Subgroups — #13129326

Order 1664.

910 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#529	C₂	1	1	yes	maximal, characteristic
2	#11719406	C₂	1	4	yes	maximal, complemented
3	#11719390	C₂	1	2	yes	maximal, complemented
4	#11719376	C₂	1	2	yes	maximal, complemented
5	#11719356	C₂	1	4	yes	maximal, complemented
6	#11719330	C₂	1	2	yes	maximal, complemented
7	#11719308	C₂	1	2	yes	maximal
8	#11719272	C₂	1	1	yes	maximal, characteristic, complemented
9	Q₈×Dic₂₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719248	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719247	C₂	1	2	yes	maximal, complemented
13	#11719246	C₂	1	2	yes	maximal, complemented
14	#11719224	C₂	1	2	yes	maximal, complemented
15	#11719223	C₂	1	2	yes	maximal, complemented
16	#11719175	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719175	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₃×#126	C₂²	1	2	yes	—
19	C₁₃×#125	C₂²	1	1	yes	characteristic
20	C₁₃×#124	C₂²	1	1	yes	characteristic
21	C₁₃×#123	C₂²	1	2	yes	—
22	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₃×#121	C₂²	1	1	yes	characteristic
24	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
25	C₄×D₄×C₁₃	C₂²	1	2	yes	—
26	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×#117	C₂²	1	2	yes	—
28	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
29	Q₈×Dic₁₃	C₂²	1	2	yes	—
30	#88198	C₂²	1	2	yes	—
31	#88190	C₂²	1	4	yes	—
32	#88190	C₂²	1	2	yes	—
33	#88189	C₂²	1	4	yes	—
34	D₄×Dic₁₃	C₂²	1	2	yes	—
35	#88180	C₂²	1	2	yes	—
36	#88180	C₂²	1	2	yes	—
37	#88180	C₂²	1	2	yes	—
38	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
39	#88178	C₂²	1	1	yes	characteristic
40	#88178	C₂²	1	1	yes	characteristic
41	#88178	C₂²	1	2	yes	—
42	#88178	C₂²	1	2	yes	—
43	#88178	C₂²	1	2	yes	—
44	#88178	C₂²	1	2	yes	—
45	#88178	C₂²	1	2	yes	—
46	#88144	C₂²	1	4	yes	—
47	#88144	C₂²	1	2	yes	—
48	#88143	C₂²	1	4	yes	—
49	#88143	C₂²	1	4	yes	—
50	#88143	C₂²	1	4	yes	—
51	#88143	C₂²	1	4	yes	—
52	#88142	C₂²	1	4	yes	—
53	#88142	C₂²	1	2	yes	—
54	#88142	C₂²	1	4	yes	—
55	#88141	C₂²	1	2	yes	—
56	#88141	C₂²	1	4	yes	—
57	#88141	C₂²	1	2	yes	—
58	#88133	C₂²	1	4	yes	—
59	#88133	C₂²	1	4	yes	—
60	#88133	C₂²	1	4	yes	—
61	#88133	C₂²	1	4	yes	—
62	#88133	C₂²	1	4	yes	—
63	#88133	C₂²	1	4	yes	—
64	#88132	C₂²	1	4	yes	—
65	#88132	C₂²	1	4	yes	—
66	#88132	C₂²	1	4	yes	—
67	#88131	C₂²	1	4	yes	—
68	#88124	C₂²	1	2	yes	—
69	#88124	C₂²	1	2	yes	—
70	#88124	C₂²	1	2	yes	—
71	#88123	C₂²	1	1	yes	characteristic
72	#88123	C₂²	1	1	yes	characteristic
73	#88123	C₂²	1	1	yes	characteristic
74	#88123	C₂²	1	1	yes	characteristic
75	#88123	C₂²	1	2	yes	—
76	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
77	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
78	C₄×Dic₂₆	C₂²	1	2	yes	—
79	C₄×Dic₂₆	C₂²	1	2	yes	—
80	C₄×Dic₂₆	C₂²	1	2	yes	—
81	C₄×Dic₂₆	C₂²	1	2	yes	—
82	C₄×Dic₂₆	C₂²	1	2	yes	—
83	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₁₃	C₂³	1	2	yes	—
86	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₂³	1	4	yes	—
91	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
92	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
93	C₂×Dic₂₆	C₂³	1	2	yes	—
94	C₂×Dic₂₆	C₂³	1	2	yes	—
95	C₂×Dic₂₆	C₂³	1	2	yes	—
96	C₂×Dic₂₆	C₂³	1	4	yes	—
