Finite Group Databasebeta

← #17901870

Subgroups — #17901870

Order 4352.

2130 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11763362C211yesmaximal, characteristic, complemented
2C2×#41×Dic17C211yesmaximal, characteristic
3#14538604C214yesmaximal, complemented
4#14538595C214yesmaximal, complemented
5#14538586C214yesmaximal, complemented
6#14538578C214yesmaximal, complemented
7#14538568C218yesmaximal, complemented
8#14537374C211yesmaximal, characteristic, complemented
9#14537373C211yesmaximal, characteristic, complemented
10C2×#11762832C211yesmaximal, characteristic, complemented
11#14537303C211yesmaximal, characteristic
12C17×#2896C211yesmaximal, characteristic
13C22×#63223C2211yescharacteristic
14#11763362—21no—
15#11763362—21no—
16#11763362—21no—
17#11763362—21no—
18#11763362C2214yes—
19#11763362C2214yescomplemented
20C2×#10587574C2212yescomplemented
21C2×#10587576C2212yescomplemented
22C2×#10587564—22no—
23#41×Dic17—22no—
24#41×Dic17—21no—
25#41×Dic17—21no—
26#41×Dic17C2214yes—
27#41×Dic17C2212yes—
28#41×Dic17C2212yes—
29C2×Q8×Dic17C2212yes—
30C2×C4×Dic34—22no—
31C2×D4×Dic17—22no—
32C2×D4×Dic17C2212yes—
33C2×#10587612—21no—
34C2×#10587612C2211yescharacteristic
35C2×#10587612C2211yescharacteristic
36C22×C4×Dic17—21no—
37C22×C4×Dic17C2211yescharacteristic
38#11763118C2218yescomplemented
39#11763114C2218yescomplemented
40#11763111C2218yescomplemented
41#11763107C2218yescomplemented
42#11763102C2218yescomplemented
43#11763097C2218yescomplemented
44#11763092C2218yescomplemented
45#11763087C2218yescomplemented
46#11762852C2214yes—
47#11762851C2214yes—
48#11762851C2214yescomplemented
49#11762849C2214yescomplemented
50#11762847C2214yescomplemented
51#11762845C2214yescomplemented
52#11762832C2214yes—
53#11762832C2212yescomplemented
54#11762832C2212yescomplemented
55C2×#10587485C2214yescomplemented
56#11762818C2212yes—
57#11762814C2212yes—
58#11762810C2214yes—
59#11762805C2214yes—
60C22×#41×C17C2211yescharacteristic
61C22×M16×C17C2211yescharacteristic
62C2×C17×#117C2211yescharacteristic
63C17×#419C2212yes—
64C17×#418C2212yes—
65C17×#417C2214yes—
66C17×#416C2214yes—
67C2×#41×C17—21no—
68C2×#41×C17—21no—
69C2×#41×C17—24no—
70C2×#41×C17Q818yescomplemented
71C2×#41×C17C2312yes—
72C2×#41×C17C2312yes—
73C22×Q8×C17C2311yescharacteristic
74C22×D4×C17—21no—
75C22×D4×C17C2311yescharacteristic
76C23×C4×C17—21no—
77C23×C4×C17C2311yescharacteristic
78C23×Dic17—22no—
79C23×Dic17D412yes—
80C22×Dic34—22no—
81C2×M16×C17—24no—
82C2×M16×C17C2312yes—
83C2×M16×C17C2312yes—
84C22×C8×C17C2312yes—
85C17×#117—21no—
86C17×#117—21no—
87C17×#117C2312yes—
88C17×#117C2312yes—
89C2×C4⋊C4×C17C2312yes—
90C2×C22⋊C4×C17—21no—
91C2×C42×C17—21no—
92C2×C22⋊Dic17—21no—
93C2×C22⋊Dic17—21no—
