Finite Group Databasebeta

← C2×#14534796 #17201003

Subgroups — C2×#14534796 #17201003

Order 4352.

2026 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14534796C2116yesmaximal, direct product factor
2C2×#11762751C211yesmaximal, characteristic, complemented
3C2×#11762750C211yesmaximal, characteristic, complemented
4C2×#11762747C211yesmaximal, characteristic, complemented
5C2×#11762738C211yesmaximal, characteristic
6C2×#11762735C211yesmaximal, characteristic
7C2×#11762731C211yesmaximal, characteristic
8C2×#11762729C211yesmaximal, characteristic, complemented
9C2×#11762722C211yesmaximal, characteristic
10C2×#11762715C211yesmaximal, characteristic, complemented
11C2×#11762700C211yesmaximal, characteristic
12C2×#11762700C211yesmaximal, characteristic
13C2×#11762700C211yesmaximal, characteristic
14C2×#11762693C211yesmaximal, characteristic, complemented
15C2×#11762693C211yesmaximal, characteristic, complemented
16C2×C4×C4⋊C4×C17C211yesmaximal, characteristic, complemented
17C23×Dic34C2211yescharacteristic
18C22×C4⋊Dic17C2211yescharacteristic
19C22×#63225C2211yescharacteristic
20C22×#63225C2211yescharacteristic
21C22×#63225C2211yescharacteristic
22C22×#63225C2211yescharacteristic
23C22×#63225C2211yescharacteristic
24C22×#63227C2211yescharacteristic
25C22×#63227C2211yescharacteristic
26C22×#63227C2211yescharacteristic
27C22×#63227C2211yescharacteristic
28C22×#63227C2211yescharacteristic
29C22×#63227C2211yescharacteristic
30C22×#63227C2211yescharacteristic
31#11762751C2218yescomplemented
32#11762750C2218yescomplemented
33#11762747C2218yescomplemented
34#11762738C2218yes—
35#11762735C2218yes—
36#11762731C2218yes—
37#11762729C2218yescomplemented
38#11762722C2218yes—
39#11762715C2218yescomplemented
40#11762700C2218yes—
41#11762700C2218yes—
42#11762700C2218yes—
43#11762693C2218yescomplemented
44#11762693C2218yescomplemented
45C2×#10587502C2211yescharacteristic
46C2×#10587502C2211yescharacteristic
47C2×#10587502C2211yescharacteristic
48C2×#10587502C2211yescharacteristic
49C2×#10587502C2211yescharacteristic
50C2×#10587502C2211yescharacteristic
51C2×#10587502C2211yescharacteristic
52C2×#10587502C2211yescharacteristic
53C2×#10587502C2211yescharacteristic
54C2×#10587502C2211yescharacteristic
55C2×#10587502C2211yescharacteristic
56C2×#10587502C2211yescharacteristic
57C2×#10587502C2211yescharacteristic
58C2×#10587502C2211yescharacteristic
59C22×C4⋊C4×C17C2211yescharacteristic
60C22×C4⋊C4×C17C2211yescharacteristic
61C22×C42×C17C2211yescharacteristic
62C22×C42×C17C2211yescharacteristic
63C22×C42×C17C2211yescharacteristic
64C4×C4⋊C4×C17C2218yescomplemented
65C2×C17×#95C2211yescharacteristic
66C2×C17×#95C2211yescharacteristic
