Finite Group Databasebeta

← #26121716

Subgroups — #26121716

Order 12032.

1254 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689603C211yesmaximal, characteristic
2C2×#15689105C211yesmaximal, characteristic
3C2×#15689096C211yesmaximal, characteristic
4#20243109C211yesmaximal, characteristic, complemented
5#20243108C211yesmaximal, characteristic, complemented
6#20243097C211yesmaximal, characteristic, complemented
7C47×#1733C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10#15689603—22no—
11#15689603—22no—
12#15689603—22no—
13#15689603—22no—
14C2×C4×Dic94—21no—
15C2×C4×D188—21no—
16C2×(C22⋊D47)⋊C4—22no—
17C2×#13093983C2211yescharacteristic
18C2×#13093982C412yescomplemented
19C22×C4⋊Dic47C2211yescharacteristic
20C2×C4⋊C4×D47C412yescomplemented
21#15689105—22no—
22#15689105C414yescomplemented
23C2×#13093942—21no—
24C2×#13093940—21no—
25#15689096—22no—
26#15689096C414yescomplemented
27C2×#13093938—22no—
28#15688886—22no—
29#15688885—22no—
30#15688882—22no—
31C22×M16×C47C2211yescharacteristic
32C2×#117×C47C2211yescharacteristic
33C2×#117×C47C2211yescharacteristic
34C47×#339—22no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350C2×C412yes—
44C2×#10625350C2×C412yes—
45C2×#10625350D412yes—
46C2×#10625350Q812yes—
47C22×Dic94D411yescharacteristic
48C22×D188D411yescharacteristic
49C22×C22⋊D47D412yes—
50C23×Dic47—21no—
51C22×C4×D47—22no—
52C22×C4×D47C2×C412yes—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329C2×C412yescomplemented
59C22×C47⋊C8—21no—
60C4×Dic94—24no—
61C4×Dic94—24no—
62C4×D188—24no—
63C4×D188—24no—
64(C22⋊D47)⋊C4—28no—
65(C22⋊D47)⋊C4—28no—
66#13093983—21no—
67#13093983—21no—
68#13093983—21no—
69#13093983C2×C412yescomplemented
70#13093982—24no—
71#13093982—24no—
72C2×C4⋊Dic47—21no—
73C2×C4⋊Dic47—21no—
74C2×C4⋊Dic47—21no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47C2×C412yes—
77C2×C4⋊Dic47D412yes—
78C2×C4⋊Dic47D412yes—
79C2×Dic47⋊C4—22no—
80C4⋊C4×D47—24no—
81C4⋊C4×D47—24no—
82C2×C22⋊Dic47—21no—
83C2×(C2×D47)⋊C4—22no—
84C2×C4×Dic47—22no—
85C2×C4×Dic47—21no—
86#13093942—24no—
87#13093940—24no—
88#13093938—28no—
89C23×C4×C47C2311yescharacteristic
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47C2×C412yescomplemented
96C22×C8×C47—21no—
97#117×C47—21no—
98#117×C47—21no—
99#117×C47—21no—
100#117×C47—21no—
101#117×C47—21no—
102#117×C47C2×C412yescomplemented
103#117×C47D412yes—
104#117×C47D412yes—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47C2×C411yescharacteristic
107C2×C4⋊C4×C47C2×C411yescharacteristic
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C42×C47—21no—
111C2×C42×C47—21no—
112C24×C47C2×D411yescharacteristic
113C23×D47C22⋊C412yes—
114C22×C4×C47—21no—
