Finite Group Databasebeta

← #17039589

Subgroups — #17039589

Order 4352.

1134 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763430C211yesmaximal, characteristic
2C2×#11762765C211yesmaximal, characteristic, complemented
3#14529756C211yesmaximal, characteristic, complemented
4#14529744C211yesmaximal, characteristic, complemented
5#14529598C211yesmaximal, characteristic, complemented
6#14529593C211yesmaximal, characteristic, complemented
7#14529220C211yesmaximal, characteristic
8#14529215C211yesmaximal, characteristic, complemented
9#14529210C211yesmaximal, characteristic
10#14529205C211yesmaximal, characteristic, complemented
11#14528617C211yesmaximal, characteristic, complemented
12#14528612C211yesmaximal, characteristic, complemented
13C4×#10587481C211yesmaximal, characteristic, complemented
14C4×#10587480C211yesmaximal, characteristic, complemented
15C17×#2314C211yesmaximal, characteristic, complemented
16C22×#63223C2211yescharacteristic
17C23×#3622C2211yescharacteristic
18#11763430—24no—
19#11763430C418yescomplemented
20C2×#10587555C2211yescharacteristic
21C2×#10587584—21no—
22C2×#10587561C2211yescharacteristic
23C2×#10587571—21no—
24C2×#10587569—21no—
25C2×#10587610C2211yescharacteristic
26C2×#10587582—21no—
27C2×#10587616C2211yescharacteristic
28C2×C4×Dic34C2211yescharacteristic
29C2×C4×D68C2211yescharacteristic
30C2×#10587481C2211yescharacteristic
31C2×#10587481C2211yescharacteristic
32C2×#10587481C2211yescharacteristic
33C2×#10587481C2211yescharacteristic
34C2×#10587480C2211yescharacteristic
35C2×#10587480C2211yescharacteristic
36C2×#10587480C2211yescharacteristic
37C2×#10587480C2211yescharacteristic
38#11762765—24no—
39C2×#10587474C2211yescharacteristic
40C2×#10587474C2211yescharacteristic
41C2×C4×#3622C2211yescharacteristic
42C2×C4×#3622C2211yescharacteristic
43#11762571C2211yescharacteristic
44#11762571C2211yescharacteristic
45#11762571C2211yescharacteristic
46#11762571C2211yescharacteristic
47#11762571C2211yescharacteristic
48#11762571C2211yescharacteristic
49#11762571C2211yescharacteristic
50#11762571C2211yescharacteristic
51C2×C17×#117C2211yescharacteristic
52C17×#388—21no—
53C17×#388—21no—
54C17×#387—21no—
55C17×#387—21no—
56C17×#384C2211yescharacteristic
57C17×#382C2211yescharacteristic
58C17×#380C2211yescharacteristic
59C17×#380C2211yescharacteristic
60C4×C4⋊C4×C17C2211yescharacteristic
61C4×C4⋊C4×C17C2211yescharacteristic
62C23×C4×C17C2311yescharacteristic
63C22×C22⋊D17—21no—
64C22×D68C2311yescharacteristic
65C22×C4×D17—21no—
66C22×Dic34—21no—
67C22×Dic34C2311yescharacteristic
68C17×#117C2×C414yes—
69C17×#117D414yes—
70C2×C4⋊C4×C17—21no—
71C2×C4⋊C4×C17—21no—
