Subgroups — #36537939

Order 22784.

640 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031564	C₂	1	1	yes	maximal, characteristic
2	#26031380	C₂	1	1	yes	maximal, characteristic
3	#26028998	C₂	1	1	yes	maximal, characteristic
4	#26019772	C₂	1	2	yes	maximal, complemented
5	#26019748	C₂	1	2	yes	maximal, complemented
6	#26019648	C₂	1	2	yes	maximal, complemented
7	#26019624	C₂	1	2	yes	maximal, complemented
8	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018909	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19151347	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3165	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668020	—	2	1	no	—
13	#19152148	C₂²	1	1	yes	characteristic
14	#19151994	—	2	1	no	—
15	#19151946	—	2	1	no	—
16	#19151916	—	2	2	no	—
17	#19151885	C₂²	1	2	yes	—
18	#19151885	C₂²	1	2	yes	—
19	#19151885	C₂²	1	2	yes	—
20	#19151883	—	2	1	no	—
21	#19151829	—	2	2	no	—
22	#19151800	C₂²	1	2	yes	—
23	#19151798	—	2	1	no	—
24	#19151677	C₂²	1	2	yes	—
25	#19151671	—	2	2	no	—
26	C₈×D₃₅₆	C₂²	1	2	yes	—
27	#19151651	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
30	#19151566	—	2	1	no	—
31	#19151351	C₂²	1	2	yes	—
32	#19151349	C₂²	1	2	yes	—
33	#19151347	C₂²	1	2	yes	—
34	#19151347	C₂²	1	1	yes	characteristic
35	#19151347	C₂²	1	2	yes	—
36	#19151347	C₂²	1	1	yes	characteristic
37	#19151344	C₂²	1	1	yes	characteristic
38	#19151344	C₂²	1	1	yes	characteristic
39	#533×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
41	#501×C₈₉	—	2	2	no	—
42	#500×C₈₉	C₂²	1	2	yes	—
43	#498×C₈₉	C₂²	1	2	yes	—
44	#428×C₈₉	—	2	1	no	—
45	#428×C₈₉	—	2	1	no	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	—	2	1	no	—
48	C₂×#13083561	—	2	2	no	—
49	#15668020	—	4	4	no	—
50	C₂×#13083557	—	2	2	no	—
51	C₂²×#10623494	—	2	1	no	—
52	C₂²×#10623494	—	2	1	no	—
53	C₂×C₈×D₈₉	—	2	2	no	—
54	#15668012	D₄	1	1	yes	characteristic
55	#15668009	D₄	1	1	yes	characteristic
56	#15668000	—	2	1	no	—
57	#15667986	—	2	1	no	—
58	#15667986	D₄	1	2	yes	—
59	C₄×D₃₅₆	—	2	1	no	—
60	C₄×D₃₅₆	C₂³	1	2	yes	—
61	#15667943	—	2	2	no	—
62	#15667943	—	2	2	no	—
63	#15667943	—	2	2	no	—
64	C₄⋊#10623494	—	2	1	no	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	C₂³	1	2	yes	—
67	C₄⋊#10623494	C₂³	1	1	yes	characteristic
68	C₄⋊#10623494	C₂³	1	1	yes	characteristic
69	C₄⋊#10623494	C₂³	1	1	yes	characteristic
70	C₄⋊#10623494	C₂³	1	1	yes	characteristic
71	#15667936	—	2	2	no	—
72	#15667932	—	2	2	no	—
73	#15667932	—	2	2	no	—
74	#15667932	—	2	2	no	—
75	C₂²⋊#10623494	—	2	1	no	—
76	#15667924	—	2	2	no	—
77	#15667924	—	2	2	no	—
78	C₄×#10623494	—	2	1	no	—
79	C₂²×Q₈×C₈₉	—	2	1	no	—
80	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
81	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
82	C₄⋊Q₈×C₈₉	—	2	1	no	—
83	C₄⋊Q₈×C₈₉	—	2	1	no	—
84	C₄⋊Q₈×C₈₉	—	2	1	no	—
85	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
86	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
88	#125×C₈₉	—	2	1	no	—
89	C₂²⋊Q₈×C₈₉	—	2	1	no	—
90	C₂²⋊Q₈×C₈₉	—	2	1	no	—
91	C₄×Q₈×C₈₉	—	2	1	no	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	#117×C₈₉	—	2	1	no	—
94	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
95	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	#107×C₈₉	—	2	2	no	—
98	#107×C₈₉	—	2	2	no	—
