Finite Group Databasebeta

← #11899719

Subgroups — #11899719

Order 1152.

765 conjugacy classes of subgroups.

The subgroup lattice has 763 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594768C211yesmaximal, characteristic, complemented
2#10594734C211yesmaximal, characteristic, complemented
3C3⋊D3×SD32C211yesmaximal, characteristic, complemented
4C3×#4916C211yesmaximal, characteristic, complemented
5C3×D3×SD32C211yesmaximal, characteristic, complemented
6#10591050C211yesmaximal, characteristic, complemented
7#10591047C211yesmaximal, characteristic, complemented
8#10591038C211yesmaximal, characteristic, complemented
9#10591036C211yesmaximal, characteristic, complemented
10#10591031C211yesmaximal, characteristic, complemented
11#10591028C211yesmaximal, characteristic, complemented
12#10590245C211yesmaximal, characteristic, complemented
13#10590242C211yesmaximal, characteristic, complemented
14D3×#800C211yesmaximal, characteristic, complemented
15#10590227C211yesmaximal, characteristic, complemented
16#82032—31nomaximal
17#82024—31nomaximal
18#64315—21no—
19#64314—21no—
20Q16×C3⋊D3C2211yescharacteristic, complemented
21D8×C3⋊D3C2211yescharacteristic
22C3×#919C2211yescharacteristic, complemented
23C3×D3×Q16C2211yescharacteristic, complemented
24C3×#912C2211yescharacteristic
25C3×D3×D8C2211yescharacteristic
26#63951—21no—
27#63946—21no—
28#63943—21no—
29#63937—21no—
30#63934—21no—
31#63925—21no—
32#63810C2211yescharacteristic
33#63810C2211yescharacteristic, complemented
34#63808C2211yescharacteristic
35#63807C2211yescharacteristic, complemented
36#63803C2211yescharacteristic
37D3×Dic12C2211yescharacteristic, complemented
38D3×D24C2211yescharacteristic
39C32×SD32C2211yescharacteristic, complemented
40#63655C2211yescharacteristic, complemented
41#63654C2211yescharacteristic, complemented
42#63627C2211yescharacteristic, complemented
43C16×C3⋊D3C2211yescharacteristic, complemented
44C3×#829C2211yescharacteristic, complemented
45C3×#828C2211yescharacteristic, complemented
46C3×#827C2211yescharacteristic, complemented
47C3×#826C2211yescharacteristic, complemented
48C3×#800C2211yescharacteristic, complemented
49C3×#800C2211yescharacteristic, complemented
50C3×D3×C16C2211yescharacteristic, complemented
51C3×D3×C16C2211yescharacteristic, complemented
52#63551C2211yescharacteristic, complemented
53#63550C2211yescharacteristic, complemented
54#63549C2211yescharacteristic, complemented
55#63548C2211yescharacteristic, complemented
56#63546C2211yescharacteristic, complemented
57#63545C2211yescharacteristic, complemented
58#63544C2211yescharacteristic, complemented
59#63543C2211yescharacteristic, complemented
60#63543C2211yescharacteristic, complemented
61#5771—31no—
62#5769—31no—
63#5766—31no—
64#5757—31no—
65C3×#508—31no—
66C2×C3×SD32—31no—
67#5195—31no—
68#5193—31no—
69#5179—31no—
70#5147—31no—