115C22×C4×C47—21no—
116C22×C4×C47—41no—
117C22×C4×C47C22×C411yescharacteristic
118C22×C4×C47C22×C411yescharacteristic
119C22×C4×C47C22×C411yescharacteristic
120C22×C4×C47C2×D411yescharacteristic
121C22×C4×C47C2×D411yescharacteristic
122C22×C4×C47C2×D411yescharacteristic
123C22×C4×C47C2×D411yescharacteristic
124C22×C4×C47C2×D411yescharacteristic
125C22×C4×C47C2×D411yescharacteristic
126C22×C4×C47C2×Q811yescharacteristic
127C22×C4×C47#4111yescharacteristic
128C22×C4×C47#4111yescharacteristic
129C22×C4×C47#4111yescharacteristic
130C22×C4×C47#4111yescharacteristic
131C2×C22⋊D47—22no—
132C2×C22⋊D47—22no—
133C2×C22⋊D47—22no—
134C2×C22⋊D47—22no—
135C2×C22⋊D47C22⋊C414yes—
136C2×C22⋊D47C4⋊C414yes—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—41no—
141C22×Dic47—82no—
142C22×Dic47C22⋊C412yes—
143#10625350—22no—
144#10625350—22no—
145#10625350—22no—
146#10625350—22no—
147#10625350—22no—
148#10625350—22no—
149#10625350—22no—
150#10625350—22no—
151#10625350—22no—
152#10625350—22no—
153#10625350—22no—
154#10625350—22no—
155#10625350—22no—
156#10625350—22no—
157#10625350—22no—
158#10625350—22no—
159C2×D188—21no—
160C2×D188—21no—
161C2×D188—21no—
162C2×D188—21no—
163C2×D188C22⋊C412yes—
164C2×D188C4⋊C412yes—
165C2×C4×D47—22no—
166C2×C4×D47—22no—
167C2×C4×D47—22no—
168C2×C4×D47—22no—
169C2×C4×D47—28no—
170C2×C4×D47—84no—
171C2×C4×D47C4214yes—
172C2×C4×D47C4⋊C414yes—
173C2×Dic94—21no—
174C2×Dic94—21no—
175C2×Dic94—21no—
176C2×Dic94—21no—
177C2×Dic94C22⋊C412yes—
178C2×Dic94C4⋊C412yes—
179M16×C47—22no—
180M16×C47—22no—
181M16×C47—41no—
182M16×C47—41no—
183C2×C8×C47—22no—
184C2×C8×C47—41no—
185C2×C8×C47—41no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—22no—
189C4⋊C4×C47—41no—
190C4⋊C4×C47C22⋊C412yes—
191C4⋊C4×C47C22⋊C412yes—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—22no—
194C22⋊C4×C47—22no—
195C22⋊C4×C47—41no—
196C42×C47—22no—
197C42×C47—22no—
198C42×C47—22no—
199C42×C47—41no—
200C22⋊Dic47—22no—
201C22⋊Dic47—41no—
202(C2×D47)⋊C4—28no—
203C4⋊Dic47—22no—
204C4⋊Dic47—22no—
205C4⋊Dic47—22no—
206C4⋊Dic47—22no—
207C4⋊Dic47—41no—
208C4⋊Dic47C22⋊C414yes—
209Dic47⋊C4—28no—
210C4×Dic47—28no—
211C4×Dic47—22no—
212C4×Dic47—41no—
213#10625329—22no—
214#10625329—22no—
215#10625329—41no—
216#10625329—41no—
217C2×C47⋊C8—22no—
218C2×C47⋊C8—41no—
219C2×C47⋊C8—41no—
220C23×C47—41no—
221C23×C47—41no—
222C23×C47C2×C22⋊C411yescharacteristic
223C23×C47C2×C22⋊C411yescharacteristic
224C23×C47C2×C4⋊C411yescharacteristic
225C23×C47#12011yescharacteristic
226C23×C47#12011yescharacteristic
227C23×C47#12311yescharacteristic
228C23×C47#12311yescharacteristic
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—42no—