94C2×C22⋊Dic17—22no—
95Q8×Dic17—22no—
96Q8×Dic17—22no—
97Q8×Dic17C2314yes—
98Q8×Dic17C2314yes—
99D4×Dic17—22no—
100D4×Dic17—22no—
101D4×Dic17—24no—
102D4×Dic17—24no—
103D4×Dic17—24no—
104D4×Dic17—24no—
105D4×Dic17C2314yes—
106D4×Dic17C2314yes—
107#10587612—24no—
108#10587612—22no—
109#10587612—22no—
110#10587612—21no—
111#10587612—21no—
112#10587612—21no—
113#10587612—21no—
114#10587612C2312yes—
115#10587612C2312yes—
116#10587612C2312yes—
117#10587612C2312yes—
118C2×C4⋊Dic17—22no—
119C2×C4⋊Dic17—22no—
120C2×C4⋊Dic17C2312yes—
121C2×C4⋊Dic17C2312yes—
122C2×#63225—22no—
123C2×#63225—22no—
124C2×C4×Dic17—24no—
125C2×C4×Dic17—22no—
126C2×C4×Dic17—22no—
127C2×C4×Dic17—21no—
128C2×C4×Dic17—21no—
129C2×C4×Dic17—22no—
130C2×C4×Dic17D411yescharacteristic
131C2×C4×Dic17D411yescharacteristic
132C2×C4×Dic17D412yes—
133C2×C4×Dic17D411yescharacteristic
134C2×C4×Dic17D411yescharacteristic
135C2×C4×Dic17C2312yes—
136C2×C4×Dic17C2311yescharacteristic
137C2×C4×Dic17C2312yes—
138C2×C4×Dic17C2311yescharacteristic
139C2×#63223—24no—
140C2×#63223C2312yes—
141C2×#63223C2312yes—
142C22×#3622C2312yes—
143#10587576—22no—
144#10587576—22no—
145#10587576C2314yes—
146#10587576C2314yes—
147#10587574—22no—
148#10587574—22no—
149#10587574C2314yes—
150#10587574C2314yes—
151#10587564—24no—
152#10587564—24no—
153#10587564—24no—
154#10587564—24no—
155C4×Dic34—24no—
156C4×Dic34—24no—
157C4×Dic34—24no—
158C4×Dic34—24no—
159C17×#103C2318yes—
160C17×#102C2318yes—
161#10587506C2318yes—
162#10587503C2318yes—
163#10587489C2318yes—
164#10587488C2318yes—
165#10587485C2318yes—
166#10587485C2318yes—
167#10587479C2318yes—
168#10587478C2318yes—
169C24×C17—21no—
170C24×C17C2×D411yescharacteristic
171#41×C17—28no—
172#41×C17—28no—
173#41×C17—24no—
174#41×C17—24no—
175#41×C17C2×Q818yes—
176#41×C17C2×Q818yescomplemented
177C2×Q8×C17—21no—
178C2×Q8×C17—22no—
179C2×Q8×C17C2×Q814yescomplemented
180C2×Q8×C17C2412yes—
181C2×D4×C17—28no—
182C2×D4×C17—22no—
183C2×D4×C17—22no—
184C2×D4×C17—21no—
185C2×D4×C17—22no—
186C2×D4×C17C2×Q814yescomplemented
187C2×D4×C17C2412yes—
188C22×C4×C17—21no—
189C22×C4×C17—28no—
190C22×C4×C17—22no—
191C22×C4×C17—22no—
192C22×C4×C17—22no—
193C22×C4×C17C2×D411yescharacteristic
194C22×C4×C17C2×D411yescharacteristic
195C22×C4×C17C2×D411yescharacteristic
196C22×C4×C17C2×Q814yes—
197C22×C4×C17#4114yes—
198C22×C4×C17C2411yescharacteristic
199C22×C4×C17C2411yescharacteristic
200C22×C4×C17C2411yescharacteristic
201C22×Dic17—22no—
202C22×Dic17—22no—
203C22×Dic17—24no—
204C22×Dic17—24no—
205C22×Dic17—44no—
206C22×Dic17—48no—
207C22×Dic17C2×D412yes—
208C22×Dic17C2×D412yes—
209C22×Dic17C2×D412yes—
210C22×Dic17C2×D412yes—
211C22×Dic17C2×D412yes—
212C22×Dic17C2×D412yes—
213C2×Dic34—24no—