71#4918—31no—
72#4918—31no—
73#4916—31no—
74#4916—31no—
75#4916—31no—
76#4916D311yescharacteristic, complemented
77#4915—31no—
78#4915—31no—
79#4914—31no—
80#4914—31no—
81D3×SD32—31no—
82D3×SD32—31no—
83D3×SD32—31no—
84D3×SD32—61no—
85D3×SD32D311yescharacteristic, complemented
86#4911—31no—
87#4911—31no—
88#4904—31no—
89C2×#800—31no—
90#4901—31no—
91#4901—31no—
92Q8×C3⋊D3—21no—
93D4×C3⋊D3—21no—
94C3×#239—21no—
95C3×D3×Q8—21no—
96C3×#237—21no—
97C3×D3×D4—21no—
98#3811—41no—
99D3×#67—41no—
100C2×#626—41no—
101#3804—41no—
102D3×D12—21no—
103#3799—21no—
104#3798—41no—
105#3798D411yescharacteristic
106#3796—21no—
107#3796—21no—
108#3796—41no—
109#3795—21no—
110#3795—41no—
111D3×Dic6—21no—
112D3×Dic6—41no—
113C32×Q16C2311yescharacteristic
114C32×D8C2311yescharacteristic
115#3756—21no—
116#3753—21no—
117#3746C2311yescharacteristic
118#3745C2311yescharacteristic
119C8×C3⋊D3C2311yescharacteristic
120C3×#216—21no—
121C3×#215—21no—
122C3×#214—21no—
123C3×#213—21no—
124C3×Dic12C2311yescharacteristic
125C3×Dic12C2311yescharacteristic
126C3×D24C2311yescharacteristic
127C3×D24C2311yescharacteristic
128C3×D3×C8C2311yescharacteristic
129C3×D3×C8C2311yescharacteristic
130#3719—21no—
131#3717—21no—
132#3716—21no—
133#3715—21no—
134#3715—21no—
135#3714—21no—
136#3712D411yescharacteristic
137#3711D411yescharacteristic
138#3711D411yescharacteristic
139C32×C16C2311yescharacteristic
140C3⋊(C3⋊C16)C2311yescharacteristic
141C3×C3⋊C16C2311yescharacteristic
142C3×C3⋊C16C2311yescharacteristic
143#3416—91noSylow
144#1010—61no—
145#1009—61no—
146#1007—61no—
147#1004—61no—
148C3×#135—31no—
149C3×#135—31no—
150C2×C3×Q16—31no—
151C2×C3×D8—31no—
152#951—61no—
153#949—61no—
154#942—61no—
155#932—61no—
156#919—31no—
157#919—31no—
158#919—31no—
159#919C2×D311yescharacteristic, complemented
160#918—61no—
161#918—61no—
162D3×Q16—31no—
163D3×Q16—31no—
164D3×Q16—31no—
165D3×Q16—61no—
166D3×Q16C2×D311yescharacteristic, complemented
167#915—61no—
168#915—61no—
169#914—61no—
170#914—61no—
171#912—31no—
172#912—31no—
173#912—31no—
174#912C2×D311yescharacteristic
175#911—61no—
176#911—61no—
177D3×D8—31no—
178D3×D8—31no—
179D3×D8—31no—
180D3×D8—61no—
181D3×D8C2×D311yescharacteristic
182C2×Dic12—31no—
183#904—31no—
184#904—31no—
185C2×D24—31no—
186#901—31no—
187#901—31no—
188C3×Q32—31no—
189C3×SD32—21no—
190C3×SD32—31no—
191C3×SD32—31no—
192C3×SD32—31no—
193C3×SD32—31no—
194C3×SD32C2×D311yescharacteristic, complemented
195C3×SD32C2×D311yescharacteristic, complemented
196C3×D16—31no—
197C2×C3×C16—31no—
198C2×C3×C16—31no—
199#829—31no—
200#829—31no—
201#829—31no—
202#829C2×D311yescharacteristic, complemented
203#828—31no—
204#828—31no—
205#828—31no—
206#828—61no—
207#828C2×D311yescharacteristic, complemented
208#827—31no—
209#827—31no—
210#827—31no—
211#827—61no—
212#827C2×D311yescharacteristic, complemented
213#826—31no—
214#826—31no—
215#826—31no—
