Subgroups — #26199737

Order 12032.

584 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254726	C₂	1	2	yes	maximal
2	#20253974	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252363	C₂	1	1	yes	maximal, characteristic
4	#20242907	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242902	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242883	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242878	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242819	C₂	1	2	yes	maximal, complemented
9	#20242812	C₂	1	2	yes	maximal, complemented
10	#20242086	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#334	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689680	C₂²	1	2	yes	—
13	#15689657	C₂²	1	1	yes	characteristic
14	#15689528	C₂²	1	1	yes	characteristic
15	#15689503	C₂²	1	1	yes	characteristic
16	#15689474	C₂²	1	2	yes	—
17	#15689431	—	2	2	no	—
18	#15689409	C₂²	1	2	yes	—
19	#15689404	C₂²	1	2	yes	—
20	#15689364	—	2	2	no	—
21	#15689364	—	2	1	no	—
22	#15689364	—	2	1	no	—
23	#15689352	—	2	2	no	—
24	#15689346	—	2	2	no	—
25	#15689334	C₂²	1	2	yes	—
26	#15689329	C₂²	1	2	yes	—
27	#15689253	C₂²	1	1	yes	characteristic
28	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
29	C₄×Dic₁₈₈	—	2	1	no	—
30	C₄×Dic₁₈₈	—	2	1	no	—
31	#15689202	C₂²	1	1	yes	characteristic
32	#15689194	—	2	1	no	—
33	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₄₇	—	2	1	no	—
35	#15689182	—	2	1	no	—
36	#15689180	C₂²	1	1	yes	characteristic
37	#15689077	—	2	1	no	—
38	#15688870	C₂²	1	2	yes	—
39	#15688870	C₂²	1	2	yes	—
40	#15688868	C₂²	1	2	yes	—
41	#15688868	C₂²	1	2	yes	—
42	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
43	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#334	C₂²	1	2	yes	—
45	C₄₇×#334	C₂²	1	1	yes	characteristic
46	C₄₇×#334	C₂²	1	1	yes	characteristic
47	C₂×Dic₁₈₈	—	2	1	no	—
48	C₂×Dic₁₈₈	—	2	1	no	—
49	C₂×Dic₁₈₈	—	2	2	no	—
50	C₂×#10625325	—	2	2	no	—
51	C₂×#10625324	—	2	1	no	—
52	C₂×C₈×D₄₇	—	2	1	no	—
53	#13094024	C₂³	1	2	yes	—
54	#13094024	C₂³	1	2	yes	—
55	#13094018	—	2	1	no	—
56	#13094016	—	2	2	no	—
57	#13094016	D₄	1	1	yes	characteristic
58	#13094012	D₄	1	1	yes	characteristic
59	#13094007	—	2	1	no	—
60	#13094003	—	2	2	no	—
61	#13094003	—	2	2	no	—
62	#13094003	D₄	1	1	yes	characteristic
63	#13093998	D₄	1	1	yes	characteristic
64	C₄×Dic₉₄	—	2	2	no	—
65	C₄×Dic₉₄	—	2	2	no	—
66	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
67	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
68	C₄×C₂²⋊D₄₇	—	2	1	no	—
69	#13093983	—	2	2	no	—
70	#13093981	—	2	1	no	—
71	#13093958	—	2	1	no	—
72	#13093958	—	2	1	no	—
73	#13093958	—	2	2	no	—
74	#13093956	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
77	Dic₄₇⋊C₈	—	2	1	no	—
78	Dic₄₇⋊C₈	—	2	1	no	—
79	#13093949	—	2	2	no	—
80	#13093949	—	2	2	no	—
81	#13093949	—	2	2	no	—
82	#13093949	—	2	2	no	—
83	#13093949	—	2	2	no	—
84	#13093946	—	2	2	no	—
85	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
86	(C₂×D₄₇)⋊C₈	—	2	1	no	—
