Subgroups — #16018869

Order 3328.

598 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125264	C₂	1	1	yes	maximal, characteristic, complemented
2	#13117095	C₂	1	2	yes	maximal, complemented
3	#13117070	C₂	1	2	yes	maximal, complemented
4	#13116886	C₂	1	1	yes	maximal, characteristic, complemented
5	#13116881	C₂	1	1	yes	maximal, characteristic, complemented
6	#13116876	C₂	1	1	yes	maximal, characteristic, complemented
7	#13116871	C₂	1	1	yes	maximal, characteristic, complemented
8	#13116774	C₂	1	2	yes	maximal, complemented
9	#13116757	C₂	1	2	yes	maximal, complemented
10	#13116635	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#529	—	2	1	no	—
13	C₂×#88158	—	2	1	no	—
14	C₂×#88158	C₂²	1	2	yes	—
15	#11719182	—	2	1	no	—
16	C₁₃×#499	C₂²	1	1	yes	characteristic
17	C₁₃×#495	C₂²	1	1	yes	characteristic
18	C₁₃×#488	—	2	1	no	—
19	C₁₃×#467	C₂²	1	1	yes	characteristic
20	C₁₃×#466	C₂²	1	1	yes	characteristic
21	C₁₃×#465	—	2	1	no	—
22	C₄×C₁₃×Q₁₆	C₂²	1	1	yes	characteristic
23	C₄×C₁₃×SD₁₆	—	2	1	no	—
24	C₄×C₁₃×D₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
26	C₂×#88069	C₂²	1	2	yes	—
27	C₂×#88068	C₂²	1	2	yes	—
28	C₂×#88067	C₂²	1	2	yes	—
29	C₂×#88066	C₂²	1	2	yes	—
30	#11718360	C₂²	1	1	yes	characteristic
31	#11718357	—	2	1	no	—
32	#11718357	C₂²	1	2	yes	—
33	#11718356	C₂²	1	1	yes	characteristic
34	#11718354	—	2	1	no	—
35	C₂²⋊#6090	C₂²	1	2	yes	—
36	#11718084	C₂²	1	2	yes	—
37	#11718084	C₂²	1	2	yes	—
38	#11718083	C₂²	1	2	yes	—
39	#11718083	C₂²	1	2	yes	—
40	C₄⋊#6090	C₂²	1	1	yes	characteristic
41	C₄⋊#6090	C₂²	1	1	yes	characteristic
42	C₄×#6090	C₂²	1	2	yes	—
43	C₂×#6127	—	2	2	no	—
44	C₂×C₁₃×Q₁₆	C₂³	1	1	yes	characteristic
45	C₂×C₁₃×SD₁₆	—	2	1	no	—
46	C₂×C₁₃×D₈	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
49	C₁₃×#126	—	4	1	no	—
50	C₁₃×#125	—	2	1	no	—
51	C₁₃×#124	—	2	1	no	—
52	C₁₃×#123	—	4	1	no	—
53	C₁₃×C₂²⋊Q₈	—	2	1	no	—
54	C₁₃×#121	—	2	1	no	—
55	C₄×Q₈×C₁₃	—	2	1	no	—
56	C₄×D₄×C₁₃	—	2	1	no	—
57	C₄×D₄×C₁₃	—	4	1	no	—
58	C₁₃×#117	—	4	1	no	—
59	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
60	#88184	—	4	1	no	—
61	#88184	—	4	1	no	—
62	C₂×Dic₅₂	—	2	1	no	—
63	C₂×Dic₅₂	C₂³	1	2	yes	—
64	#88158	—	4	2	no	—
65	#88158	—	4	2	no	—
66	#88158	—	4	4	no	—
67	C₂×D₁₀₄	—	2	1	no	—
68	C₂×D₁₀₄	C₂³	1	2	yes	—
69	C₂×#6095	—	2	2	no	—
70	C₂×#6095	—	2	2	no	—
71	#88129	—	2	2	no	—
72	#88128	—	2	1	no	—
73	C₄×D₅₂	—	4	1	no	—
74	C₄×D₅₂	—	4	1	no	—
