Finite Group Databasebeta

← #10833991

Subgroups — #10833991

Order 768.

986 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#84087C211yesmaximal, characteristic, complemented
2C2×#5238C211yesmaximal, characteristic
3C2×#4720C211yesmaximal, characteristic, complemented
4#74033C211yesmaximal, characteristic, complemented
5C3×#1788C211yesmaximal, characteristic, complemented
6#70280C211yesmaximal, characteristic, complemented
7#70262C211yesmaximal, characteristic, complemented
8#70260C211yesmaximal, characteristic, complemented
9#70253C211yesmaximal, characteristic, complemented
10#70212C211yesmaximal, characteristic, complemented
11#70194C211yesmaximal, characteristic, complemented
12#70190C211yesmaximal, characteristic, complemented
13#70187C211yesmaximal, characteristic, complemented
14#69932C211yesmaximal, characteristic, complemented
15#69504C211yesmaximal, characteristic, complemented
16#24513—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18C22×#215C2211yescharacteristic
19C22×#213C2211yescharacteristic
20C2×#930C2211yescharacteristic
21C2×#926C2211yescharacteristic
22C22×C4⋊Dic3C2211yescharacteristic
23C2×C3×#103C2211yescharacteristic
24C2×C3×#103C2211yescharacteristic
25C2×C3×#102C2211yescharacteristic
26C2×C3×#102C2211yescharacteristic
27C2×C3×C22⋊C8C2211yescharacteristic
28C3×#380C2211yescharacteristic
29#5238—24no—
30#5229C2211yescharacteristic
31#5229C2211yescharacteristic
32C2×#835C2211yescharacteristic
33#5221C2211yescharacteristic
34#5221C2211yescharacteristic
35#5220—21no—
36#5220—21no—
37C2×#832C2211yescharacteristic
38#5212—21no—
39#5212—21no—
40C2×#830C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#821C2211yescharacteristic
43C2×#815C2211yescharacteristic
44C2×Dic3⋊C8C2211yescharacteristic
45C2×Dic3⋊C8C2211yescharacteristic
46C2×C8×Dic3C2211yescharacteristic
47#4988C2211yescharacteristic
48#4988C2211yescharacteristic
49#4984C2211yescharacteristic
50#4984C2211yescharacteristic
51C2×#807C2211yescharacteristic
52C2×#807C2211yescharacteristic
53#4961—21no—
54#4961—21no—
55#4720—24no—
56#4677—21no—
57#4674—21no—
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62C2×#449—31no—
63C2×#433—31no—
64#2624—31no—
65#2311—31no—
66#2068—31no—
67#2067—31no—
68#2055—31no—
69#2054—31no—
70#1973—31no—
71#1970—31no—
72#1936—31no—
73#1933—31no—
74#1874—31no—
75#1852—31no—
76#1788D311yescharacteristic, complemented
77C2×C3×#41—22no—
78C2×C3×#41—22no—
79C2×C3×#41—22no—
80C2×C3×#41—22no—
81C2×C3×#41—41no—
82C2×C3×#41—41no—
83C22×C3×Q8C2311yescharacteristic
84C22×C3×D4—21no—
85C22×C3×D4C2311yescharacteristic
86C23×C3×C4—21no—
87C23×C3×C4C2311yescharacteristic
88C22×#67—21no—
89C23×Dic3—21no—
90C22×D12C2311yescharacteristic
91C22×C3×C8C2311yescharacteristic
92C22×C3×C8C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C22⋊C4—21no—
96C2×#217—21no—
97C2×#217—21no—
98C2×#217—21no—
99C2×#217—21no—
100C2×#217D411yescharacteristic
101C2×#217D411yescharacteristic
102C2×#215—22no—
103C2×#215—22no—
104C2×#215—41no—
105C2×#213—22no—
106C2×#213—22no—
107C2×#213—41no—
108#930—22no—
109#930—22no—
110C2×(C2×D3)⋊C4—21no—
111C2×(C2×D3)⋊C4—21no—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115#926—22no—
116#926—22no—
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—41no—
121C2×C4⋊Dic3—41no—
122C2×C4⋊Dic3D411yescharacteristic
123C2×C4⋊Dic3D411yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×C4⋊Dic3C2311yescharacteristic
126C2×C4⋊Dic3C2311yescharacteristic