87	(C₂×D₄₇)⋊C₈	—	2	1	no	—
88	#13093935	—	2	1	no	—
89	#13093934	—	2	1	no	—
90	C₈×Dic₄₇	—	2	1	no	—
91	C₂²×C₈×C₄₇	—	2	2	no	—
92	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	—	2	2	no	—
96	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
97	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
98	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂×C₂²⋊D₄₇	—	2	1	no	—
106	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₄₇	—	2	1	no	—
108	C₂×Dic₉₄	—	2	2	no	—
109	C₂×Dic₉₄	—	2	2	no	—
110	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	4	1	no	—
115	C₂×C₈×C₄₇	—	8	2	no	—
116	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₄₇	#41	1	1	yes	characteristic
123	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₂²⋊Dic₄₇	—	2	1	no	—
125	C₂²⋊Dic₄₇	—	4	2	no	—
126	(C₂×D₄₇)⋊C₄	—	2	1	no	—
127	(C₂×D₄₇)⋊C₄	—	2	1	no	—
128	(C₂×D₄₇)⋊C₄	—	2	1	no	—
129	(C₂×D₄₇)⋊C₄	—	2	1	no	—
130	C₄⋊Dic₄₇	—	2	2	no	—
131	C₄⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
136	Dic₄₇⋊C₄	—	2	1	no	—
137	Dic₄₇⋊C₄	—	2	1	no	—
138	Dic₄₇⋊C₄	—	2	1	no	—
139	Dic₄₇⋊C₄	—	2	1	no	—
140	Dic₄₇⋊C₄	—	4	2	no	—
141	Dic₄₇⋊C₄	—	4	2	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	4	2	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	Dic₁₈₈	—	4	2	no	—
147	Dic₁₈₈	—	4	2	no	—
148	Dic₁₈₈	—	8	2	no	—
149	#10625325	—	8	2	no	—
150	#10625324	—	4	2	no	—
151	C₈×D₄₇	—	4	2	no	—
152	C₂³×C₄₇	#121	1	1	yes	characteristic
153	C₂²×D₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂²⋊D₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	1	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	D₁₈₈	—	2	2	no	—
171	C₄×D₄₇	—	4	1	no	—
172	C₄×D₄₇	—	4	1	no	—
173	Dic₉₄	—	2	2	no	—
174	Dic₉₄	—	4	2	no	—
175	Dic₉₄	—	4	2	no	—
176	Dic₉₄	—	4	2	no	—
177	Dic₉₄	—	4	2	no	—
178	C₈×C₄₇	—	2	1	no	—
179	C₈×C₄₇	—	2	1	no	—
180	C₈×C₄₇	—	2	1	no	—
181	C₈×C₄₇	—	4	2	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₈×C₄₇	#135	1	2	yes	—
184	C₄₇⋊C₈	—	4	1	no	—
185	C₄₇⋊C₈	—	4	1	no	—
186	#19228	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	#473	1	2	yes	—
190	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
191	C₂×D₄₇	—	4	1	no	—
192	C₂×D₄₇	—	4	1	no	—
193	C₂×D₄₇	—	4	1	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
199	C₄×C₄₇	#575	1	1	yes	characteristic
200	C₄×C₄₇	#577	1	2	yes	—
201	Dic₄₇	—	4	1	no	—
202	Dic₄₇	—	4	1	no	—
203	Dic₄₇	—	4	1	no	—
204	Dic₄₇	—	8	2	no	—
205	Dic₄₇	—	8	2	no	—
206	#3248	—	47	2	no	—
207	#3170	—	47	1	no	—
208	#2966	—	47	1	no	—
209	#1694	—	47	1	no	—
210	#1693	—	47	1	no	—
211	#1690	—	47	1	no	—
212	#1689	—	47	1	no	—
213	#1680	—	47	2	no	—
214	#1679	—	47	2	no	—
215	C₂×#334	D₄₇	1	1	yes	characteristic, complemented
216	#1552	—	47	2	no	—
217	C₂×C₄₇	—	2	2	no	—
218	C₂×C₄₇	#3035	1	1	yes	characteristic
219	C₂×C₄₇	#3060	1	1	yes	characteristic
220	C₂×C₄₇	C₂×#473	1	1	yes	characteristic
221	D₄₇	—	8	1	no	—
222	#533	—	47	2	no	—
223	#529	—	47	1	no	—
224	#500	—	47	1	no	—
225	#494	—	47	1	no	—
226	#487	—	47	2	no	—
