Subgroups — #30824874

Order 17152.

666 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22569326	C₂	1	2	yes	maximal
2	#22558976	C₂	1	4	yes	maximal, complemented
3	#22558972	C₂	1	2	yes	maximal, complemented
4	#22558965	C₂	1	2	yes	maximal, complemented
5	#22558961	C₂	1	2	yes	maximal, complemented
6	#22558957	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863147	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#131×C₆₇	C₂	1	1	yes	maximal, characteristic
9	#16863527	—	2	2	no	—
10	#16863474	—	2	2	no	—
11	#16863468	—	2	4	no	—
12	#16863453	C₂²	1	4	yes	—
13	#16863449	C₂²	1	2	yes	—
14	#16863420	C₂²	1	4	yes	—
15	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
16	#16863149	C₂²	1	2	yes	—
17	#16863149	C₂²	1	4	yes	—
18	#16863147	C₂²	1	2	yes	—
19	#16863147	C₂²	1	4	yes	—
20	#16863147	C₂²	1	2	yes	—
21	#16863147	C₂²	1	1	yes	characteristic
22	#16863147	C₂²	1	1	yes	characteristic
23	C₂×#131×C₆₇	C₄	1	1	yes	characteristic
24	C₂×#131×C₆₇	C₄	1	1	yes	characteristic
25	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
26	#405×C₆₇	C₄	1	2	yes	—
27	#405×C₆₇	C₄	1	2	yes	—
28	#405×C₆₇	C₄	1	1	yes	characteristic
29	#405×C₆₇	C₄	1	1	yes	characteristic
30	C₄×M₁₆×C₆₇	C₂²	1	2	yes	—
31	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
34	C₂×#11761612	—	2	4	no	—
35	C₂²×C₆₇⋊C₈	—	2	2	no	—
36	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
37	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
38	C₄⋊(C₆₇⋊C₈)	C₂³	1	4	yes	—
39	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
40	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
41	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₆₇⋊C₈)	—	2	4	no	—
43	#14523954	—	2	4	no	—
44	C₄×C₆₇⋊C₈	—	2	2	no	—
45	C₂×#41×C₆₇	C₂×C₄	1	1	yes	characteristic
46	#131×C₆₇	—	2	4	no	—
47	#131×C₆₇	—	2	4	no	—
48	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
49	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
50	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
54	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
55	C₂²×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
57	C₄×Q₈×C₆₇	Q₈	1	1	yes	characteristic
58	C₄×D₄×C₆₇	D₄	1	2	yes	—
59	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
60	C₄×D₄×C₆₇	Q₈	1	2	yes	—
61	C₄×D₄×C₆₇	Q₈	1	1	yes	characteristic
62	#117×C₆₇	C₂×C₄	1	2	yes	—
63	#117×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
66	#97×C₆₇	C₂×C₄	1	2	yes	—
67	#97×C₆₇	C₂×C₄	1	2	yes	—
68	#97×C₆₇	C₂×C₄	1	2	yes	—
69	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
70	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
71	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
72	C₄×C₈×C₆₇	C₂×C₄	1	2	yes	—
73	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
74	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
75	C₄×C₈×C₆₇	C₂³	1	2	yes	—
76	#11761612	—	8	4	no	—
77	C₂×C₆₇⋊C₈	—	2	2	no	—
78	C₂×C₆₇⋊C₈	—	2	2	no	—
79	C₂×C₆₇⋊C₈	—	2	4	no	—
80	C₂×C₆₇⋊C₈	—	8	2	no	—
81	#41×C₆₇	—	2	2	no	—
82	#41×C₆₇	—	2	2	no	—
83	C₂×Q₈×C₆₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
85	C₂×D₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
