Finite Group Databasebeta

← #11876901

Subgroups — #11876901

Order 1152.

800 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594955C211yesmaximal, characteristic, complemented
2#10594949C211yesmaximal, characteristic, complemented
3#10592833C211yesmaximal, characteristic, complemented
4C3×#5134C211yesmaximal, characteristic, complemented
5C3×Dic3×M16C211yesmaximal, characteristic, complemented
6#10591165C211yesmaximal, characteristic
7#10591121C211yesmaximal, characteristic, complemented
8#10590873C211yesmaximal, characteristic, complemented
9#10590872C211yesmaximal, characteristic, complemented
10#10590863C211yesmaximal, characteristic, complemented
11#10590862C211yesmaximal, characteristic, complemented
12#10590794C211yesmaximal, characteristic, complemented
13#10590773C211yesmaximal, characteristic, complemented
14#10590766C211yesmaximal, characteristic, complemented
15#10590746C211yesmaximal, characteristic, complemented
16#80791—31nomaximal
17#78534—31nomaximal
18C2×C32×M16C2211yescharacteristic
19#64139C2211yescharacteristic
20#64133C2211yescharacteristic
21C2×#3744C2211yescharacteristic
22C3×#930C2211yescharacteristic
23C3×#924C2211yescharacteristic
24C2×C3×C4×Dic3C2211yescharacteristic
25C2×C3×#208C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic
27Dic3×#67—21no—
28#63966—21no—
29#63961—21no—
30#63952—21no—
31#63894C2211yescharacteristic
32Dic3×D12C2211yescharacteristic
33#63877—21no—
34#63869C2211yescharacteristic
35#63869C2211yescharacteristic
36#63868—21no—
37#63864C2211yescharacteristic
38#63860C2211yescharacteristic
39#63859—21no—
40#63844C2211yescharacteristic
41Dic3×Dic6C2211yescharacteristic
42#63836—21no—
43C2×#3719C2211yescharacteristic
44C2×#3714C2211yescharacteristic
45#63648C2211yescharacteristic
46#63645C2211yescharacteristic
47#63643C2211yescharacteristic
48C3×#821C2211yescharacteristic
49C3×#818C2211yescharacteristic
50C3×#816C2211yescharacteristic
51C3×#815C2211yescharacteristic
52C3×#815C2211yescharacteristic
53C3×C8×Dic3C2211yescharacteristic
54C3×C8×Dic3C2211yescharacteristic
55#63573C2211yescharacteristic
56#63573C2211yescharacteristic
57#63567C2211yescharacteristic
58#63566C2211yescharacteristic
59#63564C2211yescharacteristic
60#63563C2211yescharacteristic
61#5624—31no—
62#5600—31no—
63#5479—31no—
64#5479—31no—
65C3×#468—31no—
66C3×C4×M16—31no—
67#5168—31no—
68#5164—31no—
69#5137—31no—
70#5135—31no—
71#5134—31no—
72#5134—31no—
73#5134—61no—
74#5134D311yescharacteristic, complemented
75Dic3×M16D311yescharacteristic, complemented
76#5052—31no—
77#5039—31no—
78#4889—31no—
79#4878—31no—
80#4800—31no—
81#4789—31no—
82#4785—31no—
83#4768—31no—
84#4716—31no—
85#4711—31no—
86#4710—31no—
87#4710—31no—
88#4697—31no—
89#4697—31no—
90#4696—31no—
91#4683—31no—
92C22×C32×C4C2311yescharacteristic
93C2×#638—21no—
94C2×C4⋊(C3⋊D3)C2311yescharacteristic
95C2×#634C2311yescharacteristic
96C2×C3×#67—21no—
97C22×C3×Dic3D411yescharacteristic
98C22×C3×Dic3D411yescharacteristic
99C2×C3×D12C2311yescharacteristic
100C2×C3×Dic6C2311yescharacteristic
101C2×#624—21no—
102C2×D3×Dic3—21no—
103C32×M16—22no—
104C2×C32×C8C2311yescharacteristic
