Finite Group Databasebeta

← C29×#28903 #20323803

Subgroups — C29×#28903 #20323803

Order 7424.

730 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C29×#2513C211yesmaximal, characteristic, complemented
2C29×#2448C211yesmaximal, characteristic, complemented
3C29×#2085C211yesmaximal, characteristic, complemented
4C29×#2066C211yesmaximal, characteristic, complemented
5C29×#2054C211yesmaximal, characteristic
6C29×#2012C211yesmaximal, characteristic
7C29×#1973C211yesmaximal, characteristic, complemented
8C29×#1972C211yesmaximal, characteristic
9C29×#1958C211yesmaximal, characteristic, complemented
10C29×#1936C211yesmaximal, characteristic, complemented
11C29×#1934C211yesmaximal, characteristic, complemented
12C29×#1925C211yesmaximal, characteristic, complemented
13C29×#1880C211yesmaximal, characteristic, complemented
14C29×#1771C211yesmaximal, characteristic, complemented
15C29×#1763C211yesmaximal, characteristic, complemented
16C22×SD16×C29C2211yescharacteristic
17C22×D8×C29C2211yescharacteristic
18C2×C29×#124C2211yescharacteristic
19C2×C4×Q8×C29C2211yescharacteristic
20C2×C29×#107C2211yescharacteristic
21C2×C29×#106C2211yescharacteristic
22C2×C29×C4⋊C8C2211yescharacteristic
23C2×C29×#103C2211yescharacteristic
24C2×C29×#103C2211yescharacteristic
25C2×C29×#103C2211yescharacteristic
26C2×C29×#102C2211yescharacteristic
27C2×C29×#102C2211yescharacteristic
28C2×C29×#102C2211yescharacteristic
29C2×C29×#102C2211yescharacteristic
30C2×C29×#102C2211yescharacteristic
31C2×C29×#97C2211yescharacteristic
32C2×C29×#97C2211yescharacteristic
33C2×C4×C8×C29C2211yescharacteristic
34C29×#399—21no—
35C29×#397—21no—
36C29×#397—21no—
37C29×#397—21no—
38C29×#391C2211yescharacteristic
39C29×#390C2211yescharacteristic
40C29×#390C2211yescharacteristic
41C29×#390C2211yescharacteristic
42C29×#390C2211yescharacteristic
43C29×#390C2211yescharacteristic
44C29×#389C2211yescharacteristic
45C29×#389C2211yescharacteristic
46C29×#388—21no—
47C29×#388—21no—
48C29×#388—21no—
49C29×#388—21no—
50C29×#382C2211yescharacteristic
51C4×C4⋊C4×C29C2211yescharacteristic
52C4×C4⋊C4×C29C2211yescharacteristic
53C29×#340C2211yescharacteristic
54C29×#340C2211yescharacteristic
55C29×#340C2211yescharacteristic
56C29×#340C2211yescharacteristic
57C29×#336C2211yescharacteristic
58C29×#336C2211yescharacteristic
59C22×Q8×C29C2311yescharacteristic
60C22×D4×C29C2311yescharacteristic
61C22×D4×C29C2311yescharacteristic
62C2×SD16×C29—22no—
63C2×SD16×C29—22no—
64C2×SD16×C29—41no—
65C2×D8×C29—22no—
66C2×D8×C29—41no—
67C2×D8×C29—41no—
68C22×C8×C29C2311yescharacteristic
69C22×C8×C29C2311yescharacteristic
70C22×C8×C29C2311yescharacteristic
71C22×C8×C29C2311yescharacteristic
72C29×#124—22no—
73C29×#124—41no—
74C4×Q8×C29—22no—
75C4×Q8×C29—41no—
76C2×C4⋊C4×C29—21no—
77C2×C4⋊C4×C29—21no—
78C2×C4⋊C4×C29—21no—
79C2×C4⋊C4×C29D411yescharacteristic
80C2×C4⋊C4×C29D411yescharacteristic
81C2×C4⋊C4×C29C2311yescharacteristic
82C2×C4⋊C4×C29C2311yescharacteristic
83C2×C4⋊C4×C29C2311yescharacteristic
84C2×C4⋊C4×C29C2311yescharacteristic
85C2×C4⋊C4×C29C2311yescharacteristic
86C2×C22⋊C4×C29—21no—
87C2×C22⋊C4×C29—21no—
88C2×C22⋊C4×C29—21no—
89C2×C22⋊C4×C29—21no—
90C2×C22⋊C4×C29—21no—
91C2×C22⋊C4×C29—21no—
92C2×C22⋊C4×C29—21no—
93C2×C22⋊C4×C29—21no—
94C2×C22⋊C4×C29—21no—
95C2×C22⋊C4×C29—21no—
96C2×C22⋊C4×C29—21no—
97C2×C22⋊C4×C29—21no—
98C2×C42×C29—21no—
99C2×C42×C29—21no—
100C2×C42×C29C2311yescharacteristic
101C2×C42×C29C2311yescharacteristic
102C2×C42×C29C2311yescharacteristic
103C29×#107—41no—
104C29×#106—41no—
105C29×C4⋊C8—22no—
106C29×#103—22no—
