—	2	2	no	—
175	C₆₇⋊C₈	—	4	2	no	—
176	C₂²×C₆₇	—	2	1	no	—
177	C₂²×C₆₇	—	2	1	no	—
178	C₂²×C₆₇	—	4	2	no	—
179	C₂²×C₆₇	—	4	2	no	—
180	C₂²×C₆₇	—	4	2	no	—
181	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
182	C₂²×C₆₇	#542	1	2	yes	—
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	2	1	no	—
185	C₄×C₆₇	—	4	2	no	—
186	C₄×C₆₇	#443	1	2	yes	—
187	C₄×C₆₇	#444	1	2	yes	—
188	C₄×C₆₇	#520	1	2	yes	—
189	C₄×C₆₇	#535	1	1	yes	characteristic
190	C₄×C₆₇	#536	1	1	yes	characteristic
191	Dic₆₇	—	4	4	no	—
192	Dic₆₇	—	4	2	no	—
193	Dic₆₇	—	4	2	no	—
194	#22234	—	67	1	no	maximal, Sylow
195	C₂×C₆₇	—	2	2	no	—
196	C₂×C₆₇	—	8	2	no	—
197	C₂×C₆₇	#2326	1	1	yes	characteristic
198	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
199	C₂×C₆₇	C₂×#444	1	1	yes	characteristic
200	#3131	—	67	1	no	—
201	#2960	—	67	1	no	—
202	#2931	D₆₇	1	1	yes	characteristic
203	#1994	—	67	1	no	—
204	#1962	—	67	1	no	—
205	#1929	—	67	4	no	—
206	#1866	—	67	4	no	—
207	#1848	—	67	1	no	—
208	#1744	—	67	1	no	—
209	C₆₇	#22234	1	1	yes	characteristic, complemented, Sylow
210	C₂×#131	C₂×D₆₇	1	2	yes	—
211	#533	—	67	1	no	—
212	#532	C₂×D₆₇	1	1	yes	characteristic
213	#488	—	67	4	no	—
214	#487	—	67	1	no	—
215	#487	—	67	1	no	—
216	#486	—	67	1	no	—
217	#486	—	67	1	no	—
218	#446	—	134	1	no	—
219	#446	—	134	1	no	—
220	C₈×Q₈	—	134	1	no	—
221	C₈×Q₈	—	134	1	no	—
222	#436	—	2	1	no	—
223	#436	—	2	1	no	—
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	—	2	1	no	—
226	C₂×#108	—	67	4	no	—
227	#424	—	67	2	no	—
228	#423	—	67	1	no	—
229	#423	C₂×D₆₇	1	1	yes	characteristic
230	C₂×#104	—	67	4	no	—
231	#416	—	67	4	no	—
232	#408	C₂×D₆₇	1	2	yes	—
233	#405	—	67	2	no	—
234	C₂×C₄×C₈	—	67	1	no	—
235	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
236	C₄³	—	67	1	no	—
237	#339	—	67	4	no	—
238	#336	—	67	2	no	—
239	#336	—	67	2	no	—
240	C₂×#41	C₂²×D₆₇	1	2	yes	—
241	#131	—	4	4	no	—
242	C₂×M₁₆	—	2	2	no	—
243	C₂×M₁₆	—	67	2	no	—
244	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	67	2	no	—
247	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
248	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
249	C₄⋊Q₈	—	67	1	no	—
250	C₄⋊Q₈	—	67	1	no	—
251	C₄⋊Q₈	C₄×D₆₇	1	1	yes	characteristic
252	#127	C₄×D₆₇	1	1	yes	characteristic
253	#125	—	67	2	no	—
254	#124	C₄×D₆₇	1	2	yes	—
255	C₂²⋊Q₈	—	134	1	no	—
256	C₂²⋊Q₈	—	134	1	no	—
257	#121	—	2	1	no	—
258	#121	—	2	1	no	—
259	C₄×Q₈	—	134	1	no	—
260	C₄×Q₈	—	134	1	no	—
261	C₄×D₄	—	2	1	no	—
262	C₄×D₄	—	2	1	no	—
263	#117	—	67	2	no	—
264	C₂×C₄²	—	67	2	no	—
265	C₂×C₄²	—	134	1	no	—
266	C₂×C₄²	—	134	1	no	—
267	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
268	#108	—	268	4	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	134	2	no	—
272	C₄⋊C₈	—	134	2	no	—
273	C₄⋊C₈	—	134	1	no	—
274	C₄⋊C₈	—	134	1	no	—
275	#104	—	268	4	no	—
276	#103	—	67	4	no	—
277	#103	—	67	4	no	—
278	#102	—	67	4	no	—
279	#102	—	67	4	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	#97	—	134	2	no	—
283	C₄×C₈	—	67	1	no	—
284	C₄×C₈	—	67	1	no	—
285	C₄×C₈	—	67	2	no	—
286	C₄×C₈	—	134	2	no	—
287	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
288	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
289	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
290	C₄×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
291	#41	—	2	4	no	—
292	#41	—	2	4	no	—
293	C₂×Q₈	—	134	1	no	—
