Subgroups — #33069183

Order 18688.

710 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22621077	C₂	1	1	yes	maximal, characteristic, complemented
2	#22620874	C₂	1	1	yes	maximal, characteristic
3	C₂×#17988960	C₂	1	1	yes	maximal, characteristic
4	#22618865	C₂	1	1	yes	maximal, characteristic, complemented
5	#22609404	C₂	1	4	yes	maximal, complemented
6	#22609280	C₂	1	4	yes	maximal, complemented
7	#22608602	C₂	1	1	yes	maximal, characteristic, complemented
8	#22608598	C₂	1	1	yes	maximal, characteristic
9	C₇₃×#1564	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#11924017	—	2	1	no	—
11	C₂²×#11924017	—	2	1	no	—
12	#17989144	C₂²	1	1	yes	characteristic
13	C₂×#14556591	C₂²	1	1	yes	characteristic
14	C₂×#14556588	C₂²	1	1	yes	characteristic
15	#17988985	—	2	1	no	—
16	#17988960	—	2	1	no	—
17	#17988960	—	2	1	no	—
18	#17988960	—	2	1	no	—
19	#17988960	C₂²	1	2	yes	—
20	#17988960	C₂²	1	2	yes	—
21	#17988938	—	2	1	no	—
22	#17988934	—	2	1	no	—
23	#17988918	—	2	2	no	—
24	#17988873	C₂²	1	4	yes	complemented
25	#17988788	C₂²	1	4	yes	—
26	#17988740	—	2	2	no	—
27	#17988717	—	2	1	no	—
28	#17988717	C₂²	1	2	yes	complemented
29	C₈×Dic₁₄₆	—	2	1	no	—
30	C₈×Dic₁₄₆	C₂²	1	2	yes	complemented
31	#17988613	—	2	1	no	—
32	#17988611	C₂²	1	1	yes	characteristic
33	#17988542	—	2	1	no	—
34	#17988332	C₂²	1	4	yes	complemented
35	#17988330	C₂²	1	4	yes	—
36	#431×C₇₃	C₂²	1	1	yes	characteristic
37	#431×C₇₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic
39	#335×C₇₃	C₂²	1	2	yes	complemented
40	#334×C₇₃	C₂²	1	2	yes	complemented
41	C₂²×Dic₁₄₆	—	2	1	no	—
42	C₂²×D₂₉₂	—	2	1	no	—
43	C₂²×D₂₉₂	—	2	1	no	—
44	C₂²×D₂₉₂	—	2	1	no	—
45	C₂×#11924017	—	2	4	no	—
46	C₂×#11924017	—	2	2	no	—
47	C₂×#11924017	—	2	2	no	—
48	C₂×#11924017	—	2	2	no	—
49	C₂×#11924017	—	2	2	no	—
50	C₂×#11924017	—	4	4	no	—
51	C₂×#11924017	—	4	4	no	—
52	C₂×#11924012	—	2	1	no	—
53	#14556591	—	2	1	no	—
54	#14556591	—	2	1	no	—
55	#14556591	—	2	1	no	—
56	#14556591	D₄	1	1	yes	characteristic
57	#14556591	D₄	1	1	yes	characteristic
58	#14556591	C₂³	1	2	yes	—
59	#14556588	—	2	1	no	—
60	#14556588	—	2	1	no	—
61	#14556588	—	2	1	no	—
62	#14556588	C₂³	1	2	yes	—
63	#14556583	—	2	1	no	—
64	#14556570	—	2	1	no	—
65	#14556570	D₄	1	2	yes	—
66	C₄×Dic₁₄₆	—	2	1	no	—
67	C₄×Dic₁₄₆	C₂³	1	2	yes	—
68	#14556550	—	2	1	no	—
69	C₂×C₄⋊Dic₇₃	—	2	1	no	—
70	C₂×C₄⋊Dic₇₃	—	2	1	no	—
71	#14556523	—	2	4	no	—
72	C₄⋊#10596831	—	2	1	no	—
73	C₄⋊#10596831	C₂³	1	2	yes	—
74	#14556520	—	2	2	no	—
75	#14556520	—	2	2	no	—
76	#14556516	—	2	4	no	—
77	#14556513	—	2	4	no	—
