Subgroups — #30825975

Order 17152.

638 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	#22570218	C₂	1	1	yes	maximal, characteristic
2	#22569303	C₂	1	1	yes	maximal, characteristic, complemented
3	#22569232	C₂	1	1	yes	maximal, characteristic
4	#22559068	C₂	1	2	yes	maximal, complemented
5	#22559047	C₂	1	2	yes	maximal, complemented
6	#22559023	C₂	1	2	yes	maximal, complemented
7	C₈×#11761617	C₂	1	2	yes	maximal, complemented
8	#22558989	C₂	1	1	yes	maximal, characteristic, complemented
9	#22558653	C₂	1	1	yes	maximal, characteristic
10	#22558631	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#1453	C₂	1	1	yes	maximal, characteristic, complemented
12	#16863953	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₂₆₈	C₂²	1	1	yes	characteristic
14	#16863727	C₄	1	2	yes	—
15	#16863687	C₄	1	2	yes	—
16	#16863602	C₄	1	2	yes	—
17	#16863549	C₄	1	2	yes	—
18	#16863526	C₂²	1	2	yes	complemented
19	#16863525	—	2	2	no	—
20	C₈×Dic₁₃₄	C₂²	1	2	yes	complemented
21	C₄×#11761617	C₂²	1	2	yes	—
22	C₄×#11761617	C₂²	1	2	yes	—
23	C₈×D₂₆₈	C₂²	1	2	yes	—
24	C₈×D₂₆₈	C₂²	1	2	yes	—
25	#16863461	—	2	2	no	—
26	#16863454	—	2	2	no	—
27	#16863453	C₂²	1	1	yes	characteristic
28	#16863449	C₂²	1	1	yes	characteristic
29	C₂²⋊C₈×D₆₇	—	2	2	no	—
30	#16863149	C₂²	1	2	yes	complemented
31	#16863147	C₂²	1	2	yes	complemented
32	#16863128	C₂²	1	2	yes	complemented
33	#16863128	C₂²	1	2	yes	complemented
34	#16863125	C₂²	1	2	yes	—
35	#16863125	C₂²	1	2	yes	—
36	#431×C₆₇	C₂²	1	1	yes	characteristic
37	#431×C₆₇	C₂²	1	1	yes	characteristic
38	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
39	#322×C₆₇	C₂²	1	1	yes	characteristic, complemented
40	#322×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	#322×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₈²×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	C₂²×D₂₆₈	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₆₇	—	2	1	no	—
45	C₂×#11761617	C₂×C₄	1	2	yes	—
46	C₂×#11761617	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₆₇	—	2	2	no	—
48	C₂×C₈×D₆₇	—	2	2	no	—
49	#14524043	C₂×C₄	1	1	yes	characteristic
50	#14524043	C₂×C₄	1	1	yes	characteristic
51	#14524035	—	2	1	no	—
52	#14524022	—	2	1	no	—
53	#14524022	C₂×C₄	1	2	yes	—
54	C₄×Dic₁₃₄	—	2	1	no	—
55	C₄×Dic₁₃₄	C₂³	1	2	yes	—
56	C₄×D₂₆₈	—	2	1	no	—
57	C₄×D₂₆₈	—	2	1	no	—
58	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
59	C₄×D₂₆₈	C₂³	1	2	yes	—
60	#14524002	—	2	1	no	—
61	C₂×C₄⋊Dic₆₇	C₂×C₄	1	1	yes	characteristic
62	C₂×(C₂×D₆₇)⋊C₄	—	2	1	no	—
63	#14523975	C₂×C₄	1	2	yes	—
64	#14523975	C₂×C₄	1	2	yes	—
65	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
66	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
67	Dic₆₇⋊C₈	—	2	2	no	—
68	Dic₆₇⋊C₈	—	2	2	no	—
69	#14523968	C₂×C₄	1	2	yes	—
70	#14523968	C₂×C₄	1	2	yes	—
71	#14523965	C₂×C₄	1	2	yes	—
72	#14523965	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
74	C₂²⋊(C₆₇⋊C₈)	—	2	1	no	—
75	(C₂×D₆₇)⋊C₈	—	2	2	no	—
76	(C₂×D₆₇)⋊C₈	—	2	2	no	—
77	#14523954	—	2	1	no	—
78	#14523953	—	2	2	no	—
79	C₄×C₆₇⋊C₈	—	2	1	no	—
80	C₈×Dic₆₇	—	2	2	no	—
81	C₂×M₁₆×C₆₇	—	2	1	no	—
82	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
84	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
85	C₂²⋊C₈×C₆₇	C₂×C₄	1	2	yes	—
86	C₂²⋊C₈×C₆₇	D₄	1	2	yes	—
87	#97×C₆₇	—	2	1	no	—
88	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×D₆₇	—	2	1	no	—
95	C₂×Dic₁₃₄	—	2	1	no	—
96	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
97	C₂×D₂₆₈	—	2	1	no	—
98	C₂×D₂₆₈	—	2	4	no	—
99	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
100	C₂²×Dic₆₇	—	2	1	no	—
101	C₂×C₄×D₆₇	—	2	2	no	—
102	C₂×C₄×D₆₇	—	2	2	no	—
103	C₂×C₄×D₆₇	—	8	2	no	—
104	#11761617	—	2	4	no	—
105	#11761617	—	2	4	no	—
106	C₂×C₆₇⋊C₈	—	2	2	no	—
107	C₂×C₆₇⋊C₈	—	2	2	no	—
108	C₈×D₆₇	—	8	2	no	—
109	C₈×D₆₇	—	8	2	no	—