294	C₂×Q₈	—	134	1	no	—
295	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	134	2	no	—
302	C₂²×C₄	#11761628	1	1	yes	characteristic
303	C₂²×C₄	#11761628	1	1	yes	characteristic
304	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
305	M₁₆	—	2	4	no	—
306	M₁₆	—	4	4	no	—
307	M₁₆	—	134	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	4	no	—
312	C₂×C₈	—	67	2	no	—
313	C₂×C₈	—	67	2	no	—
314	C₂×C₈	—	134	2	no	—
315	C₂×C₈	—	134	2	no	—
316	C₂×C₈	—	134	2	no	—
317	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
318	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
319	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
320	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	1	no	—
323	C₄⋊C₄	—	67	2	no	—
324	C₄⋊C₄	—	67	2	no	—
325	C₄⋊C₄	—	134	2	no	—
326	C₄⋊C₄	—	134	2	no	—
327	C₄⋊C₄	—	134	1	no	—
328	C₄⋊C₄	—	134	1	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	2	2	no	—
331	C₂²⋊C₄	—	134	2	no	—
332	C₄²	—	268	2	no	—
333	C₄²	—	134	4	no	—
334	C₄²	—	134	2	no	—
335	C₄²	—	134	2	no	—
336	C₄²	—	134	2	no	—
337	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
341	C₂³	—	2	2	no	—
342	C₂³	C₂×#11761628	1	1	yes	characteristic
343	Q₈	—	2	4	no	—
344	Q₈	—	268	2	no	—
345	Q₈	—	268	2	no	—
346	D₄	—	2	4	no	—
347	D₄	—	4	4	no	—
348	D₄	—	4	2	no	—
349	D₄	—	4	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	268	2	no	—
356	C₂×C₄	—	268	2	no	—
357	C₂×C₄	—	134	4	no	—
358	C₂×C₄	—	134	2	no	—
359	C₂×C₄	—	134	2	no	—
360	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
361	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
362	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
363	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
364	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
366	C₂×C₄	#14524088	1	2	yes	—
367	C₂×C₄	#14524090	1	2	yes	—
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	1	no	—
372	C₈	—	4	2	no	—
373	C₈	—	268	2	no	—
374	C₈	—	134	2	no	—
375	C₈	—	134	2	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
382	C₂²	#16864011	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	2	no	—
386	C₄	—	268	4	no	—
387	C₄	—	268	2	no	—
388	C₄	—	268	2	no	—
389	C₄	#16863511	1	2	yes	—
390	C₄	#16863516	1	2	yes	—
391	C₄	#16863875	1	2	yes	—
392	C₄	#16863963	1	1	yes	characteristic
393	C₄	#16863967	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	—	8	2	no	—
396	C₂	#22562921	1	1	yes	characteristic
397	C₂	C₂×#16863511	1	1	yes	characteristic
398	C₂	C₂×#16863516	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₆₇
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₆₇×#2931	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	#532×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	#2931	D₆₇
hypocenter	C₆₇	#22234
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. #22569143	C₂	semidirect
3. #22561185	C₂	semidirect
5. #22560854	C₂	semidirect
6. #22560484	C₂	semidirect
7. #22560380	C₂	semidirect
8. #22559954	C₂	semidirect
11. #16863750	C₄	semidirect
12. #16863746	C₄	semidirect
13. #16863746	C₄	semidirect
14. #16863742	C₄	semidirect
15. #16863742	C₄	semidirect
209. C₆₇	#22234	semidirect

Maximal subgroups

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

subgroup	index
#22570531	2
#22569143	2
#22561185	2
#22561038	2
#22560854	2
#22560484	2
#22560380	2
#22559954	2
C₆₇×#2931	2
#22234	67