Finite Group Databasebeta

← #10972899

Subgroups — #10972899

Order 768.

2654 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5668C211yesmaximal, characteristic
2C2×C4×D3×Q8C211yesmaximal, characteristic, complemented
3C3×#2632C211yesmaximal, characteristic, complemented
4#82977C211yesmaximal, characteristic, complemented
5#82503C211yesmaximal, characteristic, complemented
6#78041C212yesmaximal, complemented
7#78030C212yesmaximal, complemented
8#77249C212yesmaximal, complemented
9#77189C212yesmaximal, complemented
10#77107C212yesmaximal, complemented
11#76946C212yesmaximal, complemented
12#76802C212yesmaximal, complemented
13#76781C212yesmaximal, complemented
14#75960C214yesmaximal, complemented
15#75462C214yesmaximal, complemented
16#74310C211yesmaximal, characteristic, complemented
17#74258C211yesmaximal, characteristic, complemented
18#35249—31nomaximal, Sylow
19C22×#239C2211yescharacteristic
20C22×D3×Q8C2211yescharacteristic
21C22×#237C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×C4×Q8C2211yescharacteristic
24C2×Q8×Dic3C2211yescharacteristic
25C2×#944C2211yescharacteristic
26C2×#940C2211yescharacteristic
27#5668—28no—
28C4×D3×Q8—28no—
29C2×#894C2214yes—
30C2×D3×C4⋊C4C2212yes—
31C2×D3×C4⋊C4C2211yescharacteristic
32C2×#887C2212yes—
33C2×#887C2211yescharacteristic
34C2×#885C2214yes—
35C2×#884C2212yes—
36C2×#884C2212yes—
37C2×#883C2214yes—
38C2×#67⋊C4C2212yes—
39C2×#67⋊C4C2212yes—
40C2×#875C2211yescharacteristic
41C2×C42×D3C2212yes—
42C2×C42×D3C2211yescharacteristic
43C2×C4×Dic6C2211yescharacteristic
44C2×C4×Dic6C2212yes—
45C3×#399C2212yes—
46C3×#395C2212yes—
47C3×#394C2212yes—
48C3×#393C2212yes—
49C3×#388C2214yes—
50C3×#383C2211yescharacteristic
51#5231C2212yes—
52#5230C2212yes—
53#5222C2212yes—
54#4993C2212yes—
55#4991C2212yes—
56#4989C2214yes—
57#4979C2212yes—
58#4976C2214yes—
59#4975C2214yes—
60#4957C2214yes—
61#4957C2214yes—
62#4957C2214yes—
63#4956C2214yes—
64#4950C2214yes—
65#4949C2212yes—
66#4947C2212yes—
67#4946C2214yes—
68#4944C2214yes—
69#4940C2214yes—
70#4937C2211yescharacteristic
71#4677C2212yes—
72#4673C2212yes—
73#4672C2212yes—
74#4670C2214yes—
75#4668C2214yes—
76#4667C2212yes—
77#4666C2212yes—
78#4665C2214yes—
79#4664C2212yes—
80#4656C2212yes—
81#4650C2212yes—
82#4649C2212yes—
83#4648C2212yes—
84#4647C2214yes—
85#4646C2214yes—
86C2×#532—31no—
87C22×C4×Q8—31no—
88#2854—34no—
89#2632—31no—
90#2632—31no—
91#2632—31no—
92#2632D311yescharacteristic, complemented
93#2580—32no—
94#2580—32no—
95#2567—32no—
96#2548—32no—
97#2501—32no—
98#2436—32no—
99#2406—32no—
100#2406—32no—
101#2326—34no—
102#2283—31no—
103C22×C3×Q8C2311yescharacteristic
104C22×C3×Q8C2311yescharacteristic
105C22×C3×D4C2311yescharacteristic
106C22×#67C2312yes—
107C22×#67C2312yes—
108C22×#67C2312yes—
109C23×Dic3C2312yes—
110C2×#239—24no—
111C2×#239—44no—
112C2×D3×Q8—24no—
113C2×D3×Q8—28no—
114C2×#237—24no—
115C2×#237—44no—
116C22×D12C2312yes—
117C22×D12C2311yescharacteristic
118C22×C4×D3C2312yes—
119C22×C4×D3C2312yes—
