Subgroups — #36537569

Order 22784.

714 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031382	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031172	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151945	C₂	1	1	yes	maximal, characteristic, complemented
4	#26028965	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019786	C₂	1	4	yes	maximal, complemented
6	#26019662	C₂	1	4	yes	maximal, complemented
7	#26018932	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018919	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15668018	—	2	1	no	—
11	#19152148	C₂²	1	1	yes	characteristic
12	C₂×#15668012	C₂²	1	1	yes	characteristic
13	C₂×#15668009	C₂²	1	1	yes	characteristic
14	#19151996	—	2	1	no	—
15	#19151975	—	2	1	no	—
16	#19151945	—	2	1	no	—
17	#19151945	—	2	1	no	—
18	#19151945	—	2	1	no	—
19	#19151945	—	2	1	no	—
20	#19151945	C₂²	1	2	yes	—
21	#19151945	C₂²	1	2	yes	—
22	#19151917	—	2	2	no	—
23	#19151889	C₂²	1	4	yes	complemented
24	#19151794	C₂²	1	4	yes	—
25	#19151734	—	2	2	no	—
26	#19151677	—	2	1	no	—
27	#19151677	C₂²	1	2	yes	complemented
28	C₈×D₃₅₆	—	2	1	no	—
29	C₈×D₃₅₆	C₂²	1	2	yes	complemented
30	#19151622	C₂²	1	1	yes	characteristic
31	C₂×#15667934	—	2	1	no	—
32	C₂×#15667934	—	2	1	no	—
33	#19151564	—	2	1	no	—
34	#19151346	C₂²	1	4	yes	complemented
35	#19151341	C₂²	1	4	yes	—
36	#431×C₈₉	C₂²	1	1	yes	characteristic
37	#431×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
39	#335×C₈₉	C₂²	1	2	yes	complemented
40	#334×C₈₉	C₂²	1	2	yes	complemented
41	C₂×#13083574	—	2	1	no	—
42	C₂²×Dic₁₇₈	—	2	1	no	—
43	C₂²×D₃₅₆	—	2	1	no	—
44	C₂²×D₃₅₆	—	2	1	no	—
45	C₂²×D₃₅₆	—	2	1	no	—
46	C₂×D₇₁₂	—	2	4	no	—
47	#15668018	—	4	4	no	—
48	C₂×#13083558	—	2	1	no	—
49	C₂×#13083557	—	2	2	no	—
50	C₂×C₈×D₈₉	—	2	2	no	—
51	#15668012	—	2	1	no	—
52	#15668012	—	2	1	no	—
53	#15668012	—	2	1	no	—
54	#15668012	D₄	1	1	yes	characteristic
55	#15668012	C₂³	1	2	yes	—
56	#15668009	—	2	1	no	—
57	#15668009	—	2	1	no	—
58	#15668009	—	2	1	no	—
59	#15668009	D₄	1	1	yes	characteristic
60	#15668009	C₂³	1	2	yes	—
61	#15668000	—	2	1	no	—
62	#15667986	—	2	1	no	—
63	#15667986	D₄	1	2	yes	—
64	C₄×D₃₅₆	—	2	1	no	—
65	C₄×D₃₅₆	C₂³	1	2	yes	—
66	C₂×C₄⋊Dic₈₉	—	2	1	no	—
67	C₂×C₄⋊Dic₈₉	—	2	1	no	—
68	#15667944	—	2	4	no	—
69	C₄⋊#10623494	—	2	1	no	—
70	C₄⋊#10623494	C₂³	1	2	yes	—
71	#15667934	—	2	4	no	—
72	#15667934	—	2	4	no	—
73	#15667934	—	2	2	no	—
74	#15667934	—	2	2	no	—
75	#15667934	—	2	2	no	—
76	#15667934	—	2	2	no	—
77	#15667924	—	2	2	no	—
78	#15667924	—	2	2	no	—
79	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
83	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
84	C₂²⋊C₈×C₈₉	—	2	1	no	—
85	C₂²⋊C₈×C₈₉	—	2	1	no	—
86	C₄×C₈×C₈₉	—	2	1	no	—
87	C₄×C₈×C₈₉	—	2	1	no	—
88	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
89	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
90	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×D₈₉	—	4	1	no	—
93	#13083574	—	4	2	no	—
94	#13083574	—	4	2	no	—
95	C₂×Dic₁₇₈	—	2	1	no	—
96	C₂×Dic₁₇₈	—	2	2	no	—
97	C₂×Dic₁₇₈	—	4	1	no	—
98	C₂×Dic₁₇₈	—	8	2	no	—
99	C₂×D₃₅₆	—	2	1	no	—
100	C₂×D₃₅₆	—	2	1	no	—
101	C₂×D₃₅₆	—	2	2	no	—