67C24×D17C2311yescharacteristic
68C23×C4×C17C2311yescharacteristic
69C23×C4×C17C2311yescharacteristic
70C23×C4×C17C2311yescharacteristic
71C23×C4×C17C2311yescharacteristic
72C23×C4×C17C2311yescharacteristic
73C23×C4×C17C2311yescharacteristic
74C23×C4×C17C2311yescharacteristic
75C23×Dic17C2311yescharacteristic
76C23×Dic17C2311yescharacteristic
77C23×Dic17C2311yescharacteristic
78C23×Dic17C2311yescharacteristic
79C23×Dic17C2311yescharacteristic
80C23×Dic17C2311yescharacteristic
81C23×Dic17C2311yescharacteristic
82C22×Dic34—24no—
83C22×Dic34—42no—
84C22×Dic34—42no—
85C22×Dic34C2314yes—
86C2×C4⋊C4×C17—24no—
87C2×C4⋊C4×C17—24no—
88C2×C4⋊C4×C17C2314yes—
89C2×C4⋊C4×C17C2314yes—
90C2×C42×C17—24no—
91C2×C42×C17—42no—
92C2×C42×C17—42no—
93C2×C42×C17C2314yes—
94C2×C42×C17C2314yes—
95C2×C42×C17C2314yes—
96C2×#63227—24no—
97C2×#63227—24no—
98C2×#63227—24no—
99C2×#63227—42no—
100C2×#63227—42no—
101C2×#63227—42no—
102C2×#63227—42no—
103C2×#63227C2314yes—
104C2×#63227C2314yes—
105C2×#63227C2314yes—
106C2×#63227C2314yes—
107C2×#63227C2314yes—
108C2×#63227C2314yes—
109C2×#63227C2314yes—
110C2×C4⋊Dic17—42no—
111C2×C4⋊Dic17C2314yes—
112C2×#63225—24no—
113C2×#63225—24no—
114C2×#63225—42no—
115C2×#63225—42no—
116C2×#63225—42no—
117C2×#63225C2314yes—
118C2×#63225C2314yes—
119C2×#63225C2314yes—
120C2×#63225C2314yes—
121C2×#63225C2314yes—
122C17×#95C2314yes—
123C17×#95C2314yes—
124#10587502C2314yes—
125#10587502C2314yes—
126#10587502C2314yes—
127#10587502C2314yes—
128#10587502C2314yes—
129#10587502C2314yes—
130#10587502C2314yes—
131#10587502C2314yes—
132#10587502C2314yes—
133#10587502C2314yes—
134#10587502C2314yes—
135#10587502C2314yes—
136#10587502C2314yes—
137#10587502C2314yes—
138C24×C17C2411yescharacteristic
139C23×D17—22no—
140C23×D17—22no—
141C23×D17—22no—
142C23×D17—22no—
143C23×D17—22no—
144C23×D17—22no—
145C23×D17—22no—
146C23×D17C2412yes—
147C22×C4×C17—22no—
148C22×C4×C17—22no—
149C22×C4×C17—22no—
150C22×C4×C17—22no—
151C22×C4×C17—22no—
152C22×C4×C17—22no—
153C22×C4×C17—22no—
154C22×C4×C17—22no—
155C22×C4×C17—22no—
156C22×C4×C17—22no—
157C22×C4×C17—22no—
158C22×C4×C17—22no—
159C22×C4×C17—22no—
160C22×C4×C17—22no—
161C22×C4×C17—22no—
162C22×C4×C17—22no—
163C22×C4×C17—22no—
164C22×C4×C17—22no—
165C22×C4×C17#4114yes—
166C22×C4×C17#4114yes—
167C22×C4×C17#4114yes—
168C22×C4×C17C2412yes—
169C22×C4×C17C2412yes—
170C22×C4×C17C2412yes—
171C22×C4×C17C2412yes—
172C22×C4×C17C2412yes—
173C22×C4×C17C2412yes—
174C22×C4×C17C2412yes—
175C22×Dic17—22no—
176C22×Dic17—22no—
177C22×Dic17—22no—
178C22×Dic17—22no—
179C22×Dic17—22no—
180C22×Dic17—22no—
181C22×Dic17—22no—
182C22×Dic17—22no—
183C22×Dic17—22no—
184C22×Dic17—22no—
185C22×Dic17—22no—
