Subgroups — #30748602

Order 17152.

540 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22560062	C₂	1	1	yes	maximal, characteristic, complemented
2	#22560062	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863136	C₂	1	2	yes	maximal
4	#22558090	C₂	1	2	yes	maximal, complemented
5	C₄×#124×C₆₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
7	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
8	C₂×#14523954	C₂²	1	2	yes	—
9	C₂×#14523954	C₂²	1	2	yes	—
10	#16863151	—	2	1	no	—
11	#16863151	—	2	1	no	—
12	#16863136	—	2	4	no	—
13	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₆₇	C₄	1	1	yes	characteristic
15	C₂×C₄×D₄×C₆₇	C₄	1	1	yes	characteristic
16	#391×C₆₇	C₄	1	1	yes	characteristic
17	#390×C₆₇	C₄	1	1	yes	characteristic
18	#388×C₆₇	—	2	1	no	—
19	#388×C₆₇	—	2	1	no	—
20	#382×C₆₇	C₂²	1	1	yes	characteristic
21	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
22	C₄×C₂²⋊C₄×C₆₇	—	2	1	no	—
23	C₄³×C₆₇	C₂²	1	1	yes	characteristic
24	C₂²×C₆₇⋊C₈	—	2	2	no	—
25	C₂²×C₆₇⋊C₈	—	2	2	no	—
26	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
27	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
28	#14523954	—	2	2	no	—
29	#14523954	—	2	2	no	—
30	#14523954	—	2	2	no	—
31	#14523954	—	2	2	no	—
32	C₂²×Q₈×C₆₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×D₄×C₆₇	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₆₇	—	2	1	no	—
35	#124×C₆₇	—	2	1	no	—
36	#124×C₆₇	—	2	1	no	—
37	#124×C₆₇	D₄	1	2	yes	—
38	#124×C₆₇	Q₈	1	2	yes	—
39	C₄×Q₈×C₆₇	—	4	2	no	—
40	C₄×D₄×C₆₇	—	4	2	no	—
41	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
42	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
48	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
49	C₂×C₄²×C₆₇	—	2	1	no	—
50	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
57	#95×C₆₇	—	2	1	no	—
58	#95×C₆₇	—	2	1	no	—
59	#95×C₆₇	—	2	1	no	—
60	#95×C₆₇	—	2	1	no	—
61	C₂×C₆₇⋊C₈	—	2	4	no	—
62	C₂×C₆₇⋊C₈	—	2	4	no	—
63	C₂×C₆₇⋊C₈	—	4	2	no	—
64	C₂×C₆₇⋊C₈	—	4	2	no	—
65	C₂×C₆₇⋊C₈	—	4	2	no	—
66	C₂×C₆₇⋊C₈	—	4	2	no	—
67	C₂⁴×C₆₇	—	2	1	no	—
68	C₂×Q₈×C₆₇	—	2	1	no	—
69	C₂×Q₈×C₆₇	—	4	1	no	—
70	C₂×Q₈×C₆₇	—	4	1	no	—
71	C₂×Q₈×C₆₇	C₄⋊C₄	1	2	yes	—
72	C₂×D₄×C₆₇	—	2	1	no	—
73	C₂×D₄×C₆₇	—	4	1	no	—
74	C₂×D₄×C₆₇	—	4	1	no	—
75	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₆₇	—	2	1	no	—
77	C₂²×C₄×C₆₇	—	2	1	no	—
78	C₂²×C₄×C₆₇	—	2	1	no	—
79	C₂²×C₄×C₆₇	—	4	2	no	—
80	C₂²×C₄×C₆₇	—	4	2	no	—
81	C₂²×C₄×C₆₇	—	4	2	no	—
82	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
89	C₄⋊C₄×C₆₇	—	4	1	no	—
90	C₄⋊C₄×C₆₇	—	4	1	no	—
91	C₄⋊C₄×C₆₇	—	4	2	no	—
92	C₂²⋊C₄×C₆₇	—	2	2	no	—
93	C₂²⋊C₄×C₆₇	—	2	2	no	—
94	C₂²⋊C₄×C₆₇	—	2	2	no	—
95	C₂²⋊C₄×C₆₇	—	2	2	no	—
96	C₂²⋊C₄×C₆₇	—	4	2	no	—
97	C₂²⋊C₄×C₆₇	—	4	2	no	—
98	C₂²⋊C₄×C₆₇	—	4	2	no	—