72C2×C4⋊C4×C17D411yescharacteristic
73C2×C4⋊C4×C17D411yescharacteristic
74C2×C4⋊C4×C17C2311yescharacteristic
75C2×C4⋊C4×C17C2311yescharacteristic
76C2×C4⋊C4×C17C2311yescharacteristic
77C2×C4⋊C4×C17C2311yescharacteristic
78C2×C22⋊C4×C17—21no—
79C2×C22⋊C4×C17—21no—
80C2×C22⋊C4×C17D411yescharacteristic
81C2×C22⋊C4×C17D411yescharacteristic
82C2×C42×C17—21no—
83C2×C42×C17—21no—
84C2×C42×C17C2311yescharacteristic
85C2×C42×C17C2311yescharacteristic
86C2×C22⋊Dic17—21no—
87#10587616—22no—
88#10587616C2×C414yes—
89C2×#63227—21no—
90C2×#63227—21no—
91C2×#63227—21no—
92C2×#63227—21no—
93C2×C4⋊Dic17—21no—
94C2×C4⋊Dic17C2311yescharacteristic
95C2×C4⋊Dic17C2311yescharacteristic
96#10587610—22no—
97#10587610C2×C414yes—
98C2×#63225—21no—
99C2×#63225—21no—
100C2×C4×Dic17—21no—
101C2×#63223—22no—
102C2×#63223—22no—
103C2×#63223—22no—
104C22×#3622—22no—
105C22×#3622—22no—
106C22×#3622—22no—
107C22×#3622C2311yescharacteristic
108C22×#3622C2311yescharacteristic
109C22×#3622C2311yescharacteristic
110C22×#3622C2311yescharacteristic
111#10587584—28no—
112#10587582—28no—
113#10587571—28no—
114#10587569—28no—
115#10587561—22no—
116#10587561C2×C414yes—
117C4×D68—22no—
118C4×D68C2×C414yes—
119#10587555—22no—
120#10587555C2×C414yes—
121C4×Dic34—22no—
122C4×Dic34C2×C414yes—
123C17×#95—21no—
124C17×#95—21no—
125C17×#95—21no—
126C17×#95—21no—
127C17×#95—21no—
128C17×#95—21no—
129#10587481—22no—
130#10587481—22no—
131#10587481—22no—
132#10587481—22no—
133#10587480—22no—
134#10587480—22no—
135#10587480—22no—
136#10587480—22no—
137#10587474—22no—
138#10587474—22no—
139C4×#3622—22no—
140C4×#3622—22no—
141C24×C17C2×D411yescharacteristic
142C23×D17—21no—
143C22×C4×C17—21no—
144C22×C4×C17—21no—
145C22×C4×C17—21no—
146C22×C4×C17—21no—
147C22×C4×C17—21no—
148C22×C4×C17—21no—
149C22×C4×C17—21no—
150C22×C4×C17—21no—
151C22×C4×C17C22×C412yes—
152C22×C4×C17C2×D412yes—
153C22×C4×C17C2×D411yescharacteristic
154C22×C4×C17C2×D411yescharacteristic
155C22×C4×C17C2×D411yescharacteristic
156C22×C4×C17C2×D411yescharacteristic
157C22×C4×C17C2×D411yescharacteristic
158C22×C4×C17C2411yescharacteristic
159C2×C22⋊D17—24no—
160C2×C22⋊D17—81no—
161C2×C22⋊D17—81no—
162C22×Dic17—21no—
163C22×Dic17—21no—
164C22×Dic17—21no—
165C2×D68—21no—
166C2×D68—21no—
167C2×D68—21no—
168C2×D68—21no—
169C2×D68—21no—
170C2×D68C22×C412yes—
171C2×C4×D17—24no—
172C2×C4×D17—81no—
173C2×C4×D17—81no—
174C2×Dic34—21no—
175C2×Dic34—21no—
176C2×Dic34—21no—
177C2×Dic34—21no—
178C2×Dic34—21no—
179C2×Dic34—24no—
180C2×Dic34—81no—
181C2×Dic34—81no—
182C2×Dic34C22×C412yes—
183C4⋊C4×C17—21no—
184C4⋊C4×C17—21no—
185C4⋊C4×C17—21no—
186C4⋊C4×C17—21no—
187C4⋊C4×C17—21no—
188C4⋊C4×C17—21no—