227	#479	—	94	2	no	—
228	#475	—	47	2	no	—
229	#474	—	47	2	no	—
230	#467	—	94	2	no	—
231	#467	—	94	1	no	—
232	#467	—	94	1	no	—
233	#465	—	94	2	no	—
234	#464	—	94	2	no	—
235	#462	—	47	2	no	—
236	#461	—	47	2	no	—
237	#446	—	47	1	no	—
238	C₈×Q₈	—	47	1	no	—
239	C₄×Q₁₆	—	94	1	no	—
240	C₄×Q₁₆	—	94	1	no	—
241	#436	—	47	1	no	—
242	#435	—	94	1	no	—
243	C₈×D₄	—	47	1	no	—
244	C₈×D₄	—	94	1	no	—
245	#433	—	94	1	no	—
246	#432	—	47	1	no	—
247	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
248	#405	—	94	1	no	—
249	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
250	#334	C₂×D₄₇	1	2	yes	—
251	#334	C₂×D₄₇	1	1	yes	characteristic
252	#334	C₂×D₄₇	1	1	yes	characteristic
253	#332	—	47	2	no	—
254	#332	—	47	2	no	—
255	#332	—	47	2	no	—
256	#332	—	47	2	no	—
257	C₄₇	#19228	1	1	yes	characteristic, complemented, Sylow
258	C₂×Q₁₆	—	94	2	no	—
259	C₂×Q₁₆	—	94	1	no	—
260	C₂×Q₁₆	—	94	1	no	—
261	C₂×SD₁₆	—	94	2	no	—
262	C₂×M₁₆	—	94	1	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	94	1	no	—
265	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
266	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
267	C₄⋊Q₈	—	47	2	no	—
268	C₄⋊Q₈	—	47	2	no	—
269	#126	—	94	1	no	—
270	#125	—	47	1	no	—
271	#125	—	94	2	no	—
272	#124	—	47	1	no	—
273	#123	—	94	1	no	—
274	C₂²⋊Q₈	—	47	1	no	—
275	C₂²⋊Q₈	—	94	2	no	—
276	C₂²⋊Q₈	—	94	2	no	—
277	#121	—	47	1	no	—
278	C₄×Q₈	—	47	1	no	—
279	C₄×Q₈	—	94	2	no	—
280	C₄×Q₈	—	94	2	no	—
281	C₄×D₄	—	47	1	no	—
282	C₄×D₄	—	94	1	no	—
283	#117	—	94	1	no	—
284	#117	—	94	2	no	—
285	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
286	#107	—	94	2	no	—
287	#107	—	94	1	no	—
288	#107	—	94	1	no	—
289	#106	—	94	2	no	—
290	C₄⋊C₈	—	2	2	no	—
291	C₄⋊C₈	—	47	1	no	—
292	C₄⋊C₈	—	47	1	no	—
293	C₄⋊C₈	—	94	1	no	—
294	C₄⋊C₈	—	94	1	no	—
295	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
296	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
297	#103	—	94	2	no	—
298	#103	—	94	2	no	—
299	#103	—	94	2	no	—
300	#103	—	94	2	no	—
301	#103	—	94	2	no	—
302	#102	—	94	2	no	—
303	C₂²⋊C₈	—	94	1	no	—
304	C₂²⋊C₈	—	94	1	no	—
305	C₂²⋊C₈	—	94	1	no	—
306	#97	—	94	1	no	—
307	#97	—	94	1	no	—
308	C₄×C₈	—	94	1	no	—
309	C₄×C₈	D₁₈₈	1	1	yes	characteristic
310	C₄×C₈	D₁₈₈	1	1	yes	characteristic
311	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
313	C₂×Q₈	—	47	1	no	—
314	C₂×Q₈	—	94	2	no	—
315	C₂×Q₈	—	94	2	no	—
316	C₂×D₄	—	47	1	no	—
317	C₂×D₄	—	94	1	no	—
318	C₂²×C₄	—	94	1	no	—
319	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
321	C₂²×C₄	#10625354	1	1	yes	characteristic
322	Q₁₆	—	376	2	no	—
323	Q₁₆	—	188	2	no	—
324	Q₁₆	—	188	2	no	—
325	SD₁₆	—	376	2	no	—
326	M₁₆	—	188	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	8	2	no	—
332	C₂×C₈	—	94	1	no	—
333	C₂×C₈	—	94	1	no	—
334	C₂×C₈	—	188	2	no	—
335	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
336	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
337	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