110	C₄⋊Dic₆₇	—	2	1	no	—
111	C₄⋊Dic₆₇	—	2	1	no	—
112	C₄⋊Dic₆₇	—	2	1	no	—
113	C₄⋊Dic₆₇	—	2	1	no	—
114	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
115	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
116	Dic₆₇⋊C₄	—	2	2	no	—
117	Dic₆₇⋊C₄	—	2	2	no	—
118	C₂²⋊Dic₆₇	—	2	2	no	—
119	(C₂×D₆₇)⋊C₄	—	2	2	no	—
120	(C₂×D₆₇)⋊C₄	—	2	2	no	—
121	C₄×Dic₆₇	—	2	2	no	—
122	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
125	M₁₆×C₆₇	—	4	2	no	—
126	C₂×C₈×C₆₇	—	2	1	no	—
127	C₂×C₈×C₆₇	—	2	1	no	—
128	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
132	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₆₇	#41	1	1	yes	characteristic
135	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
136	C₂³×C₆₇	C₄×D₄	1	1	yes	characteristic
137	C₂²×D₆₇	—	2	2	no	—
138	C₂²×D₆₇	—	2	4	no	—
139	C₂²×D₆₇	—	8	1	no	—
140	C₂²×D₆₇	—	8	1	no	—
141	C₂×C₄×C₆₇	—	2	2	no	—
142	C₂×C₄×C₆₇	—	2	2	no	—
143	C₂×C₄×C₆₇	—	4	1	no	—
144	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₂×Dic₆₇	—	2	2	no	—
151	C₂×Dic₆₇	—	2	2	no	—
152	C₂×Dic₆₇	—	2	2	no	—
153	C₂×Dic₆₇	—	8	1	no	—
154	D₂₆₈	—	2	4	no	—
155	D₂₆₈	—	2	2	no	—
156	D₂₆₈	#131	1	4	yes	—
157	C₄×D₆₇	—	4	2	no	—
158	C₄×D₆₇	—	4	2	no	—
159	C₄×D₆₇	—	8	2	no	—
160	Dic₁₃₄	—	2	2	no	—
161	Dic₁₃₄	—	2	2	no	—
162	Dic₁₃₄	—	8	1	no	—
163	C₈×C₆₇	—	2	2	no	—
164	C₈×C₆₇	—	2	2	no	—
165	C₈×C₆₇	—	2	2	no	—
166	C₈×C₆₇	—	2	2	no	—
167	C₈×C₆₇	—	2	2	no	—
168	C₈×C₆₇	—	4	1	no	—
169	C₆₇⋊C₈	—	4	2	no	—
170	C₆₇⋊C₈	—	4	2	no	—
171	C₂²×C₆₇	—	2	1	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂×D₆₇	—	2	4	no	—
176	C₂×D₆₇	—	4	2	no	—
177	C₂×D₆₇	—	4	2	no	—
178	C₂×D₆₇	—	8	4	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	C₂×#131	1	2	yes	—
184	C₄×C₆₇	#577	1	2	yes	—
185	Dic₆₇	—	4	2	no	—
186	Dic₆₇	—	4	2	no	—
187	Dic₆₇	—	4	2	no	—
188	#17924	—	67	1	no	maximal, Sylow
189	C₂×C₆₇	—	4	1	no	—
190	C₂×C₆₇	#2929	1	1	yes	characteristic
191	C₂×C₆₇	#2949	1	1	yes	characteristic
192	C₂×C₆₇	#2956	1	1	yes	characteristic
193	D₆₇	—	4	4	no	—
194	#3101	—	67	1	no	—
195	#2985	—	67	1	no	—
196	#2972	—	67	1	no	—
197	#1585	—	67	2	no	—
198	#1582	—	67	2	no	—
199	SD₁₆⋊C₈	—	67	2	no	—
200	C₈×SD₁₆	—	67	2	no	—
201	#1572	—	67	1	no	—
202	#1490	—	67	1	no	—
203	#1485	—	67	1	no	—
204	#1453	D₆₇	1	1	yes	characteristic, complemented
205	C₆₇	#17924	1	1	yes	characteristic, complemented, Sylow
206	#533	—	67	1	no	—
207	C₂×C₄×D₄	—	67	1	no	—
208	#483	—	67	2	no	—
209	#476	—	67	2	no	—
210	#461	—	67	2	no	—
211	#450	—	67	2	no	—
212	#446	—	67	2	no	—
213	#446	—	134	2	no	—
214	C₈×Q₈	—	67	2	no	—
215	C₄×SD₁₆	—	67	2	no	—
216	C₄×SD₁₆	—	67	2	no	—
217	C₈×D₄	—	67	2	no	—
218	C₈×D₄	—	67	2	no	—
219	C₈×D₄	—	134	2	no	—
220	#433	—	134	2	no	—
221	#432	—	67	1	no	—
222	#431	—	67	1	no	—
223	#431	C₂×D₆₇	1	1	yes	characteristic
224	#431	C₂×D₆₇	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	—	134	2	no	—
226	C₄×M₁₆	C₂×D₆₇	1	1	yes	characteristic
227	#335	—	67	2	no	—
228	#334	—	67	2	no	—
229	Q₈⋊C₈	—	67	2	no	—
230	Q₈⋊C₈	—	67	2	no	—
231	D₄⋊C₈	—	67	2	no	—
232	D₄⋊C₈	—	67	2	no	—
233	#322	C₂×D₆₇	1	1	yes	characteristic, complemented
234	#322	C₂×D₆₇	1	1	yes	characteristic, complemented
235	#322	C₂×D₆₇	1	1	yes	characteristic, complemented
236	C₈²	C₂×D₆₇	1	1	yes	characteristic, complemented
237	C₂²×D₄	—	67	1	no	—
238	C₂³×C₄	—	134	1	no	—
239	C₂×SD₁₆	—	67	2	no	—
240	C₂×SD₁₆	—	67	2	no	—
241	C₂×M₁₆	—	2	1	no	—
242	C₂²×C₈	—	134	2	no	—
243	C₂²×C₈	—	134	2	no	—
244	C₄⋊Q₈	—	67	1	no	—
245	C₄⋊Q₈	—	67	1	no	—
246	#125	—	134	1	no	—
247	C₂²⋊Q₈	—	67	2	no	—
248	C₂²⋊Q₈	—	134	1	no	—
249	C₄×Q₈	—	67	2	no	—
250	C₄×Q₈	—	134	1	no	—
251	C₄×D₄	—	67	2	no	—
252	C₄×D₄	—	67	2	no	—
253	C₄×D₄	—	134	1	no	—
254	C₄×D₄	—	134	1	no	—
255	#117	—	134	1	no	—
256	C₂×C₄⋊C₄	—	67	1	no	—
257	C₂×C₂²⋊C₄	—	134	1	no	—
258	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
259	#106	—	67	2	no	—
260	#106	—	67	2	no	—