78	#14556501	—	2	2	no	—
79	C₈×Dic₇₃	—	2	2	no	—
80	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
81	C₂²×C₈×C₇₃	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
84	C₄⋊C₈×C₇₃	C₂³	1	2	yes	—
85	C₂²⋊C₈×C₇₃	—	2	1	no	—
86	C₂²⋊C₈×C₇₃	—	2	1	no	—
87	C₄×C₈×C₇₃	—	2	1	no	—
88	C₄×C₈×C₇₃	—	2	1	no	—
89	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
90	C₄×C₈×C₇₃	D₄	1	1	yes	characteristic
91	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₇₃	C₂³	1	1	yes	characteristic
93	C₂³×D₇₃	—	4	1	no	—
94	C₂×Dic₁₄₆	—	2	1	no	—
95	C₂×Dic₁₄₆	—	2	2	no	—
96	C₂×Dic₁₄₆	—	4	2	no	—
97	C₂×Dic₁₄₆	—	4	2	no	—
98	C₂×Dic₁₄₆	—	4	1	no	—
99	C₂×Dic₁₄₆	C₂×D₄	1	2	yes	—
100	C₂×D₂₉₂	—	2	2	no	—
101	C₂×D₂₉₂	—	2	2	no	—
102	C₂×D₂₉₂	—	2	2	no	—
103	C₂×D₂₉₂	—	4	2	no	—
104	C₂×D₂₉₂	—	4	2	no	—
105	C₂×D₂₉₂	—	4	1	no	—
106	C₂×D₂₉₂	—	4	1	no	—
107	C₂×D₂₉₂	—	4	1	no	—
108	C₂×D₂₉₂	—	8	2	no	—
109	C₂×D₂₉₂	—	8	2	no	—
110	C₂²×Dic₇₃	—	4	1	no	—
111	#11924017	—	4	4	no	—
112	#11924017	—	4	4	no	—
113	#11924017	—	4	4	no	—
114	#11924017	—	4	4	no	—
115	#11924017	—	8	4	no	—
116	#11924012	—	4	2	no	—
117	C₂×#10596831	—	2	2	no	—
118	C₄⋊Dic₇₃	—	2	1	no	—
119	C₄⋊Dic₇₃	—	2	1	no	—
120	C₄⋊Dic₇₃	—	2	1	no	—
121	C₄⋊Dic₇₃	—	2	2	no	—
122	C₄⋊Dic₇₃	—	2	2	no	—
123	C₄⋊Dic₇₃	—	4	1	no	—
124	C₄⋊Dic₇₃	—	4	1	no	—
125	C₄⋊Dic₇₃	C₂×D₄	1	2	yes	—
126	#11924007	—	2	2	no	—
127	#11924007	—	2	2	no	—
128	C₂²⋊Dic₇₃	—	2	2	no	—
129	C₄×Dic₇₃	—	2	2	no	—
130	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₇₃	#41	1	1	yes	characteristic
133	C₂×C₈×C₇₃	—	2	2	no	—
134	C₂×C₈×C₇₃	—	2	2	no	—
135	C₂×C₈×C₇₃	—	2	2	no	—
136	C₂×C₈×C₇₃	SD₁₆	1	4	yes	complemented
137	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₇₃	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₇₃	#41	1	1	yes	characteristic
144	C₄²×C₇₃	C₂⁴	1	1	yes	characteristic
145	C₂³×C₇₃	#121	1	1	yes	characteristic
146	C₂²×D₇₃	—	4	2	no	—
147	C₂²×D₇₃	—	8	2	no	—
148	C₂²×D₇₃	—	8	2	no	—
149	C₂²×D₇₃	—	8	2	no	—
150	C₂×C₄×C₇₃	—	2	2	no	—
151	C₂×C₄×C₇₃	—	2	2	no	—
152	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
153	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
154	C₂×C₄×C₇₃	#121	1	1	yes	characteristic
155	C₂×C₄×C₇₃	C₂×SD₁₆	1	2	yes	—
156	C₂×C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₇₃	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₇₃	C₂×#41	1	1	yes	characteristic
160	C₂×Dic₇₃	—	2	2	no	—
161	C₂×Dic₇₃	—	2	2	no	—
162	C₂×Dic₇₃	—	4	2	no	—
163	C₂×Dic₇₃	—	8	2	no	—
164	D₂₉₂	—	4	2	no	—
165	D₂₉₂	—	4	2	no	—
166	D₂₉₂	—	4	4	no	—
167	D₂₉₂	—	8	2	no	—
168	D₂₉₂	—	8	2	no	—
