Finite Group Databasebeta

← #10801648

Subgroups — #10801648

Order 768.

902 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4894C211yesmaximal, characteristic, complemented
2C2×#4895C211yesmaximal, characteristic, complemented
3#79042C211yesmaximal, characteristic, complemented
4#79021C211yesmaximal, characteristic
5#78516C211yesmaximal, characteristic, complemented
6C3×#1950C211yesmaximal, characteristic, complemented
7#70699C211yesmaximal, characteristic, complemented
8#70699C211yesmaximal, characteristic, complemented
9#70529C211yesmaximal, characteristic, complemented
10#70467C211yesmaximal, characteristic, complemented
11#69867C211yesmaximal, characteristic, complemented
12#68946C211yesmaximal, characteristic, complemented
13#68946C211yesmaximal, characteristic, complemented
14#68927C211yesmaximal, characteristic, complemented
15#68926C211yesmaximal, characteristic, complemented
16#21519—31nomaximal, Sylow
17C2×#907C2211yescharacteristic
18C2×#907C2211yescharacteristic
19C2×#907C2211yescharacteristic
20C2×#907C2211yescharacteristic
21C2×#904C2211yescharacteristic
22C2×#904C2211yescharacteristic
23#5477C2211yescharacteristic
24C4×#235C2211yescharacteristic
25C2×C3×#108C2211yescharacteristic
26C2×C3×#108C2211yescharacteristic
27C3×#423C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C3×C4×M16C2211yescharacteristic
30C2×#825C2211yescharacteristic
31C2×#825C2211yescharacteristic
32C2×#825C2211yescharacteristic
33C2×#825C2211yescharacteristic
34C2×#825C2211yescharacteristic
35C2×#825C2211yescharacteristic
36#5129C2211yescharacteristic
37#5129C2211yescharacteristic
38#5122C2211yescharacteristic
39#5122C2211yescharacteristic
40#5113C2211yescharacteristic
41#5113C2211yescharacteristic
42C2×#815C2211yescharacteristic
43C2×C8×Dic3C2211yescharacteristic
44C4×C4⋊Dic3C2211yescharacteristic
45C2×#803C2211yescharacteristic
46#4895—24no—
47#4894—24no—
48#4849C411yescharacteristic, complemented
49#4848C411yescharacteristic, complemented
50#4845C411yescharacteristic, complemented
51#4845C411yescharacteristic, complemented
52#4844C411yescharacteristic, complemented
53#4844C411yescharacteristic, complemented
54#4843C411yescharacteristic, complemented
55#4841C411yescharacteristic, complemented
56#4836—21no—
57#4836—21no—
58#4836—21no—
59#4836—21no—
60#4707—21no—
61D3×#97—21no—
62#4689—21no—
63#4689—21no—
64C3×#341C2211yescharacteristic
65C3×#341C2211yescharacteristic
66#4555C2211yescharacteristic
67#4555C2211yescharacteristic
68#4550C2211yescharacteristic
69#4550C2211yescharacteristic
70#3035—31no—
71C2×#444—31no—
72C2×#443—31no—
73#2932—31no—
74#2875—31no—
75#1980—31no—
76#1950D311yescharacteristic, complemented
77#1929—31no—
78#1929—31no—
79#1876—31no—