214C2×Dic34—24no—
215C2×Dic34—48no—
216M16×C17—24no—
217M16×C17—24no—
218C2×C8×C17—24no—
219C2×C8×C17C2414yes—
220C4⋊C4×C17—22no—
221C4⋊C4×C17C2414yes—
222C22⋊C4×C17—22no—
223C22⋊C4×C17—22no—
224C42×C17—22no—
225C42×C17—22no—
226C22⋊Dic17—22no—
227C22⋊Dic17—22no—
228C22⋊Dic17—22no—
229C22⋊Dic17—22no—
230C22⋊Dic17—24no—
231C22⋊Dic17—24no—
232C4⋊Dic17—22no—
233C4⋊Dic17—22no—
234C4⋊Dic17—24no—
235C4⋊Dic17—24no—
236C4⋊Dic17—24no—
237C4⋊Dic17—24no—
238C4⋊Dic17C2414yes—
239C4⋊Dic17C2414yes—
240#63225—24no—
241#63225—24no—
242#63225—24no—
243#63225—24no—
244C4×Dic17—22no—
245C4×Dic17—22no—
246C4×Dic17—22no—
247C4×Dic17—22no—
248C4×Dic17—24no—
249C4×Dic17—24no—
250C4×Dic17C2×D412yes—
251C4×Dic17C2×D412yes—
252C4×Dic17C2×D412yes—
253C4×Dic17C2×D412yes—
254C4×Dic17C2×D411yescharacteristic
255C4×Dic17C2×D411yescharacteristic
256C4×Dic17C2×D411yescharacteristic
257C4×Dic17C2×D411yescharacteristic
258C4×Dic17C2412yes—
259C4×Dic17C2412yes—
260#63223—24no—
261#63223—24no—
262C2×#3622—24no—
263C2×#3622C2414yes—
264#60484—171nomaximal, Sylow
265C23×C17—24no—
266C23×C17—22no—
267C23×C17—42no—
268C23×C17—44no—
269C23×C17C22⋊Q814yes—
270C23×C17C22×D411yescharacteristic
271C23×C17C22×D411yescharacteristic
272C23×C17C22×D411yescharacteristic
273Q8×C17—24no—
274Q8×C17—22no—
275Q8×C17C22×Q814yes—
276D4×C17—28no—
277D4×C17—28no—
278D4×C17—24no—
279D4×C17—22no—
280D4×C17C22×Q814yes—
281C2×C4×C17—24no—
282C2×C4×C17—22no—
283C2×C4×C17—28no—
284C2×C4×C17—28no—
285C2×C4×C17—24no—
286C2×C4×C17—44no—
287C2×C4×C17C22⋊Q814yes—
288C2×C4×C17C22⋊Q814yes—
289C2×C4×C17C22⋊Q814yes—
290C2×C4×C17C22×D411yescharacteristic
291C2×C4×C17C22×D411yescharacteristic
292C2×C4×C17C22×D411yescharacteristic
293C2×C4×C17C22×Q812yes—
294C2×C4×C17C22×Q812yes—
295C2×C4×C17C22×Q812yes—
296C2×C4×C17C2×#4112yes—
297C2×C4×C17C2×#4112yes—
298C2×C4×C17C2×#4112yes—
299C2×C4×C17C2511yescharacteristic
300C2×Dic17—24no—
301C2×Dic17—24no—
302C2×Dic17—24no—
303C2×Dic17—24no—
304C2×Dic17—24no—
305C2×Dic17—42no—
306C2×Dic17—42no—
307C2×Dic17—42no—
308C2×Dic17—48no—
309C2×Dic17—44no—
310C2×Dic17—44no—
311C2×Dic17—48no—
312C2×Dic17C22×D412yes—
313C2×Dic17C22×D412yes—
314C2×Dic17C22×D412yes—
315C2×Dic17C22×D412yes—
316Dic34—48no—
317Dic34—48no—
318C8×C17—24no—
319#3622—24no—
320C2×#533—171no—
321C2×C4×#41—171no—
322#3080—174no—
323#3079—174no—
324#3078—174no—
325#3077—174no—
326#3076—178no—
327#2911—171no—
328#2911—171no—
329C2×#423—171no—
330#2896—171no—
331#2896D1711yescharacteristic
332C22×C17—22no—
333C22×C17—22no—
334C22×C17—22no—
335C22×C17—24no—
336C22×C17—44no—
337C22×C17—48no—
338C22×C17—44no—
339C22×C17C2×C22⋊Q812yes—
340C22×C17C2×C22⋊Q812yes—
341C22×C17C2×C22⋊Q812yes—
342C22×C17C23×D411yescharacteristic