99	C₄²×C₆₇	—	2	2	no	—
100	C₄²×C₆₇	—	2	2	no	—
101	C₄²×C₆₇	—	2	2	no	—
102	C₄²×C₆₇	—	4	1	no	—
103	C₄²×C₆₇	—	4	1	no	—
104	C₄²×C₆₇	—	4	1	no	—
105	C₄²×C₆₇	—	4	2	no	—
106	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₆₇	C₂×Q₈	1	1	yes	characteristic
108	C₄²×C₆₇	#41	1	1	yes	characteristic
109	C₄²×C₆₇	#41	1	1	yes	characteristic
110	C₂³×C₆₇	—	2	2	no	—
111	C₂³×C₆₇	—	4	1	no	—
112	C₂³×C₆₇	—	4	1	no	—
113	C₂³×C₆₇	—	4	1	no	—
114	C₂³×C₆₇	—	4	1	no	—
115	C₂³×C₆₇	—	4	1	no	—
116	C₂³×C₆₇	—	4	1	no	—
117	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
118	Q₈×C₆₇	—	4	2	no	—
119	Q₈×C₆₇	—	4	2	no	—
120	D₄×C₆₇	—	4	2	no	—
121	D₄×C₆₇	—	4	2	no	—
122	C₂×C₄×C₆₇	—	2	1	no	—
123	C₂×C₄×C₆₇	—	2	1	no	—
124	C₂×C₄×C₆₇	—	2	1	no	—
125	C₂×C₄×C₆₇	—	2	1	no	—
126	C₂×C₄×C₆₇	—	2	1	no	—
127	C₂×C₄×C₆₇	—	2	1	no	—
128	C₂×C₄×C₆₇	—	2	1	no	—
129	C₂×C₄×C₆₇	—	2	1	no	—
130	C₂×C₄×C₆₇	—	2	1	no	—
131	C₂×C₄×C₆₇	—	2	1	no	—
132	C₂×C₄×C₆₇	—	2	1	no	—
133	C₂×C₄×C₆₇	—	2	1	no	—
134	C₂×C₄×C₆₇	—	2	2	no	—
135	C₂×C₄×C₆₇	—	2	1	no	—
136	C₂×C₄×C₆₇	—	2	1	no	—
137	C₂×C₄×C₆₇	—	2	1	no	—
138	C₂×C₄×C₆₇	—	4	1	no	—
139	C₂×C₄×C₆₇	—	4	1	no	—
140	C₂×C₄×C₆₇	—	4	1	no	—
141	C₂×C₄×C₆₇	—	4	1	no	—
142	C₂×C₄×C₆₇	—	4	1	no	—
143	C₂×C₄×C₆₇	—	4	1	no	—
144	C₂×C₄×C₆₇	—	4	1	no	—
145	C₂×C₄×C₆₇	—	4	1	no	—
146	C₂×C₄×C₆₇	—	8	4	no	—
147	C₂×C₄×C₆₇	#100	1	2	yes	—
148	C₂×C₄×C₆₇	#104	1	2	yes	—
149	C₂×C₄×C₆₇	#104	1	2	yes	—
150	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	#117	1	1	yes	characteristic
152	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
156	C₆₇⋊C₈	—	4	4	no	—
157	C₆₇⋊C₈	—	4	4	no	—
158	C₂²×C₆₇	—	4	2	no	—
159	C₂²×C₆₇	—	4	2	no	—
160	C₂²×C₆₇	—	4	2	no	—
161	C₂²×C₆₇	—	8	1	no	—
162	C₂²×C₆₇	—	8	1	no	—
163	C₂²×C₆₇	—	8	1	no	—
164	C₂²×C₆₇	—	8	1	no	—
165	C₂²×C₆₇	#380	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#100	1	1	yes	characteristic
167	C₂²×C₆₇	#413	1	1	yes	characteristic
168	C₂²×C₆₇	C₂×#104	1	1	yes	characteristic
169	C₂²×C₆₇	C₂×#104	1	1	yes	characteristic
170	C₂²×C₆₇	#421	1	1	yes	characteristic
171	C₂²×C₆₇	#421	1	1	yes	characteristic
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	—	2	1	no	—
176	C₄×C₆₇	—	2	1	no	—
177	C₄×C₆₇	—	2	1	no	—
178	C₄×C₆₇	—	2	2	no	—
179	C₄×C₆₇	—	2	2	no	—
180	C₄×C₆₇	—	2	2	no	—
181	C₄×C₆₇	—	4	2	no	—
182	C₄×C₆₇	—	4	1	no	—
183	C₄×C₆₇	—	8	1	no	—
184	C₄×C₆₇	—	8	1	no	—
185	#8581	—	67	1	no	maximal, Sylow
186	C₂×C₆₇	—	8	2	no	—
187	C₂×C₆₇	#1524	1	1	yes	characteristic
188	C₂×C₆₇	#1527	1	1	yes	characteristic
189	C₂×C₆₇	#1530	1	1	yes	characteristic
190	C₂×C₆₇	#1535	1	1	yes	characteristic
191	C₂×C₆₇	#1800	1	1	yes	characteristic
192	C₂×C₆₇	#1806	1	1	yes	characteristic
193	C₂×C₆₇	#1806	1	1	yes	characteristic
194	C₄×#124	D₆₇	1	1	yes	characteristic
195	#1767	—	67	1	no	—
196	#1767	—	67	1	no	—
