Finite Group Databasebeta

← #11865879

Subgroups — #11865879

Order 1152.

1245 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64117C211yesmaximal, characteristic, complemented
2#10595029C211yesmaximal, characteristic, complemented
3C2×#63894C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5133C211yesmaximal, characteristic, complemented
6C3×#5118C211yesmaximal, characteristic, complemented
7#10591106C211yesmaximal, characteristic, complemented
8#10590860C212yesmaximal, complemented
9#10590770C212yesmaximal, complemented
10#10590765C212yesmaximal, complemented
11#10590760C212yesmaximal, complemented
12#79055—31nomaximal
13#78910—31nomaximal
14C2×#3828C2211yescharacteristic
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C2×C3×#235C2211yescharacteristic
17C22×#624—21no—
18C2×C32×M16C2211yescharacteristic
19#64117—24no—
20C2×#3745C2212yes—
21C2×#3744C2212yes—
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×C4×Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25#63978—21no—
26#63978—21no—
27C2×#3722—21no—
28#63911C2211yescharacteristic, complemented
29C4×#626—21no—
30C4×#626—21no—
31#63894—21no—
32#63894—21no—
33#63894C2212yes—
34#63894C2212yes—
35#63866C2211yescharacteristic, complemented
36#63864C2211yescharacteristic, complemented
37#63860C2211yescharacteristic, complemented
38C2×#3717C2212yes—
39#63825—24no—
40C2×#3714C2212yes—
41C3×#821C2212yescomplemented
42C3×#816C2212yescomplemented
43C3×Dic3⋊C8C2212yescomplemented
44C3×Dic3⋊C8C2212yescomplemented
45#63567C2212yescomplemented
46#63564C2212yescomplemented
47#5832—31no—
48C2×#949—31no—
49C2×#908—31no—
50C2×#908—31no—
51C2×#908—31no—
52C2×#908—61no—
53C2×#893—31no—
54#5477—31no—
55C2×C4×D12—31no—
56C3×#423—31no—
57C3×#417—31no—
58#5133—31no—
59#5133D311yescharacteristic, complemented
60#5118D311yescharacteristic, complemented
61#4966—31no—
62#4844—32no—
63#4844—32no—
64#4843—32no—
65#4841—32no—
66#4819—32no—
67#4818—32no—
68#4787—32no—
69#4786—32no—
70C23×C3⋊D3—21no—
71C22×C32×C4C2311yescharacteristic
72C2×#638—21no—
73#3828—22no—
74#3828—22no—
75C2×C4⋊(C3⋊D3)—21no—
76C2×C4⋊(C3⋊D3)—22no—
77C2×C4⋊(C3⋊D3)D414yescomplemented
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4⋊(C3⋊D3)C2312yes—
80C2×C4×C3⋊D3—21no—
81C2×#634C2311yescharacteristic
82C2×C3×#67—21no—
83C22×C3×Dic3—21no—
84C22×C3×Dic3D411yescharacteristic
85C22×C3×Dic3D411yescharacteristic
86C3×#235—22no—
87C3×#235—22no—
88C2×C3×D12C2311yescharacteristic
89C2×C3×C4×D3—21no—
90C2×C3×Dic6C2311yescharacteristic
91C2×#626—21no—
92C2×#626—21no—
93C2×#624—22no—
94C2×#624—22no—
95C2×#624—44no—
