Finite Group Databasebeta

← #13148218

Subgroups — #13148218

Order 1728.

732 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11721729C211yesmaximal, characteristic, complemented
2C9×#67⋊C4C211yesmaximal, characteristic, complemented
3C3×#63441C211yesmaximal, characteristic, complemented
4#11721282C211yesmaximal, characteristic
5#11721280C211yesmaximal, characteristic, complemented
6#11721251C211yesmaximal, characteristic, complemented
7#11721249C211yesmaximal, characteristic, complemented
8C4×#6195C211yesmaximal, characteristic, complemented
9#11721023C211yesmaximal, characteristic, complemented
10#11721020C211yesmaximal, characteristic, complemented
11D3×Dic9⋊C4C211yesmaximal, characteristic, complemented
12#11720933C211yesmaximal, characteristic, complemented
13#11720927C211yesmaximal, characteristic, complemented
14#11720926C211yesmaximal, characteristic, complemented
15#11720923C211yesmaximal, characteristic, complemented
16#10594090—31nomaximal
17#10589666—31nomaximal
18C2×#6233C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×C9×#67C2211yescharacteristic
21C22×C9×Dic3C2211yescharacteristic
22C2×C4×D3×C9C2211yescharacteristic
23C2×#6195C2211yescharacteristic
24C2×D3×Dic9C2211yescharacteristic
25C2×D3×Dic9C2211yescharacteristic
26C2×#6189C2211yescharacteristic
27C3×C9×C22⋊C4C2211yescharacteristic
28#88551C2211yescharacteristic
29#88536C2211yescharacteristic
30C4⋊(C3⋊Dic9)C2211yescharacteristic
31#88534C2211yescharacteristic
32C3×#3676C2211yescharacteristic
33C3×#3676C2211yescharacteristic
34C9×(C2×D3)⋊C4C2211yescharacteristic
35C9×Dic3⋊C4C2211yescharacteristic
36C4×C9×Dic3C2211yescharacteristic
37C3×C4⋊Dic9C2211yescharacteristic
38C3×Dic9⋊C4C2211yescharacteristic
39C3×Dic9⋊C4C2211yescharacteristic
40C3×C4×Dic9C2211yescharacteristic
41(C2×D3)⋊Dic9C2211yescharacteristic
42#88445C2211yescharacteristic
43#88445C2211yescharacteristic
44#88445C2211yescharacteristic
45Dic3⋊Dic9C2211yescharacteristic
46#88442C2211yescharacteristic
47#88442C2211yescharacteristic
48#88442C2211yescharacteristic
49Dic9⋊Dic3C2211yescharacteristic
50Dic9⋊Dic3C2211yescharacteristic
51Dic9⋊Dic3C2211yescharacteristic
52Dic9⋊Dic3C2211yescharacteristic
53#64092—31no—
54C3×#67⋊C4D311yescharacteristic
55C3×#879—31no—
56#63971—31no—
57#63969—31no—
58#63966—31no—
59#63964—31no—
60C4×#626—31no—
61#63893—31no—
62#63890—31no—
63D3×Dic3⋊C4—31no—
64#63869—31no—
65#63868—31no—
66#63867—31no—
67#63865—31no—
68C4×D4×C9—31no—
69#63501—31no—
70#63497—31no—
71#63491—31no—
72C4×#611—31no—
73#63486—31no—
74C2×Dic9⋊C4—31no—
75#63458—31no—
76#63451—31no—
77#63448—31no—
78#63445—31no—
