Subgroups — #30839232

Order 17152.

584 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22571547	C₂	1	2	yes	maximal
2	#22570795	C₂	1	1	yes	maximal, characteristic, complemented
3	#22569184	C₂	1	1	yes	maximal, characteristic
4	#22559764	C₂	1	2	yes	maximal, complemented
5	#22559757	C₂	1	2	yes	maximal, complemented
6	#22559604	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559599	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559580	C₂	1	1	yes	maximal, characteristic, complemented
9	#22559575	C₂	1	1	yes	maximal, characteristic, complemented
10	#22558907	C₂	1	2	yes	maximal, complemented
11	C₂×#335×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863953	C₂²	1	2	yes	—
13	#16863930	C₂²	1	1	yes	characteristic
14	#16863801	C₂²	1	1	yes	characteristic
15	#16863776	C₂²	1	1	yes	characteristic
16	#16863747	C₂²	1	2	yes	—
17	#16863704	—	2	2	no	—
18	#16863682	C₂²	1	2	yes	—
19	#16863677	C₂²	1	2	yes	—
20	#16863637	—	2	2	no	—
21	#16863637	—	2	1	no	—
22	#16863637	—	2	1	no	—
23	#16863625	—	2	2	no	—
24	#16863619	—	2	2	no	—
25	#16863607	C₂²	1	2	yes	—
26	#16863602	C₂²	1	2	yes	—
27	#16863526	C₂²	1	1	yes	characteristic
28	C₈×Dic₁₃₄	C₂²	1	1	yes	characteristic
29	C₄×Dic₂₆₈	—	2	1	no	—
30	C₄×Dic₂₆₈	—	2	1	no	—
31	#16863475	C₂²	1	1	yes	characteristic
32	#16863467	—	2	1	no	—
33	C₈×D₂₆₈	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₆₇	—	2	1	no	—
35	#16863455	—	2	1	no	—
36	#16863453	C₂²	1	1	yes	characteristic
37	#16863350	—	2	1	no	—
38	#16863143	C₂²	1	2	yes	—
39	#16863143	C₂²	1	2	yes	—
40	#16863141	C₂²	1	2	yes	—
41	#16863141	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₆₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
44	#335×C₆₇	C₂²	1	2	yes	—
45	#335×C₆₇	C₂²	1	1	yes	characteristic
46	#335×C₆₇	C₂²	1	1	yes	characteristic
47	C₂×Dic₂₆₈	—	2	2	no	—
48	C₂×Dic₂₆₈	—	2	1	no	—
49	C₂×Dic₂₆₈	—	2	1	no	—
50	C₂×#11761617	—	2	2	no	—
51	C₂×#11761611	—	2	1	no	—
52	C₂×C₈×D₆₇	—	2	1	no	—
53	#14524043	C₂³	1	2	yes	—
54	#14524043	C₂³	1	2	yes	—
55	#14524037	—	2	1	no	—
56	#14524035	—	2	2	no	—
57	#14524035	D₄	1	1	yes	characteristic
58	#14524031	D₄	1	1	yes	characteristic
59	#14524026	—	2	1	no	—
60	#14524022	—	2	2	no	—
61	#14524022	—	2	2	no	—
62	#14524022	D₄	1	1	yes	characteristic
63	#14524017	D₄	1	1	yes	characteristic
64	C₄×Dic₁₃₄	—	2	2	no	—
65	C₄×Dic₁₃₄	—	2	2	no	—
66	C₄×Dic₁₃₄	C₂³	1	1	yes	characteristic
67	C₄×D₂₆₈	C₂³	1	1	yes	characteristic
68	C₄×C₂²⋊D₆₇	—	2	1	no	—
69	#14524002	—	2	2	no	—
70	#14524000	—	2	1	no	—
71	#14523977	—	2	2	no	—
72	#14523977	—	2	1	no	—