105C2×C32×C8C2311yescharacteristic
106#3757—21no—
107#3752—21no—
108C4⋊(C3⋊Dic3)C2311yescharacteristic
109C4⋊(C3⋊Dic3)C2311yescharacteristic
110#3750—21no—
111#3744—22no—
112C3×#217—21no—
113C3×(C2×D3)⋊C4—21no—
114C3×C4⋊Dic3C2311yescharacteristic
115C3×C4⋊Dic3C2311yescharacteristic
116C3×Dic3⋊C4—21no—
117C3×C4×Dic3D411yescharacteristic
118C3×C4×Dic3D411yescharacteristic
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
121C3×#208—22no—
122C2×C3×C3⋊C8C2311yescharacteristic
123C2×C3×C3⋊C8C2311yescharacteristic
124C3×#204—22no—
125#3724—21no—
126#3724—21no—
127#3724—21no—
128Dic3⋊Dic3—21no—
129Dic3⋊Dic3—21no—
130Dic3⋊Dic3—21no—
131#3722—21no—
132#3722—21no—
133#3722—21no—
134(C2×D3)⋊Dic3—21no—
135(C2×D3)⋊Dic3—21no—
136(C2×D3)⋊Dic3—21no—
137Dic32—21no—
138Dic32—21no—
139#3719—22no—
140#3714—22no—
141#3183—91noSylow
142C2×C3×SD16—31no—
143C2×C3×M16—21no—
144C2×C3×M16—31no—
145C2×C3×M16C2×D311yescharacteristic
146C2×C3×M16C2×D311yescharacteristic
147C3×C22⋊Q8—31no—
148C3×#121—31no—
149C2×C3×C42—31no—
150#947—31no—
151Q8×Dic3—31no—
152C2×#216—31no—
153#936—31no—
154#935—61no—
155D4×Dic3—31no—
156D4×Dic3—61no—
157C2×#213—31no—
158#930—31no—
159#930—31no—
160#930—61no—
161#930C2×D311yescharacteristic
162#929—61no—
163#929—61no—
164C4×#67—61no—
165C4×#67—61no—
166#924—31no—
167#924—31no—
168#924—61no—
169#924C2×D311yescharacteristic
170C2×C4×Dic3C2×D311yescharacteristic
171C2×#208C2×D311yescharacteristic
172C2×Dic12—31no—
173C2×D24—31no—
174C2×#204—31no—
175C2×#204—31no—
176C2×#204—61no—
177C2×#204C2×D311yescharacteristic
178#898—61no—
179#893—31no—
180#892—61no—
181#890—31no—
182#890—31no—
183#887—31no—
184#886—61no—
185#67⋊C4—61no—
186#879—61no—
187#877—61no—
188#876—61no—
189#876—61no—
190#875—31no—
191#875—31no—
192C4×D12—31no—
193C4×D12—31no—
194#872—61no—
195#872—61no—
196#870—31no—
197#870—31no—
198C4×Dic6—31no—
199C4×Dic6—31no—
200C3×#107—31no—
201C3×#103—31no—
202C3×#102—31no—
203C3×#97—31no—
204C3×#97—31no—
205C3×C4×C8—31no—
206C3×C4×C8—31no—
207#835—31no—
208#832—31no—
209#821—31no—
210#821—31no—
211#821—31no—
212#821—31no—
213#821—61no—
214#821C2×D311yescharacteristic
215#818—31no—
216#818—31no—
217#818—61no—
218#818C2×D311yescharacteristic
219#817—31no—
220#817—31no—
221#816—31no—
222#816—31no—
223#816—31no—
224#816—31no—
225#816—61no—
226#816C2×D311yescharacteristic
227#815C2×D311yescharacteristic
228#815C2×D311yescharacteristic
229C8×Dic3C2×D311yescharacteristic
230C8×Dic3C2×D311yescharacteristic
231#810—31no—
232#809—31no—
233#808—31no—
234#808—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3⋊D3—21no—
237C22×C3×D3—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4C2×D411yescharacteristic
241C2×C32×C4C2411yescharacteristic
242#638—42no—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C4⋊(C3⋊D3)—21no—
247C4⋊(C3⋊D3)—21no—
248#634—21no—
249#634—21no—
250C3×#67—42no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—41no—
255C2×C3×Dic3—41no—
256C2×C3×Dic3C2×D411yescharacteristic
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C3×D12—21no—
261C3×D12—21no—
262C3×Dic6—21no—
263C3×Dic6—21no—
264#624—42no—