80#1876—31no—
81#1806—31no—
82#1771—31no—
83#1765—31no—
84#1764—31no—
85C2×#235C2311yescharacteristic
86C2×#235C2311yescharacteristic
87C2×#235C2311yescharacteristic
88C2×C3×M16C2311yescharacteristic
89C2×C3×M16C2311yescharacteristic
90C2×C3×M16C2311yescharacteristic
91C2×C3×M16C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C22×C3×C8C2311yescharacteristic
94C2×C3×C42C2311yescharacteristic
95#930—21no—
96#930—21no—
97C4×#67—21no—
98C4×#67—21no—
99#926C2311yescharacteristic
100C2×C4⋊Dic3—21no—
101C2×C4×Dic3C2311yescharacteristic
102C2×C4×Dic3C2311yescharacteristic
103C22×C3⋊C8C2311yescharacteristic
104C22×C3⋊C8C2311yescharacteristic
105#907—22no—
106#907—22no—
107#907—22no—
108#907—22no—
109#907—22no—
110#907—22no—
111#907—22no—
112#907D414yescomplemented
113C2×Dic12C2×C411yescharacteristic
114C2×Dic12C2×C411yescharacteristic
115#904—22no—
116#904—22no—
117#904—22no—
118#904—22no—
119C2×D24C2×C411yescharacteristic
120C2×D24C2×C411yescharacteristic
121C2×#204C2×C411yescharacteristic
122C2×#204C2×C411yescharacteristic
123C2×#204C2×C411yescharacteristic
124C2×#204C2×C411yescharacteristic
125C2×ΓL(1,𝔽25)—21no—
126C2×ΓL(1,𝔽25)—21no—
127C2×ΓL(1,𝔽25)—21no—
128C2×ΓL(1,𝔽25)—21no—
129C2×D3×C8—21no—
130C2×D3×C8—21no—
131C2×D3×C8—21no—
132C2×D3×C8—21no—
133#875C2×C411yescharacteristic
134#875C2×C411yescharacteristic
135#874C2×C411yescharacteristic
136C4×D12—21no—
137C4×D12—21no—
138C4×D12C2×C411yescharacteristic
139C4×D12C2×C411yescharacteristic
140#872—21no—
141C42×D3—21no—
142#869C2×C411yescharacteristic
143C4×Dic6C2×C411yescharacteristic
144C4×Dic6C2×C411yescharacteristic
145C3×#108—22no—
146C3×#108—22no—
147C3×C4⋊C8—21no—
148C3×C4⋊C8—21no—
149C3×C4⋊C8C2×C411yescharacteristic
150C3×C4⋊C8C2×C411yescharacteristic
151C3×C4⋊C8C2×C411yescharacteristic
152C3×C4⋊C8C2×C411yescharacteristic
153C3×#97—21no—
154C3×C4×C8—21no—
155C3⋊#95—21no—
156#825—22no—
157#825—22no—
158#825—22no—
159#825—22no—
160#825—22no—
161#825—22no—
162#821C2×C411yescharacteristic
163#821C2×C411yescharacteristic
164#821C2×C411yescharacteristic
165#821C2×C411yescharacteristic
166(C2×D3)⋊C8—21no—
167(C2×D3)⋊C8—21no—
168(C2×D3)⋊C8—21no—
169(C2×D3)⋊C8—21no—
170#816C2×C411yescharacteristic
171#816C2×C411yescharacteristic
172#816C2×C411yescharacteristic
173#816C2×C411yescharacteristic
174#815—21no—
175#815—21no—
176#815—22no—
177C8×Dic3—21no—
178C8×Dic3—21no—
179C8×Dic3—22no—
180#803D411yescharacteristic
181#803D411yescharacteristic
182#803D411yescharacteristic
183#803D411yescharacteristic
184C2×#135—31no—
185C2×#135—31no—
186C2×#131—31no—
187C2×#131—31no—
188C2×#131—31no—
189C2×#131—31no—
190#532—31no—
191C4×#41—31no—
192#464—31no—
193#464—31no—
194#463—31no—
195#463—31no—
196#462—31no—
197#461—31no—
198#460—31no—