73	#14523977	—	2	1	no	—
74	#14523975	—	2	2	no	—
75	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₆₇⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₆₇⋊C₈	—	2	1	no	—
78	Dic₆₇⋊C₈	—	2	1	no	—
79	#14523968	—	2	2	no	—
80	#14523968	—	2	2	no	—
81	#14523968	—	2	2	no	—
82	#14523968	—	2	2	no	—
83	#14523968	—	2	2	no	—
84	#14523965	—	2	2	no	—
85	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
86	(C₂×D₆₇)⋊C₈	—	2	1	no	—
87	(C₂×D₆₇)⋊C₈	—	2	1	no	—
88	#14523954	—	2	1	no	—
89	#14523953	—	2	1	no	—
90	C₈×Dic₆₇	—	2	1	no	—
91	C₂²×C₈×C₆₇	—	2	2	no	—
92	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₆₇	—	2	2	no	—
96	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
97	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
98	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₆₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
102	C₂×Dic₁₃₄	—	2	2	no	—
103	C₂×Dic₁₃₄	—	2	2	no	—
104	C₂×Dic₁₃₄	C₂×D₄	1	1	yes	characteristic
105	C₂×D₂₆₈	C₂×D₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₆₇	—	2	1	no	—
107	C₂×C₄×D₆₇	—	2	1	no	—
108	Dic₂₆₈	—	4	2	no	—
109	Dic₂₆₈	—	4	2	no	—
110	Dic₂₆₈	—	8	2	no	—
111	#11761617	—	8	2	no	—
112	#11761611	—	4	2	no	—
113	C₂×C₆₇⋊C₈	—	2	1	no	—
114	C₂×C₆₇⋊C₈	—	2	1	no	—
115	C₈×D₆₇	—	4	2	no	—
116	C₄⋊Dic₆₇	—	2	2	no	—
117	C₄⋊Dic₆₇	—	2	2	no	—
118	C₄⋊Dic₆₇	—	2	2	no	—
119	C₄⋊Dic₆₇	—	2	2	no	—
120	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
121	C₄⋊Dic₆₇	C₂×D₄	1	1	yes	characteristic
122	Dic₆₇⋊C₄	—	2	1	no	—
123	Dic₆₇⋊C₄	—	2	1	no	—
124	Dic₆₇⋊C₄	—	2	1	no	—
125	Dic₆₇⋊C₄	—	2	1	no	—
126	Dic₆₇⋊C₄	—	4	2	no	—
127	Dic₆₇⋊C₄	—	4	2	no	—
128	C₂²⋊Dic₆₇	—	2	1	no	—
129	C₂²⋊Dic₆₇	—	4	2	no	—
130	(C₂×D₆₇)⋊C₄	—	2	1	no	—
131	(C₂×D₆₇)⋊C₄	—	2	1	no	—
132	(C₂×D₆₇)⋊C₄	—	2	1	no	—
133	(C₂×D₆₇)⋊C₄	—	2	1	no	—
134	C₄×Dic₆₇	—	2	1	no	—
135	C₄×Dic₆₇	—	4	2	no	—
136	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
139	C₂×C₈×C₆₇	—	2	2	no	—
140	C₂×C₈×C₆₇	—	2	2	no	—
141	C₂×C₈×C₆₇	—	2	2	no	—
142	C₂×C₈×C₆₇	—	4	1	no	—
143	C₂×C₈×C₆₇	—	8	2	no	—
144	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₆₇	#41	1	1	yes	characteristic
151	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
152	C₂³×C₆₇	#121	1	1	yes	characteristic
153	C₂²×D₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	2	2	no	—
155	C₂×C₄×C₆₇	—	2	1	no	—
156	C₂×C₄×C₆₇	—	2	1	no	—
157	C₂×C₄×C₆₇	—	2	1	no	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
165	C₂²⋊D₆₇	—	4	2	no	—
166	C₂×Dic₆₇	—	2	1	no	—
167	C₂×Dic₆₇	—	2	1	no	—
168	C₂×Dic₆₇	—	2	1	no	—
169	C₂×Dic₆₇	—	4	2	no	—
170	C₂×Dic₆₇	—	4	2	no	—