216#826C2×D311yescharacteristic, complemented
217#812—31no—
218#812—31no—
219Dic24—31no—
220#800—31no—
221#800—31no—
222#800—31no—
223#800—31no—
224#800—61no—
225#800C2×D311yescharacteristic, complemented
226#800C2×D311yescharacteristic, complemented
227D48—31no—
228#798—31no—
229#798—31no—
230#798—31no—
231#798—31no—
232D3×C16—31no—
233D3×C16—31no—
234D3×C16—61no—
235D3×C16C2×D311yescharacteristic, complemented
236D3×C16C2×D311yescharacteristic, complemented
237C22×C3⋊D3—41no—
238C22×C3×D3—41no—
239C2×D32—41no—
240C32×Q8—21no—
241C32×D4—21no—
242#638—41no—
243C4⋊(C3⋊D3)—21no—
244C4×C3⋊D3—41no—
245C4×C3⋊D3C2×D411yescharacteristic
246#634—21no—
247#634—41no—
248C3×#67—41no—
249C3×#67—41no—
250C2×C3×Dic3—41no—
251C3×D12—21no—
252C3×D12—21no—
253C3×D12—41no—
254C3×C4×D3—41no—
255C3×C4×D3—41no—
256C3×C4×D3C2×D411yescharacteristic
257C3×C4×D3C2×D411yescharacteristic
258C3×Dic6—21no—
259C3×Dic6—21no—
260C3×Dic6—41no—
261#627—41no—
262#627D811yescharacteristic
263#626—41no—
264#626—41no—
265#626—41no—
266#626—41no—
267#626D811yescharacteristic
268#626D811yescharacteristic
269#625—41no—
270#625D811yescharacteristic
271#624—41no—
272D3×Dic3—41no—
273D3×Dic3—41no—
274D3×Dic3—41no—
275D3×Dic3—41no—
276C32×C8C2411yescharacteristic
277C3⋊(C3⋊C8)C2×D411yescharacteristic
278C3×C3⋊C8C2×D411yescharacteristic
279C3×C3⋊C8C2×D411yescharacteristic
280#578—91no—
281#576—91no—
282#510—91no—
283#510—91no—
284#510—91no—
285#509—91no—
286#509—91no—
287#509—91no—
288#508—31no—
289#508—91no—
290#508—91no—
291C2×SD32—31no—
292C2×SD32—91no—
293C2×SD32—91no—
294#504—91no—
295C3×#41—61no—
296C3×#41—61no—
297C2×C3×Q8—61no—
298C2×C3×D4—61no—
299C2×#67—121no—
300C2×#67—121no—
301#239—21no—
302#239—61no—
303#239—61no—
304#239—61no—
305#239—121no—
306D3×Q8—21no—
307D3×Q8—61no—
308D3×Q8—61no—
309D3×Q8—61no—
310D3×Q8—121no—
311D3×Q8—121no—
312#237—21no—
313#237—61no—
314#237—61no—
315#237—61no—
316#237—121no—
317#237—121no—
318#237—121no—
319D3×D4—21no—
320D3×D4—61no—
321D3×D4—61no—
322D3×D4—61no—
323D3×D4—121no—
324D3×D4—121no—
325D3×D4—121no—
326D3×D4—121no—
327#235—31no—
328#235—31no—
329#235—61no—
330#235—61no—
331#235—121no—
332#235—121no—
333#235—121no—
334#235—121no—
335C2×D12—61no—
336C2×D12—121no—
337C2×Dic6—61no—
338C2×Dic6—121no—
339C3×Q16—21no—
340C3×Q16—31no—
341C3×Q16—31no—
342C3×Q16—61no—
343C3×Q16C22×D311yescharacteristic
344C3×Q16C22×D311yescharacteristic
345C3×SD16—61no—
346C3×SD16—61no—
347C3×D8—21no—
348C3×D8—31no—
349C3×D8—31no—
350C3×D8—61no—
351C3×D8C22×D311yescharacteristic
352C3×D8C22×D311yescharacteristic
353C2×C3×C8—31no—
354C2×C3×C8—31no—
355#216—21no—
356#216—61no—
357#216—61no—
358#216—61no—
359#216—121no—
360#215—21no—
361#215—61no—
362#215—61no—
363#215—61no—
364#214—21no—
365#214—61no—
366#214—61no—
367#214—61no—
368#213—21no—
369#213—61no—
370#213—61no—
371#213—61no—
372#213—121no—
373#208—31no—