120C22×C4×D3C2311yescharacteristic
121C22×C4×D3C2311yescharacteristic
122C22×C4×D3C2311yescharacteristic
123C22×C4×D3C2312yes—
124C22×Dic6C2311yescharacteristic
125C22×Dic6C2312yes—
126C22×Dic6C2311yescharacteristic
127C3×#124—24no—
128C3×C4×Q8—24no—
129C2×C3×C4⋊C4C2312yes—
130C2×C3×C4⋊C4C2311yescharacteristic
131C2×C3×C4⋊C4C2314yes—
132C2×C3×C22⋊C4C2312yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C22⋊C4C2314yes—
136C2×C3×C42C2312yes—
137C2×C3×C42C2311yescharacteristic
138C2×#217C2314yes—
139C2×#217C2314yes—
140Q8×Dic3—24no—
141#944—24no—
142#940—24no—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2312yes—
147C2×(C2×D3)⋊C4C2312yes—
148C2×(C2×D3)⋊C4C2314yes—
149C2×(C2×D3)⋊C4C2314yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2311yescharacteristic
152C2×C4⋊Dic3C2314yes—
153C2×Dic3⋊C4C2312yes—
154C2×Dic3⋊C4C2312yes—
155C2×Dic3⋊C4C2314yes—
156C2×Dic3⋊C4C2312yes—
157C2×Dic3⋊C4C2312yes—
158C2×Dic3⋊C4C2312yes—
159C2×Dic3⋊C4C2314yes—
160C2×Dic3⋊C4C2314yes—
161C2×C4×Dic3C2314yes—
162C2×C4×Dic3C2312yes—
163C2×C4×Dic3C2312yes—
164C2×C4×Dic3C2312yes—
165C2×C4×Dic3C2311yescharacteristic
166C2×C4×Dic3C2311yescharacteristic
167C2×C4×Dic3C2311yescharacteristic
168#894—48no—
169D3×C4⋊C4—28no—
170D3×C4⋊C4—24no—
171#887—24no—
172#887—28no—
173#885—216no—
174#884—28no—
175#884—28no—
176#883—48no—
177#67⋊C4—28no—
178#67⋊C4—28no—
179#875—24no—
180C42×D3—28no—
181C42×D3D418yes—
182C4×Dic6—24no—
183C4×Dic6—28no—
184C3×#95C2314yes—
185C3×#95C2312yes—
186C3×#95C2312yes—
187C3×#95C2312yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2312yes—
193C3⋊#95C2312yes—
194C3⋊#95C2312yes—
195C22×#41—31no—
196C22×#41—31no—
197C23×Q8—31no—
198#532—68no—
199C2×C4⋊Q8—31no—
200C2×#127—31no—
201C2×#124—34no—
202C2×#124—31no—
203C2×#124C2×D311yescharacteristic
204C2×#123—34no—
205C2×#123—34no—
206C2×#121—32no—
207C2×#121—32no—
208C2×C4×Q8—31no—
209C2×C4×Q8—32no—
210C2×C4×Q8—31no—
211C2×C4×Q8—32no—
212C2×C4×Q8—31no—
213C2×C4×Q8—68no—
214C2×C4×Q8C2×D311yescharacteristic
215C2×C4×D4—32no—
216C2×C4×D4—32no—
217C22×C4⋊C4—32no—
218C22×C4⋊C4—31no—
219C22×C42—31no—
220C22×C42—32no—
221#399—32no—
222#399—32no—
223#399—32no—
224#399C2×D312yes—
225#395—32no—
226#395—32no—
227#395—32no—
228#395C2×D312yes—
229#394—32no—
230#394—32no—
231#394—32no—
232#394C2×D312yes—
233#393—32no—
234#393—32no—
235#393—32no—
236#393C2×D312yes—
237#391—34no—
238#390—34no—
239#390—34no—
240#390—34no—
241#389—34no—
242#389—34no—
243#388—34no—
244#388—34no—
245#388—34no—
246#388C2×D314yes—
247#386—34no—
248#386—34no—
249#385—34no—
250#385—34no—
251#385—34no—
252#385—34no—
253#384—34no—
254#383—31no—
255#383C2×D311yescharacteristic
256#382—32no—
257#381—32no—
258#380—32no—
259C4×C4⋊C4—32no—
260C4×C22⋊C4—32no—
261#376—32no—
262C24×C3C2412yes—
263C23×D3C2412yes—
264C23×D3C2411yescharacteristic
265C2×C3×Q8—22no—
266C2×C3×Q8—22no—
267C2×C3×Q8—24no—
268C2×C3×Q8—42no—
269C2×C3×D4—22no—
270C2×C3×D4—42no—
271C22×C3×C4C2414yes—
272C22×C3×C4C2412yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2411yescharacteristic