186C22×Dic17—22no—
187C22×Dic17—22no—
188C22×Dic17—22no—
189C22×Dic17—22no—
190C22×Dic17—22no—
191C22×Dic17—22no—
192C22×Dic17—22no—
193C22×Dic17—22no—
194C22×Dic17—22no—
195C22×Dic17—22no—
196C22×Dic17C2412yes—
197C22×Dic17C2412yes—
198C22×Dic17C2412yes—
199C22×Dic17C2412yes—
200C22×Dic17C2412yes—
201C22×Dic17C2412yes—
202C22×Dic17C2412yes—
203C2×Dic34—28no—
204C2×Dic34—44no—
205C2×Dic34—44no—
206C2×Dic34—416no—
207C4⋊C4×C17—28no—
208C4⋊C4×C17—28no—
209C42×C17—28no—
210C42×C17—44no—
211C42×C17—44no—
212#63227—28no—
213#63227—28no—
214#63227—28no—
215#63227—44no—
216#63227—44no—
217#63227—44no—
218#63227—44no—
219C4⋊Dic17—44no—
220#63225—28no—
221#63225—28no—
222#63225—44no—
223#63225—44no—
224#63225—44no—
225C2×#2650—171nomaximal, Sylow
226C23×C17C2×#4112yes—
227C23×C17C2×#4112yes—
228C23×C17C2×#4112yes—
229C23×C17H(5,𝔽2)12yes—
230C23×C17H(5,𝔽2)12yes—
231C23×C172−1+412yes—
232C23×C172−1+412yes—
233C23×C17C2511yescharacteristic
234C22×D17—22no—
235C22×D17—22no—
236C22×D17—22no—
237C22×D17—22no—
238C22×D17—22no—
239C22×D17—22no—
240C22×D17—22no—
241C22×D17—44no—
242C22×D17—44no—
243C22×D17—44no—
244C22×D17—44no—
245C22×D17—44no—
246C22×D17—44no—
247C22×D17—44no—
248C2×C4×C17—28no—
249C2×C4×C17—28no—
250C2×C4×C17—28no—
251C2×C4×C17—22no—
252C2×C4×C17—22no—
253C2×C4×C17—22no—
254C2×C4×C17—22no—
255C2×C4×C17—22no—
256C2×C4×C17—22no—
257C2×C4×C17—22no—
258C2×C4×C17—22no—
259C2×C4×C17—22no—
260C2×C4×C17—22no—
261C2×C4×C17—22no—
262C2×C4×C17—22no—
263C2×C4×C17—22no—
264C2×C4×C17—22no—
265C2×C4×C17—22no—
266C2×C4×C17—22no—
267C2×C4×C17—22no—
268C2×C4×C17—22no—
269C2×C4×C17—44no—
270C2×C4×C17—44no—
271C2×C4×C17—44no—
272C2×C4×C17—44no—
273C2×C4×C17C2×#4114yes—
274C2×C4×C17C2×#4114yes—
275C2×C4×C17C2×#4114yes—
276C2×Dic17—22no—
277C2×Dic17—22no—
278C2×Dic17—22no—
279C2×Dic17—22no—
280C2×Dic17—22no—
281C2×Dic17—22no—
282C2×Dic17—22no—
283C2×Dic17—22no—
284C2×Dic17—22no—
285C2×Dic17—22no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—22no—
289C2×Dic17—22no—
290C2×Dic17—22no—
291C2×Dic17—22no—
292C2×Dic17—22no—
293C2×Dic17—22no—
294C2×Dic17—22no—
295C2×Dic17—22no—
296C2×Dic17—22no—
297C2×Dic17—44no—
298C2×Dic17—44no—
299C2×Dic17—44no—
300C2×Dic17—44no—
301C2×Dic17—44no—
302C2×Dic17—44no—
303C2×Dic17—44no—
304Dic34—416no—
305#2650—1716no—
306C2×#400—171no—
307C2×#400—171no—
308C2×#400—171no—
309C2×#397—171no—
310C2×#397—171no—
311C2×#396—171no—
312C2×#395—171no—
313C2×#393—171no—
314C2×#391—171no—
315C2×#388—171no—
316C2×#388—171no—
317C2×#388—171no—
318C2×#387—171no—
319C2×#387—171no—
320C2×C4×C4⋊C4D1711yescharacteristic, complemented
321C22×C17#52914yes—
322C22×C17#53814yes—
323C22×C17#53914yes—
