Subgroups — #30847422

Order 17152.

692 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22573184	C₂	1	1	yes	maximal, characteristic, complemented
2	#22572538	C₂	1	2	yes	maximal, complemented
3	#22571931	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559815	C₂	1	1	yes	maximal, characteristic, complemented
5	#22559771	C₂	1	2	yes	maximal, complemented
6	#22559579	C₂	1	1	yes	maximal, characteristic, complemented
7	#22559564	C₂	1	1	yes	maximal, characteristic, complemented
8	#22559412	C₂	1	2	yes	maximal, complemented
9	#22559301	C₂	1	2	yes	maximal, complemented
10	#22559095	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14524065	—	2	1	no	—
13	#16864068	C₂²	1	2	yes	—
14	#16864051	C₂²	1	2	yes	—
15	#16863776	C₂²	1	1	yes	characteristic
16	#16863773	—	2	1	no	—
17	#16863773	C₂²	1	1	yes	characteristic
18	#16863743	C₂²	1	2	yes	—
19	#16863743	C₂²	1	2	yes	—
20	#16863716	—	2	2	no	—
21	#16863681	C₂²	1	2	yes	—
22	#16863648	—	2	2	no	—
23	#16863637	—	2	1	no	—
24	#16863602	C₂²	1	2	yes	—
25	#16863592	—	2	2	no	—
26	#16863592	C₂²	1	2	yes	—
27	#16863591	C₂²	1	2	yes	—
28	#16863560	—	2	2	no	—
29	#16863540	—	2	2	no	—
30	C₄×D₅₃₆	—	2	1	no	—
31	C₄×D₅₃₆	C₂²	1	1	yes	characteristic
32	#16863475	C₂²	1	2	yes	—
33	#16863396	—	2	2	no	—
34	#16863149	C₂²	1	1	yes	characteristic
35	#16863143	C₂²	1	2	yes	—
36	#16863139	C₂²	1	2	yes	—
37	#16863125	C₂²	1	2	yes	—
38	C₈×Q₈×C₆₇	C₂²	1	1	yes	characteristic
39	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
40	C₈×D₄×C₆₇	C₂²	1	1	yes	characteristic
41	#334×C₆₇	C₂²	1	1	yes	characteristic
42	Q₈⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
44	C₈²×C₆₇	C₂²	1	1	yes	characteristic
45	C₂×#11761629	—	2	2	no	—
46	C₂×#11761628	—	2	2	no	—
47	#14524065	—	4	4	no	—
48	C₂×Dic₂₆₈	—	2	1	no	—
49	C₂×Dic₂₆₈	—	2	1	no	—
50	C₂×#11761617	—	2	2	no	—
51	C₂×D₅₃₆	—	2	2	no	—
52	C₂×D₅₃₆	—	2	1	no	—
53	C₂×D₅₃₆	—	2	1	no	—
54	C₂×D₅₃₆	D₄	1	1	yes	characteristic
55	C₂×#11761613	—	2	2	no	—
56	C₂×#11761611	—	2	2	no	—
57	#14524043	C₂³	1	2	yes	—
58	#14524040	—	2	2	no	—
59	#14524040	C₂³	1	2	yes	—
60	#14524025	—	4	2	no	—
61	#14524022	—	2	2	no	—
62	#14524018	—	2	2	no	—
63	#14524018	—	4	2	no	—
64	#14524014	—	2	2	no	—
65	C₄×D₂₆₈	—	2	2	no	—
66	C₄×D₂₆₈	C₂³	1	2	yes	—
67	C₄⋊C₄×D₆₇	—	2	2	no	—
68	#14523977	D₄	1	1	yes	characteristic
69	#14523974	—	2	2	no	—
70	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
71	#14523968	—	2	2	no	—
72	#14523967	—	2	2	no	—
73	#14523965	—	2	2	no	—
74	#14523965	—	2	2	no	—