97	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
98	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
99	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
100	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
101	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
102	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
103	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
104	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
105	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
106	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
107	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
108	C₄²×C₁₃	C₂³	1	1	yes	characteristic
109	C₄²×C₁₃	C₂³	1	1	yes	characteristic
110	C₄²×C₁₃	C₂³	1	2	yes	—
111	C₄²×C₁₃	C₂³	1	1	yes	characteristic
112	C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
114	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
115	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
116	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
119	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
120	C₄⋊Dic₁₃	C₂³	1	2	yes	—
121	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
122	C₄⋊Dic₁₃	C₂³	1	2	yes	—
123	C₄⋊Dic₁₃	C₂³	1	2	yes	—
124	C₄⋊Dic₁₃	C₂³	1	2	yes	—
125	C₄⋊Dic₁₃	C₂³	1	2	yes	—
126	C₄⋊Dic₁₃	C₂³	1	2	yes	—
127	C₄⋊Dic₁₃	C₂³	1	2	yes	—
128	C₄⋊Dic₁₃	C₂³	1	4	yes	—
129	C₄⋊Dic₁₃	C₂³	1	4	yes	—
130	#6101	C₂³	1	2	yes	—
131	#6101	C₂³	1	2	yes	—
132	#6101	C₂³	1	4	yes	—
133	#6101	C₂³	1	4	yes	—
134	#6101	C₂³	1	2	yes	—
135	#6101	C₂³	1	2	yes	—
136	#6101	C₂³	1	4	yes	—
137	#6101	C₂³	1	4	yes	—
138	#6101	C₂³	1	4	yes	—
139	#6101	C₂³	1	4	yes	—
140	#6101	C₂³	1	4	yes	—
141	#6101	C₂³	1	4	yes	—
142	C₄×Dic₁₃	C₂³	1	4	yes	—
143	C₄×Dic₁₃	C₂³	1	2	yes	—
144	C₄×Dic₁₃	C₂³	1	2	yes	—
145	C₄×Dic₁₃	C₂³	1	4	yes	—
146	C₄×Dic₁₃	C₂³	1	4	yes	—
147	C₄×Dic₁₃	C₂³	1	4	yes	—
148	#3555	—	13	1	no	maximal, Sylow
149	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
150	C₂³×C₁₃	C₂⁴	1	2	yes	—
151	Q₈×C₁₃	—	2	2	no	—
152	D₄×C₁₃	—	2	2	no	—
153	D₄×C₁₃	—	4	2	no	—
154	C₂×C₄×C₁₃	—	2	4	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×Dic₁₃	—	4	4	no	—
168	C₂×Dic₁₃	C₂⁴	1	4	yes	—
169	C₂×Dic₁₃	C₂⁴	1	2	yes	—
170	C₂×Dic₁₃	C₂⁴	1	2	yes	—
171	C₂×Dic₁₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₃	C₂⁴	1	4	yes	—
173	C₂×Dic₁₃	C₂⁴	1	2	yes	—
174	Dic₂₆	—	2	2	no	—
175	Dic₂₆	—	2	2	no	—
176	Dic₂₆	—	2	4	no	—
177	Dic₂₆	—	4	4	no	—
178	Dic₂₆	—	4	2	no	—
179	Dic₂₆	—	4	2	no	—
180	#563	—	13	4	no	—
181	Q₈²	—	13	1	no	—
182	#557	—	13	2	no	—
183	#557	—	13	1	no	—
184	#556	—	13	2	no	—
185	#556	—	13	2	no	—
186	#556	—	13	1	no	—
187	#554	—	13	1	no	—
188	#552	—	13	2	no	—
189	#544	—	13	2	no	—
190	#542	—	13	2	no	—
191	#541	—	13	4	no	—
192	#541	—	13	2	no	—
193	#541	—	13	2	no	—
194	#533	—	13	1	no	—
195	#533	—	13	1	no	—
196	#529	D₁₃	1	1	yes	characteristic
197	C₂²×C₁₃	—	2	1	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
204	C₄×C₁₃	—	2	1	no	—
205	C₄×C₁₃	—	2	2	no	—
206	C₄×C₁₃	—	2	1	no	—
207	C₄×C₁₃	—	2	2	no	—
208	C₄×C₁₃	—	2	1	no	—
209	C₄×C₁₃	—	2	1	no	—
210	C₄×C₁₃	—	2	2	no	—
211	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
212	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
213	Dic₁₃	—	2	2	no	—
214	Dic₁₃	—	2	2	no	—