265D3×Dic3—42no—
266C32×C8—21no—
267C32×C8#4112yes—
268C3×C3⋊C8—21no—
269C3×C3⋊C8#4112yes—
270#529—91no—
271#529—91no—
272#499—91no—
273#495—91no—
274#488—91no—
275#488—91no—
276#470—91no—
277#469—91no—
278#468—31no—
279#468—91no—
280#442—91no—
281#441—91no—
282#440—91no—
283#440—91no—
284C4×M16—31no—
285C2×C3×Q8—31no—
286C2×C3×D4—31no—
287C2×C3×D4—61no—
288C22×C3×C4—21no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C2×#67—21no—
294C2×#67—61no—
295C2×#67—61no—
296C2×#67—121no—
297C22×Dic3—61no—
298C22×Dic3D1211yescharacteristic
299C22×Dic3D1211yescharacteristic
300C2×D12—31no—
301C2×D12—31no—
302C2×D12—61no—
303C2×D12C22×D311yescharacteristic
304C2×C4×D3—61no—
305C2×C4×D3—61no—
306C2×C4×D3—61no—
307C2×Dic6—31no—
308C2×Dic6—31no—
309C2×Dic6—61no—
310C2×Dic6C22×D311yescharacteristic
311C3×SD16—62no—
312C3×M16—22no—
313C3×M16—22no—
314C3×M16—42no—
315C3×M16—62no—
316C2×C3×C8—21no—
317C2×C3×C8—21no—
318C2×C3×C8—31no—
319C2×C3×C8—31no—
320C2×C3×C8C22×D311yescharacteristic
321C2×C3×C8C22×D311yescharacteristic
322C2×C3×C8C22×D311yescharacteristic
323C2×C3×C8C22×D311yescharacteristic
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—61no—
327C3×C22⋊C4—61no—
328C3×C22⋊C4—61no—
329C3×C42—31no—
330C3×C42—31no—
331C3×C42—31no—
332C3×C42—31no—
333#217—21no—
334#217—61no—
335#217—61no—
336#217—61no—
337#217—61no—
338#217—61no—
339#217—121no—
340#216—62no—
341#213—62no—
342(C2×D3)⋊C4—21no—
343(C2×D3)⋊C4—61no—
344(C2×D3)⋊C4—61no—
345(C2×D3)⋊C4—61no—
346(C2×D3)⋊C4—61no—
347(C2×D3)⋊C4—61no—
348(C2×D3)⋊C4—61no—
349(C2×D3)⋊C4—61no—
350(C2×D3)⋊C4—61no—
351(C2×D3)⋊C4—61no—
352(C2×D3)⋊C4—61no—
353(C2×D3)⋊C4—61no—
354(C2×D3)⋊C4—121no—
355C4⋊Dic3—31no—
356C4⋊Dic3—31no—
357C4⋊Dic3—31no—
358C4⋊Dic3—31no—
359C4⋊Dic3—61no—
360C4⋊Dic3—61no—
361C4⋊Dic3—61no—
362C4⋊Dic3—61no—
363C4⋊Dic3—61no—
364C4⋊Dic3C22×D311yescharacteristic
365C4⋊Dic3C22×D311yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375Dic3⋊C4—61no—
376Dic3⋊C4—61no—
377Dic3⋊C4—61no—
378Dic3⋊C4—121no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3D1211yescharacteristic
384C4×Dic3D1211yescharacteristic
385C4×Dic3C22×D311yescharacteristic
386C4×Dic3C22×D311yescharacteristic
387#208—22no—
388C2×C3⋊C8C22×D311yescharacteristic
389C2×C3⋊C8C22×D311yescharacteristic
390Dic12—62no—
391D24—62no—
392#204—22no—
393#204—62no—
394#204—62no—
395#204—122no—
396C22×C32—21no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32C22×D411yescharacteristic
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C2×C3⋊D3—41no—
403C2×C3×D3—41no—
404C2×C3×D3—41no—
405C2×C3×D3—41no—
406C32×C4—21no—
407C32×C4C2×#4111yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3⋊Dic3—41no—
410C3⋊Dic3—41no—
411C3⋊Dic3—41no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—21no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3—41no—
419C2×Q16—91no—
420C2×SD16—31no—
421C2×SD16—91no—
422C2×D8—91no—
423C2×M16—31no—
424C2×M16D3211yescharacteristic
425#126—181no—
426#126—181no—
427#125—91no—
428#125—91no—
429#124—91no—
430#124—91no—
431#123—181no—
432#123—181no—
433C22⋊Q8—31no—
434C22⋊Q8—91no—
435#121—31no—
436#121—91no—