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2412yes—
278C2×#67—24no—
279C2×#67—28no—
280C2×#67—24no—
281C2×#67—24no—
282C2×#67—28no—
283C2×#67—28no—
284C22×Dic3—24no—
285C22×Dic3—44no—
286C22×Dic3C2414yes—
287C22×Dic3C2412yes—
288C22×Dic3C2412yes—
289C22×Dic3C2411yescharacteristic
290C22×Dic3C2412yes—
291C22×Dic3C2411yescharacteristic
292C22×Dic3C2411yescharacteristic
293#239—416no—
294D3×Q8—232no—
295#237—416no—
296C2×D12—24no—
297C2×D12—28no—
298C2×D12—22no—
299C2×D12—42no—
300C2×C4×D3—24no—
301C2×C4×D3—24no—
302C2×C4×D3—24no—
303C2×C4×D3—24no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—24no—
307C2×C4×D3—28no—
308C2×C4×D3—24no—
309C2×C4×D3—44no—
310C2×C4×D3C2×D414yes—
311C2×C4×D3C2×D414yes—
312C2×C4×D3C2×D414yes—
313C2×Dic6—22no—
314C2×Dic6—24no—
315C2×Dic6—24no—
316C2×Dic6—24no—
317C2×Dic6—22no—
318C2×Dic6—42no—
319C2×Dic6#4118yescomplemented
320C3×C4⋊C4—24no—
321C3×C4⋊C4—22no—
322C3×C4⋊C4—44no—
323C3×C22⋊C4—24no—
324C3×C22⋊C4—24no—
325C3×C22⋊C4—28no—
326C3×C22⋊C4—44no—
327C3×C42—24no—
328C3×C42C2×D414yes—
329#217—28no—
330#217—44no—
331(C2×D3)⋊C4—28no—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—28no—
335(C2×D3)⋊C4—28no—
336(C2×D3)⋊C4—44no—
337(C2×D3)⋊C4—44no—
338C4⋊Dic3—22no—
339C4⋊Dic3—24no—
340C4⋊Dic3—44no—
341Dic3⋊C4—24no—
342Dic3⋊C4—24no—
343Dic3⋊C4—24no—
344Dic3⋊C4—24no—
345Dic3⋊C4—24no—
346Dic3⋊C4—28no—
347Dic3⋊C4—44no—
348Dic3⋊C4—44no—
349C4×Dic3—24no—
350C4×Dic3—24no—
351C4×Dic3—24no—
352C4×Dic3—28no—
353C4×Dic3C2×D414yes—
354C4×Dic3C2×D414yes—
355C4×Dic3C2×D414yes—
356C2×#41—64no—
357C2×#41—64no—
358C2×#41—124no—
359C2×#41—124no—
360C22×Q8—32no—
361C22×Q8—31no—
362C22×Q8—31no—
363C22×Q8—64no—
364C22×Q8—68no—
365C22×Q8C22×D311yescharacteristic
366C22×Q8C22×D311yescharacteristic
367C22×D4—32no—
368C22×D4—32no—
369C22×D4—32no—
370C22×D4—32no—
371C22×D4—31no—
372C22×D4C22×D311yescharacteristic
373C23×C4—31no—
374C23×C4—31no—
375C23×C4—31no—
376C23×C4—32no—
377C23×C4—32no—
378C23×C4—32no—
379C23×C4—32no—
380C4⋊Q8—64no—
381#127—64no—
382#124—24no—
383#124—616no—
384#124—64no—
385#123—128no—
386#123—128no—
387#121—68no—
388#121—68no—
389C4×Q8—24no—
390C4×Q8—68no—
391C4×Q8—64no—
392C4×Q8—68no—
393C4×Q8—64no—
394C4×Q8—64no—
395C4×D4—68no—
396C4×D4—68no—
397C2×C4⋊C4—32no—
398C2×C4⋊C4—32no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—32no—
401C2×C4⋊C4—31no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—34no—
407C2×C4⋊C4—34no—
408C2×C4⋊C4—64no—
409C2×C4⋊C4—68no—
410C2×C4⋊C4C22×D312yes—
411C2×C4⋊C4C22×D311yescharacteristic
412C2×C4⋊C4C22×D314yes—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—32no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4C22×D312yes—
423C2×C22⋊C4C22×D312yes—
424C2×C22⋊C4C22×D314yes—
425C2×C22⋊C4C22×D314yes—
426C2×C42—31no—
427C2×C42—31no—
428C2×C42—31no—
429C2×C42—38no—
430C2×C42—32no—
431C2×C42—32no—
432C2×C42—32no—
433C2×C42—34no—
434C2×C42—68no—
435C2×C42C22×D312yes—
436C2×C42C22×D311yescharacteristic