107C29×#103—22no—
108C29×#103—41no—
109C29×#102—22no—
110C29×#102—22no—
111C29×#102—22no—
112C29×#102—41no—
113C29×#102—41no—
114C29×#97—22no—
115C29×#97—41no—
116C4×C8×C29—41no—
117C29×#95—21no—
118C29×#95—21no—
119C29×#95—21no—
120C29×#95—21no—
121C29×#95—21no—
122C29×#95—21no—
123C29×#95—21no—
124C29×#95D411yescharacteristic
125C29×#95D411yescharacteristic
126C24×C29—21no—
127C24×C29—21no—
128C2×Q8×C29—21no—
129C2×Q8×C29—21no—
130C2×Q8×C29—21no—
131C2×Q8×C29—21no—
132C2×Q8×C29—21no—
133C2×Q8×C29#4112yes—
134C2×D4×C29—21no—
135C2×D4×C29—21no—
136C2×D4×C29—21no—
137C2×D4×C29—21no—
138C2×D4×C29—21no—
139C2×D4×C29—21no—
140C2×D4×C29—21no—
141C2×D4×C29—21no—
142C2×D4×C29—21no—
143C2×D4×C29—21no—
144C2×D4×C29—21no—
145C2×D4×C29—21no—
146C22×C4×C29—21no—
147C22×C4×C29—21no—
148C22×C4×C29—21no—
149C22×C4×C29—21no—
150C22×C4×C29—21no—
151C22×C4×C29—21no—
152C22×C4×C29C2×D411yescharacteristic
153C22×C4×C29C2×D411yescharacteristic
154C22×C4×C29C2×D411yescharacteristic
155C22×C4×C29C2×D411yescharacteristic
156C22×C4×C29C2×D411yescharacteristic
157C22×C4×C29C2×D411yescharacteristic
158C22×C4×C29C2411yescharacteristic
159SD16×C29—44no—
160D8×C29—44no—
161C2×C8×C29—21no—
162C2×C8×C29—21no—
163C2×C8×C29—21no—
164C2×C8×C29—21no—
165C2×C8×C29—21no—
166C2×C8×C29—21no—
167C2×C8×C29—21no—
168C2×C8×C29—21no—
169C2×C8×C29—21no—
170C2×C8×C29#4112yes—
171C2×C8×C29#4112yes—
172C2×C8×C29#4112yes—
173C4⋊C4×C29—21no—
174C4⋊C4×C29—21no—
175C4⋊C4×C29—21no—
176C4⋊C4×C29—21no—
177C4⋊C4×C29—21no—
178C4⋊C4×C29—21no—
179C4⋊C4×C29—21no—
180C4⋊C4×C29—21no—
181C4⋊C4×C29—21no—
182C4⋊C4×C29—21no—
183C4⋊C4×C29—41no—
184C4⋊C4×C29—41no—
185C4⋊C4×C29—42no—
186C4⋊C4×C29—81no—
187C4⋊C4×C29—81no—
188C22⋊C4×C29—42no—
189C22⋊C4×C29—42no—
190C22⋊C4×C29—42no—
191C22⋊C4×C29—42no—
192C22⋊C4×C29—42no—
193C22⋊C4×C29—42no—
194C22⋊C4×C29—81no—
195C22⋊C4×C29—81no—
196C22⋊C4×C29—81no—
197C22⋊C4×C29—81no—
198C22⋊C4×C29—81no—
199C22⋊C4×C29—81no—
200C42×C29—21no—
201C42×C29—21no—
202C42×C29—21no—
203C42×C29—21no—
204C42×C29—21no—
205C42×C29—21no—
206C42×C29—42no—
207C42×C29—81no—
208#28903C2911yesmaximal, characteristic, direct product factor, Sylow
209C23×C29—41no—
210C23×C29—41no—
211C23×C29—41no—
212C23×C29—41no—
213C23×C29—41no—
214C23×C29—41no—
215C23×C29—41no—
216C23×C29—41no—
217C23×C29—41no—
218C23×C29—41no—
219C23×C29—41no—
220C23×C29—41no—
221C23×C29—41no—
222C23×C29—41no—
223C23×C29C22×D411yescharacteristic
224Q8×C29—22no—
225Q8×C29—22no—
226Q8×C29—41no—
227Q8×C29—41no—
228D4×C29—41no—
229D4×C29—41no—
230D4×C29—41no—
231D4×C29—41no—
232D4×C29—41no—
233D4×C29—41no—
234D4×C29—41no—
235D4×C29—41no—
236C2×C4×C29—21no—
237C2×C4×C29—21no—
238C2×C4×C29—21no—
239C2×C4×C29—21no—
240C2×C4×C29—21no—
241C2×C4×C29—21no—
242C2×C4×C29—22no—
243C2×C4×C29—21no—
244C2×C4×C29—21no—
245C2×C4×C29—21no—
246C2×C4×C29—21no—
247C2×C4×C29—21no—
248C2×C4×C29—21no—
249C2×C4×C29—21no—
250C2×C4×C29—21no—
251C2×C4×C29—21no—
252C2×C4×C29—21no—
253C2×C4×C29—21no—
254C2×C4×C29—21no—
255C2×C4×C29—41no—
256C2×C4×C29—41no—
257C2×C4×C29—41no—
258C2×C4×C29—41no—
259C2×C4×C29—41no—
260C2×C4×C29—41no—
261C2×C4×C29—41no—
262C2×C4×C29—41no—
263C2×C4×C29—41no—
264C2×C4×C29—41no—
265C2×C4×C29—41no—
266C2×C4×C29—41no—
267C2×C4×C29—41no—
268C2×C4×C29—41no—
269C2×C4×C29—41no—
270C2×C4×C29—41no—
271C2×C4×C29—41no—
272C2×C4×C29C2×#4111yescharacteristic
273C2×C4×C29C2×#4111yescharacteristic
274C2×C4×C29C2×#4111yescharacteristic
275C2×C4×C29C2×#4111yescharacteristic
276C2×C4×C29H(5,𝔽2)11yescharacteristic
277C2×C4×C29H(5,𝔽2)11yescharacteristic
278C8×C29—22no—
279C8×C29—22no—