189C4⋊C4×C17—21no—
190C4⋊C4×C17—21no—
191C4⋊C4×C17—81no—
192C4⋊C4×C17—81no—
193C4⋊C4×C17C22⋊C414yes—
194C4⋊C4×C17C22⋊C414yes—
195C22⋊C4×C17—81no—
196C22⋊C4×C17—81no—
197C22⋊C4×C17C22⋊C414yes—
198C22⋊C4×C17C22⋊C414yes—
199C42×C17—81no—
200C42×C17—81no—
201C42×C17C22×C412yes—
202C42×C17C22×C412yes—
203C42×C17C2×D412yes—
204C42×C17C2×D412yes—
205C22⋊Dic17—24no—
206#63227—24no—
207#63227—24no—
208#63227—24no—
209#63227—24no—
210C4⋊Dic17—24no—
211C4⋊Dic17—21no—
212C4⋊Dic17—21no—
213C4⋊Dic17C22×C412yes—
214C4⋊Dic17C22×C412yes—
215#63225—24no—
216#63225—24no—
217C4×Dic17—24no—
218#63223—28no—
219C2×#3622—28no—
220C2×#3622—21no—
221C2×#3622—21no—
222C2×#3622—21no—
223C2×#3622—21no—
224C2×#3622—21no—
225C2×#3622—21no—
226C2×#3622—21no—
227C2×#3622—21no—
228C2×#3622#4112yes—
229C2×#3622#4112yes—
230C2×#3622#4112yes—
231C2×#3622#4112yes—
232#21412—171nomaximal, Sylow
233C23×C17—21no—
234C23×C17—21no—
235C23×C17—21no—
236C23×C17—21no—
237C23×C17—21no—
238C23×C17—21no—
239C23×C17C2×C22⋊C412yes—
240C23×C17C22×D411yescharacteristic
241C22×D17—22no—
242C22×D17—41no—
243C22×D17—41no—
244C22×D17—41no—
245C22×D17—41no—
246C22×D17—41no—
247C22×D17—41no—
248C2×C4×C17—21no—
249C2×C4×C17—21no—
250C2×C4×C17—21no—
251C2×C4×C17—21no—
252C2×C4×C17—21no—
253C2×C4×C17—21no—
254C2×C4×C17—21no—
255C2×C4×C17—21no—
256C2×C4×C17—21no—
257C2×C4×C17—21no—
258C2×C4×C17—22no—
259C2×C4×C17—22no—
260C2×C4×C17—22no—
261C2×C4×C17—22no—
262C2×C4×C17—41no—
263C2×C4×C17—41no—
264C2×C4×C17—41no—
265C2×C4×C17—41no—
266C2×C4×C17—41no—
267C2×C4×C17—41no—
268C2×C4×C17—41no—
269C2×C4×C17—41no—
270C2×C4×C17—41no—
271C2×C4×C17—41no—
272C2×C4×C17—41no—
273C2×C4×C17—41no—
274C2×C4×C17C2×C22⋊C412yes—
275C2×C4×C17C2×C22⋊C412yes—
276C2×C4×C17C2×C22⋊C412yes—
277C2×C4×C17C2×C22⋊C412yes—
278C2×C4×C17C2×C22⋊C412yes—
279C2×C4×C17C23×C411yescharacteristic
280C2×C4×C17C22×D411yescharacteristic
281C2×C4×C17C2×#4111yescharacteristic
282C2×C4×C17C2×#4111yescharacteristic
283C2×C4×C17C2×#4111yescharacteristic
284C2×C4×C17C2×#4111yescharacteristic
285C22⋊D17—84no—
286C2×Dic17—22no—
287C2×Dic17—22no—
288C2×Dic17—22no—
289C2×Dic17—41no—
290C2×Dic17—41no—
291C2×Dic17—41no—
292C2×Dic17—41no—
293C2×Dic17—41no—
294C2×Dic17—41no—
295D68—22no—
296D68—22no—
297D68—41no—
298D68—41no—
299C4×D17—84no—
300Dic34—22no—
301Dic34—22no—
302Dic34—41no—
303Dic34—41no—
304Dic34—84no—
305#3622—22no—
306#3622—22no—
307#3622—22no—
308#3622—22no—
309C2×#542—171no—
310C2×#405—171no—
311#2314D1711yescharacteristic, complemented
312#1993—171no—
313#1990—171no—
314#1959—171no—
315#1958—171no—
316#1895—171no—
317#1894—171no—
318#1893—171no—
319#1892—171no—
320#1763—171no—
321#1762—171no—