75	#88123	—	2	1	no	—
76	C₁₃×#107	C₂³	1	1	yes	characteristic
77	C₁₃×#107	C₂³	1	1	yes	characteristic
78	C₁₃×#106	—	2	1	no	—
79	C₁₃×#103	—	2	1	no	—
80	C₁₃×#103	—	2	1	no	—
81	C₁₃×#102	—	2	1	no	—
82	C₁₃×#102	—	2	1	no	—
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
87	#88069	—	4	2	no	—
88	#88068	—	4	2	no	—
89	#88067	—	4	2	no	—
90	#88066	—	4	2	no	—
91	C₂×#6090	C₂³	1	2	yes	—
92	C₂×#6090	C₂³	1	2	yes	—
93	#33778	—	13	1	no	maximal, Sylow
94	C₂×Q₈×C₁₃	—	2	1	no	—
95	C₂×D₄×C₁₃	—	2	1	no	—
96	C₂×D₄×C₁₃	—	4	1	no	—
97	C₂²×C₄×C₁₃	—	4	1	no	—
98	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
99	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
100	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₂²⋊D₁₃	—	4	2	no	—
102	#6127	—	4	4	no	—
103	#6127	—	4	4	no	—
104	C₂×D₅₂	—	2	2	no	—
105	C₂×D₅₂	—	4	1	no	—
106	C₂×D₅₂	—	4	1	no	—
107	C₂×C₄×D₁₃	—	4	2	no	—
108	C₂×Dic₂₆	—	2	2	no	—
109	C₁₃×Q₁₆	—	2	1	no	—
110	C₁₃×Q₁₆	—	2	1	no	—
111	C₁₃×SD₁₆	—	4	2	no	—
112	C₁₃×D₈	—	2	1	no	—
113	C₁₃×D₈	—	2	1	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	1	no	—
116	C₂×C₈×C₁₃	—	2	1	no	—
117	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	—	2	1	no	—
122	C₁₃×C₄⋊C₄	—	2	1	no	—
123	C₁₃×C₄⋊C₄	—	4	1	no	—
124	C₁₃×C₄⋊C₄	—	4	1	no	—
125	C₁₃×C₄⋊C₄	—	4	1	no	—
126	C₁₃×C₄⋊C₄	—	4	1	no	—
127	C₁₃×C₂²⋊C₄	—	4	1	no	—
128	C₁₃×C₂²⋊C₄	—	4	1	no	—
129	C₁₃×C₂²⋊C₄	—	4	1	no	—
130	C₁₃×C₂²⋊C₄	—	4	1	no	—
131	C₁₃×C₂²⋊C₄	—	4	1	no	—
132	C₄²×C₁₃	—	4	1	no	—
133	C₄²×C₁₃	D₈	1	1	yes	characteristic
134	C₄²×C₁₃	D₈	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
137	#6103	—	4	2	no	—
138	#6103	—	4	2	no	—
139	C₄⋊Dic₁₃	—	4	1	no	—
140	C₄⋊Dic₁₃	—	4	1	no	—
141	Dic₅₂	—	2	2	no	—
142	Dic₅₂	—	2	2	no	—
143	Dic₅₂	—	4	2	no	—
144	D₁₀₄	—	2	2	no	—
145	D₁₀₄	—	2	2	no	—
146	D₁₀₄	—	4	2	no	—
147	#6095	—	4	4	no	—
148	#6095	—	4	4	no	—
149	#6090	—	2	2	no	—
150	#6090	—	2	2	no	—
151	#3168	D₁₃	1	1	yes	characteristic, complemented
152	#3147	—	13	1	no	—
153	#2249	—	13	2	no	—
154	#2242	—	13	2	no	—
155	#2209	—	13	1	no	—
156	#2208	—	13	1	no	—
157	#2207	—	13	1	no	—
158	#2206	—	13	1	no	—
159	#2189	—	13	2	no	—
160	#2186	—	13	2	no	—
161	#2162	—	13	1	no	—
162	C₂³×C₁₃	—	4	1	no	—
163	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
164	C₂²×D₁₃	—	4	2	no	—
165	Q₈×C₁₃	—	4	1	no	—
166	Q₈×C₁₃	—	4	1	no	—
167	D₄×C₁₃	—	4	1	no	—
168	D₄×C₁₃	—	4	1	no	—
169	D₄×C₁₃	—	8	2	no	—
170	C₂×C₄×C₁₃	—	2	1	no	—