199#459—31no—
200#444—64no—
201#443—64no—
202#435—61no—
203#435—61no—
204#435—61no—
205#435—61no—
206C2×#108C2×D311yescharacteristic
207C2×#108C2×D311yescharacteristic
208#423C2×D311yescharacteristic
209C2×C4⋊C8C2×D311yescharacteristic
210C2×#104—31no—
211C2×#104—31no—
212C2×#104—31no—
213C2×#104—31no—
214C2×#104—31no—
215C2×#104—31no—
216#416—31no—
217#416—31no—
218#408—31no—
219#408—31no—
220#405—31no—
221#405—31no—
222#405—61no—
223#405—61no—
224C4×M16—61no—
225C4×M16C2×D311yescharacteristic
226C2×#97—31no—
227C2×#97—31no—
228C2×#97—61no—
229C2×C4×C8—31no—
230C4×C4⋊C4—31no—
231#341C2×D311yescharacteristic
232#341C2×D311yescharacteristic
233#339—31no—
234#339—31no—
235#336—31no—
236#336—31no—
237C22×C3×C4#4111yescharacteristic
238C22×C3×C4#4111yescharacteristic
239C22×C3×C4C2411yescharacteristic
240C2×#67—21no—
241C2×#67—21no—
242C2×#67—21no—
243C22×Dic3—21no—
244C22×Dic3—21no—
245#235—21no—
246#235—21no—
247#235—21no—
248#235—21no—
249#235—21no—
250#235—21no—
251#235—21no—
252#235—21no—
253#235—21no—
254#235—21no—
255#235C2×D412yes—
256#235#4112yes—
257C2×D12—21no—
258C2×D12—21no—
259C2×D12C22×C411yescharacteristic
260C2×D12C22×C411yescharacteristic
261C2×D12C22×C411yescharacteristic
262C2×C4×D3—21no—
263C2×C4×D3—21no—
264C2×C4×D3—21no—
265C2×C4×D3—21no—
266C2×C4×D3—21no—
267C2×Dic6C22×C411yescharacteristic
268C2×Dic6C22×C411yescharacteristic
269C2×Dic6C22×C411yescharacteristic
270C3×M16—21no—
271C3×M16—21no—
272C3×M16—21no—
273C3×M16—21no—
274C3×M16—21no—
275C3×M16—21no—
276C3×M16C2×D412yes—
277C3×M16#4112yes—
278C2×C3×C8—21no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—21no—
285C2×C3×C8—21no—
286C2×C3×C8C22×C411yescharacteristic
287C2×C3×C8C22×C411yescharacteristic
288C2×C3×C8C22×C411yescharacteristic
289C2×C3×C8C22×C411yescharacteristic
290C3×C42C22×C411yescharacteristic
291C3×C42C22×C411yescharacteristic
292C3×C42C2×D411yescharacteristic
293C3×C42C2×D411yescharacteristic
294#217—21no—
295(C2×D3)⋊C4—21no—
296(C2×D3)⋊C4—21no—
297(C2×D3)⋊C4—21no—
298(C2×D3)⋊C4—21no—
299(C2×D3)⋊C4—21no—
300(C2×D3)⋊C4—21no—
301C4⋊Dic3—21no—
302C4⋊Dic3—21no—
303C4⋊Dic3—42no—
304C4⋊Dic3C22×C411yescharacteristic
305C4⋊Dic3C22×C411yescharacteristic
306Dic3⋊C4—21no—
307Dic3⋊C4—21no—
308C4×Dic3—21no—
309C4×Dic3—21no—
310C4×Dic3—21no—
311C4×Dic3—21no—
312C4×Dic3—21no—
313C4×Dic3—21no—
314C4×Dic3—21no—
315C2×C3⋊C8—21no—
316C2×C3⋊C8—21no—
317C2×C3⋊C8C2×D411yescharacteristic
318C2×C3⋊C8C2×D411yescharacteristic
319C2×C3⋊C8C2×D411yescharacteristic
320C2×C3⋊C8C2×D411yescharacteristic
321C2×C3⋊C8C2×D412yes—
322C2×C3⋊C8#4112yes—
323Dic12—22no—
324Dic12—22no—
325D24—22no—
326D24—22no—
327#204—22no—
328#204—22no—
329#204—22no—
330#204—22no—
331ΓL(1,𝔽25)—24no—
332ΓL(1,𝔽25)—24no—