169	D₂₉₂	—	8	2	no	—
170	D₂₉₂	—	8	2	no	—
171	Dic₁₄₆	—	2	4	no	—
172	Dic₁₄₆	—	4	2	no	—
173	Dic₁₄₆	—	4	2	no	—
174	Dic₁₄₆	—	4	2	no	—
175	Dic₁₄₆	—	8	2	no	—
176	C₈×C₇₃	—	2	1	no	—
177	C₈×C₇₃	—	2	1	no	—
178	C₈×C₇₃	—	4	2	no	—
179	C₈×C₇₃	—	4	2	no	—
180	C₈×C₇₃	C₂×SD₁₆	1	2	yes	—
181	C₈×C₇₃	C₂×SD₁₆	1	2	yes	—
182	#10596831	—	4	2	no	—
183	C₂²×C₇₃	—	2	1	no	—
184	C₂²×C₇₃	—	2	1	no	—
185	C₂²×C₇₃	#460	1	2	yes	—
186	C₂²×C₇₃	C₂×#121	1	1	yes	characteristic
187	C₂×D₇₃	—	8	2	no	—
188	C₂×D₇₃	—	8	2	no	—
189	C₂×D₇₃	—	8	2	no	—
190	C₂×D₇₃	—	16	4	no	—
191	C₄×C₇₃	—	2	1	no	—
192	C₄×C₇₃	—	2	1	no	—
193	C₄×C₇₃	#460	1	2	yes	—
194	C₄×C₇₃	#471	1	2	yes	—
195	C₄×C₇₃	C₂²×SD₁₆	1	1	yes	characteristic
196	C₄×C₇₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₄×C₇₃	#577	1	2	yes	—
198	Dic₇₃	—	4	2	no	—
199	Dic₇₃	—	4	2	no	—
200	Dic₇₃	—	8	2	no	—
201	#19202	—	73	1	no	maximal, Sylow
202	C₂×C₇₃	—	2	2	no	—
203	C₂×C₇₃	C₂×#460	1	1	yes	characteristic
204	C₂×C₇₃	#3057	1	1	yes	characteristic
205	C₂×C₇₃	C₂×#471	1	1	yes	characteristic
206	D₇₃	—	16	2	no	—
207	#3229	—	73	1	no	—
208	#3208	—	73	1	no	—
209	C₂×#492	—	73	1	no	—
210	#2960	—	73	1	no	—
211	#1686	—	73	4	no	—
212	#1666	—	73	4	no	—
213	#1564	D₇₃	1	1	yes	characteristic, complemented
214	#1546	—	73	1	no	—
215	#1545	—	73	1	no	—
216	C₇₃	#19202	1	1	yes	characteristic, complemented, Sylow
217	C₂²×SD₁₆	—	146	1	no	—
218	C₂²×SD₁₆	—	146	1	no	—
219	#533	—	73	1	no	—
220	C₂×C₄⋊Q₈	—	73	1	no	—
221	C₂×#127	—	73	1	no	—
222	#498	—	146	1	no	—
223	#492	—	73	2	no	—
224	#492	—	73	2	no	—
225	#492	—	146	1	no	—
226	#492	—	146	1	no	—
227	#492	—	146	1	no	—
228	#487	—	146	1	no	—
229	#486	—	146	1	no	—
230	#483	—	146	2	no	—
231	#475	—	73	4	no	—
232	#460	—	73	4	no	—
233	#450	—	146	2	no	—
234	#446	—	73	2	no	—
235	#446	—	146	1	no	—
236	C₈×Q₈	—	73	2	no	—
237	C₈×Q₈	—	146	1	no	—
238	#431	C₂×D₇₃	1	1	yes	characteristic
239	#431	C₂×D₇₃	1	1	yes	characteristic
240	#424	—	146	1	no	—
241	#423	—	73	1	no	—
242	#405	—	146	1	no	—
243	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic
244	#335	C₂×D₇₃	1	2	yes	complemented
245	#334	C₂×D₇₃	1	2	yes	complemented
246	#332	—	73	4	no	—
247	#331	—	73	4	no	—
248	C₂²×Q₈	—	146	1	no	—
249	C₂²×D₄	—	146	1	no	—
250	C₂²×D₄	—	146	1	no	—
251	C₂²×D₄	—	146	1	no	—
252	C₂×SD₁₆	—	292	4	no	—
253	C₂×SD₁₆	—	292	4	no	—
254	C₂×SD₁₆	—	146	4	no	—
255	C₂×SD₁₆	—	146	2	no	—
256	C₂×SD₁₆	—	146	2	no	—
257	C₂×SD₁₆	—	146	2	no	—
258	C₂×SD₁₆	—	146	2	no	—
259	C₂×M₁₆	—	146	1	no	—
260	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
261	C₂²×C₈	D₂₉₂	1	1	yes	characteristic