437#95—32no—
438#95—34no—
439#95—32no—
440#95—32no—
441#95—34no—
442#95—34no—
443#95—34no—
444#95C22×D312yes—
445#95C22×D312yes—
446#95C22×D312yes—
447#95C22×D314yes—
448C23×C3—22no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—24no—
452C23×C3C2511yescharacteristic
453C22×D3—22no—
454C22×D3—22no—
455C22×D3—22no—
456C22×D3—24no—
457C22×D3—24no—
458C22×D3—24no—
459C22×D3C22×D412yes—
460C22×D3H(5,𝔽2)14yes—
461C3×Q8—28no—
462C3×Q8—44no—
463C3×D4—44no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—22no—
467C2×C3×C4—22no—
468C2×C3×C4—22no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—24no—
472C2×C3×C4—24no—
473C2×C3×C4—24no—
474C2×C3×C4—24no—
475C2×C3×C4—24no—
476C2×C3×C4C22×D412yes—
477C2×C3×C4C22×D412yes—
478C2×C3×C4C22×D412yes—
479C2×C3×C4C2×#4114yes—
480#67—48no—
481#67—48no—
482#67—48no—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—24no—
489C2×Dic3—24no—
490C2×Dic3—24no—
491C2×Dic3—24no—
492C2×Dic3—24no—
493C2×Dic3—48no—
494C2×Dic3C22×D412yes—
495C2×Dic3C22×D412yes—
496C2×Dic3C22×D412yes—
497C2×Dic3C2×#4114yes—
498C2×Dic3C2×#4114yes—
499C2×Dic32−1+414yes—
500D12—44no—
501D12—48no—
502C4×D3—216no—
503C4×D3—28no—
504C4×D3—28no—
505C4×D3—28no—
506C4×D3—48no—
507C4×D3—48no—
508Dic6—28no—
509Dic6—216no—
510Dic6—44no—
511C24—31no—
512C24—32no—
513C24C23×D312yes—
514#41—1216no—
515#41—1216no—
516C2×Q8—22no—
517C2×Q8—22no—
518C2×Q8—24no—
519C2×Q8—38no—
520C2×Q8—42no—
521C2×Q8—64no—
522C2×Q8—64no—
523C2×Q8—64no—
524C2×Q8—632no—
525C2×Q8—62no—
526C2×Q8—62no—
527C2×Q8—122no—
528C2×D4—22no—
529C2×D4—42no—
530C2×D4—64no—
531C2×D4—68no—
532C2×D4—64no—
533C2×D4—64no—
534C2×D4—68no—
535C2×D4—68no—
536C2×D4—64no—
537C2×D4—68no—
538C2×D4—62no—
539C2×D4—122no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—32no—
543C22×C4—31no—
544C22×C4—34no—
545C22×C4—34no—
546C22×C4—34no—
547C22×C4—34no—
548C22×C4—32no—
549C22×C4—32no—
550C22×C4—64no—
551C22×C4—64no—
552C22×C4—64no—
553C22×C4—64no—
554C22×C4—64no—
555C22×C4—64no—
556C22×C4—64no—
557C22×C4—68no—
558C22×C4—64no—
559C22×C4—64no—
560C22×C4—124no—
561C22×C4—124no—
562C22×C4C23×D314yes—
563C22×C4C23×D312yes—
564C22×C4C23×D312yes—
565C22×C4C23×D311yescharacteristic
566C22×C4C23×D311yescharacteristic
567C22×C4C23×D311yescharacteristic
568C22×C4C23×D312yes—
569C4⋊C4—24no—
570C4⋊C4—22no—
571C4⋊C4—44no—
572C4⋊C4—64no—
573C4⋊C4—64no—
574C4⋊C4—64no—
575C4⋊C4—64no—
576C4⋊C4—64no—
577C4⋊C4—68no—
578C4⋊C4—64no—
579C4⋊C4—62no—
580C4⋊C4—124no—
581C4⋊C4—124no—
582C4⋊C4—124no—
583C22⋊C4—24no—
584C22⋊C4—24no—
585C22⋊C4—28no—
586C22⋊C4—44no—
587C22⋊C4—68no—
588C22⋊C4—68no—
589C22⋊C4—68no—
590C22⋊C4—64no—
591C22⋊C4—64no—
592C22⋊C4—68no—
593C22⋊C4—124no—
594C22⋊C4—124no—
595C22⋊C4—124no—
596C42—24no—
597C42—34no—
598C42—34no—
599C42—34no—
600C42—64no—
601C42—64no—
602C42—68no—
603C42—64no—
604C42D3×D414yes—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—42no—
608C22×C3—48no—
609C22×C3C23×D411yescharacteristic
610C22×C3C22×#4112yes—
611C22×C3C2×H(5,𝔽2)12yes—