374#208—31no—
375Dic12—31no—
376Dic12—31no—
377Dic12—61no—
378Dic12—61no—
379Dic12C22×D311yescharacteristic
380Dic12C22×D311yescharacteristic
381D24—31no—
382D24—31no—
383D24—61no—
384D24—61no—
385D24C22×D311yescharacteristic
386D24C22×D311yescharacteristic
387#204—61no—
388#204—61no—
389ΓL(1,𝔽25)—31no—
390ΓL(1,𝔽25)—31no—
391ΓL(1,𝔽25)—31no—
392ΓL(1,𝔽25)—31no—
393D3×C8—31no—
394D3×C8—31no—
395D3×C8—61no—
396D3×C8C22×D311yescharacteristic
397D3×C8C22×D311yescharacteristic
398C3×C16—21no—
399C3×C16—31no—
400C3×C16—31no—
401C3×C16C22×D311yescharacteristic
402C3×C16C22×D311yescharacteristic
403C3⋊C16—31no—
404C3⋊C16—31no—
405C3⋊C16—61no—
406C3⋊C16C22×D311yescharacteristic
407C3⋊C16C22×D311yescharacteristic
408C22×C32—41no—
409C2×C3⋊D3—41no—
410C2×C3⋊D3—161no—
411C2×C3⋊D3C2×D811yescharacteristic
412C2×C3×D3—41no—
413C2×C3×D3—41no—
414C2×C3×D3—161no—
415C2×C3×D3C2×D811yescharacteristic
416C2×C3×D3C2×D811yescharacteristic
417D32—161no—
418C32×C4—41no—
419C32×C4C22×D411yescharacteristic
420C3⋊Dic3—41no—
421C3⋊Dic3C2×D811yescharacteristic
422C3×Dic3—41no—
423C3×Dic3—41no—
424C3×Dic3C2×D811yescharacteristic
425C3×Dic3C2×D811yescharacteristic
4262−1+4—181no—
427H(5,𝔽2)—181no—
428#137—181no—
429#137—181no—
430#137—181no—
431AGL(1,ℤ/8)—181no—
432AGL(1,ℤ/8)—181no—
433AGL(1,ℤ/8)—181no—
434#135—31no—
435#135—31no—
436#135—91no—
437#135—91no—
438#135—91no—
439#135—91no—
440C2×Q16—31no—
441C2×Q16—91no—
442C2×Q16—91no—
443C2×D8—31no—
444C2×D8—91no—
445C2×D8—91no—
446#131—91no—
447Q32—31no—
448Q32—91no—
449Q32—91no—
450SD32—31no—
451SD32—31no—
452SD32—31no—
453SD32—31no—
454SD32—91no—
455SD32—91no—
456SD32—91no—
457SD32—91no—
458SD32—91no—
459SD32D3211yescharacteristic, complemented
460D16—31no—
461D16—91no—
462D16—91no—
463M32—91no—
464M32—91no—
465M32—91no—
466C2×C16—31no—
467C2×C16—31no—
468C2×C16—91no—
469C23×C3—121no—
470C22×D3—41no—
471C22×D3—121no—
472C22×D3—121no—
473C22×D3—121no—
474C22×D3—121no—
475C22×D3—241no—
476C3×Q8—21no—
477C3×Q8—21no—
478C3×Q8—41no—
479C3×Q8—61no—
480C3×Q8—61no—
481C3×Q8—121no—
482C3×D4—21no—
483C3×D4—21no—
484C3×D4—41no—
485C3×D4—61no—
486C3×D4—61no—
487C3×D4—121no—
488C3×D4—121no—
489C3×D4—121no—
490C2×C3×C4—31no—
491C2×C3×C4—31no—
492C2×C3×C4—121no—
493C2×C3×C4—121no—
494C2×C3×C4—121no—
495#67—31no—
496#67—31no—
497#67—31no—
498#67—31no—
499#67—41no—
500#67—41no—
501#67—121no—
502#67—121no—
503#67—121no—
504#67—121no—
505#67—121no—
506#67—121no—
507#67—121no—
508#67—121no—
509#67—241no—
510C2×Dic3—41no—
511C2×Dic3—121no—
512C2×Dic3—121no—
513C2×Dic3—121no—
514C2×Dic3—121no—
515D12—21no—
516D12—21no—
517D12—31no—
518D12—31no—
519D12—41no—
520D12—61no—
521D12—61no—
522D12—121no—
523D12—121no—
524D12—121no—
525D12—121no—
526D12—121no—
527C4×D3—31no—
528C4×D3—31no—
529C4×D3—41no—
530C4×D3—41no—
531C4×D3—61no—
532C4×D3—121no—
533C4×D3—121no—
534C4×D3—121no—
535C4×D3—121no—
536C4×D3—121no—