280C8×C29—22no—
281C8×C29—41no—
282#2513C2×C2911yescharacteristic, complemented
283#2448C2×C2911yescharacteristic, complemented
284#2085C2×C2911yescharacteristic, complemented
285#2066C2×C2911yescharacteristic, complemented
286#2054C2×C2911yescharacteristic
287#2012C2×C2911yescharacteristic
288#1973C2×C2911yescharacteristic, complemented
289#1972C2×C2911yescharacteristic
290#1958C2×C2911yescharacteristic, complemented
291#1936C2×C2911yescharacteristic, complemented
292#1934C2×C2911yescharacteristic, complemented
293#1925C2×C2911yescharacteristic, complemented
294#1880C2×C2911yescharacteristic, complemented
295#1771C2×C2911yescharacteristic, complemented
296#1763C2×C2911yescharacteristic, complemented
297C22×C29—81no—
298C22×C29—81no—
299C22×C29—81no—
300C22×C29—81no—
301C22×C29—81no—
302C22×C29—81no—
303C22×C29—81no—
304C22×C29—81no—
305C22×C29—81no—
306C22×C29—81no—
307C22×C29—81no—
308C22×C29—81no—
309C22×C29—81no—
310C22×C29—81no—
311C22×C29#53211yescharacteristic
312C22×C29#54611yescharacteristic
313C22×C29#55011yescharacteristic
314C22×C29#57511yescharacteristic
315C22×C29#57511yescharacteristic
316C22×C29#57611yescharacteristic
317C22×C29#57711yescharacteristic
318C4×C29—41no—
319C4×C29—41no—
320C4×C29—41no—
321C4×C29—41no—
322C4×C29—41no—
323C4×C29—41no—
324C4×C29—42no—
325C4×C29—81no—
326C4×C29—81no—
327C4×C29—81no—
328C4×C29—81no—
329C4×C29—81no—
330C4×C29#52911yescharacteristic
331C4×C29#53811yescharacteristic
332C4×C29#55111yescharacteristic
333C4×C29#55311yescharacteristic
334C22×SD16C22×C2911yescharacteristic
335C22×D8C22×C2911yescharacteristic
336C2×#124C22×C2911yescharacteristic
337C2×C4×Q8C22×C2911yescharacteristic
338C2×#107C22×C2911yescharacteristic
339C2×#106C22×C2911yescharacteristic
340C2×C4⋊C8C22×C2911yescharacteristic
341C2×#103C22×C2911yescharacteristic
342C2×#103C22×C2911yescharacteristic
343C2×#103C22×C2911yescharacteristic
344C2×#102C22×C2911yescharacteristic
345C2×#102C22×C2911yescharacteristic
346C2×#102C22×C2911yescharacteristic
347C2×#102C22×C2911yescharacteristic
348C2×#102C22×C2911yescharacteristic
349C2×#97C22×C2911yescharacteristic
350C2×#97C22×C2911yescharacteristic
351C2×C4×C8C22×C2911yescharacteristic
352#399—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#391C22×C2911yescharacteristic
357#390C22×C2911yescharacteristic
358#390C22×C2911yescharacteristic
359#390C22×C2911yescharacteristic
360#390C22×C2911yescharacteristic
361#390C22×C2911yescharacteristic
362#389C22×C2911yescharacteristic
363#389C22×C2911yescharacteristic
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#382C22×C2911yescharacteristic
369C4×C4⋊C4C22×C2911yescharacteristic
370C4×C4⋊C4C22×C2911yescharacteristic
371#340C22×C2911yescharacteristic
372#340C22×C2911yescharacteristic
373#340C22×C2911yescharacteristic
374#340C22×C2911yescharacteristic
375#336C22×C2911yescharacteristic
376#336C22×C2911yescharacteristic
377C2×C29—161no—
378C2×C29—161no—
379C2×C29#255411yescharacteristic
380C2×C29#317911yescharacteristic
381C2×C29#318311yescharacteristic
382C2×C29#330911yescharacteristic
383C2×C29#332111yescharacteristic
384C2×C29#340111yescharacteristic
385C2×C29#340311yescharacteristic
386C22×Q8C23×C2911yescharacteristic
387C22×D4C23×C2911yescharacteristic
388C22×D4C23×C2911yescharacteristic
389C2×SD16—22no—
390C2×SD16—22no—
391C2×SD16—41no—
392C2×D8—22no—
393C2×D8—41no—
394C2×D8—41no—
395C22×C8C23×C2911yescharacteristic
396C22×C8C23×C2911yescharacteristic
397C22×C8C23×C2911yescharacteristic
398C22×C8C23×C2911yescharacteristic
399#124—22no—
400#124—41no—
401C4×Q8—22no—