338	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
339	C₄⋊C₄	—	47	1	no	—
340	C₄⋊C₄	—	47	1	no	—
341	C₄⋊C₄	—	94	1	no	—
342	C₄⋊C₄	—	94	1	no	—
343	C₄⋊C₄	—	94	1	no	—
344	C₄⋊C₄	—	94	1	no	—
345	C₄⋊C₄	—	94	2	no	—
346	C₄⋊C₄	—	94	2	no	—
347	C₄⋊C₄	—	94	2	no	—
348	C₄⋊C₄	—	94	2	no	—
349	C₄⋊C₄	—	188	2	no	—
350	C₄⋊C₄	—	188	2	no	—
351	C₂²⋊C₄	—	94	1	no	—
352	C₂²⋊C₄	—	94	1	no	—
353	C₂²⋊C₄	—	94	1	no	—
354	C₂²⋊C₄	—	94	1	no	—
355	C₂²⋊C₄	—	94	1	no	—
356	C₂²⋊C₄	—	188	2	no	—
357	C₄²	—	94	1	no	—
358	C₄²	—	188	2	no	—
359	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
360	C₄²	D₄×D₄₇	1	1	yes	characteristic
361	C₄²	#10625354	1	1	yes	characteristic
362	C₄²	C₂³×D₄₇	1	1	yes	characteristic
363	C₂³	—	94	1	no	—
364	C₂³	#13093999	1	1	yes	characteristic
365	Q₈	—	94	2	no	—
366	Q₈	—	188	2	no	—
367	Q₈	—	188	2	no	—
368	Q₈	—	188	2	no	—
369	Q₈	—	188	2	no	—
370	D₄	—	94	2	no	—
371	D₄	—	188	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	94	1	no	—
377	C₂×C₄	—	94	1	no	—
378	C₂×C₄	—	94	1	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	1	no	—
382	C₂×C₄	—	188	1	no	—
383	C₂×C₄	#13093999	1	1	yes	characteristic
384	C₂×C₄	#13093999	1	1	yes	characteristic
385	C₂×C₄	#13093999	1	1	yes	characteristic
386	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
388	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
389	C₈	—	2	1	no	—
390	C₈	—	2	1	no	—
391	C₈	—	2	1	no	—
392	C₈	—	4	2	no	—
393	C₈	—	4	2	no	—
394	C₈	—	188	1	no	—
395	C₈	—	188	1	no	—
396	C₈	#13094046	1	2	yes	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	188	1	no	—
400	C₂²	—	188	1	no	—
401	C₂²	—	188	1	no	—
402	C₂²	#15689399	1	2	yes	—
403	C₂²	C₂×#13093999	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	376	2	no	—
409	C₄	—	376	2	no	—
410	C₄	—	188	1	no	—
411	C₄	—	188	1	no	—
412	C₄	—	188	1	no	—
413	C₄	C₂×#13094046	1	1	yes	characteristic
414	C₄	#15689923	1	1	yes	characteristic
415	C₄	#15689929	1	2	yes	—
416	C₂	—	2	2	no	—
417	C₂	—	376	1	no	—
418	C₂	#20252845	1	1	yes	characteristic
419	C₂	#20253051	1	1	yes	characteristic
420	C₂	C₂×#15689399	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093999
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#334	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#13093998	D₄
hypercenter	C₂×#334	D₄₇
hypocenter	C₄₇	#19228
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#334

Complements

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

N	H ≅ G/N	type
2. #20253974	C₂	semidirect
4. #20242907	C₂	semidirect
5. #20242902	C₂	semidirect
6. #20242883	C₂	semidirect
7. #20242878	C₂	semidirect
8. #20242819	C₂	semidirect
9. #20242812	C₂	semidirect
10. #20242086	C₂	semidirect
11. C₂×C₄₇×#334	C₂	semidirect
215. C₂×#334	D₄₇	semidirect
257. C₄₇	#19228	semidirect

Maximal subgroups

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

subgroup	index
#20254726	2
#20253974	2
#20252363	2
#20242907	2
#20242902	2
#20242883	2
#20242878	2
#20242819	2
#20242812	2
#20242086	2
C₂×C₄₇×#334	2
#19228	47