Subgroups — #26124718

Order 12032.

734 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15688892	C₂	1	1	yes	maximal, characteristic
2	#20243109	C₂	1	2	yes	maximal
3	C₂×#15688882	C₂	1	2	yes	maximal
4	#20241617	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2316	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
9	C₂×C₄₇⋊#95	—	2	2	no	—
10	#15688892	C₄	1	4	yes	complemented
11	#15688885	—	2	2	no	—
12	#15688885	—	2	2	no	—
13	#15688882	—	2	4	no	—
14	C₂×#117×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#389	—	2	2	no	—
17	C₄₇×#389	—	2	2	no	—
18	C₄₇×#380	—	2	2	no	—
19	C₂³×Dic₄₇	—	2	1	no	—
20	C₂³×Dic₄₇	—	2	1	no	—
21	C₂×#10625329	—	2	2	no	—
22	C₂×#10625329	—	2	2	no	—
23	C₂×#10625329	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	C₂×C₄	1	4	yes	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	1	no	—
31	C₂×C₄⋊Dic₄₇	Q₈	1	2	yes	—
32	C₂×C₄×Dic₄₇	—	2	2	no	—
33	C₂×C₄×Dic₄₇	—	2	2	no	—
34	C₂×C₄×Dic₄₇	—	2	1	no	—
35	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
36	C₄₇⋊#95	—	4	4	no	—
37	C₂³×C₄×C₄₇	D₄	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	#117×C₄₇	—	2	2	no	—
40	#117×C₄₇	—	2	2	no	—
41	#117×C₄₇	—	2	2	no	—
42	#117×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₇	Q₈	1	2	yes	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	#95×C₄₇	—	2	4	no	—
54	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
55	C₂²×C₄×C₄₇	—	2	2	no	—
56	C₂²×C₄×C₄₇	—	2	2	no	—
57	C₂²×C₄×C₄₇	—	2	2	no	—
58	C₂²×C₄×C₄₇	—	2	2	no	—
59	C₂²×C₄×C₄₇	—	4	2	no	—
60	C₂²×C₄×C₄₇	—	4	2	no	—
61	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
62	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
65	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	#41	1	2	yes	—
68	C₂²×C₄×C₄₇	#41	1	2	yes	—
69	C₂²×C₄×C₄₇	#41	1	2	yes	—
70	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
72	C₂²×Dic₄₇	—	2	2	no	—
73	C₂²×Dic₄₇	—	2	2	no	—
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	—	2	2	no	—
76	C₂²×Dic₄₇	—	4	1	no	—
77	C₂²×Dic₄₇	—	4	1	no	—
78	C₂²×Dic₄₇	—	4	1	no	—
79	C₂²×Dic₄₇	—	4	1	no	—
80	C₂²×Dic₄₇	—	4	2	no	—
81	C₂²×Dic₄₇	—	4	2	no	—
82	C₂²×Dic₄₇	—	4	1	no	—
83	C₂²×Dic₄₇	—	4	1	no	—
84	C₄⋊C₄×C₄₇	—	2	4	no	—
85	C₄⋊C₄×C₄₇	—	2	4	no	—
86	C₄⋊C₄×C₄₇	—	2	2	no	—
87	C₄⋊C₄×C₄₇	—	2	2	no	—
88	C₄⋊C₄×C₄₇	—	2	2	no	—
89	C₄⋊C₄×C₄₇	—	2	2	no	—
90	C₄⋊C₄×C₄₇	—	8	2	no	—
91	C₄⋊C₄×C₄₇	—	8	2	no	—
92	C₂²⋊C₄×C₄₇	—	4	2	no	—
93	C₂²⋊C₄×C₄₇	—	4	2	no	—
94	C₄²×C₄₇	—	4	2	no	—
95	C₄²×C₄₇	—	4	2	no	—
96	C₄⋊Dic₄₇	—	2	4	no	—
97	C₄⋊Dic₄₇	—	4	2	no	—
98	C₄×Dic₄₇	—	2	4	no	—
99	C₄×Dic₄₇	—	4	2	no	—
100	#10625329	—	2	4	no	—
101	#10625329	—	2	4	no	—
102	#10625329	—	4	2	no	—
103	#10625329	—	4	2	no	—
104	C₂×C₄₇⋊C₈	—	2	4	no	—
105	C₂×C₄₇⋊C₈	—	4	2	no	—
106	C₂×C₄₇⋊C₈	—	4	2	no	—
107	C₂³×C₄₇	—	2	1	no	—
108	C₂³×C₄₇	—	2	1	no	—
109	C₂³×C₄₇	—	2	1	no	—
110	C₂³×C₄₇	—	2	1	no	—