102	C₂×D₃₅₆	—	2	2	no	—
103	C₂×D₃₅₆	—	2	2	no	—
104	C₂×D₃₅₆	—	4	2	no	—
105	C₂×D₃₅₆	—	4	2	no	—
106	C₂×D₃₅₆	—	4	1	no	—
107	C₂×D₃₅₆	—	4	1	no	—
108	C₂×D₃₅₆	—	4	1	no	—
109	C₂×D₃₅₆	—	8	2	no	—
110	C₂×D₃₅₆	—	8	2	no	—
111	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
112	C₂×C₂²⋊D₈₉	—	2	2	no	—
113	C₂²×Dic₈₉	—	4	1	no	—
114	C₂×C₄×D₈₉	—	2	2	no	—
115	D₇₁₂	—	8	4	no	—
116	#13083558	—	4	2	no	—
117	#13083557	—	4	4	no	—
118	C₂×#10623494	—	2	2	no	—
119	C₈×D₈₉	—	4	4	no	—
120	C₄⋊Dic₈₉	—	2	1	no	—
121	C₄⋊Dic₈₉	—	2	2	no	—
122	C₄⋊Dic₈₉	—	2	2	no	—
123	C₄⋊Dic₈₉	—	4	1	no	—
124	C₄⋊Dic₈₉	—	4	1	no	—
125	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
126	#13083551	—	2	2	no	—
127	#13083551	—	2	2	no	—
128	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	—	2	2	no	—
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₈₉	#41	1	1	yes	characteristic
142	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
143	C₂³×C₈₉	#121	1	1	yes	characteristic
144	C₂²×D₈₉	—	2	2	no	—
145	C₂²×D₈₉	—	4	2	no	—
146	C₂²×D₈₉	—	8	2	no	—
147	C₂²×D₈₉	—	8	2	no	—
148	C₂²×D₈₉	—	8	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
152	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
154	C₂×C₄×C₈₉	#135	1	2	yes	—
155	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
156	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
159	C₂²⋊D₈₉	—	4	4	no	—
160	C₂×Dic₈₉	—	2	2	no	—
161	C₂×Dic₈₉	—	4	2	no	—
162	C₂×Dic₈₉	—	8	2	no	—
163	D₃₅₆	—	2	4	no	—
164	D₃₅₆	—	4	2	no	—
165	D₃₅₆	—	4	2	no	—
166	D₃₅₆	—	4	4	no	—
167	D₃₅₆	—	4	2	no	—
168	D₃₅₆	—	4	2	no	—
169	D₃₅₆	—	8	2	no	—
170	D₃₅₆	—	8	2	no	—
171	D₃₅₆	—	8	2	no	—
172	D₃₅₆	—	8	2	no	—
173	C₄×D₈₉	—	4	2	no	—
174	C₄×D₈₉	—	4	2	no	—
175	Dic₁₇₈	—	4	2	no	—
176	Dic₁₇₈	—	8	2	no	—
177	Dic₁₇₈	—	8	2	no	—
178	C₈×C₈₉	—	2	1	no	—
179	C₈×C₈₉	—	2	1	no	—
180	C₈×C₈₉	—	2	1	no	—
181	C₈×C₈₉	—	2	1	no	—
182	C₈×C₈₉	—	4	2	no	—
183	C₈×C₈₉	—	4	2	no	—
184	#10623494	—	4	2	no	—
185	C₂²×C₈₉	—	2	1	no	—
186	C₂²×C₈₉	—	2	1	no	—
187	C₂²×C₈₉	#463	1	2	yes	—
188	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
189	C₂×D₈₉	—	4	2	no	—
190	C₂×D₈₉	—	4	2	no	—
191	C₂×D₈₉	—	4	2	no	—
192	C₂×D₈₉	—	8	2	no	—
193	C₂×D₈₉	—	8	2	no	—
194	C₂×D₈₉	—	8	2	no	—
195	C₂×D₈₉	—	16	4	no	—
196	C₄×C₈₉	—	2	1	no	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	#463	1	2	yes	—
199	C₄×C₈₉	#472	1	2	yes	—
200	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
201	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₄×C₈₉	#577	1	2	yes	—
203	Dic₈₉	—	4	2	no	—
204	Dic₈₉	—	8	2	no	—
205	#19196	—	89	1	no	maximal, Sylow
206	C₂×C₈₉	—	2	2	no	—
207	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
208	C₂×C₈₉	#3057	1	1	yes	characteristic
209	C₂×C₈₉	C₂×#472	1	1	yes	characteristic
210	D₈₉	—	8	2	no	—
211	D₈₉	—	16	2	no	—
212	#3227	—	89	1	no	—
213	#3205	—	89	1	no	—
214	C₂×#486	—	89	1	no	—
215	#2931	—	89	1	no	—
216	#1697	—	89	4	no	—
217	#1677	—	89	4	no	—
218	#1564	D₈₉	1	1	yes	characteristic, complemented
219	#1548	—	89	1	no	—
220	#1545	—	89	1	no	—
221	C₈₉	#19196	1	1	yes	characteristic, complemented, Sylow
222	C₂×#131	—	178	1	no	—
223	#532	—	89	1	no	—
224	C₂×C₄⋊Q₈	—	89	1	no	—