197	C₂×#329	—	67	2	no	—
198	#1295	—	67	2	no	—
199	C₆₇	#8581	1	1	yes	characteristic, complemented, Sylow
200	C₂×#124	C₂×D₆₇	1	1	yes	characteristic
201	C₂×C₄×Q₈	Dic₆₇	1	1	yes	characteristic
202	C₂×C₄×D₄	Dic₆₇	1	1	yes	characteristic
203	C₂×C₄⋊C₈	—	134	1	no	—
204	C₂×C₄⋊C₈	—	134	1	no	—
205	C₂×#97	—	67	2	no	—
206	C₂×#97	—	67	2	no	—
207	#391	Dic₆₇	1	1	yes	characteristic
208	#390	Dic₆₇	1	1	yes	characteristic
209	#388	—	2	1	no	—
210	#388	—	2	1	no	—
211	#382	C₂×D₆₇	1	1	yes	characteristic
212	C₄×C₂²⋊C₄	—	2	1	no	—
213	C₄×C₂²⋊C₄	—	2	1	no	—
214	C₄³	C₂×D₆₇	1	1	yes	characteristic
215	#336	—	134	1	no	—
216	#336	—	134	1	no	—
217	#329	—	134	4	no	—
218	C₂²×Q₈	C₂×Dic₆₇	1	1	yes	characteristic
219	C₂²×D₄	C₂×Dic₆₇	1	1	yes	characteristic
220	C₂³×C₄	—	2	1	no	—
221	C₂²×C₈	—	134	2	no	—
222	C₂²×C₈	—	134	2	no	—
223	#124	—	2	1	no	—
224	#124	—	2	1	no	—
225	#124	Dic₁₃₄	1	2	yes	—
226	#124	D₂₆₈	1	2	yes	—
227	C₄×Q₈	—	4	2	no	—
228	C₄×D₄	—	4	2	no	—
229	C₂×C₄⋊C₄	—	2	1	no	—
230	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
231	C₂×C₄⋊C₄	C₂×Dic₆₇	1	1	yes	characteristic
232	C₂×C₂²⋊C₄	—	2	1	no	—
233	C₂×C₂²⋊C₄	—	2	1	no	—
234	C₂×C₂²⋊C₄	—	2	1	no	—
235	C₂×C₂²⋊C₄	—	2	1	no	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	—	2	1	no	—
238	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
239	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
240	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
241	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
242	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
244	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
245	C₄⋊C₈	—	134	4	no	—
246	C₄⋊C₈	—	134	4	no	—
247	#97	—	134	2	no	—
248	#97	—	134	2	no	—
249	#97	—	134	2	no	—
250	#97	—	134	2	no	—
251	#95	—	2	1	no	—
252	#95	—	2	1	no	—
253	#95	—	2	1	no	—
254	#95	—	2	1	no	—
255	C₂⁴	—	2	1	no	—
256	C₂×Q₈	—	2	1	no	—
257	C₂×Q₈	—	4	1	no	—
258	C₂×Q₈	—	4	1	no	—
259	C₂×Q₈	C₄⋊Dic₆₇	1	2	yes	—
260	C₂×D₄	—	2	1	no	—
261	C₂×D₄	—	4	1	no	—
262	C₂×D₄	—	4	1	no	—
263	C₂×D₄	C₄⋊Dic₆₇	1	2	yes	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	4	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
274	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
277	C₂×C₈	—	268	2	no	—
278	C₂×C₈	—	268	2	no	—
279	C₂×C₈	—	268	2	no	—
280	C₂×C₈	—	268	2	no	—
281	C₂×C₈	—	134	4	no	—
282	C₂×C₈	—	134	4	no	—
283	C₄⋊C₄	—	4	1	no	—
284	C₄⋊C₄	—	4	1	no	—
285	C₄⋊C₄	—	4	2	no	—
286	C₂²⋊C₄	—	2	2	no	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₂²⋊C₄	—	2	2	no	—
290	C₂²⋊C₄	—	4	2	no	—
291	C₂²⋊C₄	—	4	2	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₄²	—	2	2	no	—
294	C₄²	—	2	2	no	—
295	C₄²	—	2	2	no	—
296	C₄²	—	4	1	no	—
297	C₄²	—	4	1	no	—
298	C₄²	—	4	1	no	—
299	C₄²	—	4	2	no	—
300	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