90	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
91	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
92	M₁₆×C₆₇	—	2	2	no	—
93	M₁₆×C₆₇	—	2	4	no	—
94	M₁₆×C₆₇	—	2	4	no	—
95	M₁₆×C₆₇	M₁₆	1	4	yes	complemented
96	C₂×C₈×C₆₇	—	2	2	no	—
97	C₂×C₈×C₆₇	—	2	4	no	—
98	C₂×C₈×C₆₇	—	2	4	no	—
99	C₂×C₈×C₆₇	M₁₆	1	4	yes	complemented
100	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
103	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
106	C₄⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
107	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
109	C₄⋊C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
110	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
111	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
112	C₂²⋊C₄×C₆₇	C₄⋊C₄	1	2	yes	—
113	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
115	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₆₇	C₂×D₄	1	2	yes	—
117	C₄²×C₆₇	C₂×Q₈	1	2	yes	—
118	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
119	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
120	C₂³×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
121	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
122	Q₈×C₆₇	—	2	2	no	—
123	D₄×C₆₇	—	2	4	no	—
124	D₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	2	2	no	—
126	C₂×C₄×C₆₇	—	2	2	no	—
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	4	no	—
129	C₂×C₄×C₆₇	—	4	1	no	—
130	C₂×C₄×C₆₇	—	4	2	no	—
131	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
133	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
138	C₂×C₄×C₆₇	C₂×M₁₆	1	2	yes	—
139	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
142	C₈×C₆₇	—	2	1	no	—
143	C₈×C₆₇	—	2	1	no	—
144	C₈×C₆₇	—	2	2	no	—
145	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
146	C₈×C₆₇	C₂×M₁₆	1	4	yes	—
147	C₈×C₆₇	C₂×M₁₆	1	2	yes	—
148	C₆₇⋊C₈	—	4	2	no	—
149	C₆₇⋊C₈	—	4	4	no	—
150	C₆₇⋊C₈	—	4	2	no	—
151	C₂²×C₆₇	—	2	1	no	—
152	C₂²×C₆₇	—	2	1	no	—
153	C₂²×C₆₇	—	2	2	no	—
154	C₂²×C₆₇	—	2	2	no	—
155	C₂²×C₆₇	—	2	2	no	—
156	C₂²×C₆₇	#423	1	2	yes	—
157	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
158	C₄×C₆₇	—	2	2	no	—
159	C₄×C₆₇	—	2	1	no	—
160	C₄×C₆₇	—	2	2	no	—
161	C₄×C₆₇	—	2	1	no	—
162	C₄×C₆₇	—	2	1	no	—
163	C₄×C₆₇	—	2	2	no	—
164	C₄×C₆₇	#423	1	2	yes	—
165	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
166	C₄×C₆₇	C₂²×M₁₆	1	1	yes	characteristic
167	C₄×C₆₇	#577	1	2	yes	—
168	#17798	—	67	1	no	maximal, Sylow
169	C₂×C₆₇	—	2	2	no	—
170	C₂×C₆₇	—	4	2	no	—
171	C₂×C₆₇	C₂×#423	1	1	yes	characteristic
172	C₂×C₆₇	#2912	1	1	yes	characteristic
173	C₂×C₆₇	#2916	1	1	yes	characteristic
174	#2989	—	67	2	no	—
175	C₄×#131	D₆₇	1	1	yes	characteristic
176	#1569	—	67	4	no	—
177	#1568	—	67	2	no	—
178	#1566	—	67	2	no	—
179	#1565	—	67	2	no	—
180	#1564	—	67	1	no	—
181	C₂×#334	—	67	1	no	—
182	C₆₇	#17798	1	1	yes	characteristic, complemented, Sylow
183	C₂×#131	Dic₆₇	1	1	yes	characteristic
184	C₂×#131	Dic₆₇	1	1	yes	characteristic
185	C₄×#41	C₂×D₆₇	1	1	yes	characteristic
186	#446	—	134	2	no	—
187	#436	—	134	2	no	—
188	#435	—	134	4	no	—
189	#432	—	67	4	no	—
190	#431	—	67	2	no	—
191	#423	—	67	4	no	—
192	C₂×C₄⋊C₈	—	67	2	no	—