127C2×C4×Dic3C2311yescharacteristic
128C2×C4×Dic3C2311yescharacteristic
129C22×C3⋊C8C2311yescharacteristic
130C22×C3⋊C8C2311yescharacteristic
131C3×#103—22no—
132C3×#103—41no—
133C3×#102—22no—
134C3×#102—41no—
135C3×C22⋊C8—22no—
136C3×#95—21no—
137#835—22no—
138#832—22no—
139C3⋊#95—21no—
140C3⋊#95—21no—
141C3⋊#95—21no—
142C3⋊#95—21no—
143C3⋊#95—21no—
144C3⋊#95—21no—
145#830D414yes—
146#821—41no—
147#821—41no—
148#815—22no—
149Dic3⋊C8—22no—
150Dic3⋊C8—22no—
151C8×Dic3—22no—
152#807—41no—
153#807—41no—
154C22×#41C2×D311yescharacteristic
155C22×SD16—31no—
156C22×D8—31no—
157C2×#121—31no—
158C2×#117—31no—
159C22×C4⋊C4—31no—
160#449—64no—
161#433—64no—
162C2×#107—31no—
163C2×#107—31no—
164C2×C4⋊C8—31no—
165C2×C4⋊C8—31no—
166C2×#103—31no—
167C2×#103C2×D311yescharacteristic
168C2×#103C2×D311yescharacteristic
169C2×#102—31no—
170C2×#102—31no—
171C2×#102—31no—
172C2×#102C2×D311yescharacteristic
173C2×#102C2×D311yescharacteristic
174C2×C22⋊C8—31no—
175C2×C22⋊C8C2×D311yescharacteristic
176C2×#97—31no—
177C2×C4×C8—31no—
178#399—61no—
179#397—61no—
180#394—61no—
181#394—61no—
182#391—31no—
183#391—31no—
184#390—31no—
185#390—31no—
186#390—31no—
187#390—31no—
188#389—31no—
189#389—31no—
190#386—61no—
191#386—61no—
192#380—61no—
193#380—61no—
194#380C2×D311yescharacteristic
195#340—31no—
196#340—31no—
197#340—31no—
198#340—31no—
199C24×C3—21no—
200C24×C3C2×D411yescharacteristic
201C23×D3—21no—
202C3×#41—44no—
203C3×#41—44no—
204C3×#41—44no—
205C3×#41—44no—
206C2×C3×Q8—21no—
207C2×C3×Q8—21no—
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8#4112yes—
212C2×C3×D4—24no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4#4112yes—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—24no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—42no—
230C22×C3×C4—42no—
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D412yes—
233C22×C3×C4#4112yes—
234C22×C3×C4C2411yescharacteristic
235C2×#67—42no—
236C2×#67—81no—
237C2×#67—81no—
238C22×Dic3—21no—
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—42no—
242C22×Dic3—81no—
243C22×Dic3—81no—
244C22×Dic3C2×D411yescharacteristic
245C22×Dic3C2×D411yescharacteristic
246C22×Dic3C2×D411yescharacteristic
247C22×Dic3C2×D411yescharacteristic
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C22⋊C4—81no—
265#217—22no—
266#217—22no—
267#217—81no—
268#217—81no—
269#217—81no—
270#217—81no—
271#215—44no—
272#213—44no—
273(C2×D3)⋊C4—42no—
274(C2×D3)⋊C4—81no—
275(C2×D3)⋊C4—81no—
276(C2×D3)⋊C4—81no—
277(C2×D3)⋊C4—81no—
278C4⋊Dic3—22no—
279C4⋊Dic3—22no—
280C4⋊Dic3—21no—
281C4⋊Dic3—21no—
282C4⋊Dic3—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—42no—
287C4⋊Dic3—81no—
288C4⋊Dic3—81no—
289C4×Dic3—21no—
290C4×Dic3—21no—
291C4×Dic3—21no—
292C4×Dic3—21no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8C2×D412yes—
298C2×C3⋊C8C2×D412yes—
299C2×#41—22no—
300C2×#41—22no—
301C2×#41—22no—
302C2×#41—22no—
303C2×#41—41no—
304C2×#41—41no—
305C22×Q8C22×D311yescharacteristic
306C22×D4—21no—
307C22×D4—31no—
308C22×D4—61no—
309C22×D4C22×D311yescharacteristic
310C23×C4—21no—
311C23×C4—61no—
312C23×C4C22×D311yescharacteristic
313C2×SD16—62no—
314C2×SD16—62no—
315C2×SD16—121no—
316C2×D8—62no—
317C2×D8—62no—
318C2×D8—121no—
319C22×C8—31no—
320C22×C8—31no—
321C22×C8C22×D311yescharacteristic
322C22×C8C22×D311yescharacteristic
323#121—62no—
324#121—62no—
325#117—62no—
326#117—62no—
327C2×C4⋊C4—31no—
328C2×C4⋊C4—31no—
329C2×C4⋊C4—31no—
330C2×C4⋊C4—31no—
331C2×C4⋊C4—31no—