111	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂³×C₄₇	#120	1	1	yes	characteristic
113	C₂³×C₄₇	#121	1	1	yes	characteristic
114	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
115	C₂³×C₄₇	#123	1	1	yes	characteristic
116	C₂³×C₄₇	#124	1	1	yes	characteristic
117	C₂³×C₄₇	#124	1	1	yes	characteristic
118	C₂×C₄×C₄₇	—	2	4	no	—
119	C₂×C₄×C₄₇	—	4	2	no	—
120	C₂×C₄×C₄₇	—	4	2	no	—
121	C₂×C₄×C₄₇	—	4	4	no	—
122	C₂×C₄×C₄₇	—	4	2	no	—
123	C₂×C₄×C₄₇	—	4	2	no	—
124	C₂×C₄×C₄₇	—	4	2	no	—
125	C₂×C₄×C₄₇	—	4	2	no	—
126	C₂×C₄×C₄₇	—	4	2	no	—
127	C₂×C₄×C₄₇	—	4	2	no	—
128	C₂×C₄×C₄₇	—	8	2	no	—
129	C₂×C₄×C₄₇	#117	1	2	yes	—
130	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
133	C₂×C₄×C₄₇	#121	1	2	yes	—
134	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
135	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
136	C₂×C₄×C₄₇	#123	1	2	yes	—
137	C₂×C₄×C₄₇	#123	1	2	yes	—
138	C₂×C₄×C₄₇	#124	1	2	yes	—
139	C₂×C₄×C₄₇	#125	1	2	yes	—
140	C₂×C₄×C₄₇	#125	1	2	yes	—
141	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#126	1	2	yes	—
143	C₂×C₄×C₄₇	#126	1	2	yes	—
144	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
145	C₂×Dic₄₇	—	2	4	no	—
146	C₂×Dic₄₇	—	4	2	no	—
147	C₂×Dic₄₇	—	4	2	no	—
148	C₂×Dic₄₇	—	4	2	no	—
149	C₂×Dic₄₇	—	4	2	no	—
150	C₂×Dic₄₇	—	4	2	no	—
151	C₂×Dic₄₇	—	4	2	no	—
152	C₂×Dic₄₇	—	4	4	no	—
153	C₂×Dic₄₇	—	4	2	no	—
154	C₂×Dic₄₇	—	8	2	no	—
155	C₂×Dic₄₇	—	8	1	no	—
156	C₂×Dic₄₇	—	8	1	no	—
157	C₄₇⋊C₈	—	4	4	no	—
158	#11296	—	47	1	no	maximal, Sylow
159	C₂²×C₄₇	—	2	1	no	—
160	C₂²×C₄₇	—	2	1	no	—
161	C₂²×C₄₇	—	2	1	no	—
162	C₂²×C₄₇	—	2	1	no	—
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	—	2	1	no	—
165	C₂²×C₄₇	—	2	1	no	—
166	C₂²×C₄₇	—	2	1	no	—
167	C₂²×C₄₇	—	2	1	no	—
168	C₂²×C₄₇	—	2	1	no	—
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	#382	1	1	yes	characteristic
172	C₂²×C₄₇	#385	1	1	yes	characteristic
173	C₂²×C₄₇	#389	1	1	yes	characteristic
174	C₂²×C₄₇	#393	1	1	yes	characteristic
175	C₂²×C₄₇	#394	1	1	yes	characteristic
176	C₂²×C₄₇	#397	1	1	yes	characteristic
177	C₂²×C₄₇	#400	1	1	yes	characteristic
178	C₂²×C₄₇	#453	1	1	yes	characteristic
179	C₂²×C₄₇	#454	1	1	yes	characteristic
180	C₂²×C₄₇	#455	1	1	yes	characteristic
181	C₂²×C₄₇	#456	1	1	yes	characteristic
182	C₄×C₄₇	—	4	4	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	—	8	2	no	—
185	C₄×C₄₇	#387	1	2	yes	—
186	C₄×C₄₇	#388	1	2	yes	—
187	C₄×C₄₇	#398	1	2	yes	—
188	C₄×C₄₇	#400	1	2	yes	—
189	Dic₄₇	—	4	4	no	—
190	Dic₄₇	—	8	2	no	—
191	#2316	D₄₇	1	1	yes	characteristic
192	C₂×#343	—	47	1	no	—
193	#1736	—	47	2	no	—
194	C₂×#339	—	47	2	no	—
195	C₄⋊#95	—	47	1	no	—
196	C₂×C₄₇	—	2	1	no	—
197	C₂×C₄₇	—	2	1	no	—
198	C₂×C₄₇	—	2	1	no	—
199	C₂×C₄₇	—	2	1	no	—
200	C₂×C₄₇	#1442	1	1	yes	characteristic
201	C₂×C₄₇	#1856	1	1	yes	characteristic
202	C₂×C₄₇	#1857	1	1	yes	characteristic
203	C₂×C₄₇	#2027	1	1	yes	characteristic