402C4×Q8—41no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4D4×C2911yescharacteristic
407C2×C4⋊C4D4×C2911yescharacteristic
408C2×C4⋊C4C23×C2911yescharacteristic
409C2×C4⋊C4C23×C2911yescharacteristic
410C2×C4⋊C4C23×C2911yescharacteristic
411C2×C4⋊C4C23×C2911yescharacteristic
412C2×C4⋊C4C23×C2911yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—21no—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—21no—
421C2×C22⋊C4—21no—
422C2×C22⋊C4—21no—
423C2×C22⋊C4—21no—
424C2×C22⋊C4—21no—
425C2×C42—21no—
426C2×C42—21no—
427C2×C42C23×C2911yescharacteristic
428C2×C42C23×C2911yescharacteristic
429C2×C42C23×C2911yescharacteristic
430#107—41no—
431#106—41no—
432C4⋊C8—22no—
433#103—22no—
434#103—22no—
435#103—41no—
436#102—22no—
437#102—22no—
438#102—22no—
439#102—41no—
440#102—41no—
441#97—22no—
442#97—41no—
443C4×C8—41no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—21no—
448#95—21no—
449#95—21no—
450#95—21no—
451#95D4×C2911yescharacteristic
452#95D4×C2911yescharacteristic
453C29#2890311yescharacteristic, direct product factor, Sylow
454C24—21no—
455C24—21no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8#41×C2912yes—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4C2×D4×C2911yescharacteristic
481C22×C4C2×D4×C2911yescharacteristic
482C22×C4C2×D4×C2911yescharacteristic
483C22×C4C2×D4×C2911yescharacteristic
484C22×C4C2×D4×C2911yescharacteristic
485C22×C4C2×D4×C2911yescharacteristic
486C22×C4C24×C2911yescharacteristic
487SD16—44no—
488D8—44no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8#41×C2912yes—
499C2×C8#41×C2912yes—
500C2×C8#41×C2912yes—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4—42no—
514C4⋊C4—81no—
515C4⋊C4—81no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—81no—
523C22⋊C4—81no—
524C22⋊C4—81no—
525C22⋊C4—81no—
526C22⋊C4—81no—
527C22⋊C4—81no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—21no—
533C42—21no—
534C42—42no—
535C42—81no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23—41no—
547C23—41no—
548C23—41no—
549C23—41no—
550C23C22×D4×C2911yescharacteristic
551Q8—22no—
552Q8—22no—
553Q8—41no—
554Q8—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—41no—
560D4—41no—
561D4—41no—
562D4—41no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4C2×#41×C2911yescharacteristic
600C2×C4C2×#41×C2911yescharacteristic
601C2×C4C2×#41×C2911yescharacteristic
602C2×C4C2×#41×C2911yescharacteristic
603C2×C4C29×H(5,𝔽2)11yescharacteristic
604C2×C4C29×H(5,𝔽2)11yescharacteristic
605C8—22no—
606C8—22no—
607C8—22no—
608C8—41no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22—81no—
623C22C29×#53211yescharacteristic
624C22C29×#54611yescharacteristic
625C22C29×#55011yescharacteristic
626C22C29×#57511yescharacteristic
627C22C29×#57511yescharacteristic
628C22C29×#57611yescharacteristic
629C22C29×#57711yescharacteristic
630C4—41no—
631C4—41no—
632C4—41no—
633C4—41no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—81no—
638C4—81no—
639C4—81no—
640C4—81no—
641C4—81no—
642C4C29×#52911yescharacteristic
643C4C29×#53811yescharacteristic
644C4C29×#55111yescharacteristic
645C4C29×#55311yescharacteristic
646C2—161no—
647C2—161no—
648C2C29×#255411yescharacteristic
649C2C29×#317911yescharacteristic
650C2C29×#318311yescharacteristic
651C2C29×#330911yescharacteristic
652C2C29×#332111yescharacteristic
653C2C29×#340111yescharacteristic
654C2C29×#340311yescharacteristic
subgroupG/H
center, socleC23×C29C22×D4
commutator, Frattini, cosocleC22×C4C24×C29
prime radicalC22×D8×C29C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ C4×C4⋊C4×C29 ◁ G