75	#14523965	—	2	2	no	—
76	#14523965	—	4	2	no	—
77	#14523965	D₄	1	2	yes	—
78	#14523963	—	2	2	no	—
79	(C₂×D₆₇)⋊C₈	—	2	2	no	—
80	C₂×SD₁₆×C₆₇	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₆₇	—	2	1	no	—
82	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
84	#106×C₆₇	D₄	1	1	yes	characteristic
85	C₄⋊C₈×C₆₇	—	2	1	no	—
86	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₆₇	C₂³	1	1	yes	characteristic
88	#103×C₆₇	D₄	1	1	yes	characteristic
89	#102×C₆₇	D₄	1	1	yes	characteristic
90	C₂²⋊C₈×C₆₇	—	2	1	no	—
91	C₄×C₈×C₆₇	—	2	1	no	—
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
95	#11761629	—	4	4	no	—
96	#11761629	—	8	2	no	—
97	#11761628	—	4	4	no	—
98	#11761628	—	8	2	no	—
99	C₂×Dic₁₃₄	—	2	2	no	—
100	C₂×D₂₆₈	—	2	2	no	—
101	C₂×D₂₆₈	—	2	2	no	—
102	C₂×D₂₆₈	—	2	2	no	—
103	C₂×D₂₆₈	—	4	2	no	—
104	C₂×D₂₆₈	—	4	2	no	—
105	C₂×D₂₆₈	C₂×D₄	1	2	yes	—
106	C₂×C₂²⋊D₆₇	—	4	2	no	—
107	C₂×C₄×D₆₇	—	2	2	no	—
108	C₂×C₄×D₆₇	—	4	2	no	—
109	C₂×C₄×D₆₇	—	4	2	no	—
110	Dic₂₆₈	—	4	2	no	—
111	Dic₂₆₈	—	8	1	no	—
112	#11761617	—	4	4	no	—
113	D₅₃₆	—	2	2	no	—
114	D₅₃₆	—	4	2	no	—
115	D₅₃₆	—	8	1	no	—
116	D₅₃₆	—	8	2	no	—
117	#11761613	—	8	2	no	—
118	#11761611	—	8	2	no	—
119	C₂×C₆₇⋊C₈	—	2	2	no	—
120	C₄⋊Dic₆₇	—	2	2	no	—
121	C₄⋊Dic₆₇	—	2	2	no	—
122	C₄⋊Dic₆₇	C₂×D₄	1	2	yes	—
123	Dic₆₇⋊C₄	—	4	2	no	—
124	C₂²⋊Dic₆₇	—	4	2	no	—
125	(C₂×D₆₇)⋊C₄	—	2	2	no	—
126	(C₂×D₆₇)⋊C₄	—	4	2	no	—
127	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₆₇	—	2	1	no	—
130	SD₁₆×C₆₇	—	2	2	no	—
131	C₂×C₈×C₆₇	—	2	1	no	—
132	C₂×C₈×C₆₇	—	2	1	no	—
133	C₂×C₈×C₆₇	—	2	1	no	—
134	C₂×C₈×C₆₇	—	4	2	no	—
135	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₄⋊C₄×C₆₇	—	2	1	no	—
140	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₆₇	—	2	1	no	—
143	C₄²×C₆₇	—	2	1	no	—
144	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
145	C₂³×C₆₇	—	2	1	no	—
146	C₂²×D₆₇	—	2	2	no	—
147	C₂²×D₆₇	—	4	2	no	—
148	Q₈×C₆₇	—	2	1	no	—
149	Q₈×C₆₇	#135	1	2	yes	complemented
150	D₄×C₆₇	—	2	1	no	—
151	D₄×C₆₇	—	2	1	no	—
152	C₂×C₄×C₆₇	—	2	1	no	—
153	C₂×C₄×C₆₇	—	2	1	no	—
154	C₂×C₄×C₆₇	—	2	1	no	—
155	C₂×C₄×C₆₇	—	4	1	no	—
156	C₂×C₄×C₆₇	—	4	1	no	—
157	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
160	C₂²⋊D₆₇	—	8	4	no	—
161	C₂×Dic₆₇	—	2	2	no	—
162	C₂×Dic₆₇	—	4	2	no	—
163	D₂₆₈	—	2	2	no	—
164	D₂₆₈	—	2	2	no	—
165	D₂₆₈	—	4	2	no	—
166	D₂₆₈	—	4	2	no	—
167	D₂₆₈	—	4	2	no	—
168	D₂₆₈	—	4	2	no	—
169	D₂₆₈	—	8	4	no	—
170	D₂₆₈	—	8	2	no	—
171	D₂₆₈	—	16	2	no	—
172	C₄×D₆₇	—	4	2	no	—