322C4×#103—171no—
323C4×#102—171no—
324C22×C17—22no—
325C22×C17—22no—
326C22×C17—22no—
327C22×C17—41no—
328C22×C17—41no—
329C22×C17—41no—
330C22×C17—41no—
331C22×C17C22×C22⋊C411yescharacteristic
332C22×C17#53211yescharacteristic
333C22×C17#53211yescharacteristic
334C22×C17#57611yescharacteristic
335C22×C17#57711yescharacteristic
336C22×C17#57711yescharacteristic
337C22×C17#57811yescharacteristic
338C2×D17—42no—
339C2×D17—42no—
340C2×D17—42no—
341C2×D17—81no—
342C2×D17—81no—
343C2×D17—81no—
344C2×D17—81no—
345C4×C17—22no—
346C4×C17—22no—
347C4×C17—22no—
348C4×C17—22no—
349C4×C17—22no—
350C4×C17—81no—
351C4×C17—81no—
352C4×C17—81no—
353C4×C17—81no—
354C4×C17C4×#4111yescharacteristic
355C4×C17C4×#4111yescharacteristic
356C4×C17#52511yescharacteristic
357C4×C17#52511yescharacteristic
358Dic17—42no—
359Dic17—42no—
360Dic17—42no—
361C22×M16—171no—
362C23×C8—171no—
363#542—178no—
364#542—344no—
365C2×C4⋊Q8—171no—
366C2×#126—341no—
367C2×#124—171no—
368C2×#124—341no—
369C2×#123—341no—
370C2×C22⋊Q8—171no—
371C2×C22⋊Q8—341no—
372C2×#121—171no—
373C2×C4×Q8—171no—
374C2×C4×D4—171no—
375C2×#117C2×D1711yescharacteristic
376C2×#103—171no—
377C2×#103—171no—
378C2×#103—171no—
379C2×#103—171no—
380C2×#102—171no—
381C2×#102—171no—
382C2×#102—171no—
383C2×#102—171no—
384#405—344no—
385C2×#97—171no—
386C2×#97—171no—
387C2×C4×C8—171no—
388C2×C4×C8—171no—
389#388—21no—
390#388—21no—
391#387—21no—
392#387—21no—
393#384C2×D1711yescharacteristic
394#382C2×D1711yescharacteristic
395#380C2×D1711yescharacteristic
396#380C2×D1711yescharacteristic
397C4×C4⋊C4C2×D1711yescharacteristic
398C4×C4⋊C4C2×D1711yescharacteristic
399#340—171no—
400#340—171no—
401#340—171no—
402#340—171no—
403#340—171no—
404#340—171no—
405#340—171no—
406#340—171no—
407C2×C17—42no—
408C2×C17#229711yescharacteristic
409C2×C17#289711yescharacteristic
410C2×C17#289811yescharacteristic
411C2×C17#317311yescharacteristic
412C2×C17#317511yescharacteristic
413C2×C17#317811yescharacteristic
414C2×C17#317911yescharacteristic
415D17—82no—
416C22×Q8—171no—
417C22×Q8—341no—
418C22×D4—171no—
419C22×D4—341no—
420C23×C4—341no—
421C23×C4C22×D1711yescharacteristic
422C2×M16—342no—
423C2×M16—342no—
424C2×M16—342no—
425C22×C8—171no—
426C22×C8—171no—
427C22×C8—171no—
428C22×C8—171no—
429C22×C8—342no—
430C22×C8—342no—
431C22×C8—342no—
432C4⋊Q8—174no—
433C4⋊Q8—342no—
434#126—348no—
435#124—174no—
436#124—348no—
437#124—342no—
438#123—348no—
439C22⋊Q8—174no—
440C22⋊Q8—342no—
441C22⋊Q8—348no—
442#121—174no—
443#121—342no—
444C4×Q8—174no—
445C4×Q8—342no—
446C4×D4—174no—
447C4×D4—342no—
448#117C4×D1714yes—
449#117D6814yes—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—171no—