232C22×D47—42no—
233C22×D47#9514yes—
234C2×C4×C47—22no—
235C2×C4×C47—22no—
236C2×C4×C47—42no—
237C2×C4×C47—42no—
238C2×C4×C47—42no—
239C2×C4×C47—81no—
240C2×C4×C47—81no—
241C2×C4×C47C2×C4211yescharacteristic
242C2×C4×C47C2×C22⋊C411yescharacteristic
243C2×C4×C47C2×C22⋊C411yescharacteristic
244C2×C4×C47C2×C22⋊C411yescharacteristic
245C2×C4×C47C2×C4⋊C411yescharacteristic
246C2×C4×C47C2×C4⋊C411yescharacteristic
247C2×C4×C47#11711yescharacteristic
248C2×C4×C47#11711yescharacteristic
249C2×C4×C47C4×D411yescharacteristic
250C2×C4×C47C4×D411yescharacteristic
251C2×C4×C47C4×D411yescharacteristic
252C2×C4×C47C4×D411yescharacteristic
253C2×C4×C47C4×D411yescharacteristic
254C2×C4×C47C4×D411yescharacteristic
255C2×C4×C47C4×D411yescharacteristic
256C2×C4×C47C4×D411yescharacteristic
257C2×C4×C47#12011yescharacteristic
258C2×C4×C47#12011yescharacteristic
259C2×C4×C47#12111yescharacteristic
260C2×C4×C47#12111yescharacteristic
261C2×C4×C47#12111yescharacteristic
262C2×C4×C47#12111yescharacteristic
263C2×C4×C47C22⋊Q811yescharacteristic
264C2×C4×C47C22⋊Q811yescharacteristic
265C2×C4×C47C22⋊Q811yescharacteristic
266C2×C4×C47C22⋊Q811yescharacteristic
267C2×C4×C47#12311yescharacteristic
268C2×C4×C47#12311yescharacteristic
269C22⋊D47—24no—
270C22⋊D47—24no—
271C22⋊D47—24no—
272C22⋊D47—24no—
273C2×Dic47—22no—
274C2×Dic47—22no—
275C2×Dic47—24no—
276C2×Dic47—44no—
277C2×Dic47—42no—
278C2×Dic47—82no—
279C2×Dic47—82no—
280C2×Dic47—81no—
281C2×Dic47—81no—
282C2×Dic47#9514yes—
283D188—22no—
284D188—22no—
285D188—22no—
286D188—22no—
287C4×D47—24no—
288C4×D47—24no—
289C4×D47—24no—
290C4×D47—24no—
291C4×D47—88no—
292Dic94—22no—
293Dic94—22no—
294Dic94—22no—
295Dic94—22no—
296C8×C47—42no—
297C47⋊C8—42no—
298#10765—471nomaximal, Sylow
299C22×C47—21no—
300C22×C47—21no—
301C22×C47—21no—
302C22×C47—21no—
303C22×C47—21no—
304C22×C47—21no—
305C22×C47—41no—
306C22×C47—41no—
307C22×C47—41no—
308C22×C47—41no—
309C22×C47C2×#9511yescharacteristic
310C22×C47#37911yescharacteristic
311C22×C47#38111yescharacteristic
312C22×C47#38511yescharacteristic
313C22×C47#38511yescharacteristic
314C22×C47#38611yescharacteristic
315C22×C47#38611yescharacteristic
316C2×D47—24no—
317C2×D47—44no—
318C2×D47—42no—
319C2×D47—42no—
320C2×D47—44no—
321C4×C47—42no—
322C4×C47—42no—
323C4×C47—82no—
324C4×C47C4×C22⋊C411yescharacteristic
325C4×C47C4×C22⋊C411yescharacteristic
326C4×C47#38011yescharacteristic
327C4×C47#38011yescharacteristic
328C4×C47#38511yescharacteristic
329C4×C47#38511yescharacteristic
330C4×C47#38611yescharacteristic
331C4×C47#38611yescharacteristic
332Dic47—24no—
333Dic47—44no—
334Dic47—82no—
335C2×#520—471no—
336C2×#413—471no—
337C2×#410—471no—
338#1736—471no—