173	C₄×D₆₇	—	4	2	no	—
174	C₄×D₆₇	—	8	4	no	—
175	C₄×D₆₇	—	8	4	no	—
176	Dic₁₃₄	—	4	2	no	—
177	Dic₁₃₄	—	4	2	no	—
178	C₈×C₆₇	—	2	1	no	—
179	C₈×C₆₇	—	2	1	no	—
180	C₈×C₆₇	—	2	1	no	—
181	C₈×C₆₇	—	4	1	no	—
182	C₈×C₆₇	—	4	1	no	—
183	C₈×C₆₇	—	4	1	no	—
184	C₈×C₆₇	AGL(1,ℤ/8)	1	2	yes	—
185	C₆₇⋊C₈	—	4	2	no	—
186	C₂²×C₆₇	—	4	1	no	—
187	C₂²×C₆₇	—	4	1	no	—
188	C₂²×C₆₇	—	4	1	no	—
189	C₂²×C₆₇	D₄²	1	1	yes	characteristic
190	C₂×D₆₇	—	4	2	no	—
191	C₂×D₆₇	—	4	2	no	—
192	C₂×D₆₇	—	4	2	no	—
193	C₂×D₆₇	—	8	2	no	—
194	C₂×D₆₇	—	8	2	no	—
195	C₂×D₆₇	—	8	2	no	—
196	C₄×C₆₇	—	2	2	no	—
197	C₄×C₆₇	—	2	1	no	—
198	C₄×C₆₇	—	4	1	no	—
199	C₄×C₆₇	—	4	1	no	—
200	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
201	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
202	C₄×C₆₇	#576	1	1	yes	characteristic
203	C₄×C₆₇	#576	1	1	yes	characteristic
204	Dic₆₇	—	4	2	no	—
205	Dic₆₇	—	8	2	no	—
206	#19908	—	67	1	no	maximal, Sylow
207	C₂×C₆₇	—	8	1	no	—
208	C₂×C₆₇	#3274	1	1	yes	characteristic
209	C₂×C₆₇	#3280	1	1	yes	characteristic
210	C₂×C₆₇	#3290	1	1	yes	characteristic
211	D₆₇	—	8	2	no	—
212	D₆₇	—	16	2	no	—
213	#3391	—	67	1	no	—
214	#3332	—	67	2	no	—
215	#3283	—	67	1	no	—
216	#1709	—	67	1	no	—
217	#1701	—	67	2	no	—
218	#1670	—	67	1	no	—
219	#1667	—	67	1	no	—
220	#1642	—	67	2	no	—
221	#1625	—	67	2	no	—
222	#1589	—	67	1	no	—
223	C₈×SD₁₆	D₆₇	1	1	yes	characteristic, complemented
224	C₆₇	#19908	1	1	yes	characteristic, complemented, Sylow
225	C₂×#135	—	134	1	no	—
226	#550	—	67	2	no	—
227	#547	—	67	2	no	—
228	#494	—	67	1	no	—
229	#493	—	67	1	no	—
230	#493	—	134	1	no	—
231	#486	—	67	2	no	—
232	#486	—	67	2	no	—
233	#481	—	134	2	no	—
234	#475	—	67	2	no	—
235	#469	—	134	2	no	—
236	#467	—	134	1	no	—
237	#461	—	67	2	no	—
238	#459	—	67	2	no	—
239	#459	—	67	2	no	—
240	#459	—	134	2	no	—
241	#452	—	134	2	no	—
242	#449	—	134	2	no	—
243	C₈×Q₈	C₂×D₆₇	1	1	yes	characteristic
244	C₄×SD₁₆	C₂×D₆₇	1	1	yes	characteristic
245	C₄×D₈	—	67	1	no	—
246	C₄×D₈	—	134	1	no	—
247	#436	—	67	2	no	—
248	C₈×D₄	C₂×D₆₇	1	1	yes	characteristic
249	#417	—	134	2	no	—
250	#335	—	67	1	no	—
251	#334	C₂×D₆₇	1	1	yes	characteristic
252	#332	—	67	2	no	—
253	#331	—	67	2	no	—
254	Q₈⋊C₈	C₂×D₆₇	1	1	yes	characteristic
255	D₄⋊C₈	—	67	2	no	—
256	D₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
257	C₈²	C₂×D₆₇	1	1	yes	characteristic
258	C₂×#41	—	134	2	no	—
259	C₂×#41	—	134	2	no	—
260	#135	—	268	4	no	—
261	C₂×Q₁₆	—	134	1	no	—
262	C₂×Q₁₆	—	134	1	no	—
263	C₂×SD₁₆	—	134	2	no	—