332C2×C4⋊C4—61no—
333C2×C4⋊C4—61no—
334C2×C4⋊C4—61no—
335C2×C4⋊C4—121no—
336C2×C4⋊C4—121no—
337C2×C4⋊C4C22×D311yescharacteristic
338C2×C4⋊C4C22×D311yescharacteristic
339C2×C22⋊C4—21no—
340C2×C22⋊C4—31no—
341C2×C22⋊C4—31no—
342C2×C22⋊C4—61no—
343C2×C22⋊C4—61no—
344C2×C22⋊C4—61no—
345C2×C22⋊C4—61no—
346C2×C22⋊C4—61no—
347C2×C22⋊C4—61no—
348C2×C22⋊C4—61no—
349C2×C22⋊C4—61no—
350C2×C22⋊C4—61no—
351C2×C42—31no—
352C2×C42—31no—
353#107—121no—
354#107—121no—
355C4⋊C8—62no—
356C4⋊C8—62no—
357#103—22no—
358#103—41no—
359#103—62no—
360#102—22no—
361#102—41no—
362#102—62no—
363#102—121no—
364#102—121no—
365C22⋊C8—22no—
366C22⋊C8—34no—
367#97—62no—
368C4×C8—62no—
369#95—21no—
370#95—61no—
371#95—61no—
372#95—61no—
373#95—61no—
374#95—61no—
375#95—61no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—21no—
380C23×C3—21no—
381C23×C3—21no—
382C23×C3—22no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3#12112yes—
390C23×C3C22×D411yescharacteristic
391C22×D3—41no—
392C22×D3—41no—
393C22×D3—41no—
394C22×D3—41no—
395C22×D3—41no—
396C22×D3—41no—
397C22×D3—41no—
398C3×Q8—22no—
399C3×Q8—22no—
400C3×Q8—41no—
401C3×Q8—41no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—48no—
405C3×D4—41no—
406C3×D4—41no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—48no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4#12112yes—
424C2×C3×C4C22×D411yescharacteristic
425C2×C3×C4C2×#4111yescharacteristic
426C2×C3×C4C2×#4111yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4H(5,𝔽2)11yescharacteristic
429C2×C3×C4H(5,𝔽2)11yescharacteristic
430#67—84no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—84no—
453D12—41no—
454D12—41no—
455D12—41no—
456D12—41no—
457C3×C8—41no—
458C3×C8—41no—
459C3⋊C8—22no—
460C3⋊C8—22no—
461C24—21no—
462C24—61no—
463C24D3×D411yescharacteristic
464#41—44no—
465#41—44no—
466#41—44no—
467#41—44no—
468C2×Q8—21no—
469C2×Q8—21no—
470C2×Q8—21no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8#23712yes—
474C2×D4—24no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—42no—
481C2×D4—42no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4—61no—
486C2×D4—61no—
487C2×D4—61no—
488C2×D4—122no—
489C2×D4—241no—
490C2×D4—241no—
491C2×D4#23712yes—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—31no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—31no—
504C22×C4—42no—
505C22×C4—42no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—122no—
510C22×C4—241no—
511C22×C4—241no—
512C22×C4#23512yes—
513C22×C4D3×D411yescharacteristic
514C22×C4D3×D412yes—
515C22×C4C23×D311yescharacteristic
516SD16—124no—
517D8—124no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—32no—
525C2×C8—32no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—61no—
529C2×C8—61no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—62no—
535C4⋊C4—62no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—122no—
543C4⋊C4—241no—
544C4⋊C4—241no—
545C22⋊C4—62no—
546C22⋊C4—62no—
547C22⋊C4—81no—
548C22⋊C4—122no—
549C22⋊C4—241no—
550C22⋊C4—241no—
551C22⋊C4—241no—
552C22⋊C4—241no—
553C22⋊C4—241no—
554C22⋊C4—241no—
555C22⋊C4—241no—
556C22⋊C4—241no—
557C42—61no—
558C42—61no—
559C42—61no—
560C42—61no—
561C22×C3—22no—
562C22×C3—22no—
563C22×C3—22no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—81no—
572C22×C3—81no—
573C22×C3—81no—
574C22×C3—81no—
575C22×C3C2×#12111yescharacteristic
576C22×C3#52511yescharacteristic
577C22×C3#53511yescharacteristic
578C22×C3#57611yescharacteristic