333ΓL(1,𝔽25)—42no—
334ΓL(1,𝔽25)—42no—
335D3×C8—24no—
336D3×C8—24no—
337D3×C8—42no—
338D3×C8—42no—
339C2×#41—31no—
340C2×#41—31no—
341C2×#41—31no—
342#135—62no—
343#135—62no—
344#135—62no—
345#135—62no—
346C2×Q16—31no—
347C2×Q16—31no—
348C2×SD16—31no—
349C2×SD16—31no—
350C2×SD16—31no—
351C2×SD16—31no—
352C2×D8—31no—
353C2×D8—31no—
354#131—34no—
355#131—62no—
356#131—62no—
357#131—62no—
358#131—62no—
359#131—62no—
360#131—62no—
361#131—62no—
362C2×M16—61no—
363C2×M16—61no—
364C2×M16—61no—
365C2×M16—61no—
366C2×M16C22×D311yescharacteristic
367C2×M16C22×D311yescharacteristic
368C2×M16C22×D311yescharacteristic
369C2×M16C22×D311yescharacteristic
370C22×C8—31no—
371C22×C8—31no—
372C22×C8—61no—
373C22×C8—61no—
374C22×C8—61no—
375C22×C8—61no—
376C22×C8C22×D311yescharacteristic
377C22×C8C22×D311yescharacteristic
378C4⋊Q8—31no—
379#127—31no—
380#124—31no—
381#124—31no—
382#121—61no—
383#121—61no—
384C4×Q8—31no—
385C4×Q8—31no—
386C4×D4—31no—
387C4×D4—31no—
388C4×D4—61no—
389C4×D4—61no—
390C4×D4—61no—
391C4×D4—61no—
392#117—31no—
393#117—61no—
394C2×C4⋊C4—61no—
395C2×C42—31no—
396C2×C42—31no—
397C2×C42—61no—
398C2×C42C22×D311yescharacteristic
399#108—22no—
400#108—22no—
401C4⋊C8—21no—
402C4⋊C8—21no—
403C4⋊C8C4×D311yescharacteristic
404C4⋊C8C4×D311yescharacteristic
405C4⋊C8C4×D311yescharacteristic
406C4⋊C8C4×D311yescharacteristic
407#104—62no—
408#104—62no—
409#104—62no—
410#104—62no—
411#104—62no—
412#104—62no—
413#103—31no—
414#103—31no—
415#103—31no—
416#103—31no—
417#102—31no—
418#102—31no—
419#102—31no—
420#102—31no—
421C22⋊C8—61no—
422C22⋊C8—61no—
423C22⋊C8—61no—
424C22⋊C8—61no—
425#97—21no—
426#97—31no—
427#97—31no—
428#97—31no—
429#97—31no—
430#97—62no—
431#97—61no—
432#97—61no—
433C4×C8—21no—
434C4×C8—62no—
435C4×C8—61no—
436C4×C8—61no—
437#95—61no—
438C23×C3C2×#4111yescharacteristic
439C22×D3—21no—
440C22×D3—21no—
441C22×D3—21no—
442C2×C3×C4—41no—
443C2×C3×C4—41no—
444C2×C3×C4C4×D411yescharacteristic
445C2×C3×C4C4×D411yescharacteristic
446C2×C3×C4C4×D411yescharacteristic
447C2×C3×C4C4×D411yescharacteristic
448C2×C3×C4C23×C411yescharacteristic
449C2×C3×C4C22×D411yescharacteristic
450C2×C3×C4C22×D411yescharacteristic
451C2×C3×C4C2×#4111yescharacteristic
452C2×C3×C4C2×#4111yescharacteristic
453C2×C3×C4C2×#4111yescharacteristic
454#67—22no—
455#67—22no—
456#67—41no—
457#67—41no—
458#67—41no—
459#67—41no—
460C2×Dic3—21no—
461C2×Dic3—22no—
462C2×Dic3—21no—
463C2×Dic3—21no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—41no—
467C2×Dic3—41no—
468C2×Dic3—41no—
469C2×Dic3—41no—
470C2×Dic3—41no—
471D12—21no—
472D12—21no—
473D12—21no—
474D12—21no—
475D12—21no—
476D12—81no—
477D12—81no—
478D12C4×D412yes—
479C4×D3—22no—
480C4×D3—22no—
481C4×D3—41no—
482C4×D3—41no—