264	C₂×SD₁₆	D₂₆₈	1	1	yes	characteristic
265	C₂×D₈	—	67	1	no	—
266	C₂×D₈	—	134	2	no	—
267	C₂×D₈	—	134	2	no	—
268	C₂×D₈	—	134	1	no	—
269	C₂×D₈	—	134	1	no	—
270	C₂×M₁₆	—	134	2	no	—
271	C₂²×C₈	—	2	1	no	—
272	C₄⋊Q₈	—	67	2	no	—
273	#127	—	67	2	no	—
274	#127	—	134	2	no	—
275	#123	—	268	2	no	—
276	C₂²⋊Q₈	—	134	2	no	—
277	#121	—	268	2	no	—
278	#121	—	134	2	no	—
279	#121	—	134	2	no	—
280	C₄×Q₈	C₂²×D₆₇	1	1	yes	characteristic
281	C₄×D₄	—	67	2	no	—
282	C₄×D₄	—	134	2	no	—
283	C₄×D₄	C₂²×D₆₇	1	1	yes	characteristic
284	C₂×C₄⋊C₄	—	134	2	no	—
285	#107	—	67	1	no	—
286	#106	—	134	2	no	—
287	#106	D₂₆₈	1	1	yes	characteristic
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	67	2	no	—
290	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
291	C₄⋊C₈	C₂²×D₆₇	1	1	yes	characteristic
292	#103	—	134	2	no	—
293	#103	—	134	2	no	—
294	#103	D₂₆₈	1	1	yes	characteristic
295	#102	—	268	2	no	—
296	#102	—	67	2	no	—
297	#102	—	134	2	no	—
298	#102	—	134	2	no	—
299	#102	—	134	2	no	—
300	#102	—	134	2	no	—
301	#102	D₂₆₈	1	1	yes	characteristic
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	134	2	no	—
304	C₄×C₈	—	2	1	no	—
305	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
308	#41	—	268	4	no	—
309	#41	—	268	4	no	—
310	#41	—	536	2	no	—
311	#41	—	536	2	no	—
312	C₂×Q₈	—	134	2	no	—
313	C₂×Q₈	C₂×D₂₆₈	1	1	yes	characteristic
314	C₂×D₄	—	268	2	no	—
315	C₂×D₄	—	268	2	no	—
316	C₂×D₄	—	268	2	no	—
317	C₂×D₄	—	67	2	no	—
318	C₂×D₄	—	134	2	no	—
319	C₂×D₄	—	134	2	no	—
320	C₂×D₄	—	134	2	no	—
321	C₂×D₄	C₂×D₂₆₈	1	1	yes	characteristic
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	268	2	no	—
324	C₂²×C₄	—	268	2	no	—
325	C₂²×C₄	—	134	2	no	—
326	Q₁₆	—	268	2	no	—
327	Q₁₆	—	536	1	no	—
328	SD₁₆	—	2	2	no	—
329	SD₁₆	—	268	4	no	—
330	D₈	—	268	2	no	—
331	D₈	—	536	1	no	—
332	D₈	—	536	2	no	—
333	D₈	—	536	2	no	—
334	D₈	—	134	2	no	—
335	M₁₆	—	536	2	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	4	2	no	—
340	C₂×C₈	—	134	2	no	—
341	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
342	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
343	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
344	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	268	2	no	—
347	C₄⋊C₄	—	67	2	no	—
348	C₄⋊C₄	—	134	2	no	—
349	C₄⋊C₄	—	134	2	no	—
350	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
351	C₄⋊C₄	C₂×D₂₆₈	1	1	yes	characteristic
352	C₂²⋊C₄	—	2	1	no	—
353	C₂²⋊C₄	—	268	2	no	—
354	C₂²⋊C₄	—	268	2	no	—