96C32×M16—22no—
97C2×C32×C8C2312yes—
98#3745—24no—
99#3744—24no—
100C3×C4⋊Dic3—21no—
101C3×C4⋊Dic3C2312yes—
102C3×C4×Dic3D411yescharacteristic
103C3×C4×Dic3D411yescharacteristic
104C3×C4×Dic3C2311yescharacteristic
105C3×C4×Dic3C2311yescharacteristic
106C3×#208—22no—
107C2×C3×C3⋊C8C2312yes—
108Dic3⋊Dic3—21no—
109Dic3⋊Dic3—21no—
110#3722—21no—
111#3722—21no—
112#3722—22no—
113#3722—22no—
114(C2×D3)⋊Dic3—21no—
115(C2×D3)⋊Dic3—21no—
116#3717—24no—
117#3714—24no—
118#3036—91noSylow
119C2×C3×#41—31no—
120C2×#235—31no—
121C2×#235—31no—
122C2×#235—61no—
123C2×#235C2×D311yescharacteristic
124C22×D12—31no—
125C22×D12—31no—
126C22×D12—61no—
127C22×C4×D3—61no—
128C22×C4×D3—61no—
129C2×C3×M16—21no—
130C2×C3×M16—31no—
131C2×C3×M16C2×D311yescharacteristic
132C2×C3×M16C2×D311yescharacteristic
133C2×C3×C4⋊C4—31no—
134C2×C3×C42—31no—
135#949—64no—
136#947—31no—
137#944—31no—
138C2×#215—32no—
139#940—31no—
140#939—61no—
141#939—61no—
142#936—31no—
143C2×#213—32no—
144#930—61no—
145#930—61no—
146C4×#67—61no—
147C4×#67—61no—
148C2×(C2×D3)⋊C4—61no—
149C2×(C2×D3)⋊C4—61no—
150C2×C4⋊Dic3C2×D311yescharacteristic
151C2×C4×Dic3C2×D311yescharacteristic
152C2×#208C2×D311yescharacteristic
153#908—64no—
154#908—64no—
155#908—68no—
156#908—64no—
157C2×D24—32no—
158C2×D24—32no—
159C2×D24—32no—
160C2×D24—62no—
161C2×#204—32no—
162C2×#204—32no—
163C2×#204—32no—
164C2×#204—62no—
165#893—32no—
166#893—32no—
167#893—61no—
168#893—61no—
169#875—31no—
170#875—31no—
171#874—31no—
172C4×D12—32no—
173C4×D12—32no—
174C4×D12—61no—
175C4×D12—61no—
176C4×D12—61no—
177C4×D12—61no—
178#869—31no—
179C3×C4⋊C8—32no—
180C3×C4⋊C8—32no—
181C3×#103—32no—
182C3×#102—32no—
183#821—32no—
184#821C2×D312yescomplemented
185#816—32no—
186#816C2×D312yescomplemented
187Dic3⋊C8C2×D312yescomplemented
188Dic3⋊C8C2×D312yescomplemented
189#810—32no—
190#809—32no—
191C23×C32C2×D411yescharacteristic
192C22×C3⋊D3—24no—
193C22×C3⋊D3—22no—
194C22×C3⋊D3—21no—
195C22×C3⋊D3—42no—
196C22×C3⋊D3—42no—
197C22×C3×D3—21no—
198C2×C32×C4C2×D411yescharacteristic
199C2×C32×C4C2×D412yes—
200C2×C32×C4#4112yes—
201C2×C32×C4C2411yescharacteristic
202#638—42no—
203C2×C3⋊Dic3—21no—
204C4⋊(C3⋊D3)—21no—
205C4⋊(C3⋊D3)—24no—
206C4⋊(C3⋊D3)—22no—
207C4⋊(C3⋊D3)—21no—
208C4⋊(C3⋊D3)C2×D414yes—
209C4×C3⋊D3—42no—
210#634—21no—
211#634—21no—
212C3×#67—42no—
213C2×C3×Dic3—22no—
214C2×C3×Dic3—21no—
215C2×C3×Dic3—22no—
216C2×C3×Dic3—41no—
217C2×C3×Dic3—42no—
218C2×C3×Dic3C2×D411yescharacteristic
219C2×C3×Dic3C2×D411yescharacteristic
220C2×C3×Dic3C2×D411yescharacteristic
221C2×C3×Dic3C2×D411yescharacteristic
222C3×D12—21no—
223C3×D12—21no—