193	#405	Dic₆₇	1	1	yes	characteristic
194	#405	Dic₆₇	1	2	yes	—
195	#405	Dic₆₇	1	2	yes	—
196	#405	Dic₆₇	1	1	yes	characteristic
197	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
198	C₄×M₁₆	C₂×D₆₇	1	2	yes	—
199	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
200	C₂×C₄×C₈	C₂×D₆₇	1	2	yes	—
201	#335	—	67	2	no	—
202	#335	—	67	4	no	—
203	#334	—	67	2	no	—
204	#334	—	67	2	no	—
205	#334	—	67	1	no	—
206	#334	—	67	1	no	—
207	#334	—	67	4	no	—
208	C₂×#41	C₂×Dic₆₇	1	1	yes	characteristic
209	#131	—	2	4	no	—
210	#131	—	2	4	no	—
211	C₂×M₁₆	—	134	4	no	—
212	C₂×M₁₆	C₂×Dic₆₇	1	1	yes	characteristic
213	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
214	C₂×M₁₆	C₂×Dic₆₇	1	2	yes	—
215	C₂×M₁₆	C₂×Dic₆₇	1	1	yes	characteristic
216	C₂²×C₈	—	134	2	no	—
217	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
218	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
219	C₂²×C₈	C₂×Dic₆₇	1	2	yes	—
220	C₂²×C₈	C₂×Dic₆₇	1	1	yes	characteristic
221	C₄×Q₈	Dic₁₃₄	1	1	yes	characteristic
222	C₄×Q₈	D₂₆₈	1	1	yes	characteristic
223	C₄×D₄	Dic₁₃₄	1	2	yes	—
224	C₄×D₄	Dic₁₃₄	1	1	yes	characteristic
225	C₄×D₄	D₂₆₈	1	2	yes	—
226	C₄×D₄	D₂₆₈	1	1	yes	characteristic
227	#117	C₂×Dic₆₇	1	2	yes	—
228	#117	C₂×Dic₆₇	1	1	yes	characteristic
229	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
230	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
231	C₄⋊C₈	—	67	4	no	—
232	C₄⋊C₈	—	67	2	no	—
233	C₄⋊C₈	—	67	2	no	—
234	C₄⋊C₈	—	134	2	no	—
235	C₄⋊C₈	—	134	4	no	—
236	C₂²⋊C₈	—	134	2	no	—
237	C₂²⋊C₈	—	134	4	no	—
238	#97	—	134	4	no	—
239	#97	C₂×Dic₆₇	1	2	yes	—
240	#97	C₂×Dic₆₇	1	2	yes	—
241	#97	C₂×Dic₆₇	1	2	yes	—
242	C₄×C₈	—	134	2	no	—
243	C₄×C₈	C₂×Dic₆₇	1	2	yes	—
244	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
245	C₄×C₈	C₂×Dic₆₇	1	1	yes	characteristic
246	C₄×C₈	C₂×Dic₆₇	1	2	yes	—
247	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
248	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
249	C₄×C₈	C₂²×D₆₇	1	2	yes	—
250	#41	—	2	2	no	—
251	#41	—	2	2	no	—
252	C₂×Q₈	C₄⋊Dic₆₇	1	1	yes	characteristic
253	C₂×D₄	C₄⋊Dic₆₇	1	2	yes	—
254	C₂×D₄	C₄⋊Dic₆₇	1	1	yes	characteristic
255	C₂²×C₄	C₂²×Dic₆₇	1	2	yes	—
256	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
257	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
258	C₂²×C₄	C₂×D₂₆₈	1	2	yes	—
259	C₂²×C₄	C₂×Dic₁₃₄	1	2	yes	—
260	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
261	M₁₆	—	2	2	no	—
262	M₁₆	—	2	4	no	—
263	M₁₆	—	2	4	no	—
264	M₁₆	—	536	4	no	—
265	M₁₆	#11761612	1	4	yes	complemented
266	C₂×C₈	—	2	2	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	2	4	no	—
269	C₂×C₈	—	536	2	no	—
270	C₂×C₈	—	134	2	no	—
271	C₂×C₈	—	134	2	no	—
272	C₂×C₈	—	134	4	no	—
273	C₂×C₈	#11761612	1	4	yes	complemented
274	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
275	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
276	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
277	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
278	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
279	C₂×C₈	C₂²×Dic₆₇	1	1	yes	characteristic
280	C₄⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