579C22×C3#57611yescharacteristic
580C22×C3#57711yescharacteristic
581C22×C3#57811yescharacteristic
582C2×D3—81no—
583C2×D3—81no—
584C2×D3—81no—
585C2×D3—81no—
586C2×D3—81no—
587C2×D3—81no—
588C2×D3—81no—
589C3×C4—22no—
590C3×C4—42no—
591C3×C4—81no—
592C3×C4—81no—
593C3×C4#54611yescharacteristic
594C3×C4#54611yescharacteristic
595C3×C4#55111yescharacteristic
596C3×C4#55111yescharacteristic
597Dic3—41no—
598Dic3—41no—
599Dic3—41no—
600Dic3—41no—
601Dic3—81no—
602Dic3—81no—
603Dic3—81no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—22no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—121no—
618C23—121no—
619C23—121no—
620C23—121no—
621C23—121no—
622C23—121no—
623C23—121no—
624C23#88412yes—
625C23C2×D3×D411yescharacteristic
626Q8—22no—
627Q8—22no—
628Q8—41no—
629Q8—41no—
630D4—22no—
631D4—22no—
632D4—48no—
633D4—41no—
634D4—41no—
635D4—121no—
636D4—121no—
637D4—121no—
638D4—121no—
639D4—244no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—48no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—61no—
662C2×C4—61no—
663C2×C4—61no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—244no—
678C2×C4#88412yes—
679C2×C4C2×#23511yescharacteristic
680C2×C4C2×D3×D411yescharacteristic
681C2×C4C2×#23711yescharacteristic
682C2×C4C2×#23711yescharacteristic
683C2×C4#100411yescharacteristic
684C2×C4#100411yescharacteristic
685C8—41no—
686C8—41no—
687C8—62no—
688C8—62no—
689C2×C3—42no—
690C2×C3—82no—
691C2×C3#241111yescharacteristic
692C2×C3#306111yescharacteristic
693C2×C3#306211yescharacteristic
694C2×C3#311911yescharacteristic
695C2×C3#312411yescharacteristic
696C2×C3#322011yescharacteristic
697C2×C3#322511yescharacteristic
698D3—161no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—241no—
714C22—241no—
715C22—241no—
716C22—241no—
717C22—241no—
718C22—241no—
719C22—241no—
720C22C2×#88411yescharacteristic
721C22#558611yescharacteristic
722C22#559211yescharacteristic
723C22#576911yescharacteristic
724C22#577011yescharacteristic
725C22#577411yescharacteristic
726C22#577911yescharacteristic
727C4—22no—
728C4—42no—
729C4—81no—
730C4—81no—
731C4—121no—
732C4—121no—
733C4—121no—
734C4—121no—
735C4—241no—
736C4—241no—
737C4—241no—
738C4#549511yescharacteristic
739C4#549511yescharacteristic
740C4#559111yescharacteristic
741C4#559111yescharacteristic
742C3#2451311yescharacteristic, complemented, Sylow
743C2—42no—
744C2—82no—
745C2—481no—
746C2#7382511yescharacteristic
747C2#7884011yescharacteristic
748C2#7889111yescharacteristic
749C2#8007311yescharacteristic
750C2#8011811yescharacteristic
751C2#8021811yescharacteristic
752C2#8022411yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1788C2
socleC23×C3C22×D4
prime radicalC2×#5238C2
hypercenter#1788D3
hypocenterC3#24513
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1788

Complements

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

NH ≅ G/Ntype
1. #84087C2semidirect
3. C2×#4720C2semidirect
4. #74033C2semidirect
5. C3×#1788C2semidirect
6. #70280C2semidirect
7. #70262C2semidirect
8. #70260C2semidirect
9. #70253C2semidirect
10. #70212C2semidirect
11. #70194C2semidirect
12. #70190C2semidirect
13. #70187C2semidirect
14. #69932C2semidirect
15. #69504C2semidirect
76. #1788D3semidirect
742. C3#24513semidirect

Maximal subgroups

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

subgroupindex
#840872
C2×#52382
C2×#47202
#740332
C3×#17882
#702802
#702622
#702602
#702532
#702122
#701942
#701902
#701872
#699322
#695042
#245133