612C22×C3C2×2−1+412yes—
613C2×D3—22no—
614C2×D3—22no—
615C2×D3—28no—
616C2×D3—42no—
617C2×D3—42no—
618C2×D3—42no—
619C2×D3—48no—
620C2×D3#53514yes—
621C3×C4—22no—
622C3×C4—24no—
623C3×C4—22no—
624C3×C4—22no—
625C3×C4—42no—
626C3×C4—42no—
627C3×C4—44no—
628Dic3—24no—
629Dic3—22no—
630Dic3—42no—
631Dic3—42no—
632Dic3—44no—
633Dic3#52514yes—
634Dic3#53614yes—
635C23—22no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—32no—
640C23—34no—
641C23—62no—
642C23—62no—
643C23—62no—
644C23—64no—
645C23—64no—
646C23—64no—
647C23C24×D311yescharacteristic
648Q8—28no—
649Q8—44no—
650Q8—616no—
651Q8—68no—
652Q8—124no—
653D4—44no—
654D4—124no—
655D4—128no—
656D4—128no—
657D4—128no—
658D4—128no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—24no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—32no—
672C2×C4—32no—
673C2×C4—34no—
674C2×C4—34no—
675C2×C4—32no—
676C2×C4—34no—
677C2×C4—68no—
678C2×C4—68no—
679C2×C4—68no—
680C2×C4—616no—
681C2×C4—62no—
682C2×C4—62no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—64no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—64no—
690C2×C4—64no—
691C2×C4—128no—
692C2×C4—128no—
693C2×C4—128no—
694C2×C4C2×D3×D412yes—
695C2×C4C2×D3×D412yes—
696C2×C4C2×D3×D412yes—
697C2×C4D3×#4114yes—
698C2×C3—82no—
699C2×C3C2×#52511yescharacteristic
700C2×C3C2×#53511yescharacteristic
701C2×C3C2×#53611yescharacteristic
702C2×C3#352214yes—
703D3—24no—
704D3—82no—
705C22—34no—
706C22—42no—
707C22—48no—
708C22—42no—
709C22—42no—
710C22—62no—
711C22—68no—
712C22—62no—
713C22—122no—
714C22—128no—
715C22—122no—
716C22—122no—
717C22C22×D3×D411yescharacteristic
718C22C2×D3×#4112yes—
719C22D3×H(5,𝔽2)12yes—
720C22D3×2−1+412yes—
721C4—22no—
722C4—24no—
723C4—22no—
724C4—22no—
725C4—34no—
726C4—34no—
727C4—44no—
728C4—42no—
729C4—42no—
730C4—64no—
731C4—62no—
732C4—124no—
733C4—122no—
734C4—122no—
735C3#3524911yescharacteristic, complemented, Sylow
736C2—64no—
737C2—82no—
738C2—242no—
739C2D3×#52511yescharacteristic
740C2D3×#53511yescharacteristic
741C2D3×#53611yescharacteristic
742C2#8655814yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2632C2
prime radicalC2×#5668C2
hypercenter#2632D3
hypocenterC3#35249
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2632

Complements

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

NH ≅ G/Ntype
2. C2×C4×D3×Q8C2semidirect
3. C3×#2632C2semidirect
4. #82977C2semidirect
5. #82503C2semidirect
6. #78041C2semidirect
7. #78030C2semidirect
8. #77249C2semidirect
9. #77189C2semidirect
10. #77107C2semidirect
11. #76946C2semidirect
12. #76802C2semidirect
13. #76781C2semidirect
14. #75960C2semidirect
15. #75462C2semidirect
16. #74310C2semidirect
17. #74258C2semidirect
92. #2632D3semidirect
319. C2×Dic6#41semidirect
735. C3#35249semidirect

Maximal subgroups

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

subgroupindex
C2×#56682
C2×C4×D3×Q82
C3×#26322
#829772
#825032
#780412
#780302
#772492
#771892
#771072
#769462
#768022
#767812
#759602
#754622
#743102
#742582
#352493