339#1736—471no—
340#1733—471no—
341#1733D4711yescharacteristic, complemented
342C2×C47—21no—
343C2×C47—21no—
344C2×C47—21no—
345C2×C47—21no—
346C2×C47—21no—
347C2×C47—21no—
348C2×C47C22⋊#9511yescharacteristic
349C2×C47#179511yescharacteristic
350C2×C47#179611yescharacteristic
351D47—44no—
352C22×#41—471no—
353C22×M16—471no—
354C22×M16C2×D4711yescharacteristic
355#520—942no—
356#520—942no—
357#520—942no—
358#520—942no—
359C2×C4×Q8—941no—
360C2×C4×D4—941no—
361C2×C4×D4—942no—
362C2×#117—472no—
363C2×#117—471no—
364C2×#117C2×D4711yescharacteristic
365C2×#117C2×D4711yescharacteristic
366C22×C4⋊C4—471no—
367C22×C4⋊C4—472no—
368#413—474no—
369#413—942no—
370C2×#101—941no—
371C2×#100—941no—
372#410—474no—
373#410—942no—
374C2×#99—942no—
375#340—942no—
376#340—942no—
377#339—22no—
378#339—942no—
379C47#1076511yescharacteristic, complemented, Sylow
380C2×#41—472no—
381C2×#41—472no—
382C2×#41—472no—
383C2×#41—472no—
384C2×#41—941no—
385C2×#41—941no—
386C2×#41—941no—
387C2×#41—941no—
388C2×#41—941no—
389C2×#41—941no—
390C2×#41—941no—
391C2×#41—941no—
392C22×Q8—471no—
393C22×D4—472no—
394C22×D4—471no—
395C23×C4—472no—
396C23×C4—942no—
397C23×C4—941no—
398C23×C4C22×D4711yescharacteristic
399C2×M16—21no—
400C2×M16—21no—
401C2×M16—21no—
402C2×M16—21no—
403C2×M16—21no—
404C2×M16—472no—
405C2×M16—941no—
406C2×M16—941no—
407C2×M16—941no—
408C2×M16—941no—
409C2×M16—941no—
410C2×M16C4×D4712yescomplemented
411C22×C8—21no—
412C22×C8—941no—
413C4×Q8—944no—
414C4×Q8—944no—
415C4×D4—944no—
416C4×D4—944no—
417C4×D4—948no—
418C4×D4—948no—
419#117—21no—
420#117—21no—
421#117—21no—
422#117—21no—
423#117—21no—
424#117—472no—
425#117—944no—
426#117—944no—
427#117—941no—
428#117—941no—
429#117—941no—
430#117C4×D4712yescomplemented
431#117D18812yes—
432#117C22⋊D4712yes—
433C2×C4⋊C4—21no—
434C2×C4⋊C4—472no—
435C2×C4⋊C4—472no—
436C2×C4⋊C4—472no—
437C2×C4⋊C4—944no—
438C2×C4⋊C4—942no—
439C2×C4⋊C4—941no—
440C2×C4⋊C4—941no—
441C2×C4⋊C4—941no—
442C2×C4⋊C4—944no—
443C2×C4⋊C4—941no—
444C2×C4⋊C4C4×D4711yescharacteristic
445C2×C4⋊C4C4×D4711yescharacteristic
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—942no—
449C2×C22⋊C4—941no—
450C2×C42—21no—
451C2×C42—21no—
452C2×C42—942no—
453C2×C42—941no—
454#101—944no—
455#100—944no—
456#99—948no—
457C24—472no—
458C24D4×D4711yescharacteristic
459#41—942no—
460#41—942no—
461#41—942no—
462#41—942no—
463#41—942no—
464#41—942no—
465#41—942no—
466#41—942no—
467#41—942no—
468#41—942no—
469#41—942no—
470#41—942no—
471#41—942no—
472#41—942no—
473#41—942no—
474#41—942no—
475C2×Q8—472no—
476C2×Q8—472no—
477C2×Q8—941no—
478C2×Q8—941no—
479C2×Q8—941no—
480C2×Q8—941no—
481C2×D4—474no—
482C2×D4—474no—
483C2×D4—472no—