224C3×C4×D3—42no—
225C3×Dic6—21no—
226C3×Dic6—21no—
227#626—42no—
228#626—42no—
229#624—44no—
230#624—44no—
231C32×C8—22no—
232C3×C3⋊C8—22no—
233C2×AGL(1,ℤ/8)—91no—
234C2×AGL(1,ℤ/8)—91no—
235#532—91no—
236C2×C4×D4—91no—
237#463—92no—
238#463—92no—
239#461—92no—
240#459—92no—
241#423—31no—
242#417—31no—
243#417—91no—
244C23×D3—61no—
245C23×D3—61no—
246C23×D3—121no—
247C3×#41—62no—
248C3×#41—62no—
249C2×C3×Q8—31no—
250C2×C3×D4—31no—
251C2×C3×D4—61no—
252C22×C3×C4—21no—
253C22×C3×C4—31no—
254C22×C3×C4—31no—
255C22×C3×C4—61no—
256C22×C3×C4—61no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C2×#67—21no—
260C2×#67—61no—
261C2×#67—61no—
262C2×#67—61no—
263C2×#67—61no—
264C2×#67—121no—
265C22×Dic3—21no—
266C22×Dic3D1211yescharacteristic
267C22×Dic3D1211yescharacteristic
268#235—22no—
269#235—22no—
270#235—64no—
271#235—62no—
272#235—62no—
273#235—62no—
274#235—62no—
275#235—122no—
276C2×D12—34no—
277C2×D12—34no—
278C2×D12—32no—
279C2×D12—32no—
280C2×D12—31no—
281C2×D12—31no—
282C2×D12—62no—
283C2×D12—61no—
284C2×D12—64no—
285C2×D12—61no—
286C2×D12—62no—
287C2×D12—61no—
288C2×D12—62no—
289C2×D12—61no—
290C2×D12—61no—
291C2×D12—122no—
292C2×D12—121no—
293C2×D12C22×D311yescharacteristic
294C2×C4×D3—21no—
295C2×C4×D3—62no—
296C2×C4×D3—62no—
297C2×C4×D3—61no—
298C2×C4×D3—61no—
299C2×C4×D3—62no—
300C2×C4×D3—62no—
301C2×C4×D3—121no—
302C2×C4×D3—124no—
303C2×C4×D3—124no—
304C2×Dic6—31no—
305C2×Dic6—31no—
306C2×Dic6—61no—
307C2×Dic6C22×D311yescharacteristic
308C3×M16—24no—
309C3×M16—22no—
310C3×M16—22no—
311C3×M16—62no—
312C2×C3×C8—22no—
313C2×C3×C8—32no—
314C2×C3×C8C22×D312yes—
315C2×C3×C8C22×D312yes—
316C3×C4⋊C4—32no—
317C3×C4⋊C4—61no—
318C3×C42—31no—
319C3×C42—31no—
320C3×C42—31no—
321C3×C42—31no—
322#217—61no—
323#217—61no—
324#215—64no—
325#213—64no—
326(C2×D3)⋊C4—62no—
327(C2×D3)⋊C4—62no—
328(C2×D3)⋊C4—61no—
329(C2×D3)⋊C4—61no—
330(C2×D3)⋊C4—61no—
331(C2×D3)⋊C4—61no—
332(C2×D3)⋊C4—62no—
333(C2×D3)⋊C4—62no—
334(C2×D3)⋊C4—61no—
335(C2×D3)⋊C4—61no—
336C4⋊Dic3—21no—
337C4⋊Dic3—61no—
338C4⋊Dic3—61no—
339C4⋊Dic3C22×D312yes—
340Dic3⋊C4—61no—
341Dic3⋊C4—61no—
342C4×Dic3D1211yescharacteristic
343C4×Dic3D1211yescharacteristic
344C4×Dic3C22×D311yescharacteristic
345C4×Dic3C22×D311yescharacteristic
346#208—22no—
347C2×C3⋊C8C22×D312yes—
348D24—64no—
349D24—64no—
350D24—68no—
351D24—64no—
352#204—64no—
353#204—64no—
354#204—68no—
355#204—64no—
356C22×C32—21no—
357C22×C32—21no—
358C22×C32#12112yes—
359C22×C32C22×D411yescharacteristic
360C2×C3⋊D3—24no—
361C2×C3⋊D3—41no—
362C2×C3⋊D3—48no—
363C2×C3⋊D3—42no—
364C2×C3⋊D3—42no—
365C2×C3⋊D3—41no—
366C2×C3⋊D3—41no—