215	Dic₁₃	—	2	4	no	—
216	Dic₁₃	—	2	2	no	—
217	Dic₁₃	—	2	4	no	—
218	Dic₁₃	—	2	2	no	—
219	C₄⋊Q₈	—	13	2	no	—
220	C₄⋊Q₈	—	13	4	no	—
221	C₄⋊Q₈	—	13	2	no	—
222	C₄⋊Q₈	—	13	4	no	—
223	C₄⋊Q₈	—	13	1	no	—
224	C₄⋊Q₈	—	13	1	no	—
225	C₄⋊Q₈	—	13	1	no	—
226	C₄⋊Q₈	—	13	1	no	—
227	C₄⋊Q₈	—	13	2	no	—
228	#126	—	13	4	no	—
229	#126	—	13	4	no	—
230	#126	—	13	4	no	—
231	#126	—	13	4	no	—
232	#126	—	13	4	no	—
233	#126	—	13	4	no	—
234	#126	C₂×D₁₃	1	2	yes	—
235	#125	—	13	4	no	—
236	#125	—	13	4	no	—
237	#125	—	13	4	no	—
238	#125	—	13	2	no	—
239	#125	—	13	4	no	—
240	#125	—	13	4	no	—
241	#125	—	13	2	no	—
242	#125	—	13	2	no	—
243	#125	—	13	2	no	—
244	#125	C₂×D₁₃	1	1	yes	characteristic
245	#124	—	13	2	no	—
246	#124	—	13	4	no	—
247	#124	C₂×D₁₃	1	1	yes	characteristic
248	#123	—	13	4	no	—
249	#123	C₂×D₁₃	1	2	yes	—
250	C₂²⋊Q₈	—	13	2	no	—
251	C₂²⋊Q₈	—	13	1	no	—
252	C₂²⋊Q₈	—	13	1	no	—
253	C₂²⋊Q₈	—	13	2	no	—
254	C₂²⋊Q₈	—	13	2	no	—
255	C₂²⋊Q₈	—	13	2	no	—
256	C₂²⋊Q₈	—	13	2	no	—
257	C₂²⋊Q₈	—	13	4	no	—
258	C₂²⋊Q₈	—	13	4	no	—
259	C₂²⋊Q₈	—	13	4	no	—
260	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
261	#121	C₂×D₁₃	1	1	yes	characteristic
262	C₄×Q₈	—	13	2	no	—
263	C₄×Q₈	—	13	4	no	—
264	C₄×Q₈	—	13	2	no	—
265	C₄×Q₈	—	13	2	no	—
266	C₄×Q₈	—	13	2	no	—
267	C₄×Q₈	—	13	1	no	—
268	C₄×Q₈	—	13	2	no	—
269	C₄×Q₈	—	13	2	no	—
270	C₄×Q₈	—	13	1	no	—
271	C₄×Q₈	—	13	2	no	—
272	C₄×Q₈	—	13	2	no	—
273	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
274	C₄×D₄	—	13	2	no	—
275	C₄×D₄	C₂×D₁₃	1	2	yes	—
276	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
277	#117	—	13	2	no	—
278	#117	—	13	2	no	—
279	#117	—	13	2	no	—
280	#117	—	13	4	no	—
281	#117	C₂×D₁₃	1	2	yes	—
282	C₂×C₄⋊C₄	—	13	2	no	—
283	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
284	C₂×C₁₃	—	4	1	no	—
285	C₂×C₁₃	—	4	2	no	—
286	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
287	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
288	C₂×C₁₃	#585	1	1	yes	characteristic
289	C₂×Q₈	—	13	1	no	—
290	C₂×Q₈	—	13	1	no	—
291	C₂×Q₈	—	13	2	no	—
292	C₂×Q₈	—	13	2	no	—
293	C₂×Q₈	—	13	2	no	—
294	C₂×Q₈	—	13	4	no	—
295	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
296	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
297	C₂×D₄	C₂²×D₁₃	1	2	yes	—
298	C₂²×C₄	—	13	4	no	—
299	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
300	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
301	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
302	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
303	C₄⋊C₄	—	13	1	no	—
304	C₄⋊C₄	—	13	2	no	—
305	C₄⋊C₄	—	13	4	no	—
306	C₄⋊C₄	—	13	2	no	—
307	C₄⋊C₄	—	13	2	no	—
308	C₄⋊C₄	—	13	1	no	—
309	C₄⋊C₄	—	13	2	no	—
310	C₄⋊C₄	—	13	4	no	—
311	C₄⋊C₄	—	13	2	no	—
312	C₄⋊C₄	—	13	2	no	—
313	C₄⋊C₄	—	13	2	no	—
314	C₄⋊C₄	—	13	2	no	—
315	C₄⋊C₄	—	13	4	no	—
316	C₄⋊C₄	—	13	4	no	—
317	C₄⋊C₄	—	13	4	no	—
318	C₄⋊C₄	—	13	4	no	—
319	C₄⋊C₄	—	13	4	no	—
320	C₄⋊C₄	—	13	2	no	—
321	C₄⋊C₄	—	13	2	no	—
322	C₄⋊C₄	—	13	2	no	—
323	C₄⋊C₄	—	13	4	no	—
324	C₄⋊C₄	—	13	4	no	—
325	C₄⋊C₄	—	13	4	no	—
326	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
327	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
328	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
329	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
