Subgroups — #30869417

Order 17152.

722 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863527	C₂	1	2	yes	maximal
2	#22561150	C₂	1	2	yes	maximal
3	#22560775	C₂	1	2	yes	maximal
4	#22560775	C₂	1	2	yes	maximal
5	#22560768	C₂	1	2	yes	maximal
6	#22560768	C₂	1	2	yes	maximal
7	#22560326	C₂	1	1	yes	maximal, characteristic
8	#22559958	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic
10	#16863527	—	2	8	no	—
11	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×#14523954	C₂²	1	2	yes	—
15	C₂×#14523954	C₂²	1	1	yes	characteristic
16	C₂×#14523954	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
18	#16863151	C₂²	1	1	yes	characteristic
19	#16863151	C₂²	1	2	yes	—
20	#16863151	C₂²	1	2	yes	—
21	#16863151	C₂²	1	2	yes	—
22	#16863151	C₂²	1	2	yes	—
23	#16863151	C₂²	1	2	yes	—
24	#16863151	C₂²	1	2	yes	—
25	#16863151	C₂²	1	1	yes	characteristic
26	#16863151	C₂²	1	2	yes	—
27	C₂×C₄⋊Q₈×C₆₇	C₄	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₆₇	C₂²	1	2	yes	—
29	#391×C₆₇	C₄	1	2	yes	—
30	#389×C₆₇	C₄	1	2	yes	—
31	#389×C₆₇	C₄	1	1	yes	characteristic
32	#389×C₆₇	C₄	1	1	yes	characteristic
33	#384×C₆₇	C₄	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
36	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₄³×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
39	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
40	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
41	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
42	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
43	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
44	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
45	#14523954	—	2	4	no	—
46	#14523954	—	2	2	no	—
47	#14523954	D₄	1	4	yes	—
48	C₄×C₆₇⋊C₈	—	2	4	no	—
49	C₂²×Q₈×C₆₇	C₂×C₄	1	2	yes	—
50	C₄⋊Q₈×C₆₇	—	2	4	no	—
51	C₄×Q₈×C₆₇	—	2	4	no	—
52	C₄×Q₈×C₆₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
68	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
71	#95×C₆₇	C₂×C₄	1	2	yes	—
72	#95×C₆₇	C₂×C₄	1	2	yes	—
73	#95×C₆₇	C₂×C₄	1	2	yes	—
74	#95×C₆₇	C₂×C₄	1	2	yes	—
75	C₂×C₆₇⋊C₈	—	2	2	no	—
76	C₂×C₆₇⋊C₈	—	2	2	no	—
77	C₂×C₆₇⋊C₈	—	2	2	no	—
78	C₂×C₆₇⋊C₈	—	2	2	no	—
79	C₂×C₆₇⋊C₈	—	2	2	no	—
80	C₂×C₆₇⋊C₈	—	2	2	no	—
81	C₂×C₆₇⋊C₈	—	2	2	no	—
82	C₂×C₆₇⋊C₈	—	2	2	no	—
83	C₂×C₆₇⋊C₈	—	2	2	no	—
84	C₂×C₆₇⋊C₈	—	2	2	no	—
85	C₂×C₆₇⋊C₈	—	2	2	no	—
86	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
87	C₂×Q₈×C₆₇	—	2	4	no	—
88	C₂×Q₈×C₆₇	—	2	4	no	—
89	C₂×Q₈×C₆₇	—	4	2	no	—
90	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
101	C₄⋊C₄×C₆₇	—	2	4	no	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	4	no	—
104	C₄⋊C₄×C₆₇	—	2	4	no	—
105	C₄⋊C₄×C₆₇	—	2	2	no	—
106	C₄⋊C₄×C₆₇	—	2	4	no	—
107	C₄⋊C₄×C₆₇	—	4	1	no	—
108	C₄⋊C₄×C₆₇	—	4	1	no	—
109	C₄⋊C₄×C₆₇	M₁₆	1	4	yes	—
110	C₄²×C₆₇	—	2	2	no	—
111	C₄²×C₆₇	—	2	2	no	—
112	C₄²×C₆₇	—	2	2	no	—
113	C₄²×C₆₇	—	2	2	no	—
114	C₄²×C₆₇	—	2	2	no	—
115	C₄²×C₆₇	—	2	2	no	—
116	C₄²×C₆₇	—	2	2	no	—
117	C₄²×C₆₇	—	2	2	no	—
118	C₄²×C₆₇	—	4	1	no	—
119	C₄²×C₆₇	—	4	1	no	—
120	C₄²×C₆₇	C₂×D₄	1	2	yes	—
121	C₄²×C₆₇	#41	1	2	yes	—
122	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
123	Q₈×C₆₇	—	4	8	no	—
124	C₂×C₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	2	1	no	—
126	C₂×C₄×C₆₇	—	2	1	no	—
127	C₂×C₄×C₆₇	—	2	1	no	—
128	C₂×C₄×C₆₇	—	2	1	no	—
129	C₂×C₄×C₆₇	—	2	1	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	1	no	—