99	#106×C₈₉	—	2	2	no	—
100	#106×C₈₉	—	2	2	no	—
101	#97×C₈₉	D₄	1	2	yes	—
102	C₄×C₈×C₈₉	C₂³	1	2	yes	—
103	#13083574	—	4	2	no	—
104	#13083574	—	4	2	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×D₃₅₆	—	2	1	no	—
107	C₂×D₃₅₆	—	2	1	no	—
108	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
109	C₂×C₂²⋊D₈₉	—	2	2	no	—
110	C₂×C₄×D₈₉	—	2	2	no	—
111	#13083561	—	8	2	no	—
112	#13083557	—	4	4	no	—
113	C₂×#10623494	—	2	1	no	—
114	C₂×#10623494	—	2	1	no	—
115	C₂×#10623494	—	2	2	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₂×#10623494	—	4	2	no	—
119	C₂×#10623494	—	8	1	no	—
120	C₈×D₈₉	—	4	4	no	—
121	C₄⋊Dic₈₉	—	2	1	no	—
122	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
123	#13083551	—	2	2	no	—
124	#13083551	—	2	2	no	—
125	C₂×Q₈×C₈₉	—	2	1	no	—
126	C₂×Q₈×C₈₉	—	2	1	no	—
127	C₂×Q₈×C₈₉	—	2	2	no	—
128	C₂×Q₈×C₈₉	—	4	1	no	—
129	C₂×Q₈×C₈₉	—	8	2	no	—
130	C₂²×C₄×C₈₉	—	4	1	no	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
134	M₁₆×C₈₉	—	2	2	no	—
135	M₁₆×C₈₉	SD₁₆	1	4	yes	complemented
136	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
138	C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₄⋊C₄×C₈₉	—	2	2	no	—
140	C₄⋊C₄×C₈₉	—	2	1	no	—
141	C₄⋊C₄×C₈₉	—	2	2	no	—
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₄⋊C₄×C₈₉	—	4	1	no	—
145	C₄⋊C₄×C₈₉	—	4	1	no	—
146	C₄⋊C₄×C₈₉	—	4	1	no	—
147	C₄⋊C₄×C₈₉	—	4	1	no	—
148	C₂²⋊C₄×C₈₉	—	4	1	no	—
149	C₄²×C₈₉	—	4	1	no	—
150	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
151	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₈₉	#41	1	1	yes	characteristic
153	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
154	C₂³×C₈₉	#121	1	1	yes	characteristic
155	C₂²×D₈₉	—	2	2	no	—
156	Q₈×C₈₉	—	4	1	no	—
157	Q₈×C₈₉	—	4	1	no	—
158	Q₈×C₈₉	—	8	1	no	—
159	Q₈×C₈₉	—	8	2	no	—
160	Q₈×C₈₉	—	8	2	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	4	1	no	—
164	C₂×C₄×C₈₉	—	4	1	no	—
165	C₂×C₄×C₈₉	—	4	1	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	—	8	2	no	—
168	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
169	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
170	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
172	C₂×C₄×C₈₉	#137	1	2	yes	—
173	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
176	C₂²⋊D₈₉	—	4	4	no	—
177	C₂×Dic₈₉	—	2	2	no	—
178	D₃₅₆	—	2	2	no	—
179	D₃₅₆	—	2	2	no	—
180	D₃₅₆	—	4	2	no	—
181	D₃₅₆	—	8	1	no	—
182	C₄×D₈₉	—	4	2	no	—
183	C₄×D₈₉	—	4	2	no	—
184	Dic₁₇₈	—	4	2	no	—
185	C₈×C₈₉	—	2	2	no	—
186	C₈×C₈₉	C₂×SD₁₆	1	4	yes	—
187	#10623494	—	4	1	no	—
188	#10623494	—	4	1	no	—
189	#10623494	—	4	1	no	—
190	#10623494	—	4	2	no	—
191	#10623494	—	4	1	no	—
192	C₂²×C₈₉	—	2	1	no	—
193	C₂²×C₈₉	—	2	1	no	—
194	C₂²×C₈₉	#461	1	2	yes	—
195	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
196	C₂×D₈₉	—	4	2	no	—
197	C₂×D₈₉	—	4	2	no	—
198	C₂×D₈₉	—	4	2	no	—
199	C₄×C₈₉	—	2	1	no	—
200	C₄×C₈₉	—	2	1	no	—
201	C₄×C₈₉	—	2	1	no	—
202	C₄×C₈₉	—	8	1	no	—
203	C₄×C₈₉	—	8	2	no	—
204	C₄×C₈₉	—	8	1	no	—
205	C₄×C₈₉	#461	1	2	yes	—
206	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
207	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
208	C₄×C₈₉	#577	1	1	yes	characteristic
209	C₄×C₈₉	#578	1	1	yes	characteristic
210	Dic₈₉	—	4	2	no	—
211	#19233	—	89	1	no	maximal, Sylow