483C4×D3—41no—
484C4×D3—41no—
485C4×D3—81no—
486C4×D3—81no—
487Dic6—21no—
488Dic6—21no—
489Dic6—21no—
490Dic6—21no—
491Dic6—21no—
492Dic6C4×D412yes—
493C3×C8—21no—
494C3×C8—21no—
495C3×C8—21no—
496C3×C8—21no—
497C3×C8—22no—
498C3×C8—22no—
499C3×C8—41no—
500C3×C8—41no—
501C3⋊C8—21no—
502C3⋊C8—21no—
503C3⋊C8#12112yes—
504C3⋊C8#12112yes—
505#41—32no—
506#41—32no—
507#41—61no—
508#41—61no—
509#41—61no—
510#41—61no—
511#41—61no—
512#41—61no—
513#41—61no—
514#41—61no—
515#41—61no—
516#41—61no—
517C2×Q8—31no—
518C2×Q8—31no—
519C2×Q8—31no—
520C2×D4—31no—
521C2×D4—31no—
522C2×D4—31no—
523C2×D4—61no—
524C2×D4—61no—
525C2×D4—61no—
526C2×D4—61no—
527C2×D4—61no—
528C22×C4—61no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—61no—
533C22×C4—61no—
534C22×C4—61no—
535C22×C4#23911yescharacteristic
536C22×C4#23911yescharacteristic
537C22×C4C23×D311yescharacteristic
538Q16—62no—
539Q16—62no—
540SD16—62no—
541SD16—62no—
542SD16—62no—
543SD16—62no—
544D8—62no—
545D8—62no—
546M16—21no—
547M16—21no—
548M16—21no—
549M16—21no—
550M16—21no—
551M16—21no—
552M16—64no—
553M16—64no—
554M16—122no—
555M16—122no—
556M16D3×D412yes—
557M16#23912yes—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—32no—
567C2×C8—31no—
568C2×C8—31no—
569C2×C8—32no—
570C2×C8—31no—
571C2×C8—31no—
572C2×C8—64no—
573C2×C8—64no—
574C2×C8—61no—
575C2×C8—61no—
576C2×C8—122no—
577C2×C8—122no—
578C2×C8C2×C4×D311yescharacteristic
579C2×C8C2×C4×D311yescharacteristic
580C2×C8C2×C4×D311yescharacteristic
581C2×C8C2×C4×D311yescharacteristic
582C4⋊C4—31no—
583C4⋊C4—31no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C4⋊C4—61no—
587C4⋊C4—61no—
588C4⋊C4—122no—
589C22⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C22⋊C4—61no—
595C22⋊C4—61no—
596C42—61no—
597C42—61no—
598C42—61no—
599C42—61no—
600C42—61no—
601C42—61no—
602C42—61no—
603C42C2×C4×D311yescharacteristic
604C42C2×C4×D311yescharacteristic
605C42D3×D411yescharacteristic
606C42D3×D411yescharacteristic
607C22×C3—21no—
608C22×C3—21no—
609C22×C3C2×C4×D411yescharacteristic
610C22×C3#52911yescharacteristic
611C22×C3#53211yescharacteristic
612C2×D3—22no—
613C2×D3—41no—
614C2×D3—41no—
615C2×D3—41no—
616C2×D3—41no—
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C2×D3—41no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4C2×C4×D411yescharacteristic
626C3×C4C4×#4111yescharacteristic
627C3×C4C2×#12111yescharacteristic
628C3×C4#52511yescharacteristic
629Dic3—22no—
630Dic3—42no—
631Dic3—41no—
632Dic3—41no—
633Dic3—41no—
634Dic3—41no—
635Dic3—81no—
636C23—61no—
637C23—61no—
638C23—61no—
639C23C2×#23911yescharacteristic
640Q8—32no—
641Q8—61no—
642Q8—61no—
643Q8—61no—
644Q8—61no—
645Q8—61no—
646D4—32no—
647D4—62no—
648D4—62no—
649D4—61no—
650D4—61no—
651D4—61no—
