Subgroups — #31009083

Order 17152.

648 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573310	C₂	1	2	yes	maximal, complemented
2	#443×D₆₇	C₂	1	1	yes	maximal, characteristic
3	#22562052	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562051	C₂	1	1	yes	maximal, characteristic, complemented
5	#22562050	C₂	1	1	yes	maximal, characteristic, complemented
6	#22562044	C₂	1	2	yes	maximal, complemented
7	#22562043	C₂	1	2	yes	maximal, complemented
8	#364×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#22561835	C₂	1	2	yes	maximal, complemented
10	#22561802	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#2171	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₆₇	C₄	1	1	yes	characteristic
13	#131×D₆₇	C₂²	1	2	yes	—
14	#16863814	—	2	2	no	—
15	#16863814	C₂²	1	2	yes	complemented
16	#16863813	C₂²	1	2	yes	complemented
17	#16863812	—	2	2	no	—
18	#16863812	C₂²	1	2	yes	complemented
19	C₂×#14523982	—	2	2	no	—
20	C₂×#14523982	C₂²	1	1	yes	characteristic
21	C₂×#14523982	C₂²	1	1	yes	characteristic
22	M₃₂×D₆₇	—	2	2	no	—
23	M₃₂×D₆₇	C₂²	1	2	yes	—
24	#16863514	C₂²	1	1	yes	characteristic
25	#16863513	C₄	1	1	yes	characteristic
26	#16863512	C₄	1	1	yes	characteristic
27	#16863511	C₂²	1	2	yes	—
28	#16863510	C₄	1	2	yes	—
29	#108×D₆₇	C₄	1	1	yes	characteristic
30	#104×D₆₇	C₄	1	2	yes	—
31	C₄×C₈×D₆₇	C₂²	1	1	yes	characteristic
32	#16863217	C₂²	1	1	yes	characteristic, complemented
33	#16863216	C₂²	1	2	yes	complemented
34	#16863181	C₂²	1	2	yes	complemented
35	#16863180	C₂²	1	2	yes	complemented
36	#16863179	C₂²	1	2	yes	complemented
37	#16863172	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₆₇	C₂²	1	1	yes	characteristic, complemented
40	#504×C₆₇	C₂²	1	2	yes	complemented
41	#443×C₆₇	C₂²	1	1	yes	characteristic
42	#364×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#350×C₆₇	C₂²	1	2	yes	complemented
44	#346×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	#41×D₆₇	C₂×C₄	1	2	yes	—
46	#14524066	C₈	1	1	yes	characteristic
47	#14524065	C₂×C₄	1	1	yes	characteristic
48	#14524064	C₈	1	2	yes	—
49	#14524063	C₂×C₄	1	2	yes	—
50	#14524062	C₈	1	1	yes	characteristic
51	Q₁₆×D₆₇	C₈	1	1	yes	characteristic
52	SD₁₆×D₆₇	C₈	1	2	yes	—
53	D₈×D₆₇	C₈	1	1	yes	characteristic
54	#14524051	—	2	2	no	—
55	#14524051	C₂×C₄	1	2	yes	—
56	#14524050	C₂×C₄	1	2	yes	—
57	#14524049	—	2	2	no	—
58	#14524049	C₂³	1	2	yes	—
59	M₁₆×D₆₇	—	2	2	no	—
60	M₁₆×D₆₇	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₆₇	—	2	2	no	—
62	C₂×C₈×D₆₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₆₇	C₂³	1	1	yes	characteristic
64	C₄²×D₆₇	C₂×C₄	1	1	yes	characteristic
65	#14523983	—	2	2	no	—
66	#14523983	C₂³	1	2	yes	—
67	#14523982	—	2	2	no	—
68	#14523982	—	2	1	no	—
69	#14523982	—	2	1	no	—
70	#14523982	—	2	2	no	—
71	#14523982	—	2	2	no	—
72	#14523982	D₄	1	2	yes	—