261	C₄⋊C₈	—	67	2	no	—
262	C₄⋊C₈	—	67	2	no	—
263	C₄⋊C₈	—	134	2	no	—
264	C₄⋊C₈	—	134	2	no	—
265	C₄⋊C₈	C₄×D₆₇	1	2	yes	—
266	C₄⋊C₈	D₂₆₈	1	2	yes	—
267	#103	—	67	2	no	—
268	#103	—	67	2	no	—
269	#102	—	67	2	no	—
270	#102	—	67	2	no	—
271	C₂²⋊C₈	—	134	1	no	—
272	C₂²⋊C₈	—	134	1	no	—
273	C₂²⋊C₈	—	134	2	no	—
274	C₂²⋊C₈	—	134	2	no	—
275	C₂²⋊C₈	C₄×D₆₇	1	2	yes	—
276	C₂²⋊C₈	D₂₆₈	1	2	yes	—
277	#97	—	2	1	no	—
278	#97	—	134	2	no	—
279	#97	—	134	1	no	—
280	C₄×C₈	—	134	2	no	—
281	C₄×C₈	—	134	1	no	—
282	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
283	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
284	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
285	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
286	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
287	C₄×C₈	C₂²×D₆₇	1	1	yes	characteristic
288	C₂⁴	—	134	1	no	—
289	C₂×Q₈	—	67	2	no	—
290	C₂×Q₈	—	134	1	no	—
291	C₂×D₄	—	67	2	no	—
292	C₂×D₄	—	134	4	no	—
293	C₂×D₄	—	134	1	no	—
294	C₂²×C₄	—	536	2	no	—
295	C₂²×C₄	—	134	2	no	—
296	C₂²×C₄	—	134	1	no	—
297	C₂²×C₄	—	134	2	no	—
298	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
300	C₂²×C₄	#11761628	1	1	yes	characteristic
301	SD₁₆	—	134	4	no	—
302	SD₁₆	—	134	4	no	—
303	M₁₆	—	4	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	536	2	no	—
307	C₂×C₈	—	536	2	no	—
308	C₂×C₈	—	134	2	no	—
309	C₂×C₈	—	134	2	no	—
310	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
311	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
312	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
313	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
314	C₄⋊C₄	—	67	2	no	—
315	C₄⋊C₄	—	67	2	no	—
316	C₄⋊C₄	—	134	1	no	—
317	C₄⋊C₄	—	134	1	no	—
318	C₄⋊C₄	—	134	1	no	—
319	C₄⋊C₄	—	134	2	no	—
320	C₄⋊C₄	—	134	1	no	—
321	C₄⋊C₄	—	134	2	no	—
322	C₂²⋊C₄	—	134	2	no	—
323	C₂²⋊C₄	—	134	2	no	—
324	C₂²⋊C₄	—	134	2	no	—
325	C₄²	—	134	2	no	—
326	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
327	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
328	C₄²	#11761628	1	1	yes	characteristic
329	C₄²	C₂³×D₆₇	1	1	yes	characteristic
330	C₂³	—	536	1	no	—
331	C₂³	—	536	1	no	—
332	C₂³	—	134	4	no	—
333	C₂³	—	134	2	no	—
334	C₂³	C₄×D₂₆₈	1	1	yes	characteristic
335	Q₈	—	536	1	no	—
336	Q₈	—	134	2	no	—
337	Q₈	—	134	2	no	—
338	D₄	—	67	4	no	—
339	D₄	—	134	4	no	—
340	D₄	—	134	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	4	1	no	—
344	C₂×C₄	—	268	2	no	—
345	C₂×C₄	—	268	2	no	—
346	C₂×C₄	—	536	2	no	—
347	C₂×C₄	—	536	1	no	—
348	C₂×C₄	—	134	2	no	—
349	C₂×C₄	—	134	2	no	—
350	C₂×C₄	—	134	2	no	—
351	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
352	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
353	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
354	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
356	C₂×C₄	C₂×#11761628	1	1	yes	characteristic
357	C₈	—	2	2	no	—
358	C₈	—	2	2	no	—
359	C₈	—	2	2	no	—
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	268	2	no	—
364	C₈	—	268	2	no	—
365	C₂²	—	2	1	no	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	268	2	no	—
369	C₂²	—	268	2	no	—
370	C₂²	—	536	4	no	—
371	C₂²	—	134	4	no	—
372	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
373	C₄	—	2	1	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	2	1	no	—
377	C₄	—	268	2	no	—
378	C₄	—	268	2	no	—
379	C₄	—	268	2	no	—
380	C₄	#131×D₆₇	1	2	yes	—
381	C₄	#16864208	1	2	yes	—
382	C₂	—	4	1	no	—
383	C₂	—	268	4	no	—
384	C₂	#22568905	1	1	yes	characteristic
385	C₂	#22569070	1	1	yes	characteristic
386	C₂	#22569120	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₄²	C₂³×D₆₇
Fitting	C₆₇×#1453	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂²×D₂₆₈	C₂×C₄
cosocle	C₄²×C₆₇	C₂⁴
hypercenter	#1453	D₆₇
hypocenter	C₆₇	#17924
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1453