453C2×C4⋊C4—171no—
454C2×C4⋊C4—341no—
455C2×C4⋊C4—341no—
456C2×C4⋊C4—341no—
457C2×C4⋊C4C22⋊D1711yescharacteristic
458C2×C4⋊C4C22⋊D1711yescharacteristic
459C2×C4⋊C4C22×D1711yescharacteristic
460C2×C4⋊C4C22×D1711yescharacteristic
461C2×C4⋊C4C22×D1711yescharacteristic
462C2×C4⋊C4C22×D1711yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—341no—
466C2×C22⋊C4—341no—
467C2×C22⋊C4—341no—
468C2×C22⋊C4—341no—
469C2×C22⋊C4—341no—
470C2×C22⋊C4C22⋊D1711yescharacteristic
471C2×C22⋊C4C22⋊D1711yescharacteristic
472C2×C42—21no—
473C2×C42—21no—
474C2×C42—341no—
475C2×C42C22×D1711yescharacteristic
476C2×C42C22×D1711yescharacteristic
477#103—342no—
478#103—342no—
479#103—342no—
480#103—342no—
481#102—342no—
482#102—342no—
483#102—342no—
484#102—342no—
485#97—342no—
486#97—342no—
487C4×C8—342no—
488C4×C8—342no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—21no—
493#95—21no—
494#95—21no—
495C17#2141211yescharacteristic, complemented, Sylow
496C24—341no—
497C24C2×C22⋊D1711yescharacteristic
498C2×Q8—172no—
499C2×Q8—341no—
500C2×Q8—344no—
501C2×Q8—341no—
502C2×Q8—341no—
503C2×Q8—341no—
504C2×Q8—341no—
505C2×Q8—1361no—
506C2×Q8—1361no—
507C2×D4—172no—
508C2×D4—344no—
509C2×D4—341no—
510C2×D4—341no—
511C2×D4—341no—
512C2×D4—341no—
513C2×D4—341no—
514C2×D4—1361no—
515C2×D4—1361no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—341no—
525C22×C4—341no—
526C22×C4—341no—
527C22×C4—344no—
528C22×C4—1361no—
529C22×C4—1361no—
530C22×C4C2×C4×D1712yes—
531C22×C4C2×D6812yes—
532C22×C4C2×C22⋊D1711yescharacteristic
533C22×C4C2×C22⋊D1711yescharacteristic
534C22×C4C2×C22⋊D1711yescharacteristic
535C22×C4C2×C22⋊D1711yescharacteristic
536C22×C4C2×C22⋊D1711yescharacteristic
537C22×C4C23×D1711yescharacteristic
538M16—348no—
539C2×C8—172no—
540C2×C8—172no—
541C2×C8—172no—
542C2×C8—172no—
543C2×C8—348no—
544C2×C8—341no—
545C2×C8—341no—
546C2×C8—341no—
547C2×C8—341no—
548C2×C8—341no—
549C2×C8—341no—
550C2×C8—341no—
551C2×C8—341no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—81no—
561C4⋊C4—81no—
562C4⋊C4—172no—
563C4⋊C4—172no—
564C4⋊C4—341no—
565C4⋊C4—341no—
566C4⋊C4—344no—
567C4⋊C4—344no—
568C4⋊C4—344no—
569C4⋊C4#6322714yes—
570C4⋊C4#6322714yes—
571C22⋊C4—81no—
572C22⋊C4—81no—
573C22⋊C4—344no—
574C22⋊C4—344no—
575C22⋊C4—344no—
576C22⋊C4—344no—
577C22⋊C4—344no—
578C22⋊C4#6322714yes—
579C22⋊C4#6322714yes—
580C42—81no—
581C42—81no—
582C42—344no—
583C42C2×C4×D1712yes—
584C42C2×C4×D1712yes—
585C42C2×D6812yes—
586C42C2×D6812yes—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—342no—
594C23—681no—
595C23—681no—
596C23—681no—
597C23—681no—
598C23—681no—
599C23—681no—
600C23C2×#6322712yes—
601C23C22×C22⋊D1711yescharacteristic