73	#14523982	D₄	1	2	yes	—
74	C₂×C₆₇⋊C₁₆	—	2	2	no	—
75	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
76	C₂×C₆₇⋊C₁₆	C₂³	1	1	yes	characteristic
77	C₁₆×D₆₇	—	2	2	no	—
78	C₁₆×D₆₇	—	2	2	no	—
79	C₁₆×D₆₇	—	2	2	no	—
80	#14523979	C₂×C₄	1	1	yes	characteristic
81	#14523978	C₂×C₄	1	2	yes	—
82	#14523971	C₂×C₄	1	2	yes	—
83	#14523970	C₂×C₄	1	2	yes	—
84	#14523969	C₂×C₄	1	2	yes	—
85	C₄×C₆₇⋊C₈	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₆₇	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₆₇	C₂³	1	1	yes	characteristic
88	#135×C₆₇	C₂×C₄	1	1	yes	characteristic
89	#131×C₆₇	C₂³	1	2	yes	—
90	M₃₂×C₆₇	—	2	2	no	—
91	M₃₂×C₆₇	C₂³	1	2	yes	—
92	C₂×C₁₆×C₆₇	—	2	2	no	—
93	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₆₇	C₂³	1	1	yes	characteristic
95	#108×C₆₇	C₂×C₄	1	1	yes	characteristic
96	#104×C₆₇	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
98	#11761629	C₂×C₈	1	2	yes	—
99	#11761628	—	2	2	no	—
100	#11761628	C₂²×C₄	1	2	yes	—
101	#11761627	—	2	2	no	—
102	#11761627	C₂×C₈	1	2	yes	—
103	Q₈×D₆₇	C₂×C₈	1	2	yes	—
104	D₄×D₆₇	—	2	2	no	—
105	D₄×D₆₇	C₂×C₈	1	2	yes	—
106	C₂×C₄×D₆₇	—	2	2	no	—
107	C₂×C₄×D₆₇	—	2	1	no	—
108	C₂×C₄×D₆₇	C₂²×C₄	1	1	yes	characteristic
109	Dic₂₆₈	C₂×C₈	1	1	yes	characteristic
110	#11761618	C₂×C₈	1	2	yes	—
111	#11761617	C₂×C₈	1	2	yes	—
112	#11761616	C₂×C₈	1	2	yes	—
113	#11761615	C₂×C₈	1	2	yes	—
114	D₅₃₆	C₂×C₈	1	1	yes	characteristic
115	#11761613	C₂×C₈	1	2	yes	—
116	#11761612	—	2	2	no	—
117	#11761612	C₂²×C₄	1	2	yes	—
118	#11761611	—	2	2	no	—
119	#11761611	—	2	2	no	—
120	#11761611	—	2	2	no	—
121	C₂×C₆₇⋊C₈	—	2	2	no	—
122	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₆₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
124	C₈×D₆₇	—	2	2	no	—
125	C₈×D₆₇	—	2	2	no	—
126	C₈×D₆₇	—	2	2	no	—
127	C₈×D₆₇	C₂×C₈	1	1	yes	characteristic
128	C₈×D₆₇	C₂×C₈	1	1	yes	characteristic
129	C₈×D₆₇	C₂×C₈	1	1	yes	characteristic
130	C₈×D₆₇	C₂×C₈	1	1	yes	characteristic
131	C₈×D₆₇	C₂×D₄	1	1	yes	characteristic
132	C₈×D₆₇	C₂×D₄	1	1	yes	characteristic
133	C₈×D₆₇	#41	1	1	yes	characteristic
134	C₈×D₆₇	#41	1	1	yes	characteristic
135	C₄×Dic₆₇	—	2	1	no	—
136	C₄×Dic₆₇	C₂²×C₄	1	1	yes	characteristic
137	C₆₇⋊C₁₆	—	2	2	no	—
138	C₆₇⋊C₁₆	—	2	1	no	—
139	C₆₇⋊C₁₆	C₂×D₄	1	2	yes	—
140	#41×C₆₇	C₂²×C₄	1	2	yes	—
141	Q₁₆×C₆₇	C₂×C₈	1	1	yes	characteristic
142	SD₁₆×C₆₇	C₂×C₈	1	2	yes	—
143	D₈×C₆₇	C₂×C₈	1	1	yes	characteristic
144	M₁₆×C₆₇	—	2	2	no	—
145	M₁₆×C₆₇	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₆₇	—	2	2	no	—
147	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
149	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
150	C₁₆×C₆₇	—	2	2	no	—
151	C₁₆×C₆₇	—	2	1	no	—
152	C₁₆×C₆₇	C₂×D₄	1	2	yes	—
153	C₂²×D₆₇	—	2	2	no	—
154	C₂²×D₆₇	#131	1	1	yes	characteristic
155	Q₈×C₆₇	C₂²×C₈	1	2	yes	—
156	D₄×C₆₇	—	2	2	no	—