79#63445—61no—
80#63441D311yescharacteristic, complemented
81#63440—31no—
82#63438—31no—
83#63432—31no—
84C23×C3×C9C2311yescharacteristic
85C22×C3⋊D9C2311yescharacteristic
86C22×D3×C9C2311yescharacteristic
87C2×C3×C4×C9C2311yescharacteristic
88C2×C3×C4×C9C2311yescharacteristic
89#6233—41no—
90C2×C3⋊Dic9C2311yescharacteristic
91C2×C3⋊Dic9C2311yescharacteristic
92C2×C3⋊Dic9C2311yescharacteristic
93C4×C3⋊D9—41no—
94C9×#67—22no—
95C2×C9×Dic3—41no—
96C2×C9×Dic3C2311yescharacteristic
97C2×C9×Dic3C2311yescharacteristic
98C2×C9×Dic3C2311yescharacteristic
99C2×C3×Dic9C2311yescharacteristic
100C2×C3×Dic9C2311yescharacteristic
101C2×C3×Dic9C2311yescharacteristic
102C2×C3×Dic9C2311yescharacteristic
103C4×D3×C9—41no—
104#6195—22no—
105D3×Dic9—22no—
106D3×Dic9—41no—
107#6189—41no—
108#5707—91no—
109#5564—91no—
110C2×#638—31no—
111C2×C4×C3⋊D3—31no—
112C2×C3×#67C2×D311yescharacteristic
113C22×C3×Dic3C2×D311yescharacteristic
114C2×C3×C4×D3C2×D311yescharacteristic
115C2×#627—31no—
116C2×#626—31no—
117C2×D3×Dic3—31no—
118C2×D3×Dic3—31no—
119C32×C22⋊C4C2×D311yescharacteristic
120#3757—31no—
121#3752—31no—
122C4⋊(C3⋊Dic3)—31no—
123#3750—31no—
124C3×#217—31no—
125C3×#217—31no—
126C3×(C2×D3)⋊C4C2×D311yescharacteristic
127C3×C4⋊Dic3—31no—
128C3×Dic3⋊C4—31no—
129C3×Dic3⋊C4—31no—
130C3×Dic3⋊C4C2×D311yescharacteristic
131C3×C4×Dic3—31no—
132C3×C4×Dic3C2×D311yescharacteristic
133#3724—31no—
134#3724—31no—
135#3724—31no—
136Dic3⋊Dic3—31no—
137Dic3⋊Dic3—31no—
138Dic3⋊Dic3—31no—
139Dic3⋊Dic3—31no—
140Dic3⋊Dic3—31no—
141#3722—31no—
142#3722—31no—
143#3722—31no—
144(C2×D3)⋊Dic3—31no—
145C2×D4×C9—31no—
146C22×C4×C9—31no—
147C22×C4×C9—31no—
148C2×#611—31no—
149C2×#611—31no—
150C2×#611—61no—
151C22×Dic9—31no—
152C22×Dic9—31no—
153C2×C4×D9—31no—
154C2×C4×D9—61no—
155C2×Dic18—31no—
156C9×C4⋊C4—31no—
157C9×C22⋊C4—21no—
158C9×C22⋊C4—31no—
159C9×C22⋊C4C2×D311yescharacteristic
160C42×C9—31no—
161#3676—31no—
162#3676—31no—
163#3676—61no—
164#3676C2×D311yescharacteristic
165#3676C2×D311yescharacteristic
166(C2×D9)⋊C4—31no—
167(C2×D9)⋊C4—31no—
168(C2×D9)⋊C4—31no—
169(C2×D9)⋊C4—31no—
170(C2×D9)⋊C4—61no—
171C4⋊Dic9—31no—
172C4⋊Dic9—31no—
173C4⋊Dic9—61no—
174C4⋊Dic9C2×D311yescharacteristic
175Dic9⋊C4—31no—
176Dic9⋊C4—31no—
177Dic9⋊C4—31no—
178Dic9⋊C4—31no—
179Dic9⋊C4—31no—
180Dic9⋊C4—31no—
181Dic9⋊C4—31no—
182Dic9⋊C4—31no—
183Dic9⋊C4—61no—
184Dic9⋊C4C2×D311yescharacteristic
185Dic9⋊C4C2×D311yescharacteristic
186C4×Dic9C2×D311yescharacteristic
187C22×C3×C9—21no—
188C22×C3×C9—21no—
189C22×C3×C9—21no—
190C22×C3×C9C2411yescharacteristic
191C2×C3⋊D9—21no—
192C2×C3⋊D9—21no—
193C2×C3⋊D9—21no—