367C2×C3×D3—41no—
368C2×C3×D3—41no—
369C2×C3×D3—41no—
370C32×C4#12112yes—
371C32×C4C22×D411yescharacteristic
372C32×C4C2×#4111yescharacteristic
373C3⋊Dic3—41no—
374C3×Dic3—21no—
375C3×Dic3—21no—
376C3×Dic3—21no—
377C3×Dic3—41no—
378C3×Dic3—42no—
379C3×Dic3AGL(1,ℤ/8)12yescomplemented
380C2×#41—31no—
381C2×#41—91no—
382C22×D4—91no—
383C23×C4—181no—
384AGL(1,ℤ/8)—184no—
385AGL(1,ℤ/8)—184no—
386C2×SD16—92no—
387C2×SD16—92no—
388C2×D8—92no—
389C2×D8—92no—
390C2×M16—31no—
391C2×M16D3211yescharacteristic
392C4⋊Q8—91no—
393#127—91no—
394#124—91no—
395#124—91no—
396#121—181no—
397#121—181no—
398C4×D4—92no—
399C4×D4—92no—
400C4×D4—181no—
401C4×D4—181no—
402C4×D4—181no—
403C4×D4—181no—
404C2×C4⋊C4—31no—
405C2×C22⋊C4—181no—
406C2×C42—31no—
407C4⋊C8—32no—
408C4⋊C8—32no—
409#103—32no—
410#103—92no—
411#102—32no—
412#102—92no—
413C23×C3—21no—
414C23×C3—61no—
415C23×C3C2×D1211yescharacteristic
416C23×C3D3×D411yescharacteristic
417C22×D3—21no—
418C22×D3—64no—
419C22×D3—64no—
420C22×D3—62no—
421C22×D3—62no—
422C22×D3—61no—
423C22×D3—61no—
424C22×D3—121no—
425C22×D3—122no—
426C22×D3—124no—
427C22×D3—122no—
428C22×D3—122no—
429C22×D3—122no—
430C22×D3—122no—
431C22×D3—242no—
432C22×D3—242no—
433C3×Q8—61no—
434C3×Q8—61no—
435C3×D4—61no—
436C3×D4—61no—
437C3×D4—122no—
438C2×C3×C4—21no—
439C2×C3×C4—22no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—31no—
445C2×C3×C4—31no—
446C2×C3×C4—62no—
447C2×C3×C4—61no—
448C2×C3×C4—62no—
449C2×C3×C4—121no—
450C2×C3×C4—122no—
451C2×C3×C4—122no—
452C2×C3×C4C2×D1211yescharacteristic
453C2×C3×C4#23512yes—
454C2×C3×C4D3×D411yescharacteristic
455C2×C3×C4D3×D412yes—
456C2×C3×C4D3×D412yes—
457C2×C3×C4#23912yes—
458C2×C3×C4C23×D311yescharacteristic
459C2×C3×C4C23×D311yescharacteristic
460#67—42no—
461#67—122no—
462#67—124no—
463#67—122no—
464#67—122no—
465#67—122no—
466C2×Dic3—22no—
467C2×Dic3—22no—
468C2×Dic3—21no—
469C2×Dic3—41no—
470C2×Dic3—42no—
471C2×Dic3—61no—
472C2×Dic3—61no—
473C2×Dic3—121no—
474C2×Dic3C2×D1211yescharacteristic
475C2×Dic3C2×D1211yescharacteristic
476C2×Dic3C2×D1211yescharacteristic
477C2×Dic3C2×D1211yescharacteristic
478D12—21no—
479D12—21no—
480D12—34no—
481D12—34no—
482D12—64no—
483D12—62no—
484D12—64no—
485D12—64no—
486D12—62no—
487D12—61no—
488D12—61no—
489D12—61no—
490D12—62no—
491D12—61no—
492D12—122no—
493D12—124no—
494D12—121no—
495D12—122no—
496D12—122no—
497C4×D3—42no—
498C4×D3—124no—
499C4×D3—124no—
500C4×D3—124no—
501C4×D3—124no—
502C4×D3—122no—
503C4×D3—122no—
504C4×D3—124no—
505Dic6—21no—
506Dic6—21no—
507Dic6—62no—
508Dic6—61no—
509Dic6—61no—
510Dic6—61no—
511Dic6—61no—
512Dic6—121no—