133	C₂×C₄×C₆₇	—	2	2	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	2	no	—
136	C₂×C₄×C₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	1	no	—
138	C₂×C₄×C₆₇	—	2	1	no	—
139	C₂×C₄×C₆₇	—	2	2	no	—
140	C₂×C₄×C₆₇	—	2	1	no	—
141	C₂×C₄×C₆₇	—	2	2	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	2	1	no	—
144	C₂×C₄×C₆₇	—	2	1	no	—
145	C₂×C₄×C₆₇	—	2	1	no	—
146	C₂×C₄×C₆₇	—	2	2	no	—
147	C₂×C₄×C₆₇	—	2	2	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
153	C₂×C₄×C₆₇	#131	1	2	yes	—
154	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
157	C₂×C₄×C₆₇	2₋¹⁺⁴	1	2	yes	—
158	C₆₇⋊C₈	—	2	4	no	—
159	C₆₇⋊C₈	—	4	2	no	—
160	C₆₇⋊C₈	—	4	2	no	—
161	C₆₇⋊C₈	—	4	2	no	—
162	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
163	C₂²×C₆₇	#519	1	1	yes	characteristic
164	C₂²×C₆₇	#519	1	1	yes	characteristic
165	C₂²×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#131	1	1	yes	characteristic
167	C₂²×C₆₇	#568	1	1	yes	characteristic
168	C₂²×C₆₇	#568	1	1	yes	characteristic
169	C₄×C₆₇	—	2	2	no	—
170	C₄×C₆₇	—	2	4	no	—
171	C₄×C₆₇	—	2	2	no	—
172	C₄×C₆₇	—	2	2	no	—
173	C₄×C₆₇	—	2	2	no	—
174	C₄×C₆₇	—	4	2	no	—
175	C₄×C₆₇	—	4	2	no	—
176	C₄×C₆₇	—	4	2	no	—
177	C₄×C₆₇	—	4	1	no	—
178	C₄×C₆₇	—	4	1	no	—
179	C₄×C₆₇	#536	1	2	yes	—
180	C₄×C₆₇	#541	1	2	yes	—
181	#22244	—	67	1	no	maximal, Sylow
182	C₂×C₆₇	#2327	1	1	yes	characteristic
183	C₂×C₆₇	D₄×M₁₆	1	1	yes	characteristic
184	C₂×C₆₇	#2935	1	1	yes	characteristic
185	C₂×C₆₇	#2983	1	1	yes	characteristic
186	C₂×C₆₇	#2984	1	1	yes	characteristic
187	C₂×C₆₇	#2985	1	1	yes	characteristic
188	C₂×C₆₇	#2987	1	1	yes	characteristic
189	C₂×#446	—	67	2	no	—
190	C₄×C₄⋊Q₈	D₆₇	1	1	yes	characteristic
191	#1985	—	67	2	no	—
192	#1917	—	67	2	no	—
193	#1917	—	67	2	no	—
194	#1916	—	67	2	no	—
195	#1916	—	67	2	no	—
196	#1831	—	67	1	no	—
197	#1745	—	67	1	no	—
198	C₆₇	#22244	1	1	yes	characteristic, complemented, Sylow
199	C₂×C₄⋊Q₈	Dic₆₇	1	1	yes	characteristic
200	C₂×C₄×Q₈	C₂×D₆₇	1	2	yes	—
201	#446	—	134	8	no	—
202	C₂×C₄⋊C₈	—	67	2	no	—
203	C₂×C₄⋊C₈	—	67	2	no	—
204	C₂×C₄⋊C₈	—	67	2	no	—
205	C₂×#97	—	67	1	no	—
206	C₂×#97	—	67	2	no	—
207	C₂×#97	—	67	1	no	—
208	C₂×C₄×C₈	—	67	2	no	—
209	#391	Dic₆₇	1	2	yes	—
210	#389	Dic₆₇	1	2	yes	—
211	#389	Dic₆₇	1	1	yes	characteristic
212	#389	Dic₆₇	1	1	yes	characteristic
213	#384	Dic₆₇	1	1	yes	characteristic
214	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂×D₆₇	1	2	yes	—
216	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
217	C₄³	C₂×D₆₇	1	1	yes	characteristic
218	#336	—	67	1	no	—
219	#336	—	67	2	no	—
220	#336	—	67	1	no	—
221	#336	—	67	2	no	—
222	#336	—	67	2	no	—
223	#336	—	67	2	no	—
224	#336	—	67	2	no	—
225	#336	—	67	2	no	—
226	#336	—	67	2	no	—
227	C₂²×Q₈	C₂×Dic₆₇	1	2	yes	—
228	C₂²×C₈	—	67	2	no	—
229	C₂²×C₈	—	67	2	no	—
230	C₂²×C₈	—	67	2	no	—
231	C₂²×C₈	—	67	2	no	—
232	C₄⋊Q₈	—	2	4	no	—
233	C₄×Q₈	—	2	4	no	—
234	C₄×Q₈	—	2	4	no	—
235	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
238	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
239	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
242	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
244	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
246	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
247	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
248	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
249	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