171	C₂×C₄×C₁₃	—	2	1	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	—	4	1	no	—
174	C₂×C₄×C₁₃	—	4	1	no	—
175	C₂×C₄×C₁₃	—	4	1	no	—
176	C₂×C₄×C₁₃	—	4	1	no	—
177	C₂×C₄×C₁₃	—	8	2	no	—
178	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
181	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
184	C₂²⋊D₁₃	—	8	4	no	—
185	C₂×Dic₁₃	—	4	2	no	—
186	D₅₂	—	4	2	no	—
187	D₅₂	—	4	2	no	—
188	D₅₂	—	8	2	no	—
189	D₅₂	—	8	2	no	—
190	C₄×D₁₃	—	8	4	no	—
191	Dic₂₆	—	4	2	no	—
192	Dic₂₆	—	4	2	no	—
193	C₈×C₁₃	—	2	1	no	—
194	C₈×C₁₃	—	2	1	no	—
195	C₈×C₁₃	AGL(1,ℤ/8)	1	2	yes	—
196	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
197	C₈×C₁₃	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×#135	—	13	2	no	—
199	C₂×#135	—	26	1	no	—
200	#532	—	26	1	no	—
201	#529	—	2	1	no	—
202	C₂×Q₃₂	—	13	2	no	—
203	C₂×SD₃₂	—	13	2	no	—
204	C₂×SD₃₂	—	13	2	no	—
205	C₂×D₁₆	—	13	2	no	—
206	#499	C₂×D₁₃	1	1	yes	characteristic
207	#495	—	13	2	no	—
208	#495	—	26	1	no	—
209	#495	C₂×D₁₃	1	1	yes	characteristic
210	#494	—	13	1	no	—
211	#493	—	13	1	no	—
212	#492	—	26	1	no	—
213	#488	—	2	1	no	—
214	#467	C₂×D₁₃	1	1	yes	characteristic
215	#466	C₂×D₁₃	1	1	yes	characteristic
216	#465	—	2	1	no	—
217	C₄×Q₁₆	C₂×D₁₃	1	1	yes	characteristic
218	C₄×SD₁₆	—	2	1	no	—
219	C₄×D₈	C₂×D₁₃	1	1	yes	characteristic
220	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
221	C₄⋊C₁₆	—	13	1	no	—
222	C₄⋊C₁₆	—	13	1	no	—
223	#358	—	13	2	no	—
224	#358	—	13	2	no	—
225	#357	—	13	2	no	—
226	#357	—	13	2	no	—
227	C₂²⋊C₁₆	—	13	2	no	—
228	C₄×C₁₆	—	13	2	no	—
229	C₂²×C₁₃	—	2	1	no	—
230	C₂²×C₁₃	—	2	1	no	—
231	C₂²×C₁₃	—	2	1	no	—
232	C₂²×C₁₃	—	8	1	no	—
233	C₂²×C₁₃	—	8	1	no	—
234	C₂²×C₁₃	—	8	1	no	—
235	C₂²×C₁₃	C₂²×D₈	1	1	yes	characteristic
236	C₂×D₁₃	—	8	2	no	—
237	C₂×D₁₃	—	8	2	no	—
238	C₂×D₁₃	—	8	2	no	—
239	C₄×C₁₃	—	2	1	no	—
240	C₄×C₁₃	—	2	1	no	—
241	C₄×C₁₃	—	2	1	no	—
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	8	1	no	—
244	C₄×C₁₃	—	8	1	no	—
245	C₄×C₁₃	—	8	1	no	—
246	C₄×C₁₃	#508	1	2	yes	—
247	C₄×C₁₃	#535	1	1	yes	characteristic
248	C₄×C₁₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
249	Dic₁₃	—	8	2	no	—
250	C₂×#41	—	26	2	no	—
251	#135	—	52	2	no	—
252	#135	—	52	2	no	—
253	#135	—	52	4	no	—
254	C₂×Q₁₆	—	13	2	no	—
255	C₂×Q₁₆	—	26	1	no	—
256	C₂×Q₁₆	C₂²×D₁₃	1	1	yes	characteristic
257	C₂×SD₁₆	—	2	1	no	—
258	C₂×SD₁₆	—	26	2	no	—
259	C₂×SD₁₆	—	26	2	no	—
260	C₂×D₈	—	13	2	no	—
261	C₂×D₈	—	26	1	no	—
262	C₂×D₈	C₂²×D₁₃	1	1	yes	characteristic