301	C₄²	C₂×Dic₁₃₄	1	1	yes	characteristic
302	C₄²	#11761628	1	1	yes	characteristic
303	C₄²	#11761628	1	1	yes	characteristic
304	C₂³	—	2	2	no	—
305	C₂³	—	4	1	no	—
306	C₂³	—	4	1	no	—
307	C₂³	—	4	1	no	—
308	C₂³	—	4	1	no	—
309	C₂³	—	4	1	no	—
310	C₂³	—	4	1	no	—
311	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	D₄	—	4	2	no	—
315	D₄	—	4	2	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	2	1	no	—
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	4	1	no	—
333	C₂×C₄	—	4	1	no	—
334	C₂×C₄	—	4	1	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	8	4	no	—
341	C₂×C₄	#14523960	1	2	yes	—
342	C₂×C₄	#14523970	1	2	yes	—
343	C₂×C₄	#14523970	1	2	yes	—
344	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
345	C₂×C₄	#14524002	1	1	yes	characteristic
346	C₂×C₄	#14524017	1	1	yes	characteristic
347	C₂×C₄	#14524017	1	1	yes	characteristic
348	C₂×C₄	#14524022	1	1	yes	characteristic
349	C₂×C₄	#14524022	1	1	yes	characteristic
350	C₈	—	268	4	no	—
351	C₈	—	268	4	no	—
352	C₂²	—	4	2	no	—
353	C₂²	—	4	2	no	—
354	C₂²	—	4	2	no	—
355	C₂²	—	8	1	no	—
356	C₂²	—	8	1	no	—
357	C₂²	—	8	1	no	—
358	C₂²	—	8	1	no	—
359	C₂²	#16863256	1	1	yes	characteristic
360	C₂²	C₂×#14523960	1	1	yes	characteristic
361	C₂²	#16863380	1	1	yes	characteristic
362	C₂²	C₂×#14523970	1	1	yes	characteristic
363	C₂²	C₂×#14523970	1	1	yes	characteristic
364	C₂²	#16863413	1	1	yes	characteristic
365	C₂²	#16863413	1	1	yes	characteristic
366	C₄	—	2	2	no	—
367	C₄	—	2	2	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	1	no	—
370	C₄	—	2	1	no	—
371	C₄	—	2	1	no	—
372	C₄	—	2	1	no	—
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	4	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	8	1	no	—
378	C₄	—	8	1	no	—
379	C₂	—	8	2	no	—
380	C₂	#22558797	1	1	yes	characteristic
381	C₂	#22558807	1	1	yes	characteristic
382	C₂	#22558820	1	1	yes	characteristic
383	C₂	#22558840	1	1	yes	characteristic
384	C₂	#22560201	1	1	yes	characteristic
385	C₂	#22560229	1	1	yes	characteristic
386	C₂	#22560229	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₆₇
commutator	C₂²×C₄×C₆₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₆₇
Fitting	C₄×#124×C₆₇	C₂
socle	C₂³×C₆₇	C₂×C₂²⋊C₄
prime radical	C₂²×D₄×C₆₇	C₂×C₄
cosocle	C₂×C₄²×C₆₇	C₂³
hypercenter	C₄×#124	D₆₇
hypocenter	C₆₇	#8581
LCS	G ▷ C₂²×C₄×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#124

Complements

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

N	H ≅ G/N	type
1. #22560062	C₂	semidirect
2. #22560062	C₂	semidirect
4. #22558090	C₂	semidirect
199. C₆₇	#8581	semidirect

Maximal subgroups

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

subgroup	index
#22560062	2
C₂×#16863136	2
#22558090	2
C₄×#124×C₆₇	2
#8581	67