324C22×C17#54114yes—
325C22×C17#54214yes—
326C22×C17#54214yes—
327C22×C17#54214yes—
328C22×C17C22×#4111yescharacteristic
329C22×C17C22×#4111yescharacteristic
330C22×C17C22×#4111yescharacteristic
331C22×C17C2×H(5,𝔽2)11yescharacteristic
332C22×C17C2×H(5,𝔽2)11yescharacteristic
333C22×C17C2×2−1+411yescharacteristic
334C22×C17C2×2−1+411yescharacteristic
335C2×D17—42no—
336C2×D17—42no—
337C2×D17—42no—
338C2×D17—42no—
339C2×D17—42no—
340C2×D17—42no—
341C2×D17—42no—
342C2×D17—88no—
343C4×C17—24no—
344C4×C17—24no—
345C4×C17—24no—
346C4×C17—42no—
347C4×C17—42no—
348C4×C17—42no—
349C4×C17—42no—
350Dic17—42no—
351Dic17—42no—
352Dic17—42no—
353Dic17—42no—
354Dic17—42no—
355Dic17—42no—
356Dic17—42no—
357C23×Q8—171no—
358C22×C4⋊C4—171no—
359C22×C4⋊C4—171no—
360C22×C4⋊C4—171no—
361C22×C4⋊C4—171no—
362C22×C4⋊C4—171no—
363C22×C4⋊C4—171no—
364C22×C4⋊C4C2×D1711yescharacteristic
365C22×C4⋊C4C2×D1711yescharacteristic
366C22×C22⋊C4—171no—
367C22×C22⋊C4—171no—
368C22×C22⋊C4—171no—
369C22×C22⋊C4—171no—
370C22×C22⋊C4—171no—
371C22×C22⋊C4—171no—
372C22×C22⋊C4—171no—
373C22×C42C2×D1711yescharacteristic
374C22×C42C2×D1711yescharacteristic
375C22×C42C2×D1711yescharacteristic
376#400—178no—
377#400—178no—
378#400—178no—
379#397—178no—
380#397—178no—
381#396—178no—
382#395—178no—
383#393—178no—
384#391—178no—
385#388—178no—
386#388—178no—
387#388—178no—
388#387—178no—
389#387—178no—
390C4×C4⋊C4C2×D1718yescomplemented
391C2×#95—171no—
392C2×#95—171no—
393C2×#95—171no—
394C2×#95—171no—
395C2×#95—171no—
396C2×#95—171no—
397C2×#95—171no—
398C2×#95—171no—
399C2×#95—171no—
400C2×#95—171no—
401C2×#95—171no—
402C2×#95—171no—
403C2×#95—171no—
404C2×#95—171no—
405C2×#95C2×D1711yescharacteristic
406C2×#95C2×D1711yescharacteristic
407C2×C17#265018yescomplemented
408C2×C17C2×#52911yescharacteristic
409C2×C17C2×#53811yescharacteristic
410C2×C17C2×#53911yescharacteristic
411C2×C17C2×#54111yescharacteristic
412C2×C17C2×#54211yescharacteristic
413C2×C17C2×#54211yescharacteristic
414C2×C17C2×#54211yescharacteristic
415D17—82no—
416C25—171no—
417C22×Q8—174no—
418C22×Q8—344no—
419C22×Q8—682no—
420C22×Q8—682no—
421C23×C4—171no—
422C23×C4—171no—
423C23×C4—171no—
424C23×C4—171no—
425C23×C4—171no—
426C23×C4—171no—
427C23×C4—171no—
428C23×C4C22×D1711yescharacteristic
429C23×C4C22×D1711yescharacteristic
430C23×C4C22×D1711yescharacteristic
431C23×C4C22×D1711yescharacteristic
432C23×C4C22×D1711yescharacteristic
433C23×C4C22×D1711yescharacteristic
434C23×C4C22×D1711yescharacteristic
435C2×C4⋊C4—24no—
436C2×C4⋊C4—24no—
437C2×C4⋊C4—174no—
438C2×C4⋊C4—174no—
439C2×C4⋊C4—174no—
440C2×C4⋊C4—174no—
441C2×C4⋊C4—174no—
442C2×C4⋊C4—174no—
443C2×C4⋊C4—344no—
444C2×C4⋊C4—344no—