171	D₂₆₈	—	2	1	no	—
172	D₂₆₈	—	2	1	no	—
173	C₄×D₆₇	—	4	1	no	—
174	C₄×D₆₇	—	4	1	no	—
175	Dic₁₃₄	—	2	1	no	—
176	Dic₁₃₄	—	2	1	no	—
177	Dic₁₃₄	—	4	2	no	—
178	Dic₁₃₄	—	4	2	no	—
179	Dic₁₃₄	—	4	2	no	—
180	Dic₁₃₄	—	4	2	no	—
181	C₈×C₆₇	—	2	1	no	—
182	C₈×C₆₇	—	2	1	no	—
183	C₈×C₆₇	—	2	1	no	—
184	C₈×C₆₇	—	4	2	no	—
185	C₈×C₆₇	—	4	2	no	—
186	C₈×C₆₇	#135	1	2	yes	—
187	C₆₇⋊C₈	—	4	1	no	—
188	C₆₇⋊C₈	—	4	1	no	—
189	C₂²×C₆₇	—	2	1	no	—
190	C₂²×C₆₇	—	2	1	no	—
191	C₂²×C₆₇	#473	1	2	yes	—
192	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
193	C₂×D₆₇	—	4	1	no	—
194	C₂×D₆₇	—	4	1	no	—
195	C₂×D₆₇	—	4	1	no	—
196	C₄×C₆₇	—	2	1	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	2	1	no	—
199	C₄×C₆₇	—	2	1	no	—
200	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
201	C₄×C₆₇	#575	1	1	yes	characteristic
202	C₄×C₆₇	#576	1	1	yes	characteristic
203	C₄×C₆₇	#578	1	1	yes	characteristic
204	Dic₆₇	—	4	1	no	—
205	Dic₆₇	—	4	1	no	—
206	Dic₆₇	—	4	1	no	—
207	Dic₆₇	—	8	2	no	—
208	Dic₆₇	—	8	2	no	—
209	#19223	—	67	1	no	maximal, Sylow
210	C₂×C₆₇	—	2	2	no	—
211	C₂×C₆₇	#3035	1	1	yes	characteristic
212	C₂×C₆₇	#3061	1	1	yes	characteristic
213	C₂×C₆₇	C₂×#473	1	1	yes	characteristic
214	D₆₇	—	8	1	no	—
215	#3248	—	67	2	no	—
216	#3170	—	67	1	no	—
217	#2966	—	67	1	no	—
218	#1700	—	67	2	no	—
219	#1699	—	67	2	no	—
220	#1674	—	67	1	no	—
221	#1673	—	67	1	no	—
222	#1670	—	67	1	no	—
223	#1669	—	67	1	no	—
224	C₂×#335	D₆₇	1	1	yes	characteristic, complemented
225	#1552	—	67	2	no	—
226	C₆₇	#19223	1	1	yes	characteristic, complemented, Sylow
227	#533	—	67	2	no	—
228	#529	—	67	1	no	—
229	#500	—	67	1	no	—
230	#494	—	67	1	no	—
231	#487	—	67	2	no	—
232	#479	—	134	2	no	—
233	#475	—	67	2	no	—
234	#474	—	67	2	no	—
235	#467	—	134	2	no	—
236	#467	—	134	1	no	—
237	#467	—	134	1	no	—
238	#465	—	134	2	no	—
239	#464	—	134	2	no	—
240	#462	—	67	2	no	—
241	#461	—	67	2	no	—
242	#446	—	67	1	no	—
243	C₈×Q₈	—	67	1	no	—
244	C₄×Q₁₆	—	134	1	no	—
245	C₄×Q₁₆	—	134	1	no	—
246	#436	—	67	1	no	—
247	#435	—	134	1	no	—
248	C₈×D₄	—	67	1	no	—
249	C₈×D₄	—	134	1	no	—
250	#433	—	134	1	no	—
251	#432	—	67	1	no	—
252	C₂×C₄⋊C₈	C₂×D₆₇	1	2	yes	—
253	#405	—	134	1	no	—
254	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
255	#335	C₂×D₆₇	1	1	yes	characteristic
256	#335	C₂×D₆₇	1	1	yes	characteristic
257	#335	C₂×D₆₇	1	2	yes	—
258	#332	—	67	2	no	—
259	#332	—	67	2	no	—
260	#332	—	67	2	no	—
261	#332	—	67	2	no	—
262	C₂×Q₁₆	—	134	2	no	—
263	C₂×Q₁₆	—	134	1	no	—
264	C₂×Q₁₆	—	134	1	no	—
265	C₂×SD₁₆	—	134	2	no	—
266	C₂×M₁₆	—	134	1	no	—
267	C₂²×C₈	—	2	2	no	—