343C4×C17—24no—
344C4×C17—44no—
345C4×C17C2×C22⋊Q812yes—
346C4×C17C2×C22⋊Q812yes—
347C4×C17C2×C22⋊Q812yes—
348C4×C17C23×Q811yescharacteristic
349C4×C17C22×#4111yescharacteristic
350Dic17—22no—
351Dic17—22no—
352Dic17—22no—
353Dic17—44no—
354Dic17—44no—
355Dic17#57514yes—
356C22×#41C2×D1711yescharacteristic
357C22×M16—171no—
358C22×M16C2×D1711yescharacteristic
359#533—174no—
360#533—174no—
361#533—341no—
362#533—341no—
363#533—341no—
364#533—341no—
365C2×C4⋊Q8—172no—
366C2×#125—172no—
367C2×C22⋊Q8—342no—
368C4×#41—174no—
369C4×#41—172no—
370C4×#41—172no—
371C4×#41—342no—
372C4×#41—341no—
373C4×#41—341no—
374C2×C4×Q8—172no—
375C2×C4×Q8—342no—
376C2×C4×D4—172no—
377C2×C4×D4—342no—
378C2×#117—171no—
379C2×#117—171no—
380C2×#117—341no—
381C2×#117C2×D1711yescharacteristic
382C22×C42—171no—
383C22×C42—341no—
384#479—178no—
385#479—178no—
386#478—178no—
387#478—178no—
388#477—178no—
389#476—178no—
390#475—178no—
391#474—178no—
392#428—174no—
393#428—174no—
394#428—174no—
395#428—174no—
396#427—174no—
397#427—174no—
398#423—174no—
399#423—172no—
400#423—172no—
401C2×C4⋊C8—174no—
402#419—172no—
403#419C2×D1712yes—
404#418—172no—
405#418C2×D1712yes—
406#417—174no—
407#417C2×D1714yes—
408#416—174no—
409#416C2×D1714yes—
410C2×C17—22no—
411C2×C17—22no—
412C2×C17—22no—
413C2×C17—44no—
414C2×C17C22×C22⋊Q811yescharacteristic
415C2×C17C2×#57512yes—
416C2×#41—21no—
417C2×#41—21no—
418C2×#41—24no—
419C2×#41Dic3418yescomplemented
420C2×#41C22×D1712yes—
421C2×#41C22×D1712yes—
422C22×Q8—342no—
423C22×Q8C22×D1711yescharacteristic
424C22×D4—21no—
425C22×D4C22×D1711yescharacteristic
426C23×C4—21no—
427C23×C4—172no—
428C23×C4—342no—
429C23×C4C22×D1711yescharacteristic
430C2×M16—24no—
431C2×M16—172no—
432C2×M16—172no—
433C2×M16—344no—
434C2×M16C22×D1712yes—
435C2×M16C22×D1712yes—
436C22×C8—172no—
437C22×C8C22×D1712yes—
438C4⋊Q8—174no—
439C4⋊Q8—174no—
440C4⋊Q8—342no—
441C4⋊Q8—342no—
442#125—174no—
443#125—174no—
444#125—342no—
445#125—342no—
446C22⋊Q8—344no—
447C22⋊Q8—344no—
448C22⋊Q8—344no—
449C22⋊Q8—344no—
450C4×Q8—174no—
451C4×Q8—174no—
452C4×Q8—344no—
453C4×Q8—344no—
454C4×Q8—344no—
455C4×Q8—344no—
456C4×Q8—342no—
457C4×Q8—342no—
458C4×D4—174no—
459C4×D4—174no—
460C4×D4—342no—
461C4×D4—342no—
462C4×D4—344no—
463C4×D4—344no—
464C4×D4—344no—
465C4×D4—344no—
466#117—21no—
467#117—21no—
468#117—172no—
469#117—172no—
470#117—172no—
471#117—172no—
472#117—342no—
473#117—342no—
474#117—344no—
475#117—341no—
476#117—341no—
477#117—341no—
478#117—341no—
479#117C22×D1712yes—
480#117C22×D1712yes—
481C2×C4⋊C4—172no—
482C2×C4⋊C4—172no—
483C2×C4⋊C4—342no—
484C2×C4⋊C4—342no—
485C2×C4⋊C4—342no—
486C2×C4⋊C4—342no—
487C2×C4⋊C4C22×D1712yes—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—342no—