194C2×D3×C9—21no—
195C2×D3×C9—21no—
196C2×D3×C9#4112yes—
197C3×C4×C9—21no—
198C3×C4×C9—21no—
199C3⋊Dic9—21no—
200C3⋊Dic9—21no—
201C3⋊Dic9—21no—
202C9×Dic3—21no—
203C9×Dic3—21no—
204C9×Dic3—21no—
205C3×Dic9—21no—
206C3×Dic9—21no—
207C3×Dic9—21no—
208C3×Dic9—21no—
209C3×#126—91no—
210C3×C4×D4—31no—
211#939—91no—
212#935—91no—
213#929—91no—
214C4×#67—91no—
215#924—91no—
216C2×Dic3⋊C4—91no—
217#898—91no—
218#897—91no—
219#896—91no—
220#896—91no—
221#894—91no—
222D3×C4⋊C4—91no—
223#890—91no—
224#889—91no—
225#886—91no—
226#886—91no—
227#884—91no—
228#883—91no—
229#883—91no—
230#883—91no—
231#883—181no—
232#67⋊C4D911yescharacteristic, complemented
233#879—31no—
234#878—91no—
235#878—91no—
236#876—91no—
237C4×D12—91no—
238#870—91no—
239#870—91no—
240C23×C32C22×D311yescharacteristic
241C22×C3⋊D3—31no—
242C22×C3×D3C22×D311yescharacteristic
243C2×C32×C4C22×D311yescharacteristic
244C2×C32×C4C22×D311yescharacteristic
245#638—121no—
246C2×C3⋊Dic3—31no—
247C2×C3⋊Dic3—31no—
248C2×C3⋊Dic3—31no—
249C4×C3⋊D3—121no—
250C3×#67—22no—
251C2×C3×Dic3—31no—
252C2×C3×Dic3—31no—
253C2×C3×Dic3—31no—
254C2×C3×Dic3—31no—
255C2×C3×Dic3—41no—
256C2×C3×Dic3C22×D311yescharacteristic
257C2×C3×Dic3C22×D311yescharacteristic
258C2×C3×Dic3C22×D311yescharacteristic
259C3×C4×D3—41no—
260#627—121no—
261#626—62no—
262D3×Dic3—62no—
263D3×Dic3—121no—
264C23×C9—21no—
265C23×C9—31no—
266C23×C9C22×D311yescharacteristic
267C22×D9—31no—
268C22×D9—61no—
269D4×C9—62no—
270C2×C4×C9—21no—
271C2×C4×C9—21no—
272C2×C4×C9—31no—
273C2×C4×C9—31no—
274C2×C4×C9—31no—
275C2×C4×C9—121no—
276C2×C4×C9—121no—
277C2×C4×C9C22×D311yescharacteristic
278C2×C4×C9C22×D311yescharacteristic
279#611—62no—
280#611—121no—
281#611—122no—
282C2×Dic9—31no—
283C2×Dic9—31no—
284C2×Dic9—31no—
285C2×Dic9—61no—
286C2×Dic9—61no—
287C2×Dic9—61no—
288C2×Dic9—62no—
289C2×Dic9—121no—
290C2×Dic9C22×D311yescharacteristic
291C2×Dic9C22×D311yescharacteristic
292C2×Dic9C22×D311yescharacteristic
293C2×Dic9C22×D311yescharacteristic
294C4×D9—121no—
295C4×D9—122no—
296Dic18—121no—
297#539—271noSylow
298C2×C3×C9—41no—
299C2×C3×C9C2×#4111yescharacteristic
300C2×C3×C9H(5,𝔽2)11yescharacteristic
301C2×C3×C92−1+411yescharacteristic
302C3⋊D9—41no—
303D3×C9—22no—
304C2×C3×D4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C2×#67—91no—
308C2×#67—91no—
309C2×#67—91no—
310C2×#67—181no—
311C2×#67C2×D911yescharacteristic
312C22×Dic3—91no—
313C22×Dic3—91no—
314C22×Dic3C2×D911yescharacteristic
315C2×D12—91no—
316C2×C4×D3—91no—
317C2×C4×D3—91no—
318C2×C4×D3—91no—
319C2×C4×D3—91no—
320C2×C4×D3—181no—
321C2×C4×D3C2×D911yescharacteristic
322C2×Dic6—91no—