263	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
264	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
265	C₄⋊Q₈	—	26	1	no	—
266	#127	—	26	1	no	—
267	#126	—	4	1	no	—
268	#125	—	2	1	no	—
269	#124	—	2	1	no	—
270	#124	—	26	2	no	—
271	#123	—	4	1	no	—
272	C₂²⋊Q₈	—	2	1	no	—
273	#121	—	2	1	no	—
274	#121	—	52	1	no	—
275	#121	—	52	1	no	—
276	C₄×Q₈	—	2	1	no	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	4	1	no	—
279	C₄×D₄	—	52	1	no	—
280	C₄×D₄	—	52	1	no	—
281	#117	—	4	1	no	—
282	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
283	Q₃₂	—	52	2	no	—
284	SD₃₂	—	52	2	no	—
285	SD₃₂	—	52	2	no	—
286	D₁₆	—	52	2	no	—
287	C₂×C₁₆	—	13	2	no	—
288	C₂×C₁₆	—	13	2	no	—
289	#107	C₂²×D₁₃	1	1	yes	characteristic
290	#107	C₂²×D₁₃	1	1	yes	characteristic
291	#106	—	2	1	no	—
292	#103	—	2	1	no	—
293	#103	—	2	1	no	—
294	#102	—	2	1	no	—
295	#102	—	2	1	no	—
296	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
297	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
300	C₂×C₁₃	—	4	1	no	—
301	C₂×C₁₃	—	16	1	no	—
302	C₂×C₁₃	#3205	1	1	yes	characteristic
303	C₂×C₁₃	C₂×#508	1	1	yes	characteristic
304	C₂×C₁₃	#3414	1	1	yes	characteristic
305	D₁₃	—	16	2	no	—
306	#41	—	52	4	no	—
307	#41	—	52	4	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	26	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	26	2	no	—
313	C₂×D₄	—	52	2	no	—
314	C₂×D₄	—	52	1	no	—
315	C₂×D₄	—	52	1	no	—
316	C₂²×C₄	—	4	1	no	—
317	C₂²×C₄	—	52	2	no	—
318	C₂²×C₄	#6104	1	1	yes	characteristic
319	C₂²×C₄	#6104	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
321	Q₁₆	—	2	1	no	—
322	Q₁₆	—	2	1	no	—
323	Q₁₆	—	26	2	no	—
324	Q₁₆	—	26	2	no	—
325	Q₁₆	—	52	2	no	—
326	SD₁₆	—	4	2	no	—
327	SD₁₆	—	52	4	no	—
328	SD₁₆	—	52	4	no	—
329	D₈	—	2	1	no	—
330	D₈	—	2	1	no	—
331	D₈	—	26	2	no	—
332	D₈	—	26	2	no	—
333	D₈	—	52	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
338	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
339	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
340	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
341	C₄⋊C₄	—	2	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	4	1	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	52	1	no	—
348	C₄⋊C₄	—	52	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	—	4	1	no	—
352	C₂²⋊C₄	—	4	1	no	—
353	C₂²⋊C₄	—	4	1	no	—
354	C₂²⋊C₄	—	52	2	no	—
355	C₂²⋊C₄	—	52	2	no	—
356	C₄²	—	4	1	no	—