268	C₂²×C₈	—	134	1	no	—
269	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
270	C₂²×C₈	D₂₆₈	1	1	yes	characteristic
271	C₄⋊Q₈	—	67	2	no	—
272	C₄⋊Q₈	—	67	2	no	—
273	#126	—	134	1	no	—
274	#125	—	67	1	no	—
275	#125	—	134	2	no	—
276	#124	—	67	1	no	—
277	#123	—	134	1	no	—
278	C₂²⋊Q₈	—	67	1	no	—
279	C₂²⋊Q₈	—	134	2	no	—
280	C₂²⋊Q₈	—	134	2	no	—
281	#121	—	67	1	no	—
282	C₄×Q₈	—	67	1	no	—
283	C₄×Q₈	—	134	2	no	—
284	C₄×Q₈	—	134	2	no	—
285	C₄×D₄	—	67	1	no	—
286	C₄×D₄	—	134	1	no	—
287	#117	—	134	2	no	—
288	#117	—	134	1	no	—
289	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
290	#107	—	134	2	no	—
291	#107	—	134	1	no	—
292	#107	—	134	1	no	—
293	#106	—	134	2	no	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	67	1	no	—
296	C₄⋊C₈	—	67	1	no	—
297	C₄⋊C₈	—	134	1	no	—
298	C₄⋊C₈	—	134	1	no	—
299	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
300	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
301	#103	—	134	2	no	—
302	#103	—	134	2	no	—
303	#103	—	134	2	no	—
304	#103	—	134	2	no	—
305	#103	—	134	2	no	—
306	#102	—	134	2	no	—
307	C₂²⋊C₈	—	134	1	no	—
308	C₂²⋊C₈	—	134	1	no	—
309	C₂²⋊C₈	—	134	1	no	—
310	#97	—	134	1	no	—
311	#97	—	134	1	no	—
312	C₄×C₈	—	134	1	no	—
313	C₄×C₈	D₂₆₈	1	1	yes	characteristic
314	C₄×C₈	D₂₆₈	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
317	C₂×Q₈	—	67	1	no	—
318	C₂×Q₈	—	134	2	no	—
319	C₂×Q₈	—	134	2	no	—
320	C₂×D₄	—	67	1	no	—
321	C₂×D₄	—	134	1	no	—
322	C₂²×C₄	—	134	1	no	—
323	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
325	C₂²×C₄	#11761629	1	1	yes	characteristic
326	Q₁₆	—	268	2	no	—
327	Q₁₆	—	268	2	no	—
328	Q₁₆	—	536	2	no	—
329	SD₁₆	—	536	2	no	—
330	M₁₆	—	268	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	8	2	no	—
336	C₂×C₈	—	268	2	no	—
337	C₂×C₈	—	134	1	no	—
338	C₂×C₈	—	134	1	no	—
339	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
340	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
341	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
342	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
343	C₄⋊C₄	—	268	2	no	—
344	C₄⋊C₄	—	268	2	no	—
345	C₄⋊C₄	—	67	1	no	—
346	C₄⋊C₄	—	67	1	no	—
347	C₄⋊C₄	—	134	2	no	—
348	C₄⋊C₄	—	134	2	no	—
349	C₄⋊C₄	—	134	2	no	—
350	C₄⋊C₄	—	134	2	no	—
351	C₄⋊C₄	—	134	1	no	—
352	C₄⋊C₄	—	134	1	no	—
353	C₄⋊C₄	—	134	1	no	—
354	C₄⋊C₄	—	134	1	no	—
355	C₂²⋊C₄	—	268	2	no	—
356	C₂²⋊C₄	—	134	1	no	—
357	C₂²⋊C₄	—	134	1	no	—
358	C₂²⋊C₄	—	134	1	no	—
359	C₂²⋊C₄	—	134	1	no	—
360	C₂²⋊C₄	—	134	1	no	—
361	C₄²	—	268	2	no	—
362	C₄²	—	134	1	no	—
363	C₄²	D₄×D₆₇	1	1	yes	characteristic