157	D₄×C₆₇	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₆₇	—	2	2	no	—
159	C₂×C₄×C₆₇	—	2	1	no	—
160	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
161	C₂²⋊D₆₇	—	2	2	no	—
162	C₂²⋊D₆₇	—	2	2	no	—
163	C₂²⋊D₆₇	—	2	2	no	—
164	C₂×Dic₆₇	—	2	1	no	—
165	C₂×Dic₆₇	—	2	2	no	—
166	C₂×Dic₆₇	#131	1	1	yes	characteristic
167	D₂₆₈	—	2	2	no	—
168	D₂₆₈	C₂²×C₈	1	2	yes	—
169	C₄×D₆₇	—	2	2	no	—
170	C₄×D₆₇	—	2	2	no	—
171	C₄×D₆₇	—	2	2	no	—
172	C₄×D₆₇	—	4	2	no	—
173	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
174	C₄×D₆₇	C₄×D₄	1	1	yes	characteristic
175	C₄×D₆₇	C₂²×C₈	1	1	yes	characteristic
176	C₄×D₆₇	C₂²×C₈	1	1	yes	characteristic
177	Dic₁₃₄	—	2	2	no	—
178	Dic₁₃₄	C₂²×C₈	1	2	yes	—
179	C₈×C₆₇	—	2	2	no	—
180	C₈×C₆₇	C₂²×C₈	1	1	yes	characteristic
181	C₈×C₆₇	C₂²×C₈	1	1	yes	characteristic
182	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
184	C₆₇⋊C₈	—	2	2	no	—
185	C₆₇⋊C₈	C₄×D₄	1	1	yes	characteristic
186	C₆₇⋊C₈	C₄×D₄	1	1	yes	characteristic
187	C₆₇⋊C₈	C₂²×C₈	1	1	yes	characteristic
188	C₆₇⋊C₈	C₂²×C₈	1	1	yes	characteristic
189	C₂²×C₆₇	—	2	2	no	—
190	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
191	C₂×D₆₇	—	2	2	no	—
192	C₂×D₆₇	—	4	1	no	—
193	C₂×D₆₇	—	8	2	no	—
194	C₂×D₆₇	C₈×D₄	1	1	yes	characteristic
195	C₂×D₆₇	C₈×D₄	1	1	yes	characteristic
196	C₄×C₆₇	—	2	2	no	—
197	C₄×C₆₇	—	4	1	no	—
198	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₆₇	C₂³×C₈	1	1	yes	characteristic
200	Dic₆₇	—	2	2	no	—
201	Dic₆₇	—	2	2	no	—
202	Dic₆₇	C₈×D₄	1	1	yes	characteristic
203	Dic₆₇	C₈×D₄	1	1	yes	characteristic
204	#33443	—	67	1	no	maximal, Sylow
205	C₂×C₆₇	—	2	1	no	—
206	C₂×C₆₇	—	4	2	no	—
207	C₂×C₆₇	C₂×C₈×D₄	1	1	yes	characteristic
208	D₆₇	—	2	1	no	—
209	D₆₇	—	2	1	no	—
210	D₆₇	—	4	2	no	—
211	#3407	—	67	2	no	—
212	C₂×#443	—	67	1	no	—
213	#2171	—	67	1	no	—
214	#2171	—	67	1	no	—
215	#2171	—	67	1	no	—
216	#2171	D₆₇	1	1	yes	characteristic, complemented
217	#2170	—	67	2	no	—
218	#2170	—	67	2	no	—
219	C₂×#364	—	67	1	no	—
220	#2117	—	67	2	no	—
221	C₄×M₃₂	—	67	1	no	—
222	C₆₇	#33443	1	1	yes	characteristic, complemented, Sylow
223	C₂×#135	—	67	1	no	—
224	C₂×#131	—	67	2	no	—
225	#504	—	67	2	no	—
226	#504	—	67	2	no	—
227	#504	—	67	2	no	—
228	#504	—	134	2	no	—
229	#504	—	134	2	no	—
230	#504	C₂×D₆₇	1	2	yes	complemented
231	C₂×M₃₂	—	67	1	no	—
232	C₂×M₃₂	—	67	1	no	—
233	C₂×M₃₂	—	67	2	no	—
234	C₂×M₃₂	—	134	2	no	—
235	C₂×M₃₂	—	134	2	no	—
236	#443	—	67	1	no	—
237	#443	—	67	2	no	—
238	#443	—	67	1	no	—
239	#443	—	67	2	no	—
240	#443	—	67	1	no	—
241	#443	C₂×D₆₇	1	1	yes	characteristic
242	C₂×#108	—	67	1	no	—
243	C₂×#104	—	67	2	no	—
244	C₂×C₄×C₈	—	67	1	no	—
245	#364	—	67	2	no	—
246	#364	—	67	1	no	—
247	#364	C₂×D₆₇	1	1	yes	characteristic, complemented
248	#350	—	67	2	no	—
249	#350	—	67	2	no	—
250	#350	—	67	2	no	—