652D4—61no—
653D4—61no—
654D4—121no—
655D4—121no—
656D4—121no—
657D4—121no—
658D4—241no—
659D4—241no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—61no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—62no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—61no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—241no—
680C2×C4—241no—
681C2×C4#89311yescharacteristic
682C2×C4#89311yescharacteristic
683C2×C4#89311yescharacteristic
684C2×C4#89311yescharacteristic
685C2×C4C22×C4×D311yescharacteristic
686C2×C4C2×D3×D411yescharacteristic
687C2×C4C2×D3×D411yescharacteristic
688C2×C4C2×#23911yescharacteristic
689C2×C4D3×#4111yescharacteristic
690C2×C4D3×#4111yescharacteristic
691C8—21no—
692C8—21no—
693C8—21no—
694C8—21no—
695C8—22no—
696C8—22no—
697C8—32no—
698C8—32no—
699C8—41no—
700C8—41no—
701C8—61no—
702C8—61no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3C4×#12111yescharacteristic
706C2×C3#295611yescharacteristic
707C2×C3#295711yescharacteristic
708D3—42no—
709D3—81no—
710D3—81no—
711C22—21no—
712C22—21no—
713C22—62no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—121no—
718C22—121no—
719C22—121no—
720C22—121no—
721C22—121no—
722C22C2×#89311yescharacteristic
723C22#569111yescharacteristic
724C22#572511yescharacteristic
725C4—21no—
726C4—21no—
727C4—21no—
728C4—21no—
729C4—62no—
730C4—122no—
731C4—121no—
732C4—121no—
733C4—121no—
734C4—121no—
735C4—241no—
736C4C4×D3×D411yescharacteristic
737C4C4×#23911yescharacteristic
738C4D3×#12111yescharacteristic
739C4#562711yescharacteristic
740C3#2151911yescharacteristic, complemented, Sylow
741C2—21no—
742C2—21no—
743C2—122no—
744C2—241no—
745C2—241no—
746C2#7596411yescharacteristic
747C2#7924911yescharacteristic
748C2#7925811yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1950C2
socleC22×C3C2×C4×D4
prime radical#79021C2
cosocleC22×C3×C4C24
hypercenter#1950D3
hypocenterC3#21519
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
1. C2×#4894C2semidirect
2. C2×#4895C2semidirect
3. #79042C2semidirect
5. #78516C2semidirect
6. C3×#1950C2semidirect
7. #70699C2semidirect
8. #70699C2semidirect
9. #70529C2semidirect
10. #70467C2semidirect
11. #69867C2semidirect
12. #68946C2semidirect
13. #68946C2semidirect
14. #68927C2semidirect
15. #68926C2semidirect
48. #4849C4semidirect
49. #4848C4semidirect
50. #4845C4semidirect
51. #4845C4semidirect
52. #4844C4semidirect
53. #4844C4semidirect
54. #4843C4semidirect
55. #4841C4semidirect
76. #1950D3semidirect
112. #907D4semidirect
740. C3#21519semidirect

Maximal subgroups

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

subgroupindex
C2×#48942
C2×#48952
#790422
#790212
#785162
C3×#19502
#706992
#705292
#704672
#698672
#689462
#689272
#689262
#215193