330	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
331	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
332	C₂²⋊C₄	—	13	2	no	—
333	C₂²⋊C₄	—	13	4	no	—
334	C₂²⋊C₄	—	13	2	no	—
335	C₂²⋊C₄	—	13	4	no	—
336	C₂²⋊C₄	—	13	4	no	—
337	C₂²⋊C₄	—	13	4	no	—
338	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
339	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
340	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
341	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
342	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
343	C₄²	—	13	4	no	—
344	C₄²	—	13	2	no	—
345	C₄²	—	13	2	no	—
346	C₄²	—	13	4	no	—
347	C₄²	—	13	4	no	—
348	C₄²	—	13	4	no	—
349	C₄²	C₂²×D₁₃	1	1	yes	characteristic
350	C₄²	C₂²×D₁₃	1	1	yes	characteristic
351	C₄²	C₂²×D₁₃	1	1	yes	characteristic
352	C₄²	C₂²×D₁₃	1	1	yes	characteristic
353	C₄²	C₂²×D₁₃	1	2	yes	—
354	C₁₃	#3555	1	1	yes	characteristic, complemented, Sylow
355	C₂³	C₂³×D₁₃	1	1	yes	characteristic
356	C₂³	C₂³×D₁₃	1	2	yes	—
357	Q₈	—	2	2	no	—
358	Q₈	—	26	2	no	—
359	Q₈	—	26	2	no	—
360	Q₈	—	26	4	no	—
361	Q₈	—	52	2	no	—
362	Q₈	—	52	2	no	—
363	Q₈	—	52	4	no	—
364	D₄	—	2	2	no	—
365	D₄	—	4	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	13	4	no	—
371	C₂×C₄	—	13	2	no	—
372	C₂×C₄	—	13	2	no	—
373	C₂×C₄	—	13	2	no	—
374	C₂×C₄	—	13	4	no	—
375	C₂×C₄	—	13	2	no	—
376	C₂×C₄	—	52	4	no	—
377	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₁₃	1	2	yes	—
379	C₂×C₄	C₂³×D₁₃	1	2	yes	—
380	C₂×C₄	C₂³×D₁₃	1	2	yes	—
381	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
382	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
383	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
384	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
385	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	2	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	2	no	—
392	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
393	C₄	—	2	1	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	2	no	—
397	C₄	—	2	1	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	2	no	—
400	C₄	—	26	2	no	—
401	C₄	—	26	2	no	—
402	C₄	—	26	4	no	—
403	C₄	—	26	2	no	—
404	C₄	—	26	4	no	—
405	C₄	—	26	2	no	—
406	C₄	#88257	1	2	yes	—
407	C₄	#88257	1	2	yes	—
408	C₂	—	4	1	no	—
409	C₂	—	4	2	no	—
410	C₂	C₂×#88257	1	1	yes	characteristic
411	C₂	C₂×#88257	1	1	yes	characteristic
412	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#529	C₂
prime radical	C₁₃×#121	C₂²
hypercenter	#529	D₁₃
hypocenter	C₁₃	#3555
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
2. #11719406	C₂	semidirect
3. #11719390	C₂	semidirect
4. #11719376	C₂	semidirect
5. #11719356	C₂	semidirect
6. #11719330	C₂	semidirect
8. #11719272	C₂	semidirect
9. Q₈×Dic₂₆	C₂	semidirect
10. #11719248	C₂	semidirect
11. #11719247	C₂	semidirect
12. #11719247	C₂	semidirect
13. #11719246	C₂	semidirect
14. #11719224	C₂	semidirect
15. #11719223	C₂	semidirect
16. #11719175	C₂	semidirect
17. #11719175	C₂	semidirect
354. C₁₃	#3555	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#529	2
#11719406	2
#11719390	2
#11719376	2
#11719356	2
#11719330	2
#11719308	2
#11719272	2
Q₈×Dic₂₆	2
#11719248	2
#11719247	2
#11719246	2
#11719224	2
#11719223	2
#11719175	2
#3555	13