204	C₂×C₄₇	#2028	1	1	yes	characteristic
205	C₂×C₄₇	#2039	1	1	yes	characteristic
206	C₂×C₄₇	#2040	1	1	yes	characteristic
207	C₂²×M₁₆	—	47	2	no	—
208	C₂×#117	C₂×D₄₇	1	2	yes	—
209	C₂²×C₄⋊C₄	—	47	1	no	—
210	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
211	C₂²×C₄²	—	47	1	no	—
212	#389	—	2	2	no	—
213	#389	—	2	2	no	—
214	#380	—	2	2	no	—
215	C₂×#95	—	94	2	no	—
216	#343	—	47	4	no	—
217	#340	—	94	2	no	—
218	#340	—	94	2	no	—
219	#339	—	94	4	no	—
220	C₄₇	#11296	1	1	yes	characteristic, complemented, Sylow
221	C₂³×C₄	—	94	1	no	—
222	C₂³×C₄	—	94	1	no	—
223	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
224	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
225	C₂×M₁₆	—	47	4	no	—
226	C₂×M₁₆	—	94	2	no	—
227	C₂×M₁₆	—	94	2	no	—
228	C₂×M₁₆	—	94	2	no	—
229	C₂×M₁₆	—	94	2	no	—
230	C₂×M₁₆	—	94	2	no	—
231	C₂²×C₈	—	94	2	no	—
232	#117	—	2	2	no	—
233	#117	—	2	2	no	—
234	#117	—	2	2	no	—
235	#117	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	—	47	2	no	—
241	C₂×C₄⋊C₄	—	94	2	no	—
242	C₂×C₄⋊C₄	—	94	2	no	—
243	C₂×C₄⋊C₄	—	94	1	no	—
244	C₂×C₄⋊C₄	Dic₉₄	1	2	yes	—
245	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
246	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
247	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	47	2	no	—
251	C₂×C₄²	—	94	2	no	—
252	C₂×C₄²	—	94	2	no	—
253	C₂×C₄²	—	94	1	no	—
254	#95	—	2	4	no	—
255	#95	—	188	4	no	—
256	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
257	C₂²×C₄	—	2	2	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	94	2	no	—
264	C₂²×C₄	—	94	2	no	—
265	C₂²×C₄	—	94	2	no	—
266	C₂²×C₄	—	94	2	no	—
267	C₂²×C₄	—	188	2	no	—
268	C₂²×C₄	—	188	2	no	—
269	C₂²×C₄	—	188	1	no	—
270	C₂²×C₄	—	188	1	no	—
271	C₂²×C₄	—	188	1	no	—
272	C₂²×C₄	—	188	1	no	—
273	C₂²×C₄	—	188	1	no	—
274	C₂²×C₄	—	188	1	no	—
275	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
276	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
278	C₂²×C₄	#10625350	1	2	yes	—
279	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
280	C₂²×C₄	#10625352	1	2	yes	—
281	C₂²×C₄	#10625352	1	1	yes	characteristic
282	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
283	C₂²×C₄	#10625354	1	2	yes	—
284	C₂²×C₄	#10625354	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
286	M₁₆	—	94	4	no	—
287	M₁₆	—	94	4	no	—
288	M₁₆	—	188	2	no	—
289	M₁₆	—	188	2	no	—
290	C₂×C₈	—	94	4	no	—
291	C₂×C₈	—	188	2	no	—
292	C₂×C₈	—	188	2	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	8	2	no	—
300	C₄⋊C₄	—	8	2	no	—
301	C₄⋊C₄	—	94	4	no	—
302	C₄⋊C₄	—	188	2	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₂²⋊C₄	—	4	2	no	—
305	C₄²	—	4	2	no	—
306	C₄²	—	4	2	no	—
307	C₄²	—	94	4	no	—
308	C₄²	—	188	2	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
314	C₂³	#13093993	1	1	yes	characteristic
315	C₂³	#13093995	1	1	yes	characteristic
316	C₂³	#13094000	1	1	yes	characteristic