437C4×Q8—91no—
438C4×Q8—91no—
439C4×D4—91no—
440C4×D4—91no—
441C4×D4—181no—
442C4×D4—181no—
443#117—181no—
444#117—181no—
445C2×C42—31no—
446#107—31no—
447#107—91no—
448#106—91no—
449#106—91no—
450#103—31no—
451#103—91no—
452#103—91no—
453#103—91no—
454#102—31no—
455#102—91no—
456#102—91no—
457#102—91no—
458#97—31no—
459#97—31no—
460C4×C8—31no—
461C4×C8—31no—
462C23×C3—21no—
463C23×C3—61no—
464C23×C3C2×D1211yescharacteristic
465C23×C3D3×D411yescharacteristic
466C22×D3—21no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—121no—
470C3×Q8—61no—
471C3×Q8—61no—
472C3×D4—61no—
473C3×D4—61no—
474C3×D4—122no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—31no—
482C2×C3×C4—31no—
483C2×C3×C4—31no—
484C2×C3×C4—31no—
485C2×C3×C4—41no—
486C2×C3×C4—41no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—121no—
491C2×C3×C4—121no—
492C2×C3×C4C2×D1211yescharacteristic
493C2×C3×C4D3×D411yescharacteristic
494C2×C3×C4C23×D311yescharacteristic
495C2×C3×C4C23×D311yescharacteristic
496#67—42no—
497#67—122no—
498#67—122no—
499#67—242no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—41no—
504C2×Dic3—41no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—121no—
512C2×Dic3—121no—
513C2×Dic3—121no—
514C2×Dic3—122no—
515C2×Dic3C2×D1211yescharacteristic
516C2×Dic3C2×D1211yescharacteristic
517C2×Dic3C2×D1211yescharacteristic
518C2×Dic3C2×D1211yescharacteristic
519D12—21no—
520D12—21no—
521D12—61no—
522D12—61no—
523D12—61no—
524D12—61no—
525D12—121no—
526D12—121no—
527C4×D3—122no—
528C4×D3—122no—
529C4×D3—122no—
530Dic6—21no—
531Dic6—21no—
532Dic6—61no—
533Dic6—61no—
534Dic6—61no—
535Dic6—61no—
536Dic6—121no—
537Dic6—121no—
538C3×C8—21no—
539C3×C8—21no—
540C3×C8—22no—
541C3×C8—32no—
542C3×C8—41no—
543C3×C8—61no—
544C3×C8#23512yes—
545C3×C8#23712yes—
546C3⋊C8—21no—
547C3⋊C8#23512yes—
548C2×C32—41no—
549C2×C32#53211yescharacteristic
550C2×C32#57511yescharacteristic
551C2×C32#57511yescharacteristic
552C3⋊D3—81no—
553C3×D3—81no—
554C2×Q8—31no—
555C2×Q8—91no—
556C2×D4—31no—
557C2×D4—61no—
558C2×D4—91no—
559C2×D4—181no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—181no—
563C22×C4—181no—
564C22×C4C2×D3211yescharacteristic
565Q16—182no—
566SD16—62no—
567SD16—182no—
568D8—182no—
569M16—22no—
570M16—62no—
571C2×C8—31no—
572C2×C8—31no—
573C2×C8C2×D3211yescharacteristic
574C2×C8C2×D3211yescharacteristic
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—61no—
578C4⋊C4—91no—
579C4⋊C4—91no—
580C4⋊C4—181no—
581C4⋊C4—181no—
582C4⋊C4—181no—
583C4⋊C4—181no—
584C4⋊C4—181no—
585C4⋊C4—181no—
586C4⋊C4—181no—
587C22⋊C4—61no—
588C22⋊C4—61no—
589C22⋊C4—181no—
590C22⋊C4—181no—
591C22⋊C4—181no—
592C22⋊C4—181no—
593C22⋊C4—181no—
594C22⋊C4—181no—
595C22⋊C4—181no—
596C22⋊C4—181no—
597C42—31no—
598C42—31no—
599C42—31no—
600C42—31no—
601C42—181no—
602C42—181no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—41no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3—121no—
616C22×C3C22×D1211yescharacteristic
617C22×C3C2×D3×D411yescharacteristic
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C2×D3—121no—
622C2×D3—121no—
623C2×D3—121no—
624C2×D3—121no—