251	#350	C₂×D₆₇	1	2	yes	complemented
252	#346	—	67	1	no	—
253	#346	C₂×D₆₇	1	1	yes	characteristic, complemented
254	C₄×C₁₆	—	67	1	no	—
255	C₄×C₁₆	—	67	1	no	—
256	C₂×#41	—	67	2	no	—
257	#135	—	67	2	no	—
258	#135	—	67	1	no	—
259	#135	—	67	2	no	—
260	#135	—	67	1	no	—
261	#135	—	67	1	no	—
262	#135	C₄×D₆₇	1	1	yes	characteristic
263	C₂×Q₁₆	—	67	1	no	—
264	C₂×SD₁₆	—	67	2	no	—
265	C₂×D₈	—	67	1	no	—
266	#131	—	67	2	no	—
267	#131	—	67	2	no	—
268	#131	—	67	2	no	—
269	#131	—	134	2	no	—
270	#131	—	134	2	no	—
271	#131	C₂²×D₆₇	1	2	yes	—
272	C₂×M₁₆	—	67	2	no	—
273	C₂×M₁₆	—	134	2	no	—
274	C₂²×C₈	—	67	1	no	—
275	C₂²×C₈	—	67	1	no	—
276	C₂²×C₈	—	134	2	no	—
277	C₂×C₄²	—	67	1	no	—
278	M₃₂	—	2	2	no	—
279	M₃₂	—	67	2	no	—
280	M₃₂	—	67	2	no	—
281	M₃₂	—	67	2	no	—
282	M₃₂	—	134	2	no	—
283	M₃₂	—	134	1	no	—
284	M₃₂	—	134	1	no	—
285	M₃₂	—	134	2	no	—
286	M₃₂	—	134	2	no	—
287	M₃₂	—	134	2	no	—
288	M₃₂	C₂²×D₆₇	1	2	yes	—
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	67	1	no	—
291	C₂×C₁₆	—	67	1	no	—
292	C₂×C₁₆	—	134	2	no	—
293	C₂×C₁₆	—	134	2	no	—
294	C₂×C₁₆	—	134	2	no	—
295	C₂×C₁₆	—	134	2	no	—
296	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₆₇	1	1	yes	characteristic
298	#108	—	67	2	no	—
299	#108	—	67	1	no	—
300	#108	C₄×D₆₇	1	1	yes	characteristic
301	#104	—	67	2	no	—
302	#104	—	67	2	no	—
303	#104	—	67	2	no	—
304	#104	C₄×D₆₇	1	2	yes	—
305	C₄×C₈	—	67	1	no	—
306	C₄×C₈	—	67	1	no	—
307	C₄×C₈	—	67	1	no	—
308	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
309	#41	—	67	2	no	—
310	#41	—	67	2	no	—
311	#41	—	67	2	no	—
312	#41	—	134	2	no	—
313	#41	—	134	2	no	—
314	#41	C₂×C₄×D₆₇	1	2	yes	—
315	C₂×Q₈	—	67	2	no	—
316	C₂×D₄	—	67	2	no	—
317	C₂×D₄	—	134	2	no	—
318	C₂²×C₄	—	67	1	no	—
319	C₂²×C₄	—	134	1	no	—
320	C₂²×C₄	—	134	2	no	—
321	Q₁₆	—	67	2	no	—
322	Q₁₆	—	67	1	no	—
323	Q₁₆	C₈×D₆₇	1	1	yes	characteristic
324	SD₁₆	—	67	2	no	—
325	SD₁₆	—	67	2	no	—
326	SD₁₆	—	67	2	no	—
327	SD₁₆	C₈×D₆₇	1	2	yes	—
328	D₈	—	67	2	no	—
329	D₈	—	67	1	no	—
330	D₈	C₈×D₆₇	1	1	yes	characteristic
331	M₁₆	—	2	2	no	—
332	M₁₆	—	67	2	no	—
333	M₁₆	—	134	2	no	—
334	M₁₆	—	134	2	no	—
335	M₁₆	—	134	2	no	—
336	M₁₆	—	134	2	no	—
337	M₁₆	C₂×C₄×D₆₇	1	2	yes	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	67	1	no	—
340	C₂×C₈	—	67	1	no	—
341	C₂×C₈	—	67	1	no	—
342	C₂×C₈	—	67	1	no	—
343	C₂×C₈	—	67	1	no	—
344	C₂×C₈	—	67	1	no	—
345	C₂×C₈	—	67	1	no	—
346	C₂×C₈	—	67	1	no	—
347	C₂×C₈	—	67	1	no	—
348	C₂×C₈	—	67	1	no	—
349	C₂×C₈	—	134	2	no	—
350	C₂×C₈	—	134	2	no	—
351	C₂×C₈	—	134	2	no	—
352	C₂×C₈	—	134	2	no	—
353	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
355	C₄²	—	67	1	no	—
356	C₄²	—	134	1	no	—
357	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
358	C₁₆	—	2	2	no	—
359	C₁₆	—	2	1	no	—
360	C₁₆	—	67	2	no	—
361	C₁₆	—	134	2	no	—
362	C₁₆	—	134	1	no	—
363	C₁₆	D₄×D₆₇	1	2	yes	—