281	C₄⋊C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
282	C₄⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
283	C₄⋊C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
284	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
285	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
286	C₂²⋊C₄	C₄⋊Dic₆₇	1	2	yes	—
287	C₄²	C₂²×Dic₆₇	1	1	yes	characteristic
288	C₄²	C₂²×Dic₆₇	1	2	yes	—
289	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
290	C₄²	C₂×D₂₆₈	1	2	yes	—
291	C₄²	C₂×Dic₁₃₄	1	2	yes	—
292	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
293	C₄²	C₂³×D₆₇	1	1	yes	characteristic
294	C₂³	C₂×C₄⋊Dic₆₇	1	2	yes	—
295	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
296	Q₈	—	2	2	no	—
297	D₄	—	2	4	no	—
298	D₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	4	1	no	—
304	C₂×C₄	—	4	2	no	—
305	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
306	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
307	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
308	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
309	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
310	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
311	C₂×C₄	C₂×#11761612	1	2	yes	—
312	C₂×C₄	C₂×#11761612	1	2	yes	—
313	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
314	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
315	C₂×C₄	C₂²×Dic₁₃₄	1	1	yes	characteristic
316	C₈	—	2	1	no	—
317	C₈	—	2	1	no	—
318	C₈	—	2	2	no	—
319	C₈	—	268	4	no	—
320	C₈	—	268	2	no	—
321	C₈	—	268	2	no	—
322	C₈	C₂×#11761612	1	2	yes	—
323	C₈	C₂×#11761612	1	4	yes	—
324	C₈	C₂×#11761612	1	2	yes	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	2	2	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	2	2	no	—
330	C₂²	#16863420	1	2	yes	—
331	C₂²	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
332	C₄	—	2	2	no	—
333	C₄	—	2	1	no	—
334	C₄	—	2	2	no	—
335	C₄	—	2	1	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	2	no	—
338	C₄	#16863420	1	2	yes	—
339	C₄	C₂²×#11761612	1	1	yes	characteristic
340	C₄	C₂²×#11761612	1	1	yes	characteristic
341	C₄	#16864208	1	2	yes	—
342	C₂	—	2	2	no	—
343	C₂	—	4	2	no	—
344	C₂	C₂×#16863420	1	1	yes	characteristic
345	C₂	#22568804	1	1	yes	characteristic
346	C₂	#22568820	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₄×#131×C₆₇	C₂
socle	C₂²×C₆₇	C₂²×C₄⋊C₄
prime radical	C₂×#41×C₆₇	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	C₄×#131	D₆₇
hypocenter	C₆₇	#17798
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ C₄×#131

Complements

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

N	H ≅ G/N	type
2. #22558976	C₂	semidirect
3. #22558972	C₂	semidirect
4. #22558965	C₂	semidirect
5. #22558961	C₂	semidirect
6. #22558957	C₂	semidirect
7. C₂×#16863147	C₂	semidirect
95. M₁₆×C₆₇	M₁₆	semidirect
99. C₂×C₈×C₆₇	M₁₆	semidirect
182. C₆₇	#17798	semidirect
265. M₁₆	#11761612	semidirect
273. C₂×C₈	#11761612	semidirect

Maximal subgroups

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

subgroup	index
#22569326	2
#22558976	2
#22558972	2
#22558965	2
#22558961	2
#22558957	2
C₂×#16863147	2
C₄×#131×C₆₇	2
#17798	67