Complements

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

N	H ≅ G/N	type
2. #22569303	C₂	semidirect
4. #22559068	C₂	semidirect
5. #22559047	C₂	semidirect
6. #22559023	C₂	semidirect
7. C₈×#11761617	C₂	semidirect
8. #22558989	C₂	semidirect
10. #22558631	C₂	semidirect
11. C₆₇×#1453	C₂	semidirect
18. #16863526	C₂²	semidirect
20. C₈×Dic₁₃₄	C₂²	semidirect
30. #16863149	C₂²	semidirect
31. #16863147	C₂²	semidirect
32. #16863128	C₂²	semidirect
33. #16863128	C₂²	semidirect
39. #322×C₆₇	C₂²	semidirect
40. #322×C₆₇	C₂²	semidirect
41. #322×C₆₇	C₂²	semidirect
42. C₈²×C₆₇	C₂²	semidirect
204. #1453	D₆₇	semidirect
205. C₆₇	#17924	semidirect
233. #322	C₂×D₆₇	semidirect
234. #322	C₂×D₆₇	semidirect
235. #322	C₂×D₆₇	semidirect
236. C₈²	C₂×D₆₇	semidirect

Maximal subgroups

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

subgroup	index
#22570218	2
#22569303	2
#22569232	2
#22559068	2
#22559047	2
#22559023	2
C₈×#11761617	2
#22558989	2
#22558653	2
#22558631	2
C₆₇×#1453	2
#17924	67