445C2×C4⋊C4—682no—
446C2×C4⋊C4—682no—
447C2×C4⋊C4—682no—
448C2×C4⋊C4—682no—
449C2×C4⋊C4C22×D1714yes—
450C2×C4⋊C4C22×D1714yes—
451C2×C22⋊C4—174no—
452C2×C22⋊C4—174no—
453C2×C22⋊C4—174no—
454C2×C22⋊C4—174no—
455C2×C22⋊C4—174no—
456C2×C22⋊C4—174no—
457C2×C22⋊C4—174no—
458C2×C22⋊C4—344no—
459C2×C22⋊C4—344no—
460C2×C22⋊C4—344no—
461C2×C22⋊C4—682no—
462C2×C22⋊C4—682no—
463C2×C22⋊C4—682no—
464C2×C22⋊C4—682no—
465C2×C42—24no—
466C2×C42—42no—
467C2×C42—42no—
468C2×C42C22×D1714yes—
469C2×C42C22×D1714yes—
470C2×C42C22×D1714yes—
471#95—174no—
472#95—174no—
473#95—174no—
474#95—174no—
475#95—174no—
476#95—174no—
477#95—174no—
478#95—174no—
479#95—174no—
480#95—174no—
481#95—174no—
482#95—174no—
483#95—174no—
484#95—174no—
485#95C22×D1714yes—
486#95C22×D1714yes—
487C17C2×#265011yescharacteristic, complemented, Sylow
488C24—172no—
489C24—342no—
490C24—342no—
491C24—342no—
492C24—342no—
493C24—342no—
494C24—342no—
495C24—342no—
496C24C23×D1711yescharacteristic
497C2×Q8—348no—
498C2×Q8—684no—
499C2×Q8—684no—
500C2×Q8—6816no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—172no—
520C22×C4—172no—
521C22×C4—172no—
522C22×C4—172no—
523C22×C4—172no—
524C22×C4—172no—
525C22×C4—172no—
526C22×C4—342no—
527C22×C4—342no—
528C22×C4—342no—
529C22×C4—342no—
530C22×C4—342no—
531C22×C4—342no—
532C22×C4—342no—
533C22×C4—342no—
534C22×C4—342no—
535C22×C4—342no—
536C22×C4—342no—
537C22×C4—342no—
538C22×C4—342no—
539C22×C4—342no—
540C22×C4—342no—
541C22×C4—342no—
542C22×C4—342no—
543C22×C4—342no—
544C22×C4—342no—
545C22×C4—342no—
546C22×C4—342no—
547C22×C4#6325214yes—
548C22×C4#6325214yes—
549C22×C4#6325214yes—
550C22×C4C23×D1712yes—
551C22×C4C23×D1712yes—
552C22×C4C23×D1712yes—
553C22×C4C23×D1712yes—
554C22×C4C23×D1712yes—
555C22×C4C23×D1712yes—
556C22×C4C23×D1712yes—
557C4⋊C4—28no—
558C4⋊C4—28no—
559C4⋊C4—348no—
560C4⋊C4—348no—
561C4⋊C4—684no—
562C4⋊C4—684no—
563C4⋊C4—684no—
564C4⋊C4—684no—
565C22⋊C4—348no—
566C22⋊C4—348no—
567C22⋊C4—348no—
568C22⋊C4—684no—
569C22⋊C4—684no—
570C22⋊C4—684no—
571C22⋊C4—684no—
572C42—28no—
573C42—44no—
574C42—44no—
575C23—342no—
576C23—342no—
577C23—342no—
578C23—342no—
579C23—342no—
580C23—342no—
581C23—342no—
582C23—684no—
583C23—684no—
584C23—684no—
585C23—684no—
586C23—684no—
587C23—684no—
588C23—684no—
589C23C2×#6325212yes—
590C23C2×#6325212yes—
591C23C2×#6325212yes—
592C23#1058769112yes—
593C23#1058769412yes—
594C23#1058769612yes—
595C23#1058769712yes—
596C23C24×D1711yescharacteristic
597Q8—6816no—
598C2×C4—28no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—28no—
606C2×C4—28no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—44no—
622C2×C4—44no—
623C2×C4—342no—
624C2×C4—342no—
625C2×C4—342no—