250	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
251	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
253	C₄⋊C₈	—	134	4	no	—
254	C₄⋊C₈	—	134	4	no	—
255	C₄⋊C₈	—	134	4	no	—
256	#97	—	67	4	no	—
257	#97	—	134	4	no	—
258	#97	—	134	2	no	—
259	C₄×C₈	—	134	4	no	—
260	#95	C₂×Dic₆₇	1	2	yes	—
261	#95	C₂×Dic₆₇	1	2	yes	—
262	#95	C₂×Dic₆₇	1	2	yes	—
263	#95	C₂×Dic₆₇	1	2	yes	—
264	C₂×Q₈	—	2	4	no	—
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	4	2	no	—
267	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
270	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
271	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
272	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
274	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
275	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
277	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
278	C₂×C₈	—	67	4	no	—
279	C₂×C₈	—	134	2	no	—
280	C₂×C₈	—	134	2	no	—
281	C₂×C₈	—	134	2	no	—
282	C₂×C₈	—	134	2	no	—
283	C₂×C₈	—	134	2	no	—
284	C₂×C₈	—	134	2	no	—
285	C₂×C₈	—	134	2	no	—
286	C₂×C₈	—	134	2	no	—
287	C₂×C₈	—	134	2	no	—
288	C₂×C₈	—	134	2	no	—
289	C₂×C₈	—	134	2	no	—
290	C₄⋊C₄	—	2	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	4	no	—
296	C₄⋊C₄	—	4	1	no	—
297	C₄⋊C₄	—	4	1	no	—
298	C₄⋊C₄	#11761612	1	4	yes	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	—	2	2	no	—
307	C₄²	—	4	1	no	—
308	C₄²	—	4	1	no	—
309	C₄²	D₄×D₆₇	1	2	yes	—
310	C₄²	#11761627	1	2	yes	—
311	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
312	Q₈	—	4	8	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	1	no	—
315	C₂×C₄	—	2	1	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	2	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
339	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
340	C₂×C₄	C₂×#11761612	1	2	yes	—
341	C₂×C₄	C₂×#11761612	1	4	yes	—
342	C₂×C₄	#14524050	1	2	yes	—
343	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
344	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
345	C₂×C₄	#14524091	1	2	yes	—
346	C₂×C₄	#14524091	1	2	yes	—
347	C₈	—	268	2	no	—
348	C₈	—	268	2	no	—
349	C₈	—	268	2	no	—
350	C₈	—	134	4	no	—
351	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
352	C₂²	#16863874	1	1	yes	characteristic
353	C₂²	#16863874	1	1	yes	characteristic
354	C₂²	C₂²×#11761612	1	1	yes	characteristic
355	C₂²	C₂×#14524050	1	1	yes	characteristic
356	C₂²	#16864163	1	1	yes	characteristic
357	C₂²	#16864163	1	1	yes	characteristic
358	C₄	—	2	2	no	—
359	C₄	—	2	2	no	—
360	C₄	—	2	2	no	—
361	C₄	—	2	4	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	#16863971	1	2	yes	—
369	C₄	#16864007	1	2	yes	—
370	C₂	#22562929	1	1	yes	characteristic
371	C₂	D₄×#11761612	1	1	yes	characteristic
372	C₂	#22568953	1	1	yes	characteristic
373	C₂	#22569294	1	1	yes	characteristic
374	C₂	#22569298	1	1	yes	characteristic
375	C₂	#22569304	1	1	yes	characteristic
376	C₂	#22569315	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator, socle, prime radical	C₂³×C₆₇	C₂³×C₄
Fitting	C₄×C₄⋊Q₈×C₆₇	C₂
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₆₇
hypocenter	C₆₇	#22244
LCS	G ▷ C₂³×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
198. C₆₇	#22244	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863527	2
#22561150	2
#22560775	2
#22560768	2
#22560326	2
#22559958	2
C₄×C₄⋊Q₈×C₆₇	2
#22244	67