537C4×D3—121no—
538C4×D3—121no—
539C4×D3—121no—
540C4×D3—241no—
541C4×D3D3×D411yescharacteristic
542C4×D3D3×D411yescharacteristic
543Dic6—21no—
544Dic6—21no—
545Dic6—31no—
546Dic6—31no—
547Dic6—41no—
548Dic6—61no—
549Dic6—61no—
550Dic6—121no—
551Dic6—121no—
552Dic6—121no—
553Dic6—121no—
554Dic6—121no—
555Dic6—241no—
556C3×C8—21no—
557C3×C8—31no—
558C3×C8—31no—
559C3×C8C23×D311yescharacteristic
560C3×C8C23×D311yescharacteristic
561C3⋊C8—31no—
562C3⋊C8—31no—
563C3⋊C8—61no—
564C3⋊C8D3×D411yescharacteristic
565C3⋊C8D3×D411yescharacteristic
566C2×C32—81no—
567C2×C32C22×D811yescharacteristic
568C3⋊D3—21no—
569C3⋊D3—81no—
570C3×D3—21no—
571C3×D3—21no—
572C3×D3—81no—
573C3×D3—81no—
574#41—61no—
575#41—61no—
576#41—91no—
577#41—181no—
578#41—181no—
579#41—181no—
580#41—181no—
581#41—361no—
582#41—361no—
583#41—361no—
584#41—361no—
585C2×Q8—61no—
586C2×Q8—181no—
587C2×Q8—181no—
588C2×Q8—361no—
589C2×D4—61no—
590C2×D4—181no—
591C2×D4—181no—
592C2×D4—361no—
593C2×D4—361no—
594C2×D4—361no—
595Q16—31no—
596Q16—31no—
597Q16—61no—
598Q16—91no—
599Q16—181no—
600Q16—181no—
601Q16C2×D3211yescharacteristic
602SD16—61no—
603SD16—61no—
604SD16—181no—
605SD16—181no—
606SD16—181no—
607SD16—181no—
608D8—31no—
609D8—31no—
610D8—61no—
611D8—91no—
612D8—181no—
613D8—181no—
614D8C2×D3211yescharacteristic
615M16—91no—
616M16—91no—
617M16—91no—
618C2×C8—31no—
619C2×C8—31no—
620C2×C8—91no—
621C16—31no—
622C16—31no—
623C16—91no—
624C16C2×D3211yescharacteristic
625C22×C3—31no—
626C22×C3—31no—
627C22×C3—41no—
628C22×C3—41no—
629C22×C3—81no—
630C22×C3—121no—
631C22×C3—121no—
632C22×C3—481no—
633C2×D3—31no—
634C2×D3—31no—
635C2×D3—41no—
636C2×D3—41no—
637C2×D3—61no—
638C2×D3—121no—
639C2×D3—121no—
640C2×D3—161no—
641C2×D3—241no—
642C2×D3—481no—
643C2×D3—481no—
644C2×D3—481no—
645C2×D3—482no—
646C2×D3—481no—
647C2×D3D3×D811yescharacteristic
648C2×D3D3×D811yescharacteristic
649C3×C4—21no—
650C3×C4—31no—
651C3×C4—31no—
652C3×C4—41no—
653C3×C4—41no—
654C3×C4—81no—
655C3×C4—121no—
656C3×C4—121no—
657C3×C4C2×D3×D411yescharacteristic
658C3×C4C2×D3×D411yescharacteristic
659Dic3—31no—
660Dic3—31no—
661Dic3—41no—
662Dic3—41no—
663Dic3—61no—
664Dic3—121no—
665Dic3—121no—
666Dic3—241no—
667Dic3D3×D811yescharacteristic
668Dic3D3×D811yescharacteristic
669C32#341611yescharacteristic, complemented, Sylow
670C23—121no—
671C23—361no—
672C23—361no—
673Q8—21no—
674Q8—61no—
675Q8—61no—
676Q8—91no—
677Q8—121no—
678Q8—181no—
679Q8—361no—
680Q8—361no—
681D4—21no—
682D4—61no—
683D4—61no—
684D4—91no—
685D4—91no—
686D4—91no—
687D4—121no—
688D4—121no—
689D4—121no—
690D4—181no—
691D4—361no—
692D4—361no—
693D4—361no—
694D4—361no—
695D4—361no—
696D4—361no—
697C2×C4—31no—
698C2×C4—31no—
699C2×C4—91no—
700C2×C4—121no—
701C2×C4—121no—
702C2×C4—121no—
703C2×C4—361no—
704C2×C4—361no—
705C2×C4—361no—
706C2×C4—361no—
707C2×C4—361no—
708C2×C4—361no—
709C8—31no—