323C2×Dic6—91no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—91no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—91no—
328C3×C22⋊C4—21no—
329C3×C22⋊C4—31no—
330C3×C22⋊C4—91no—
331C3×C22⋊C4—91no—
332C3×C22⋊C4C2×D911yescharacteristic
333C3×C22⋊C4D3211yescharacteristic
334C3×C42—31no—
335C3×C42—91no—
336#217—31no—
337#217—31no—
338#217—91no—
339#217—91no—
340#217—91no—
341#217—181no—
342(C2×D3)⋊C4—91no—
343(C2×D3)⋊C4—91no—
344(C2×D3)⋊C4—91no—
345(C2×D3)⋊C4—91no—
346(C2×D3)⋊C4—91no—
347(C2×D3)⋊C4—91no—
348(C2×D3)⋊C4—91no—
349(C2×D3)⋊C4—91no—
350(C2×D3)⋊C4—91no—
351(C2×D3)⋊C4—181no—
352(C2×D3)⋊C4C2×D911yescharacteristic
353C4⋊Dic3—31no—
354C4⋊Dic3—91no—
355C4⋊Dic3—91no—
356C4⋊Dic3—91no—
357C4⋊Dic3—91no—
358C4⋊Dic3—91no—
359C4⋊Dic3—91no—
360C4⋊Dic3—91no—
361C4⋊Dic3—181no—
362Dic3⋊C4—31no—
363Dic3⋊C4—31no—
364Dic3⋊C4—91no—
365Dic3⋊C4—91no—
366Dic3⋊C4—91no—
367Dic3⋊C4—91no—
368Dic3⋊C4—91no—
369Dic3⋊C4—91no—
370Dic3⋊C4—91no—
371Dic3⋊C4—91no—
372Dic3⋊C4—91no—
373Dic3⋊C4—91no—
374Dic3⋊C4—91no—
375Dic3⋊C4—91no—
376Dic3⋊C4—91no—
377Dic3⋊C4—181no—
378Dic3⋊C4C2×D911yescharacteristic
379C4×Dic3—31no—
380C4×Dic3C2×D911yescharacteristic
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32C23×D311yescharacteristic
385C2×C3⋊D3—61no—
386C2×C3⋊D3—61no—
387C2×C3⋊D3—61no—
388C2×C3×D3—21no—
389C2×C3×D3—21no—
390C2×C3×D3#23512yes—
391C32×C4—21no—
392C32×C4—21no—
393C3⋊Dic3—61no—
394C3⋊Dic3—61no—
395C3⋊Dic3—61no—
396C3×Dic3—21no—
397C3×Dic3—21no—
398C3×Dic3—21no—
399C3×Dic3—61no—
400C3×Dic3—61no—
401C3×Dic3—61no—
402C3×Dic3—61no—
403C22×C9—21no—
404C22×C9—21no—
405C22×C9—21no—
406C22×C9—21no—
407C22×C9—32no—
408C22×C9—41no—
409C22×C9—41no—
410C22×C9—41no—
411C22×C9—61no—
412C22×C9—61no—
413C22×C9C23×D311yescharacteristic
414C2×D9—62no—
415C2×D9—61no—
416C2×D9—61no—
417C2×D9—61no—
418C2×D9—121no—
419C2×D9—121no—
420C4×C9—21no—
421C4×C9—21no—
422C4×C9—41no—
423C4×C9—41no—
424C4×C9—61no—
425C4×C9—61no—
426C4×C9—61no—
427Dic9—21no—
428Dic9—21no—
429Dic9—21no—
430Dic9—21no—
431Dic9—61no—
432Dic9—61no—
433Dic9—61no—
434Dic9—121no—
435Dic9—121no—
436Dic9—121no—
437#126—91no—
438#126—271no—
439#125—271no—
440#125—271no—
441#123—271no—
442#123—271no—
443#123—271no—
444#123—271no—
445C22⋊Q8—271no—
446C22⋊Q8—271no—
447C22⋊Q8—271no—
448#121—271no—
449C4×D4—31no—
450C4×D4—271no—
451C2×C4⋊C4—271no—
452C3×C9#53911yescharacteristic, complemented, Sylow
453C23×C3—21no—
454C23×C3—31no—
455C23×C3C22×D911yescharacteristic
456C23×C3C2×D3211yescharacteristic
457C22×D3—91no—
458C22×D3—91no—
459C22×D3—181no—
460C22×D3C22×D911yescharacteristic
461C3×D4—62no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—31no—