490C2×C22⋊C4—341no—
491C2×C22⋊C4—341no—
492C2×C42—21no—
493C2×C42—171no—
494C2×C42—172no—
495C2×C42—171no—
496C2×C42—171no—
497C2×C42—171no—
498C2×C42—172no—
499C2×C42—171no—
500C2×C42—171no—
501C2×C42—172no—
502C2×C42—342no—
503C2×C42—342no—
504C2×C42—344no—
505C2×C42—342no—
506C2×C42—341no—
507C2×C42—341no—
508#107—178no—
509#107—178no—
510#106—178no—
511#106—178no—
512C4⋊C8—178no—
513C4⋊C8—178no—
514#103—178no—
515#103C22×D1718yes—
516#102—178no—
517#102C22×D1718yes—
518C17#6048411yescharacteristic, complemented, Sylow
519C24—21no—
520C24D4×D1711yescharacteristic
521#41—24no—
522#41—24no—
523#41—28no—
524#41—28no—
525#41C2×Dic3418yes—
526#41C2×Dic3418yescomplemented
527C2×Q8—21no—
528C2×Q8—22no—
529C2×Q8—344no—
530C2×Q8—344no—
531C2×Q8—688no—
532C2×Q8C2×Dic3414yescomplemented
533C2×Q8C23×D1712yes—
534C2×D4—22no—
535C2×D4—22no—
536C2×D4—28no—
537C2×D4—21no—
538C2×D4—22no—
539C2×D4C2×Dic3414yescomplemented
540C2×D4C23×D1712yes—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—28no—
545C22×C4—22no—
546C22×C4—172no—
547C22×C4—172no—
548C22×C4—172no—
549C22×C4—172no—
550C22×C4—172no—
551C22×C4—172no—
552C22×C4—344no—
553C22×C4—344no—
554C22×C4—342no—
555C22×C4—342no—
556C22×C4—684no—
557C22×C4—688no—
558C22×C4C2×Dic3414yes—
559C22×C4D4×D1711yescharacteristic
560C22×C4D4×D1711yescharacteristic
561C22×C4D4×D1711yescharacteristic
562C22×C4#6325414yes—
563C22×C4C23×D1711yescharacteristic
564C22×C4C23×D1711yescharacteristic
565C22×C4C23×D1711yescharacteristic
566M16—24no—
567M16—24no—
568M16—344no—
569M16—344no—
570C2×C8—24no—
571C2×C8—174no—
572C2×C8—344no—
573C2×C8C23×D1714yes—
574C4⋊C4—22no—
575C4⋊C4—174no—
576C4⋊C4—174no—
577C4⋊C4—344no—
578C4⋊C4—344no—
579C4⋊C4—344no—
580C4⋊C4—344no—
581C4⋊C4—344no—
582C4⋊C4—344no—
583C4⋊C4—344no—
584C4⋊C4—344no—
585C4⋊C4—342no—
586C4⋊C4—342no—
587C4⋊C4C23×D1714yes—
588C22⋊C4—22no—
589C22⋊C4—22no—
590C22⋊C4—344no—
591C22⋊C4—344no—
592C22⋊C4—342no—
593C22⋊C4—342no—
594C22⋊C4—342no—
595C22⋊C4—342no—
596C42—22no—
597C42—22no—
598C42—171no—
599C42—171no—
600C42—171no—
601C42—171no—
602C42—172no—
603C42—172no—
604C42—172no—
605C42—172no—
606C42—172no—
607C42—172no—
608C42—344no—
609C42—344no—
610C42—342no—
611C42—342no—
612C42—342no—
613C42—342no—
614C23—24no—
615C23—22no—
616C23—42no—
617C23—44no—
618C23#1058756414yes—
619C23C2×D4×D1711yescharacteristic
620C23C2×D4×D1711yescharacteristic
621C23C2×D4×D1711yescharacteristic
622Q8—24no—
623Q8—22no—
624Q8—688no—
625Q8—688no—
626Q8C22×Dic3414yes—
627D4—28no—
628D4—28no—
629D4—24no—
630D4—22no—
631D4C22×Dic3414yes—
632C2×C4—24no—
633C2×C4—22no—
634C2×C4—28no—
635C2×C4—28no—
636C2×C4—24no—
637C2×C4—44no—
638C2×C4—172no—
639C2×C4—172no—
640C2×C4—172no—
641C2×C4—172no—