513C3×C8—24no—
514C3×C8—22no—
515C3×C8—22no—
516C3×C8—62no—
517C3⋊C8—22no—
518C2×C32—22no—
519C2×C32C2×#12111yescharacteristic
520C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
521C2×C32#57511yescharacteristic
522C3⋊D3—44no—
523C3⋊D3—81no—
524C3×D3—81no—
525C24—181no—
526#41—62no—
527#41—62no—
528#41—182no—
529#41—182no—
530C2×Q8—31no—
531C2×Q8—91no—
532C2×D4—31no—
533C2×D4—61no—
534C2×D4—92no—
535C2×D4—91no—
536C2×D4—94no—
537C2×D4—181no—
538C2×D4—181no—
539C2×D4—181no—
540C2×D4—182no—
541C2×D4—181no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—61no—
545C22×C4—61no—
546C22×C4—182no—
547C22×C4—182no—
548C22×C4—181no—
549C22×C4—364no—
550C22×C4C2×D3211yescharacteristic
551SD16—184no—
552SD16—184no—
553D8—184no—
554D8—184no—
555M16—22no—
556M16—62no—
557C2×C8—32no—
558C2×C8C2×D3212yes—
559C4⋊C4—32no—
560C4⋊C4—61no—
561C4⋊C4—181no—
562C4⋊C4—181no—
563C22⋊C4—182no—
564C22⋊C4—182no—
565C22⋊C4—181no—
566C22⋊C4—181no—
567C22⋊C4—181no—
568C22⋊C4—181no—
569C42—31no—
570C42—31no—
571C42—31no—
572C42—31no—
573C22×C3—21no—
574C22×C3—21no—
575C22×C3—21no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—22no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—121no—
582C22×C3—121no—
583C22×C3—121no—
584C22×C3#88412yes—
585C22×C3#89512yes—
586C22×C3C22×D1211yescharacteristic
587C22×C3C2×D3×D411yescharacteristic
588C2×D3—41no—
589C2×D3—41no—
590C2×D3—41no—
591C2×D3—64no—
592C2×D3—64no—
593C2×D3—124no—
594C2×D3—128no—
595C2×D3—128no—
596C2×D3—122no—
597C2×D3—122no—
598C2×D3—122no—
599C2×D3—122no—
600C2×D3—122no—
601C2×D3—121no—
602C2×D3—121no—
603C2×D3—121no—
604C2×D3—121no—
605C2×D3—121no—
606C2×D3—121no—
607C2×D3—242no—
608C2×D3—242no—
609C2×D3—241no—
610C2×D3—241no—
611C2×D3—248no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—22no—
615C3×C4—32no—
616C3×C4—61no—
617C3×C4—61no—
618C3×C4—61no—
619C3×C4—122no—
620C3×C4—121no—
621C3×C4#88412yes—
622C3×C4#89512yes—
623C3×C4C2×#23511yescharacteristic
624C3×C4C2×D3×D411yescharacteristic
625C3×C4C2×D3×D411yescharacteristic
626C3×C4C2×#23911yescharacteristic
627Dic3—21no—
628Dic3—21no—
629Dic3—21no—
630Dic3—41no—
631Dic3—42no—
632Dic3—122no—
633Dic3—121no—
634Dic3—121no—
635Dic3#90812yescomplemented
636C32#303611yescharacteristic, complemented, Sylow
637C23—61no—
638C23—182no—
639C23—184no—
640C23—181no—
641C23—362no—
642C23—362no—
643C23D3×D1211yescharacteristic
644Q8—61no—
645Q8—61no—
646Q8—181no—
647Q8—181no—
648D4—61no—
649D4—61no—
650D4—94no—
651D4—122no—
652D4—182no—
653D4—181no—
654D4—181no—
655D4—184no—
656D4—362no—
657D4—362no—
658D4—362no—
659C2×C4—31no—
660C2×C4—31no—