465C2×C3×C4—31no—
466C2×C3×C4—31no—
467C2×C3×C4—91no—
468C2×C3×C4—91no—
469C2×C3×C4—91no—
470C2×C3×C4—91no—
471C2×C3×C4—121no—
472C2×C3×C4—121no—
473C2×C3×C4C22×D911yescharacteristic
474C2×C3×C4C22×D911yescharacteristic
475C2×C3×C4C2×D3211yescharacteristic
476C2×C3×C4C2×D3211yescharacteristic
477#67—22no—
478#67—182no—
479#67—361no—
480#67—361no—
481#67—362no—
482C2×Dic3—31no—
483C2×Dic3—31no—
484C2×Dic3—31no—
485C2×Dic3—31no—
486C2×Dic3—41no—
487C2×Dic3—91no—
488C2×Dic3—91no—
489C2×Dic3—91no—
490C2×Dic3—91no—
491C2×Dic3—91no—
492C2×Dic3—91no—
493C2×Dic3—181no—
494C2×Dic3—181no—
495C2×Dic3—181no—
496C2×Dic3—182no—
497C2×Dic3—361no—
498C2×Dic3C22×D911yescharacteristic
499C2×Dic3C22×D911yescharacteristic
500C2×Dic3C22×D911yescharacteristic
501D12—182no—
502C4×D3—41no—
503C4×D3—182no—
504C4×D3—361no—
505C4×D3—361no—
506C4×D3—361no—
507C4×D3—362no—
508Dic6—361no—
509Dic6—361no—
510C2×C32—41no—
511C2×C32C2×#23511yescharacteristic
512C2×C32#100411yescharacteristic
513C2×C32#101011yescharacteristic
514C3⋊D3—121no—
515C3×D3—22no—
516C2×C9—21no—
517C2×C9—21no—
518C2×C9—21no—
519C2×C9—41no—
520C2×C9—62no—
521C2×C9—81no—
522C2×C9D3×#4111yescharacteristic
523C2×C9#100911yescharacteristic
524C2×C9#101011yescharacteristic
525D9—122no—
526D9—121no—
527C2×Q8—271no—
528C2×D4—31no—
529C2×D4—271no—
530C2×D4—271no—
531C22×C4—31no—
532C22×C4—31no—
533C22×C4—271no—
534C22×C4—271no—
535C22×C4—271no—
536C4⋊C4—31no—
537C4⋊C4—91no—
538C4⋊C4—91no—
539C4⋊C4—91no—
540C4⋊C4—271no—
541C4⋊C4—271no—
542C4⋊C4—271no—
543C4⋊C4—271no—
544C4⋊C4—271no—
545C4⋊C4—271no—
546C4⋊C4—271no—
547C4⋊C4—271no—
548C4⋊C4—271no—
549C4⋊C4—271no—
550C22⋊C4—31no—
551C22⋊C4—91no—
552C22⋊C4—91no—
553C22⋊C4—271no—
554C22⋊C4—271no—
555C22⋊C4—271no—
556C22⋊C4—271no—
557C22⋊C4—271no—
558C22⋊C4—271no—
559C22⋊C4D3×D911yescharacteristic
560C42—31no—
561C42—91no—
562C22×C3—21no—
563C22×C3—21no—
564C22×C3—21no—
565C22×C3—21no—
566C22×C3—21no—
567C22×C3—21no—
568C22×C3—21no—
569C22×C3—32no—
570C22×C3—41no—
571C22×C3—41no—
572C22×C3—41no—
573C22×C3—61no—
574C22×C3—61no—
575C22×C3C23×D911yescharacteristic
576C22×C3C22×D3211yescharacteristic
577C2×D3—21no—
578C2×D3—21no—
579C2×D3—182no—
580C2×D3—181no—
581C2×D3—181no—
582C2×D3—181no—
583C2×D3—181no—
584C2×D3—181no—
585C2×D3—181no—
586C2×D3—361no—
587C2×D3—361no—
588C2×D3#369712yes—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—41no—
595C3×C4—61no—
596C3×C4—61no—
597C3×C4—61no—
598C3×C4—181no—
599C3×C4—181no—
600C3×C4—181no—
601C3×C4—181no—
602Dic3—21no—
603Dic3—21no—
604Dic3—21no—
605Dic3—61no—
606Dic3—61no—
607Dic3—61no—
608Dic3—61no—