364	C₂³	—	67	1	no	—
365	C₂³	—	134	2	no	—
366	Q₈	—	67	2	no	—
367	Q₈	—	134	2	no	—
368	Q₈	C₂×C₈×D₆₇	1	2	yes	—
369	D₄	—	2	2	no	—
370	D₄	—	67	2	no	—
371	D₄	—	134	2	no	—
372	D₄	—	134	2	no	—
373	D₄	—	134	2	no	—
374	D₄	—	134	2	no	—
375	D₄	C₂×C₈×D₆₇	1	2	yes	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	268	2	no	—
379	C₂×C₄	—	67	1	no	—
380	C₂×C₄	—	67	1	no	—
381	C₂×C₄	—	67	1	no	—
382	C₂×C₄	—	67	1	no	—
383	C₂×C₄	—	67	1	no	—
384	C₂×C₄	—	134	2	no	—
385	C₂×C₄	—	134	2	no	—
386	C₂×C₄	—	134	2	no	—
387	C₂×C₄	—	134	1	no	—
388	C₂×C₄	—	134	2	no	—
389	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	67	1	no	—
392	C₈	—	67	1	no	—
393	C₈	—	67	1	no	—
394	C₈	—	67	1	no	—
395	C₈	—	134	2	no	—
396	C₈	C₂×C₈×D₆₇	1	1	yes	characteristic
397	C₈	C₂×C₈×D₆₇	1	1	yes	characteristic
398	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
399	C₈	#41×D₆₇	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	268	1	no	—
402	C₂²	—	536	2	no	—
403	C₂²	—	67	1	no	—
404	C₂²	—	67	1	no	—
405	C₂²	—	134	2	no	—
406	C₂²	#131×D₆₇	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	67	1	no	—
410	C₄	—	67	1	no	—
411	C₄	—	134	2	no	—
412	C₄	—	134	2	no	—
413	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
414	C₄	C₂²×C₈×D₆₇	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	4	2	no	—
417	C₂	—	268	2	no	—
418	C₂	—	134	1	no	—
419	C₂	—	134	1	no	—
420	C₂	C₈×D₄×D₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₆₇×#2171	C₂
socle	C₂×C₆₇	C₂×C₈×D₄
prime radical	#135×D₆₇	C₄
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	#2171	D₆₇
hypocenter	C₆₇	#33443
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2171

Complements

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

N	H ≅ G/N	type
1. #22573310	C₂	semidirect
3. #22562052	C₂	semidirect
4. #22562051	C₂	semidirect
5. #22562050	C₂	semidirect
6. #22562044	C₂	semidirect
7. #22562043	C₂	semidirect
8. #364×D₆₇	C₂	semidirect
9. #22561835	C₂	semidirect
10. #22561802	C₂	semidirect
11. C₆₇×#2171	C₂	semidirect
15. #16863814	C₂²	semidirect
16. #16863813	C₂²	semidirect
18. #16863812	C₂²	semidirect
32. #16863217	C₂²	semidirect
33. #16863216	C₂²	semidirect
34. #16863181	C₂²	semidirect
35. #16863180	C₂²	semidirect
36. #16863179	C₂²	semidirect
37. #16863172	C₂²	semidirect
38. C₁₆×Dic₆₇	C₂²	semidirect
39. C₁₆×Dic₆₇	C₂²	semidirect
40. #504×C₆₇	C₂²	semidirect
42. #364×C₆₇	C₂²	semidirect
43. #350×C₆₇	C₂²	semidirect
44. #346×C₆₇	C₂²	semidirect
216. #2171	D₆₇	semidirect
222. C₆₇	#33443	semidirect
230. #504	C₂×D₆₇	semidirect
247. #364	C₂×D₆₇	semidirect
251. #350	C₂×D₆₇	semidirect
253. #346	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22573310	2
#443×D₆₇	2
#22562052	2
#22562051	2
#22562050	2
#22562044	2
#22562043	2
#364×D₆₇	2
#22561835	2
#22561802	2
C₆₇×#2171	2
#33443	67