710C8—31no—
711C8—91no—
712C8C22×D3211yescharacteristic
713C2×C3—21no—
714C2×C3—61no—
715C2×C3—61no—
716C2×C3—81no—
717C2×C3—81no—
718C2×C3—161no—
719C2×C3—241no—
720C2×C3—241no—
721C2×C3C2×D3×D811yescharacteristic
722C2×C3C2×D3×D811yescharacteristic
723D3—21no—
724D3—21no—
725D3—62no—
726D3—61no—
727D3—61no—
728D3—81no—
729D3—81no—
730D3—241no—
731D3—241no—
732D3—481no—
733C22—31no—
734C22—31no—
735C22—41no—
736C22—91no—
737C22—121no—
738C22—121no—
739C22—361no—
740C22—481no—
741C22—1441no—
742C22—1441no—
743C4—31no—
744C4—31no—
745C4—41no—
746C4—91no—
747C4—121no—
748C4—121no—
749C4—361no—
750C4D32×D411yescharacteristic
751C3—21no—
752C3#8202411yescharacteristic, complemented
753C3#8203211yescharacteristic, complemented
754C2—61no—
755C2—61no—
756C2—81no—
757C2—181no—
758C2—241no—
759C2—241no—
760C2—721no—
761C2D32×D811yescharacteristic
subgroupG/H
centerC2D32×D8
commutator, cosocleC32×C8C24
FrattiniC8C22×D32
FittingC32×SD32C22
socleC2×C32C22×D8
hypercenterSD32D32
hypocenterC32#3416
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #10594768C2semidirect
2. #10594734C2semidirect
3. C3⋊D3×SD32C2semidirect
4. C3×#4916C2semidirect
5. C3×D3×SD32C2semidirect
6. #10591050C2semidirect
7. #10591047C2semidirect
8. #10591038C2semidirect
9. #10591036C2semidirect
10. #10591031C2semidirect
11. #10591028C2semidirect
12. #10590245C2semidirect
13. #10590242C2semidirect
14. D3×#800C2semidirect
15. #10590227C2semidirect
20. Q16×C3⋊D3C22semidirect
22. C3×#919C22semidirect
23. C3×D3×Q16C22semidirect
33. #63810C22semidirect
35. #63807C22semidirect
37. D3×Dic12C22semidirect
39. C32×SD32C22semidirect
40. #63655C22semidirect
41. #63654C22semidirect
42. #63627C22semidirect
43. C16×C3⋊D3C22semidirect
44. C3×#829C22semidirect
45. C3×#828C22semidirect
46. C3×#827C22semidirect
47. C3×#826C22semidirect
48. C3×#800C22semidirect
49. C3×#800C22semidirect
50. C3×D3×C16C22semidirect
51. C3×D3×C16C22semidirect
52. #63551C22semidirect
53. #63550C22semidirect
54. #63549C22semidirect
55. #63548C22semidirect
56. #63546C22semidirect
57. #63545C22semidirect
58. #63544C22semidirect
59. #63543C22semidirect
60. #63543C22semidirect
76. #4916D3semidirect
85. D3×SD32D3semidirect
159. #919C2×D3semidirect
166. D3×Q16C2×D3semidirect
194. C3×SD32C2×D3semidirect
195. C3×SD32C2×D3semidirect
202. #829C2×D3semidirect
207. #828C2×D3semidirect
212. #827C2×D3semidirect
216. #826C2×D3semidirect
225. #800C2×D3semidirect
226. #800C2×D3semidirect
235. D3×C16C2×D3semidirect
236. D3×C16C2×D3semidirect
459. SD32D32semidirect
669. C32#3416semidirect
752. C3#82024semidirect
753. C3#82032semidirect

Maximal subgroups

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

subgroupindex
#105947682
#105947342
C3⋊D3×SD322
C3×#49162
C3×D3×SD322
#105910502
#105910472
#105910382
#105910362
#105910312
#105910282
#105902452
#105902422
D3×#8002
#105902272
#820323
#820243