225	C₂×#127	—	89	1	no	—
226	#498	—	178	1	no	—
227	#493	—	178	1	no	—
228	#486	—	89	2	no	—
229	#486	—	89	2	no	—
230	#486	—	178	1	no	—
231	#486	—	178	1	no	—
232	#486	—	178	1	no	—
233	#486	—	178	1	no	—
234	#481	—	178	2	no	—
235	#476	—	89	4	no	—
236	#459	—	89	4	no	—
237	#447	—	178	2	no	—
238	#436	—	89	2	no	—
239	#436	—	178	1	no	—
240	C₈×D₄	—	89	2	no	—
241	C₈×D₄	—	178	1	no	—
242	#431	C₂×D₈₉	1	1	yes	characteristic
243	#431	C₂×D₈₉	1	1	yes	characteristic
244	#423	—	89	1	no	—
245	C₂×#102	—	178	1	no	—
246	C₂×#102	—	178	1	no	—
247	#408	—	178	1	no	—
248	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
249	#335	C₂×D₈₉	1	2	yes	complemented
250	#334	C₂×D₈₉	1	2	yes	complemented
251	#333	—	89	4	no	—
252	#331	—	89	4	no	—
253	C₂×#41	—	178	1	no	—
254	C₂²×Q₈	—	178	1	no	—
255	C₂²×D₄	—	178	1	no	—
256	C₂²×D₄	—	178	1	no	—
257	C₂²×D₄	—	178	1	no	—
258	C₂×D₈	—	178	4	no	—
259	#131	—	356	4	no	—
260	C₂×M₁₆	—	178	1	no	—
261	C₂×M₁₆	—	178	2	no	—
262	C₂²×C₈	—	178	2	no	—
263	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
264	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
265	C₄⋊Q₈	—	89	1	no	—
266	C₄⋊Q₈	—	89	2	no	—
267	C₄⋊Q₈	—	178	1	no	—
268	C₄⋊Q₈	—	178	1	no	—
269	C₄⋊Q₈	—	178	1	no	—
270	#127	—	89	1	no	—
271	#127	—	89	2	no	—
272	#127	—	178	1	no	—
273	#127	—	178	1	no	—
274	#127	—	178	1	no	—
275	#124	—	178	1	no	—
276	#121	—	89	2	no	—
277	#121	—	178	1	no	—
278	C₄×D₄	—	89	2	no	—
279	C₄×D₄	—	178	1	no	—
280	C₂×C₄⋊C₄	—	178	1	no	—
281	C₂×C₄⋊C₄	—	178	1	no	—
282	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
283	#106	—	178	4	no	—
284	C₄⋊C₈	—	89	2	no	—
285	C₄⋊C₈	—	178	1	no	—
286	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
287	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
288	#102	—	178	4	no	—
289	#102	—	178	4	no	—
290	#102	—	178	2	no	—
291	#102	—	178	2	no	—
292	#102	—	178	2	no	—
293	#102	—	178	2	no	—
294	C₂²⋊C₈	—	2	1	no	—
295	C₂²⋊C₈	—	2	1	no	—
296	C₂²⋊C₈	—	178	2	no	—
297	C₂²⋊C₈	—	178	2	no	—
298	C₄×C₈	—	2	1	no	—
299	C₄×C₈	—	2	1	no	—
300	C₄×C₈	D₃₅₆	1	1	yes	characteristic
301	C₄×C₈	D₃₅₆	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
304	C₂⁴	—	356	1	no	—
305	#41	—	356	2	no	—
306	#41	—	356	2	no	—
307	C₂×Q₈	—	356	1	no	—
308	C₂×Q₈	—	178	2	no	—
309	C₂×Q₈	—	178	1	no	—
310	C₂×Q₈	—	712	2	no	—
311	C₂×D₄	—	89	2	no	—
312	C₂×D₄	—	356	1	no	—
313	C₂×D₄	—	356	1	no	—
314	C₂×D₄	—	356	1	no	—
315	C₂×D₄	—	356	2	no	—
316	C₂×D₄	—	356	2	no	—
317	C₂×D₄	—	178	2	no	—
318	C₂×D₄	—	178	1	no	—
319	C₂×D₄	—	178	1	no	—
320	C₂×D₄	—	178	2	no	—
321	C₂×D₄	—	178	2	no	—
322	C₂×D₄	—	178	2	no	—
323	C₂×D₄	—	712	2	no	—
324	C₂×D₄	—	712	2	no	—
325	C₂²×C₄	—	356	1	no	—
326	C₂²×C₄	—	178	2	no	—
327	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
328	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
329	C₂²×C₄	#13083575	1	1	yes	characteristic
330	D₈	—	712	4	no	—
331	M₁₆	—	356	4	no	—
332	M₁₆	—	356	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	356	4	no	—
338	C₂×C₈	—	178	2	no	—
339	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
340	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
341	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