355	C₂²⋊C₄	—	134	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	C₂³×D₆₇	1	1	yes	characteristic
358	C₂³	—	2	1	no	—
359	C₂³	—	268	2	no	—
360	C₂³	—	134	2	no	—
361	Q₈	—	2	1	no	—
362	Q₈	—	268	2	no	—
363	Q₈	—	268	2	no	—
364	Q₈	#14524065	1	2	yes	complemented
365	D₄	—	2	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	268	2	no	—
368	D₄	—	268	2	no	—
369	D₄	—	268	2	no	—
370	D₄	—	268	2	no	—
371	D₄	—	536	4	no	—
372	D₄	—	536	2	no	—
373	D₄	—	536	4	no	—
374	D₄	—	1072	2	no	—
375	D₄	—	134	2	no	—
376	D₄	—	134	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	268	2	no	—
383	C₂×C₄	—	268	2	no	—
384	C₂×C₄	—	268	2	no	—
385	C₂×C₄	—	536	4	no	—
386	C₂×C₄	—	536	4	no	—
387	C₂×C₄	—	134	2	no	—
388	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
390	C₂×C₄	#14524089	1	1	yes	characteristic
391	C₈	—	2	1	no	—
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	4	1	no	—
397	C₈	—	268	2	no	—
398	C₈	#14524070	1	2	yes	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	268	2	no	—
403	C₂²	—	268	2	no	—
404	C₂²	—	268	2	no	—
405	C₂²	—	536	2	no	—
406	C₂²	—	536	2	no	—
407	C₂²	—	536	2	no	—
408	C₂²	D₄×D₂₆₈	1	1	yes	characteristic
409	C₄	—	2	2	no	—
410	C₄	—	2	1	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	268	2	no	—
414	C₄	—	536	2	no	—
415	C₄	C₂×#14524065	1	1	yes	characteristic
416	C₄	C₂×#14524070	1	1	yes	characteristic
417	C₄	#16864198	1	1	yes	characteristic
418	C₄	#16864201	1	1	yes	characteristic
419	C₂	—	8	1	no	—
420	C₂	—	536	2	no	—
421	C₂	—	1072	2	no	—
422	C₂	#22571830	1	1	yes	characteristic
423	C₂	#22571896	1	1	yes	characteristic
424	C₂	#22571996	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₂₆₈
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₈×SD₁₆×C₆₇	C₂
socle	C₂²×C₆₇	D₄²
hypercenter	C₈×SD₁₆	D₆₇
hypocenter	C₆₇	#19908
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #22573184	C₂	semidirect
2. #22572538	C₂	semidirect
3. #22571931	C₂	semidirect
4. #22559815	C₂	semidirect
5. #22559771	C₂	semidirect
6. #22559579	C₂	semidirect
7. #22559564	C₂	semidirect
8. #22559412	C₂	semidirect
9. #22559301	C₂	semidirect
10. #22559095	C₂	semidirect
11. C₈×SD₁₆×C₆₇	C₂	semidirect
149. Q₈×C₆₇	#135	semidirect
223. C₈×SD₁₆	D₆₇	semidirect
224. C₆₇	#19908	semidirect
364. Q₈	#14524065	semidirect

Maximal subgroups

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

subgroup	index
#22573184	2
#22572538	2
#22571931	2
#22559815	2
#22559771	2
#22559579	2
#22559564	2
#22559412	2
#22559301	2
#22559095	2
C₈×SD₁₆×C₆₇	2
#19908	67