484C2×D4—472no—
485C2×D4—942no—
486C2×D4—942no—
487C2×D4—942no—
488C2×D4—942no—
489C2×D4—941no—
490C2×D4—941no—
491C2×D4—941no—
492C2×D4—941no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—41no—
496C22×C4—472no—
497C22×C4—474no—
498C22×C4—474no—
499C22×C4—948no—
500C22×C4—942no—
501C22×C4—942no—
502C22×C4—942no—
503C22×C4—942no—
504C22×C4—942no—
505C22×C4—942no—
506C22×C4—942no—
507C22×C4—3764no—
508C22×C4—3762no—
509C22×C4—1881no—
510C22×C4C2×C4×D4711yescharacteristic
511C22×C4C2×C4×D4711yescharacteristic
512C22×C4C2×C4×D4711yescharacteristic
513C22×C4C2×D18811yescharacteristic
514C22×C4#1062535011yescharacteristic
515C22×C4#1062535011yescharacteristic
516C22×C4D4×D4711yescharacteristic
517C22×C4D4×D4711yescharacteristic
518C22×C4D4×D4711yescharacteristic
519C22×C4D4×D4711yescharacteristic
520C22×C4#1062535211yescharacteristic
521C22×C4Q8×D4711yescharacteristic
522C22×C4#1062535411yescharacteristic
523C22×C4C2×C22⋊D4711yescharacteristic
524M16—22no—
525M16—22no—
526M16—41no—
527M16—41no—
528M16—942no—
529M16—942no—
530M16—1881no—
531M16—1881no—
532C2×C8—22no—
533C2×C8—41no—
534C2×C8—41no—
535C2×C8—942no—
536C2×C8—1881no—
537C2×C8—1881no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—22no—
541C4⋊C4—41no—
542C4⋊C4—474no—
543C4⋊C4—948no—
544C4⋊C4—942no—
545C4⋊C4—942no—
546C4⋊C4—942no—
547C4⋊C4—942no—
548C4⋊C4—1881no—
549C4⋊C4(C2×D47)⋊C412yes—
550C4⋊C4(C2×D47)⋊C412yes—
551C22⋊C4—22no—
552C22⋊C4—22no—
553C22⋊C4—22no—
554C22⋊C4—41no—
555C22⋊C4—948no—
556C22⋊C4—942no—
557C22⋊C4—1881no—
558C42—22no—
559C42—22no—
560C42—22no—
561C42—41no—
562C42—948no—
563C42—942no—
564C42—1881no—
565C23—41no—
566C23—41no—
567C23—474no—
568C23—942no—
569C23—942no—
570C23—1882no—
571C23—1882no—
572C23C22⋊C4×D4711yescharacteristic
573C23C22⋊C4×D4711yescharacteristic
574C23C4⋊C4×D4711yescharacteristic
575C23#1309399211yescharacteristic
576C23#1309399411yescharacteristic
577C23#1309400611yescharacteristic
578C23#1309400911yescharacteristic
579Q8—942no—
580Q8—942no—
581Q8—942no—
582Q8—942no—
583D4—944no—
584D4—944no—
585D4—944no—
586D4—944no—
587D4—942no—
588D4—942no—
589D4—942no—
590D4—942no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—81no—
597C2×C4—81no—
598C2×C4—474no—
599C2×C4—942no—
600C2×C4—942no—
601C2×C4—944no—
602C2×C4—944no—
603C2×C4—944no—
604C2×C4—944no—
605C2×C4—944no—
606C2×C4—3768no—
607C2×C4—3761no—
608C2×C4—3761no—
609C2×C4—3762no—
610C2×C4—3762no—
611C2×C4—1882no—
612C2×C4—1884no—
613C2×C4C42×D4711yescharacteristic
614C2×C4C22⋊C4×D4711yescharacteristic
615C2×C4C22⋊C4×D4711yescharacteristic
616C2×C4C2×(C2×D47)⋊C411yescharacteristic
617C2×C4C4⋊C4×D4711yescharacteristic
618C2×C4C4⋊C4×D4711yescharacteristic