625C2×D3—121no—
626C2×D3—121no—
627C2×D3—241no—
628C2×D3—241no—
629C2×D3—241no—
630C3×C4—21no—
631C3×C4—21no—
632C3×C4—21no—
633C3×C4—21no—
634C3×C4—41no—
635C3×C4—61no—
636C3×C4—61no—
637C3×C4—61no—
638C3×C4—61no—
639C3×C4—121no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4C2×#23511yescharacteristic
643C3×C4C2×#23511yescharacteristic
644C3×C4C2×#23711yescharacteristic
645C3×C4D3×#4111yescharacteristic
646Dic3—21no—
647Dic3—21no—
648Dic3—21no—
649Dic3—21no—
650Dic3—41no—
651Dic3—41no—
652Dic3—41no—
653Dic3—121no—
654Dic3—121no—
655Dic3—121no—
656Dic3—121no—
657Dic3—121no—
658Dic3—121no—
659Dic3—241no—
660Dic3—241no—
661Dic3—241no—
662C32#318311yescharacteristic, complemented, Sylow
663C23—61no—
664C23—181no—
665C23D3×D1211yescharacteristic
666Q8—61no—
667Q8—61no—
668Q8—181no—
669Q8—181no—
670D4—61no—
671D4—61no—
672D4—122no—
673D4—181no—
674D4—181no—
675D4—362no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—31no—
679C2×C4—31no—
680C2×C4—31no—
681C2×C4—31no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—121no—
686C2×C4—121no—
687C2×C4—181no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—362no—
691C2×C4—362no—
692C2×C4D3×D1211yescharacteristic
693C2×C4C22×D3211yescharacteristic
694C8—21no—
695C8—32no—
696C8—61no—
697C8#380412yes—
698C2×C3—21no—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—41no—
702C2×C3—41no—
703C2×C3—81no—
704C2×C3—241no—
705C2×C3#547711yescharacteristic
706C2×C3#559611yescharacteristic
707C2×C3#574811yescharacteristic
708C2×C3#574811yescharacteristic
709C2×C3#577311yescharacteristic
710C2×C3#577711yescharacteristic
711D3—81no—
712D3—241no—
713D3—241no—
714D3—481no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—361no—
722C22—361no—
723C22—361no—
724C22C2×D3×D1211yescharacteristic
725C4—21no—
726C4—61no—
727C4—61no—
728C4—61no—
729C4—61no—
730C4—121no—
731C4—121no—
732C4—121no—
733C4—361no—
734C4—361no—
735C4—361no—
736C4D3×#23511yescharacteristic
737C4C2×#380411yescharacteristic
738C3—21no—
739C3#7853411yescharacteristic, complemented
740C3#8079111yescharacteristic, complemented
741C2—41no—
742C2—241no—
743C2—721no—
744C2#1059471111yescharacteristic
745C2#1059471211yescharacteristic
746C2#1059491011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radical#10591165C2
hypercenterC2×M16D32
hypocenterC32#3183
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10594955C2semidirect
2. #10594949C2semidirect
3. #10592833C2semidirect
4. C3×#5134C2semidirect
5. C3×Dic3×M16C2semidirect
7. #10591121C2semidirect
8. #10590873C2semidirect
9. #10590872C2semidirect
10. #10590863C2semidirect
11. #10590862C2semidirect
12. #10590794C2semidirect
13. #10590773C2semidirect
14. #10590766C2semidirect
15. #10590746C2semidirect
74. #5134D3semidirect
75. Dic3×M16D3semidirect
662. C32#3183semidirect
739. C3#78534semidirect
740. C3#80791semidirect

Maximal subgroups

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

subgroupindex
#105949552
#105949492
#105928332
C3×#51342
C3×Dic3×M162
#105911652
#105911212
#105908732
#105908722
#105908632
#105908622
#105907942
#105907732
#105907662
#105907462
#807913
#785343