212	C₂×C₈₉	—	2	2	no	—
213	C₂×C₈₉	C₂×#461	1	1	yes	characteristic
214	C₂×C₈₉	#3063	1	1	yes	characteristic
215	C₂×C₈₉	#3068	1	1	yes	characteristic
216	D₈₉	—	8	2	no	—
217	#3246	—	89	1	no	—
218	#3227	—	89	1	no	—
219	#3165	D₈₉	1	1	yes	characteristic, complemented
220	#2935	—	89	1	no	—
221	#1695	—	89	2	no	—
222	#1691	—	89	2	no	—
223	#1675	—	89	2	no	—
224	#1671	—	89	2	no	—
225	#1565	—	89	1	no	—
226	#1542	—	89	1	no	—
227	C₂×#333	—	89	1	no	—
228	C₈₉	#19233	1	1	yes	characteristic, complemented, Sylow
229	C₂×#131	—	178	1	no	—
230	#533	C₂×D₈₉	1	1	yes	characteristic
231	#532	—	89	1	no	—
232	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
233	#501	—	2	2	no	—
234	#500	C₂×D₈₉	1	2	yes	—
235	#498	—	178	1	no	—
236	#498	C₂×D₈₉	1	2	yes	—
237	#486	—	178	1	no	—
238	#481	—	178	2	no	—
239	#476	—	89	2	no	—
240	#476	—	89	2	no	—
241	#476	—	89	2	no	—
242	#475	—	178	1	no	—
243	#465	—	178	2	no	—
244	#461	—	89	2	no	—
245	#460	—	178	1	no	—
246	#436	—	89	2	no	—
247	#435	—	178	2	no	—
248	C₈×D₄	—	89	2	no	—
249	#431	—	89	1	no	—
250	#428	—	2	1	no	—
251	#428	—	2	1	no	—
252	C₂×C₄⋊C₈	—	89	1	no	—
253	C₂×C₄⋊C₈	—	89	1	no	—
254	#408	—	178	1	no	—
255	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
256	#335	—	89	2	no	—
257	#334	—	89	2	no	—
258	#333	—	89	2	no	—
259	#333	—	89	2	no	—
260	#333	—	89	1	no	—
261	#333	—	89	1	no	—
262	#332	—	89	1	no	—
263	#332	—	89	1	no	—
264	C₂×#41	—	178	1	no	—
265	C₂²×Q₈	—	2	1	no	—
266	C₂×SD₁₆	—	178	2	no	—
267	#131	—	356	4	no	—
268	C₂×M₁₆	—	178	2	no	—
269	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
270	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
271	C₂²×C₈	—	178	1	no	—
272	C₂²×C₈	—	178	2	no	—
273	C₂²×C₈	—	178	1	no	—
274	C₄⋊Q₈	—	2	1	no	—
275	C₄⋊Q₈	—	2	1	no	—
276	C₄⋊Q₈	—	2	1	no	—
277	C₄⋊Q₈	—	89	1	no	—
278	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
279	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
280	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
281	#127	—	89	1	no	—
282	#125	—	2	1	no	—
283	#124	—	178	1	no	—
284	C₂²⋊Q₈	—	2	1	no	—
285	C₂²⋊Q₈	—	2	1	no	—
286	#121	—	89	2	no	—
287	#121	—	178	1	no	—
288	C₄×Q₈	—	2	1	no	—
289	C₄×Q₈	—	2	1	no	—
290	C₄×D₄	—	89	2	no	—
291	C₄×D₄	—	178	1	no	—
292	#117	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
296	#107	—	2	2	no	—
297	#107	—	2	2	no	—
298	#106	—	2	2	no	—
299	#106	—	2	2	no	—
300	#106	—	178	2	no	—
301	#106	—	178	2	no	—
302	#106	—	178	2	no	—
303	C₄⋊C₈	—	89	1	no	—
304	C₄⋊C₈	—	89	1	no	—
305	C₄⋊C₈	—	89	1	no	—
306	C₄⋊C₈	—	89	1	no	—
307	C₄⋊C₈	—	89	2	no	—
308	C₄⋊C₈	—	178	1	no	—
309	C₄⋊C₈	—	178	1	no	—
310	#103	—	178	2	no	—
311	#102	—	178	2	no	—
312	#102	—	178	2	no	—
313	#102	—	178	2	no	—
314	C₂²⋊C₈	—	178	1	no	—
315	C₂²⋊C₈	—	178	2	no	—
316	C₂²⋊C₈	—	178	2	no	—
317	#97	C₂²⋊D₈₉	1	2	yes	—
318	C₄×C₈	—	178	1	no	—
319	C₄×C₈	C₂²×D₈₉	1	2	yes	—
320	#41	—	356	2	no	—
321	#41	—	356	2	no	—
322	C₂×Q₈	—	2	1	no	—
323	C₂×Q₈	—	2	1	no	—
324	C₂×Q₈	—	2	2	no	—
325	C₂×Q₈	—	4	1	no	—
326	C₂×Q₈	—	8	2	no	—
327	C₂×Q₈	—	178	1	no	—
328	C₂×D₄	—	89	2	no	—
329	C₂×D₄	—	178	2	no	—
330	C₂×D₄	—	178	1	no	—
331	C₂×D₄	—	178	1	no	—
332	C₂²×C₄	—	4	1	no	—
333	C₂²×C₄	—	178	2	no	—
334	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
336	C₂²×C₄	#13083573	1	1	yes	characteristic
337	SD₁₆	—	712	2	no	—