642C2×C4—344no—
643C2×C4—344no—
644C2×C4—344no—
645C2×C4—344no—
646C2×C4—344no—
647C2×C4—688no—
648C2×C4—682no—
649C2×C4—682no—
650C2×C4—682no—
651C2×C4—688no—
652C2×C4—684no—
653C2×C4—684no—
654C2×C4#1058756414yes—
655C2×C4#1058756414yes—
656C2×C4#1058756414yes—
657C2×C4C22×Dic3412yes—
658C2×C4C22×Dic3412yes—
659C2×C4C22×Dic3412yes—
660C2×C4C2×D4×D1711yescharacteristic
661C2×C4C2×D4×D1711yescharacteristic
662C2×C4C2×D4×D1711yescharacteristic
663C2×C4C2×#6325412yes—
664C2×C4C2×#6325412yes—
665C2×C4C2×#6325412yes—
666C2×C4C24×D1711yescharacteristic
667C8—24no—
668C8—344no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—24no—
673C22—44no—
674C22—48no—
675C22—44no—
676C22C2×#1058756412yes—
677C22C2×#1058756412yes—
678C22C2×#1058756412yes—
679C22C22×D4×D1711yescharacteristic
680C4—24no—
681C4—44no—
682C4—174no—
683C4—342no—
684C4—342no—
685C4—342no—
686C4—684no—
687C4—684no—
688C4C2×#1058756412yes—
689C4C2×#1058756412yes—
690C4C2×#1058756412yes—
691C4C23×Dic3411yescharacteristic
692C4C22×#6325411yescharacteristic
693C2—22no—
694C2—22no—
695C2—22no—
696C2—44no—
697C2C22×#1058756411yescharacteristic
698C2D17×#57512yes—
subgroupG/H
centerC2×C4C2×D4×D17
commutator, cosocleC2×C4×C17C25
FrattiniC2×C4C24×D17
FittingC17×#2896C2
socleC22×C17C23×D4
prime radicalC22×#41×C17C22
hypercenter#2896D17
hypocenterC17#60484
LCSG ▷ C2×C4×C17 ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #2896

Complements

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

NH ≅ G/Ntype
1. C2×#11763362C2semidirect
3. #14538604C2semidirect
4. #14538595C2semidirect
5. #14538586C2semidirect
6. #14538578C2semidirect
7. #14538568C2semidirect
8. #14537374C2semidirect
9. #14537373C2semidirect
10. C2×#11762832C2semidirect
19. #11763362C22semidirect
20. C2×#10587574C22semidirect
21. C2×#10587576C22semidirect
38. #11763118C22semidirect
39. #11763114C22semidirect
40. #11763111C22semidirect
41. #11763107C22semidirect
42. #11763102C22semidirect
43. #11763097C22semidirect
44. #11763092C22semidirect
45. #11763087C22semidirect
48. #11762851C22semidirect
49. #11762849C22semidirect
50. #11762847C22semidirect
51. #11762845C22semidirect
53. #11762832C22semidirect
54. #11762832C22semidirect
55. C2×#10587485C22semidirect
70. C2×#41×C17Q8semidirect
176. #41×C17C2×Q8semidirect
179. C2×Q8×C17C2×Q8semidirect
186. C2×D4×C17C2×Q8semidirect
419. C2×#41Dic34semidirect
518. C17#60484semidirect
526. #41C2×Dic34semidirect
532. C2×Q8C2×Dic34semidirect
539. C2×D4C2×Dic34semidirect

Maximal subgroups

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

subgroupindex
C2×#117633622
C2×#41×Dic172
#145386042
#145385952
#145385862
#145385782
#145385682
#145373742
#145373732
C2×#117628322
#145373032
C17×#28962
#6048417