357	C₄²	#6104	1	1	yes	characteristic
358	C₄²	#6104	1	1	yes	characteristic
359	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
360	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
361	C₁₆	—	26	2	no	—
362	C₁₆	—	26	2	no	—
363	C₁₃	#33778	1	1	yes	characteristic, complemented, Sylow
364	C₂³	—	4	1	no	—
365	C₂³	—	52	2	no	—
366	C₂³	C₂×#6104	1	1	yes	characteristic
367	Q₈	—	4	1	no	—
368	Q₈	—	4	1	no	—
369	Q₈	—	52	2	no	—
370	Q₈	—	52	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	1	no	—
373	D₄	—	8	2	no	—
374	D₄	—	52	2	no	—
375	D₄	—	52	2	no	—
376	D₄	—	104	2	no	—
377	D₄	—	104	4	no	—
378	D₄	—	104	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	8	2	no	—
387	C₂×C₄	—	52	2	no	—
388	C₂×C₄	—	104	4	no	—
389	C₂×C₄	C₂×#6104	1	1	yes	characteristic
390	C₂×C₄	C₂×#6104	1	1	yes	characteristic
391	C₂×C₄	C₂×#6104	1	1	yes	characteristic
392	C₂×C₄	C₂×#6104	1	1	yes	characteristic
393	C₂×C₄	C₂×#6104	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	#88203	1	2	yes	—
398	C₈	#88256	1	1	yes	characteristic
399	C₈	#88256	1	1	yes	characteristic
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	104	2	no	—
407	C₂²	—	104	2	no	—
408	C₂²	—	104	2	no	—
409	C₂²	C₂²×#6104	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	1	no	—
417	C₄	—	104	2	no	—
418	C₄	#11718855	1	2	yes	—
419	C₄	C₂×#88203	1	1	yes	characteristic
420	C₄	#11719535	1	1	yes	characteristic
421	C₂	—	4	1	no	—
422	C₂	—	16	1	no	—
423	C₂	—	208	2	no	—
424	C₂	#13125751	1	1	yes	characteristic
425	C₂	C₂×#11718855	1	1	yes	characteristic
426	C₂	#13127970	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#6104
commutator, cosocle	C₂×C₈×C₁₃	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#3168	C₂
socle	C₂²×C₁₃	C₂²×D₈
hypercenter	#3168	D₁₃
hypocenter	C₁₃	#33778
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #13125264	C₂	semidirect
2. #13117095	C₂	semidirect
3. #13117070	C₂	semidirect
4. #13116886	C₂	semidirect
5. #13116881	C₂	semidirect
6. #13116876	C₂	semidirect
7. #13116871	C₂	semidirect
8. #13116774	C₂	semidirect
9. #13116757	C₂	semidirect
10. #13116635	C₂	semidirect
11. C₁₃×#3168	C₂	semidirect
151. #3168	D₁₃	semidirect
363. C₁₃	#33778	semidirect

Maximal subgroups

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

subgroup	index
#13125264	2
#13117095	2
#13117070	2
#13116886	2
#13116881	2
#13116876	2
#13116871	2
#13116774	2
#13116757	2
#13116635	2
C₁₃×#3168	2
#33778	13