262	C₄⋊Q₈	—	73	1	no	—
263	C₄⋊Q₈	—	73	1	no	—
264	C₄⋊Q₈	—	73	2	no	—
265	C₄⋊Q₈	—	146	1	no	—
266	C₄⋊Q₈	—	146	1	no	—
267	C₄⋊Q₈	—	146	1	no	—
268	#127	—	73	2	no	—
269	#127	—	146	1	no	—
270	#127	—	146	1	no	—
271	#127	—	146	1	no	—
272	#125	—	146	1	no	—
273	C₂²⋊Q₈	—	73	2	no	—
274	C₂²⋊Q₈	—	146	1	no	—
275	C₄×Q₈	—	73	2	no	—
276	C₄×Q₈	—	146	1	no	—
277	#117	—	146	1	no	—
278	C₂×C₄⋊C₄	—	146	1	no	—
279	C₂×C₄⋊C₄	—	146	1	no	—
280	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
281	#106	—	146	4	no	—
282	C₄⋊C₈	—	73	2	no	—
283	C₄⋊C₈	—	146	2	no	—
284	C₄⋊C₈	—	146	2	no	—
285	C₄⋊C₈	—	146	1	no	—
286	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
287	C₄⋊C₈	C₂²×D₇₃	1	2	yes	—
288	#103	—	146	4	no	—
289	#102	—	146	4	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	C₂²⋊C₈	—	2	1	no	—
292	#97	—	146	2	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	—	146	2	no	—
296	C₄×C₈	D₂₉₂	1	1	yes	characteristic
297	C₄×C₈	D₂₉₂	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₇₃	1	1	yes	characteristic
300	C₂⁴	—	292	1	no	—
301	C₂×Q₈	—	292	1	no	—
302	C₂×Q₈	—	292	2	no	—
303	C₂×Q₈	—	292	2	no	—
304	C₂×Q₈	—	73	2	no	—
305	C₂×Q₈	—	146	2	no	—
306	C₂×Q₈	—	146	1	no	—
307	C₂×D₄	—	292	1	no	—
308	C₂×D₄	—	292	1	no	—
309	C₂×D₄	—	292	1	no	—
310	C₂×D₄	—	292	2	no	—
311	C₂×D₄	—	292	2	no	—
312	C₂×D₄	—	584	2	no	—
313	C₂×D₄	—	584	2	no	—
314	C₂×D₄	—	146	2	no	—
315	C₂×D₄	—	146	2	no	—
316	C₂×D₄	—	146	2	no	—
317	C₂²×C₄	—	292	1	no	—
318	C₂²×C₄	D₄×D₇₃	1	1	yes	characteristic
319	C₂²×C₄	C₂×D₂₉₂	1	1	yes	characteristic
320	C₂²×C₄	#11924029	1	1	yes	characteristic
321	SD₁₆	—	292	4	no	—
322	SD₁₆	—	292	4	no	—
323	SD₁₆	—	292	4	no	—
324	SD₁₆	—	292	4	no	—
325	SD₁₆	—	584	4	no	—
326	M₁₆	—	292	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	146	2	no	—
331	C₂×C₈	#11924017	1	4	yes	complemented
332	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
333	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
334	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
335	C₂×C₈	C₂×D₂₉₂	1	1	yes	characteristic
336	C₄⋊C₄	—	292	1	no	—
337	C₄⋊C₄	—	292	1	no	—
338	C₄⋊C₄	—	73	2	no	—
339	C₄⋊C₄	—	146	2	no	—
340	C₄⋊C₄	—	146	2	no	—
341	C₄⋊C₄	—	146	2	no	—
342	C₄⋊C₄	—	146	1	no	—
343	C₄⋊C₄	—	146	1	no	—
344	C₄⋊C₄	—	146	1	no	—
345	C₄⋊C₄	—	146	2	no	—
346	C₂²⋊C₄	—	146	2	no	—
347	C₄²	—	146	2	no	—
348	C₄²	D₄×D₇₃	1	1	yes	characteristic
349	C₄²	C₂×D₂₉₂	1	1	yes	characteristic
350	C₄²	#11924029	1	1	yes	characteristic
351	C₄²	C₂³×D₇₃	1	1	yes	characteristic
352	C₂³	—	292	2	no	—
353	C₂³	—	584	2	no	—
354	C₂³	—	584	2	no	—
355	C₂³	—	584	2	no	—