626C2×C4—342no—
627C2×C4—342no—
628C2×C4—342no—
629C2×C4—342no—
630C2×C4—342no—
631C2×C4—342no—
632C2×C4—342no—
633C2×C4—342no—
634C2×C4—342no—
635C2×C4—342no—
636C2×C4—342no—
637C2×C4—342no—
638C2×C4—342no—
639C2×C4—342no—
640C2×C4—342no—
641C2×C4—342no—
642C2×C4—342no—
643C2×C4—342no—
644C2×C4—684no—
645C2×C4—684no—
646C2×C4—684no—
647C2×C4—684no—
648C2×C4—684no—
649C2×C4—684no—
650C2×C4—684no—
651C2×C4C2×#6325214yes—
652C2×C4C2×#6325214yes—
653C2×C4C2×#6325214yes—
654C22—682no—
655C22—682no—
656C22—682no—
657C22—682no—
658C22—682no—
659C22—682no—
660C22—682no—
661C22—1368no—
662C22#1176334314yes—
663C22#1176339214yes—
664C22#1176340614yes—
665C22#1176341714yes—
666C22#1176342414yes—
667C22#1176343014yes—
668C22#1176343114yes—
669C22C22×#6325211yescharacteristic
670C22C22×#6325211yescharacteristic
671C22C22×#6325211yescharacteristic
672C22C2×#1058769111yescharacteristic
673C22C2×#1058769611yescharacteristic
674C22C2×#1058769711yescharacteristic
675C22C2×#1058769411yescharacteristic
676C4—24no—
677C4—24no—
678C4—24no—
679C4—42no—
680C4—42no—
681C4—42no—
682C4—42no—
683C4—682no—
684C4—682no—
685C4—682no—
686C4—682no—
687C4—682no—
688C4—682no—
689C4—682no—
690C2—1362no—
691C2#1453479618yesdirect product factor
692C2C2×#1176334311yescharacteristic
693C2C2×#1176339211yescharacteristic
694C2C2×#1176340611yescharacteristic
695C2C2×#1176341711yescharacteristic
696C2C2×#1176342411yescharacteristic
697C2C2×#1176343011yescharacteristic
698C2C2×#1176343111yescharacteristic
subgroupG/H
centerC24C23×D17
commutator, cosocleC23×C17C25
FrattiniC23C24×D17
FittingC2×C4×C4⋊C4×C17C2
socleC24×C17C24
prime radicalC24×D17C23
hypercenterC2×C4×C4⋊C4D17
hypocenterC17C2×#2650
LCSG ▷ C23×C17 ▷ C17
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. #14534796C2direct (N × H)
2. C2×#11762751C2semidirect
3. C2×#11762750C2semidirect
4. C2×#11762747C2semidirect
8. C2×#11762729C2semidirect
10. C2×#11762715C2semidirect
14. C2×#11762693C2semidirect
15. C2×#11762693C2semidirect
16. C2×C4×C4⋊C4×C17C2semidirect
31. #11762751C22semidirect
32. #11762750C22semidirect
33. #11762747C22semidirect
37. #11762729C22semidirect
39. #11762715C22semidirect
43. #11762693C22semidirect
44. #11762693C22semidirect
64. C4×C4⋊C4×C17C22semidirect
320. C2×C4×C4⋊C4D17semidirect
390. C4×C4⋊C4C2×D17semidirect
407. C2×C17#2650semidirect
487. C17C2×#2650semidirect
691. C2#14534796direct (N × H)

Maximal subgroups

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

subgroupindex
#145347962
C2×#117627512
C2×#117627502
C2×#117627472
C2×#117627382
C2×#117627352
C2×#117627312
C2×#117627292
C2×#117627222
C2×#117627152
C2×#117627002
C2×#117626932
C2×C4×C4⋊C4×C172
C2×#265017