619C2×C4#1309398111yescharacteristic
620C2×C4#1309398211yescharacteristic
621C2×C4(C22⋊D47)⋊C411yescharacteristic
622C2×C4(C22⋊D47)⋊C411yescharacteristic
623C2×C4C4×C22⋊D4711yescharacteristic
624C2×C4C4×C22⋊D4711yescharacteristic
625C2×C4#1309398611yescharacteristic
626C2×C4#1309398611yescharacteristic
627C2×C4C4×D18811yescharacteristic
628C2×C4C4×D18811yescharacteristic
629C2×C4#1309399211yescharacteristic
630C2×C4#1309399411yescharacteristic
631C2×C4#1309399511yescharacteristic
632C2×C4#1309399711yescharacteristic
633C2×C4#1309399711yescharacteristic
634C2×C4#1309399911yescharacteristic
635C2×C4#1309400011yescharacteristic
636C2×C4#1309400211yescharacteristic
637C2×C4#1309400211yescharacteristic
638C2×C4#1309400411yescharacteristic
639C2×C4#1309400611yescharacteristic
640C2×C4#1309400911yescharacteristic
641C8—42no—
642C8—1882no—
643C22—21no—
644C22—21no—
645C22—21no—
646C22—21no—
647C22—21no—
648C22—21no—
649C22—41no—
650C22—41no—
651C22—41no—
652C22—41no—
653C22—944no—
654C22—1884no—
655C22—1884no—
656C22—1882no—
657C22—1882no—
658C22#95×D4711yescharacteristic
659C22#1568897811yescharacteristic
660C22#1568898511yescharacteristic
661C22#1568899411yescharacteristic
662C22#1568899711yescharacteristic
663C22#1568899911yescharacteristic
664C22#1568900111yescharacteristic
665C4—42no—
666C4—42no—
667C4—82no—
668C4—944no—
669C4—3762no—
670C4—1884no—
671C4#1568897011yescharacteristic
672C4C4×(C2×D47)⋊C411yescharacteristic
673C4#1568898011yescharacteristic
674C4#1568898211yescharacteristic
675C4#1568899411yescharacteristic
676C4#1568899711yescharacteristic
677C4#1568899911yescharacteristic
678C4#1568900111yescharacteristic
679C2—21no—
680C2—21no—
681C2—21no—
682C2—21no—
683C2—21no—
684C2—21no—
685C2—1884no—
686C2(C2×D47)⋊#9511yescharacteristic
687C2#2024335711yescharacteristic
688C2#2024336211yescharacteristic
subgroupG/H
centerC22#15688978
commutatorC2×C4×C47C2×C42
FrattiniC23×C4C22×D47
FittingC47×#1733C2
socleC22×C47#379
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1733D47
hypocenterC47#10765
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
4. #20243109C2semidirect
5. #20243108C2semidirect
6. #20243097C2semidirect
7. C47×#1733C2semidirect
18. C2×#13093982C4semidirect
20. C2×C4⋊C4×D47C4semidirect
22. #15689105C4semidirect
26. #15689096C4semidirect
58. C2×#10625329C2×C4semidirect
69. #13093983C2×C4semidirect
95. C2×M16×C47C2×C4semidirect
102. #117×C47C2×C4semidirect
341. #1733D47semidirect
379. C47#10765semidirect
410. C2×M16C4×D47semidirect
430. #117C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896032
C2×#156891052
C2×#156890962
#202431092
#202431082
#202430972
C47×#17332
#1076547