356	C₂³	#14556566	1	1	yes	characteristic
357	Q₈	—	292	2	no	—
358	Q₈	—	292	2	no	—
359	Q₈	—	292	2	no	—
360	Q₈	—	584	2	no	—
361	Q₈	—	146	4	no	—
362	D₄	—	292	2	no	—
363	D₄	—	292	4	no	—
364	D₄	—	292	2	no	—
365	D₄	—	584	2	no	—
366	D₄	—	584	2	no	—
367	D₄	—	584	2	no	—
368	D₄	—	584	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	292	2	no	—
372	C₂×C₄	—	584	2	no	—
373	C₂×C₄	—	146	2	no	—
374	C₂×C₄	—	146	2	no	—
375	C₂×C₄	#14556566	1	1	yes	characteristic
376	C₂×C₄	#14556566	1	1	yes	characteristic
377	C₂×C₄	#14556566	1	1	yes	characteristic
378	C₂×C₄	C₂×#11924017	1	2	yes	—
379	C₂×C₄	#14556619	1	2	yes	—
380	C₂×C₄	C₂×D₄×D₇₃	1	1	yes	characteristic
381	C₂×C₄	C₂²×D₂₉₂	1	1	yes	characteristic
382	C₂×C₄	C₂×#11924029	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	1	no	—
385	C₈	—	4	2	no	—
386	C₈	—	4	2	no	—
387	C₈	—	292	2	no	—
388	C₈	C₂×#11924017	1	2	yes	—
389	C₈	C₂×#11924017	1	2	yes	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	584	2	no	—
393	C₂²	—	584	2	no	—
394	C₂²	—	584	2	no	—
395	C₂²	—	1168	4	no	—
396	C₂²	#17988788	1	2	yes	—
397	C₂²	C₂×#14556566	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	292	2	no	—
401	C₄	—	292	2	no	—
402	C₄	—	584	2	no	—
403	C₄	#17988788	1	2	yes	—
404	C₄	#17988851	1	2	yes	—
405	C₄	C₂²×#11924017	1	1	yes	characteristic
406	C₄	C₂×#14556619	1	1	yes	characteristic
407	C₄	#17989394	1	2	yes	—
408	C₂	—	2	2	no	—
409	C₂	—	1168	2	no	—
410	C₂	C₂×#17988788	1	1	yes	characteristic
411	C₂	#22619571	1	1	yes	characteristic
412	C₂	C₂×#17988851	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#14556566
commutator, cosocle	C₄²×C₇₃	C₂⁴
Frattini	C₄²	C₂³×D₇₃
Fitting	C₇₃×#1564	C₂
socle	C₂²×C₇₃	C₂×#121
prime radical	C₂×#14556588	C₂²
hypercenter	#1564	D₇₃
hypocenter	C₇₃	#19202
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
1. #22621077	C₂	semidirect
4. #22618865	C₂	semidirect
5. #22609404	C₂	semidirect
6. #22609280	C₂	semidirect
7. #22608602	C₂	semidirect
9. C₇₃×#1564	C₂	semidirect
24. #17988873	C₂²	semidirect
28. #17988717	C₂²	semidirect
30. C₈×Dic₁₄₆	C₂²	semidirect
34. #17988332	C₂²	semidirect
39. #335×C₇₃	C₂²	semidirect
40. #334×C₇₃	C₂²	semidirect
136. C₂×C₈×C₇₃	SD₁₆	semidirect
213. #1564	D₇₃	semidirect
216. C₇₃	#19202	semidirect
244. #335	C₂×D₇₃	semidirect
245. #334	C₂×D₇₃	semidirect
331. C₂×C₈	#11924017	semidirect

Maximal subgroups

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

subgroup	index
#22621077	2
#22620874	2
C₂×#17988960	2
#22618865	2
#22609404	2
#22609280	2
#22608602	2
#22608598	2
C₇₃×#1564	2
#19202	73