342	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
343	C₄⋊C₄	—	89	2	no	—
344	C₄⋊C₄	—	356	1	no	—
345	C₄⋊C₄	—	356	1	no	—
346	C₄⋊C₄	—	178	2	no	—
347	C₄⋊C₄	—	178	2	no	—
348	C₄⋊C₄	—	178	1	no	—
349	C₂²⋊C₄	—	178	2	no	—
350	C₂²⋊C₄	—	178	2	no	—
351	C₄²	D₄×D₈₉	1	1	yes	characteristic
352	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
353	C₄²	#13083575	1	1	yes	characteristic
354	C₄²	C₂³×D₈₉	1	1	yes	characteristic
355	C₂³	—	356	2	no	—
356	C₂³	—	178	2	no	—
357	C₂³	—	712	2	no	—
358	C₂³	—	712	2	no	—
359	C₂³	—	712	2	no	—
360	C₂³	#15667987	1	1	yes	characteristic
361	Q₈	—	356	2	no	—
362	Q₈	—	712	2	no	—
363	Q₈	—	712	2	no	—
364	D₄	—	356	4	no	—
365	D₄	—	356	2	no	—
366	D₄	—	356	4	no	—
367	D₄	—	356	2	no	—
368	D₄	—	356	2	no	—
369	D₄	—	356	2	no	—
370	D₄	—	178	4	no	—
371	D₄	—	712	2	no	—
372	D₄	—	712	2	no	—
373	D₄	—	712	2	no	—
374	D₄	—	712	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	356	2	no	—
378	C₂×C₄	—	356	2	no	—
379	C₂×C₄	—	356	2	no	—
380	C₂×C₄	—	178	2	no	—
381	C₂×C₄	—	712	2	no	—
382	C₂×C₄	#15667987	1	1	yes	characteristic
383	C₂×C₄	#15667987	1	1	yes	characteristic
384	C₂×C₄	#15667987	1	1	yes	characteristic
385	C₂×C₄	#15668034	1	2	yes	—
386	C₂×C₄	#15668040	1	2	yes	—
387	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
388	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
389	C₂×C₄	C₂×#13083575	1	1	yes	characteristic
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	4	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	356	2	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	356	2	no	—
400	C₂²	—	356	2	no	—
401	C₂²	—	356	2	no	—
402	C₂²	—	1424	4	no	—
403	C₂²	—	712	2	no	—
404	C₂²	—	712	2	no	—
405	C₂²	—	712	2	no	—
406	C₂²	#19151814	1	2	yes	—
407	C₂²	C₂×#15667987	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	356	2	no	—
411	C₄	—	712	2	no	—
412	C₄	#19151814	1	2	yes	—
413	C₄	#19151869	1	2	yes	—
414	C₄	C₂×#15668034	1	1	yes	characteristic
415	C₄	C₂×#15668040	1	1	yes	characteristic
416	C₄	#19152405	1	2	yes	—
417	C₂	—	2	2	no	—
418	C₂	—	1424	2	no	—
419	C₂	—	712	2	no	—
420	C₂	C₂×#19151814	1	1	yes	characteristic
421	C₂	#26029892	1	1	yes	characteristic
422	C₂	C₂×#19151869	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667987
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1564	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26031172	C₂
hypercenter	#1564	D₈₉
hypocenter	C₈₉	#19196
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #26031382	C₂	semidirect
3. C₂×#19151945	C₂	semidirect
4. #26028965	C₂	semidirect
5. #26019786	C₂	semidirect
6. #26019662	C₂	semidirect
7. #26018932	C₂	semidirect
8. #26018919	C₂	semidirect
9. C₈₉×#1564	C₂	semidirect
23. #19151889	C₂²	semidirect
27. #19151677	C₂²	semidirect
29. C₈×D₃₅₆	C₂²	semidirect
34. #19151346	C₂²	semidirect
39. #335×C₈₉	C₂²	semidirect
40. #334×C₈₉	C₂²	semidirect
218. #1564	D₈₉	semidirect
221. C₈₉	#19196	semidirect
249. #335	C₂×D₈₉	semidirect
250. #334	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26031382	2
#26031172	2
C₂×#19151945	2
#26028965	2
#26019786	2
#26019662	2
#26018932	2
#26018919	2
C₈₉×#1564	2
#19196	89