364	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
365	C₄²	#11761629	1	1	yes	characteristic
366	C₄²	C₂³×D₆₇	1	1	yes	characteristic
367	C₂³	—	134	1	no	—
368	C₂³	#14524018	1	1	yes	characteristic
369	Q₈	—	268	2	no	—
370	Q₈	—	268	2	no	—
371	Q₈	—	268	2	no	—
372	Q₈	—	268	2	no	—
373	Q₈	—	134	1	no	—
374	Q₈	—	134	1	no	—
375	D₄	—	268	2	no	—
376	D₄	—	134	1	no	—
377	D₄	—	134	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	268	1	no	—
384	C₂×C₄	—	268	1	no	—
385	C₂×C₄	—	268	2	no	—
386	C₂×C₄	—	268	2	no	—
387	C₂×C₄	—	134	1	no	—
388	C₂×C₄	—	134	1	no	—
389	C₂×C₄	—	134	1	no	—
390	C₂×C₄	#14524018	1	1	yes	characteristic
391	C₂×C₄	#14524018	1	1	yes	characteristic
392	C₂×C₄	#14524018	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
394	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
395	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	2	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	—	268	1	no	—
402	C₈	—	268	1	no	—
403	C₈	#14524065	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	268	1	no	—
407	C₂²	—	268	1	no	—
408	C₂²	—	268	1	no	—
409	C₂²	#16863672	1	2	yes	—
410	C₂²	C₂×#14524018	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	268	1	no	—
416	C₄	—	268	1	no	—
417	C₄	—	268	1	no	—
418	C₄	—	536	2	no	—
419	C₄	—	536	2	no	—
420	C₄	C₂×#14524065	1	1	yes	characteristic
421	C₄	#16864196	1	1	yes	characteristic
422	C₄	#16864197	1	1	yes	characteristic
423	C₄	#16864209	1	1	yes	characteristic
424	C₂	—	2	2	no	—
425	C₂	—	536	1	no	—
426	C₂	#22569666	1	1	yes	characteristic
427	C₂	#22569881	1	1	yes	characteristic
428	C₂	C₂×#16863672	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14524018
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#335×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#121
prime radical	#14524017	D₄
hypercenter	C₂×#335	D₆₇
hypocenter	C₆₇	#19223
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#335

Complements

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

N	H ≅ G/N	type
2. #22570795	C₂	semidirect
4. #22559764	C₂	semidirect
5. #22559757	C₂	semidirect
6. #22559604	C₂	semidirect
7. #22559599	C₂	semidirect
8. #22559580	C₂	semidirect
9. #22559575	C₂	semidirect
10. #22558907	C₂	semidirect
11. C₂×#335×C₆₇	C₂	semidirect
224. C₂×#335	D₆₇	semidirect
226. C₆₇	#19223	semidirect

Maximal subgroups

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

subgroup	index
#22571547	2
#22570795	2
#22569184	2
#22559764	2
#22559757	2
#22559604	2
#22559599	2
#22559580	2
#22559575	2
#22558907	2
C₂×#335×C₆₇	2
#19223	67