317	C₂³	#13094007	1	1	yes	characteristic
318	C₂³	#13094011	1	1	yes	characteristic
319	C₂³	#13094013	1	1	yes	characteristic
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	2	no	—
322	C₂×C₄	—	4	2	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	8	2	no	—
331	C₂×C₄	—	94	4	no	—
332	C₂×C₄	—	376	2	no	—
333	C₂×C₄	—	376	1	no	—
334	C₂×C₄	—	376	1	no	—
335	C₂×C₄	—	188	4	no	—
336	C₂×C₄	—	188	2	no	—
337	C₂×C₄	—	188	2	no	—
338	C₂×C₄	—	188	2	no	—
339	C₂×C₄	—	188	2	no	—
340	C₂×C₄	—	188	2	no	—
341	C₂×C₄	—	188	2	no	—
342	C₂×C₄	—	188	2	no	—
343	C₂×C₄	#13093982	1	2	yes	—
344	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
345	C₂×C₄	#13093986	1	1	yes	characteristic
346	C₂×C₄	#13093989	1	1	yes	characteristic
347	C₂×C₄	#13093996	1	2	yes	—
348	C₂×C₄	#13094000	1	2	yes	—
349	C₂×C₄	#13094003	1	2	yes	—
350	C₂×C₄	#13094005	1	2	yes	—
351	C₂×C₄	#13094009	1	2	yes	—
352	C₂×C₄	#13094013	1	2	yes	—
353	C₂×C₄	#13094014	1	2	yes	—
354	C₂×C₄	#13094015	1	2	yes	—
355	C₂×C₄	#13094015	1	1	yes	characteristic
356	C₂×C₄	#13094019	1	2	yes	—
357	C₂×C₄	#13094019	1	2	yes	—
358	C₂×C₄	#13094023	1	1	yes	characteristic
359	C₈	—	188	4	no	—
360	C₂²	—	2	1	no	—
361	C₂²	—	2	1	no	—
362	C₂²	—	2	1	no	—
363	C₂²	—	2	1	no	—
364	C₂²	—	2	1	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	#15688988	1	1	yes	characteristic
373	C₂²	#15688996	1	1	yes	characteristic
374	C₂²	#15689019	1	1	yes	characteristic
375	C₂²	#15689034	1	1	yes	characteristic
376	C₂²	#15689037	1	1	yes	characteristic
377	C₂²	#15689049	1	1	yes	characteristic
378	C₂²	#15689061	1	1	yes	characteristic
379	C₂²	#15689291	1	1	yes	characteristic
380	C₂²	#15689296	1	1	yes	characteristic
381	C₂²	#15689301	1	1	yes	characteristic
382	C₂²	#15689306	1	1	yes	characteristic
383	C₄	—	4	4	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	376	2	no	—
387	C₄	—	188	4	no	—
388	C₄	#15689004	1	2	yes	—
389	C₄	#15689013	1	2	yes	—
390	C₄	#15689056	1	2	yes	—
391	C₄	#15689062	1	2	yes	—
392	C₂	—	2	1	no	—
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	1	no	—
396	C₂	#20241647	1	1	yes	characteristic
397	C₂	#20243598	1	1	yes	characteristic
398	C₂	#20243603	1	1	yes	characteristic
399	C₂	#20244541	1	1	yes	characteristic
400	C₂	#20244546	1	1	yes	characteristic
401	C₂	#20244609	1	1	yes	characteristic
402	C₂	#20244614	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093993
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#2316	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#2316	D₄₇
hypocenter	C₄₇	#11296
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #2316

Complements

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

N	H ≅ G/N	type
10. #15688892	C₄	semidirect
220. C₄₇	#11296	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15688892	2
#20243109	2
C₂×#15688882	2
#20241617	2
C₄₇×#2316	2
#11296	47