609Dic3—181no—
610Dic3—181no—
611Dic3—181no—
612Dic3—181no—
613Dic3—181no—
614Dic3—181no—
615Dic3—361no—
616Dic3—361no—
617Dic3—361no—
618C32#556411yescharacteristic
619C9—21no—
620C9#570711yescharacteristic, complemented
621C23—31no—
622C23—271no—
623C23C2×D3×D911yescharacteristic
624Q8—1081no—
625D4—62no—
626D4—542no—
627D4—1081no—
628C2×C4—31no—
629C2×C4—31no—
630C2×C4—31no—
631C2×C4—91no—
632C2×C4—91no—
633C2×C4—91no—
634C2×C4—91no—
635C2×C4—121no—
636C2×C4—121no—
637C2×C4—271no—
638C2×C4—271no—
639C2×C4—271no—
640C2×C4—542no—
641C2×C4—1081no—
642C2×C4—1081no—
643C2×C4C2×D3×D911yescharacteristic
644C2×C4C2×D3×D911yescharacteristic
645C2×C3—21no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—41no—
649C2×C3—41no—
650C2×C3—62no—
651C2×C3—81no—
652C2×C3C2×#369711yescharacteristic
653C2×C3#6371011yescharacteristic
654C2×C3#6371611yescharacteristic
655C2×C3D3×#23511yescharacteristic
656C2×C3#6430911yescharacteristic
657C2×C3#6431411yescharacteristic
658D3—22no—
659D3—362no—
660D3—361no—
661D3—361no—
662C22—21no—
663C22—21no—
664C22—21no—
665C22—32no—
666C22—61no—
667C22—61no—
668C22—541no—
669C22—541no—
670C22—541no—
671C22C22×D3×D911yescharacteristic
672C4—21no—
673C4—21no—
674C4—61no—
675C4—61no—
676C4—61no—
677C4—181no—
678C4—181no—
679C4—181no—
680C4—181no—
681C4—541no—
682C4—541no—
683C4—541no—
684C3—21no—
685C3#1058966611yescharacteristic, complemented
686C3#1059409011yescharacteristic
687C2—41no—
688C2—62no—
689C2—1081no—
690C2D3×#369711yescharacteristic
691C2#1172249411yescharacteristic
692C2#1172250011yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C22⋊C4C22
socleC22×C32C23×D3
prime radical#11721282C2
hypercenterC22⋊C4D3×D9
hypocenterC3×C9#539
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C22⋊C4

Complements

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

NH ≅ G/Ntype
1. #11721729C2semidirect
2. C9×#67⋊C4C2semidirect
3. C3×#63441C2semidirect
5. #11721280C2semidirect
6. #11721251C2semidirect
7. #11721249C2semidirect
8. C4×#6195C2semidirect
9. #11721023C2semidirect
10. #11721020C2semidirect
11. D3×Dic9⋊C4C2semidirect
12. #11720933C2semidirect
13. #11720927C2semidirect
14. #11720926C2semidirect
15. #11720923C2semidirect
80. #63441D3semidirect
232. #67⋊C4D9semidirect
452. C3×C9#539semidirect
620. C9#5707semidirect
685. C3#10589666semidirect

Maximal subgroups

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

subgroupindex
#117217292
C9×#67⋊C42
C3×#634412
#117212822
#117212802
#117212512
#117212492
C4×#61952
#117210232
#117210202
D3×Dic9⋊C42
#117209332
#117209272
#117209262
#117209232
#105940903
#105896663