Complements

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

NH ≅ G/Ntype
1. C29×#2513C2semidirect
2. C29×#2448C2semidirect
3. C29×#2085C2semidirect
4. C29×#2066C2semidirect
7. C29×#1973C2semidirect
9. C29×#1958C2semidirect
10. C29×#1936C2semidirect
11. C29×#1934C2semidirect
12. C29×#1925C2semidirect
13. C29×#1880C2semidirect
14. C29×#1771C2semidirect
15. C29×#1763C2semidirect
208. #28903C29direct (N × H)
282. #2513C2×C29semidirect
283. #2448C2×C29semidirect
284. #2085C2×C29semidirect
285. #2066C2×C29semidirect
288. #1973C2×C29semidirect
290. #1958C2×C29semidirect
291. #1936C2×C29semidirect
292. #1934C2×C29semidirect
293. #1925C2×C29semidirect
294. #1880C2×C29semidirect
295. #1771C2×C29semidirect
296. #1763C2×C29semidirect
453. C29#28903direct (N × H)

Maximal subgroups

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

subgroupindex
C29×#25132
C29×#24482
C29×#20852
C29×#20662
C29×#20542
C29×#20122
C29×#19732
C29×#19722
C29×#19582
C29×#19362
C29×#19342
C29×#19252
C29×#18802
C29×#17712
C29×#17632
#2890329