661C2×C4—31no—
662C2×C4—31no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—121no—
667C2×C4—122no—
668C2×C4—122no—
669C2×C4—181no—
670C2×C4—364no—
671C2×C4—364no—
672C2×C4—362no—
673C2×C4#379912yes—
674C2×C4D3×D1211yescharacteristic
675C2×C4#381112yes—
676C2×C4C22×D3211yescharacteristic
677C8—22no—
678C8—62no—
679C2×C3—22no—
680C2×C3—22no—
681C2×C3—21no—
682C2×C3—21no—
683C2×C3—21no—
684C2×C3—42no—
685C2×C3—241no—
686C2×C3C2×#88411yescharacteristic
687C2×C3C2×#89511yescharacteristic
688C2×C3C2×#90811yescharacteristic
689C2×C3#574811yescharacteristic
690C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
691C2×C3#577711yescharacteristic
692D3—81no—
693D3—124no—
694D3—124no—
695D3—244no—
696D3—242no—
697D3—241no—
698D3—241no—
699C22—21no—
700C22—21no—
701C22—121no—
702C22—121no—
703C22—121no—
704C22—184no—
705C22—368no—
706C22—362no—
707C22—362no—
708C22—361no—
709C22—361no—
710C22—361no—
711C22#6391012yes—
712C22C2×D3×D1211yescharacteristic
713C4—32no—
714C4—61no—
715C4—61no—
716C4—61no—
717C4—122no—
718C4—121no—
719C4—361no—
720C4#6391012yes—
721C4C2×#379911yescharacteristic
722C4C2×#381111yescharacteristic
723C3—21no—
724C3#7891011yescharacteristic, complemented
725C3#7905511yescharacteristic, complemented
726C2—22no—
727C2—241no—
728C2—364no—
729C2—721no—
730C2D3×#90811yescharacteristic
731C2#1059471111yescharacteristic
732C2C2×#6391011yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
hypercenterC2×M16D32
hypocenterC32#3036
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. C2×#64117C2semidirect
2. #10595029C2semidirect
3. C2×#63894C2semidirect
4. C2×#63825C2semidirect
5. C3×#5133C2semidirect
6. C3×#5118C2semidirect
7. #10591106C2semidirect
8. #10590860C2semidirect
9. #10590770C2semidirect
10. #10590765C2semidirect
11. #10590760C2semidirect
28. #63911C22semidirect
35. #63866C22semidirect
36. #63864C22semidirect
37. #63860C22semidirect
41. C3×#821C22semidirect
42. C3×#816C22semidirect
43. C3×Dic3⋊C8C22semidirect
44. C3×Dic3⋊C8C22semidirect
45. #63567C22semidirect
46. #63564C22semidirect
59. #5133D3semidirect
60. #5118D3semidirect
77. C2×C4⋊(C3⋊D3)D4semidirect
184. #821C2×D3semidirect
186. #816C2×D3semidirect
187. Dic3⋊C8C2×D3semidirect
188. Dic3⋊C8C2×D3semidirect
379. C3×Dic3AGL(1,ℤ/8)semidirect
635. Dic3#908semidirect
636. C32#3036semidirect
724. C3#78910semidirect
725. C3#79055semidirect

Maximal subgroups

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

subgroupindex
C2×#641172
#105950292
C2×#638942
C2×#638252
C3×#51332
C3×#51182
#105911062
#105908602
#105907702
#105907652
#105907602
#790553
#789103