602Q8—342no—
603Q8—342no—
604Q8—681no—
605Q8—681no—
606Q8—1364no—
607D4—342no—
608D4—342no—
609D4—681no—
610D4—681no—
611D4—1364no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—342no—
639C2×C4—342no—
640C2×C4—342no—
641C2×C4—681no—
642C2×C4—681no—
643C2×C4—681no—
644C2×C4—681no—
645C2×C4—681no—
646C2×C4—681no—
647C2×C4—1364no—
648C2×C4C2×#6322712yes—
649C2×C4C2×#6322712yes—
650C2×C4C2×#6322712yes—
651C2×C4C2×#6322712yes—
652C2×C4C2×#6322712yes—
653C2×C4C22×C4×D1711yescharacteristic
654C2×C4C22×D6811yescharacteristic
655C2×C4#41×D1711yescharacteristic
656C2×C4#41×D1711yescharacteristic
657C2×C4#41×D1711yescharacteristic
658C2×C4#41×D1711yescharacteristic
659C8—342no—
660C8—342no—
661C8—342no—
662C8—342no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—682no—
671C22—682no—
672C22—682no—
673C22—1361no—
674C22—1361no—
675C22—1361no—
676C22—1361no—
677C22C22×#6322711yescharacteristic
678C22#1176335511yescharacteristic
679C22#1176335511yescharacteristic
680C22#1176361211yescharacteristic
681C22#1176361711yescharacteristic
682C22#1176362011yescharacteristic
683C22#1176362411yescharacteristic
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4—81no—
693C4—682no—
694C4—682no—
695C4—682no—
696C4#1176327711yescharacteristic
697C4#1176327711yescharacteristic
698C4#1176332111yescharacteristic
699C4#1176332111yescharacteristic
700C2—42no—
701C2—1362no—
702C2#1453127211yescharacteristic
703C2#1453730711yescharacteristic
704C2#1453731411yescharacteristic
705C2#1453939511yescharacteristic
706C2#1453941711yescharacteristic
707C2#1453945411yescharacteristic
708C2#1453946911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D17
commutatorC2×C4×C17C23×C4
FrattiniC22×C4C23×D17
FittingC17×#2314C2
socleC23×C17C22×D4
prime radicalC2×#10587616C22
cosocleC22×C4×C17C24
hypercenter#2314D17
hypocenterC17#21412
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2314

Complements

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

NH ≅ G/Ntype
2. C2×#11762765C2semidirect
3. #14529756C2semidirect
4. #14529744C2semidirect
5. #14529598C2semidirect
6. #14529593C2semidirect
8. #14529215C2semidirect
10. #14529205C2semidirect
11. #14528617C2semidirect
12. #14528612C2semidirect
13. C4×#10587481C2semidirect
14. C4×#10587480C2semidirect
15. C17×#2314C2semidirect
19. #11763430C4semidirect
311. #2314D17semidirect
495. C17#21412semidirect

Maximal subgroups

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

subgroupindex
C2×#117634302
C2×#117627652
#145297562
#145297442
#145295982
#145295932
#145292202
#145292152
#145292102
#145292052
#145286172
#145286122
C4×#105874812
C4×#105874802
C17×#23142
#2141217