338	M₁₆	—	2	2	no	—
339	M₁₆	—	356	4	no	—
340	M₁₆	#13083561	1	4	yes	complemented
341	C₂×C₈	—	356	2	no	—
342	C₂×C₈	—	356	4	no	—
343	C₂×C₈	—	178	1	no	—
344	C₂×C₈	—	178	1	no	—
345	C₂×C₈	—	178	2	no	—
346	C₂×C₈	—	178	1	no	—
347	C₂×C₈	—	178	1	no	—
348	C₂×C₈	—	712	1	no	—
349	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
350	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	—	4	1	no	—
359	C₄⋊C₄	—	4	1	no	—
360	C₄⋊C₄	—	4	1	no	—
361	C₄⋊C₄	—	89	2	no	—
362	C₄⋊C₄	—	178	1	no	—
363	C₂²⋊C₄	—	4	1	no	—
364	C₂²⋊C₄	—	178	2	no	—
365	C₂²⋊C₄	—	178	2	no	—
366	C₄²	—	4	1	no	—
367	C₄²	D₄×D₈₉	1	1	yes	characteristic
368	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
369	C₄²	#13083573	1	1	yes	characteristic
370	C₄²	C₂³×D₈₉	1	1	yes	characteristic
371	C₂³	—	178	2	no	—
372	C₂³	#15667983	1	1	yes	characteristic
373	Q₈	—	4	1	no	—
374	Q₈	—	4	1	no	—
375	Q₈	—	8	1	no	—
376	Q₈	—	8	2	no	—
377	Q₈	—	8	2	no	—
378	Q₈	—	356	2	no	—
379	D₄	—	356	4	no	—
380	D₄	—	356	2	no	—
381	D₄	—	178	2	no	—
382	D₄	—	178	2	no	—
383	D₄	—	712	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	356	2	no	—
392	C₂×C₄	—	356	2	no	—
393	C₂×C₄	—	178	2	no	—
394	C₂×C₄	#15667983	1	1	yes	characteristic
395	C₂×C₄	#15667983	1	1	yes	characteristic
396	C₂×C₄	#15667983	1	1	yes	characteristic
397	C₂×C₄	C₂×#13083561	1	2	yes	—
398	C₂×C₄	#15668043	1	2	yes	—
399	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
401	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	356	1	no	—
404	C₈	—	356	2	no	—
405	C₈	—	356	1	no	—
406	C₈	—	356	1	no	—
407	C₈	—	356	1	no	—
408	C₈	C₂×#13083561	1	4	yes	—
409	C₂²	—	2	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	356	2	no	—
412	C₂²	—	356	2	no	—
413	C₂²	—	356	2	no	—
414	C₂²	#19151800	1	2	yes	—
415	C₂²	C₂×#15667983	1	1	yes	characteristic
416	C₄	—	2	1	no	—
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	8	1	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	1	no	—
422	C₄	—	356	2	no	—
423	C₄	#19151800	1	2	yes	—
424	C₄	C₂²×#13083561	1	1	yes	characteristic
425	C₄	C₂×#15668043	1	1	yes	characteristic
426	C₄	#19152407	1	1	yes	characteristic
427	C₄	#19152414	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	712	2	no	—
430	C₂	C₂×#19151800	1	1	yes	characteristic
431	C₂	#26029937	1	1	yes	characteristic
432	C₂	#26029976	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667983
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3165	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#19152148	C₂²
hypercenter	#3165	D₈₉
hypocenter	C₈₉	#19233
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3165

Complements

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

N	H ≅ G/N	type
4. #26019772	C₂	semidirect
5. #26019748	C₂	semidirect
6. #26019648	C₂	semidirect
7. #26019624	C₂	semidirect
8. #26019004	C₂	semidirect
9. #26018909	C₂	semidirect
10. C₂×#19151347	C₂	semidirect
11. C₈₉×#3165	C₂	semidirect
135. M₁₆×C₈₉	SD₁₆	semidirect
219. #3165	D₈₉	semidirect
228. C₈₉	#19233	semidirect
340. M₁₆	#13083561	semidirect

Maximal subgroups

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

subgroup	index
#26031564	2
#26031380	2
#26028998	2
#26019772	2
#26019748	2
#26019648	2
#26019624	2
#26019004	2
#26018909	2
C₂×#19151347	2
C₈₉×#3165	2
#19233	89