Finite Group Databasebeta

← #10823554

Subgroups — #10823554

Order 768.

1114 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5625C211yesmaximal, characteristic, complemented
2C2×Dic3×SD16C211yesmaximal, characteristic, complemented
3#82633C211yesmaximal, characteristic
4C2×#4757C211yesmaximal, characteristic, complemented
5C3×#2000C211yesmaximal, characteristic
6#72057C211yesmaximal, characteristic, complemented
7#71695C211yesmaximal, characteristic, complemented
8#71685C211yesmaximal, characteristic
9#70246C211yesmaximal, characteristic, complemented
10#70220C211yesmaximal, characteristic, complemented
11#70164C211yesmaximal, characteristic, complemented
12#69936C211yesmaximal, characteristic, complemented
13#69907C211yesmaximal, characteristic, complemented
14#68828C211yesmaximal, characteristic, complemented
15#68781C211yesmaximal, characteristic, complemented
16#23584—31nomaximal, Sylow
17C22×C3×SD16C2211yescharacteristic
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C2×#944C2211yescharacteristic
22C2×D4×Dic3C2211yescharacteristic
23C22×#214C2211yescharacteristic
24C2×#926C2211yescharacteristic
25C2×#924C2211yescharacteristic
26#5625—24no—
27#5625—24no—
28C2×#890—21no—
29C2×#890C2211yescharacteristic
30C2×#889—21no—
31C2×#887C2211yescharacteristic
32C2×#879—21no—
33C2×#879—21no—
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39#5221—21no—
40#5221C2211yescharacteristic
41#5220—21no—
42C2×#832C2211yescharacteristic
43#5212C2211yescharacteristic
44C2×#830C2211yescharacteristic
45Dic3×SD16—24no—
46C2×#817C2211yescharacteristic
47C2×#816C2211yescharacteristic
48C2×#816C2211yescharacteristic
49C2×#815C2211yescharacteristic
50C2×C8×Dic3C2211yescharacteristic
51#4984C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53C2×#810C2211yescharacteristic
54C2×#807C2211yescharacteristic
55#4951—21no—
56#4950—21no—
57#4757—24no—
58C3×#340C2211yescharacteristic
59#4551C2211yescharacteristic
60#4550C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#541—31no—
65C2×#440—31no—
66C2×C4×SD16—31no—
67#2324—31no—
68#2059—31no—
69#2043—31no—
70#2036—31no—
71#2035—31no—
72#2025—31no—
73#2013—31no—
74#2000—31no—
75#2000D311yescharacteristic
76#1763—31no—
77C4×#103—31no—
78#1750—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C23×Dic3—21no—
84C22×Dic6C2311yescharacteristic
85C2×C3×SD16—22no—
86C2×C3×SD16—22no—
87C2×C3×SD16—22no—
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×C22⋊Q8—22no—
91C3×C22⋊Q8—22no—
92C3×#121—22no—
93C3×#121—22no—
94C2×C3×C4⋊C4—21no—
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C22⋊C4—21no—
98C2×C3×C22⋊C4—21no—
99C2×#217—21no—
100C2×#217—21no—
101C2×#217—21no—
102C2×#217—21no—
103C2×#217—21no—
104C2×#217D411yescharacteristic
105C2×#217D411yescharacteristic
106Q8×Dic3—22no—
107Q8×Dic3D414yescomplemented
108#944—22no—
109#944—22no—
110D4×Dic3—22no—
111D4×Dic3—22no—
112C2×#214—22no—
113C2×#214—22no—
114C2×#214—22no—
115#926—22no—
116#926—22no—
117C2×C4⋊Dic3—21no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3D411yescharacteristic
121C2×C4⋊Dic3D411yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125#924—22no—
126#924—22no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×Dic3⋊C4—21no—
130C2×Dic3⋊C4—21no—
131C2×Dic3⋊C4—21no—
132C2×C4×Dic3—21no—
133C2×C4×Dic3—21no—
134C2×C4×Dic3—21no—
135C2×C4×Dic3C2311yescharacteristic
136C2×C4×Dic3C2311yescharacteristic
137C22×C3⋊C8C2311yescharacteristic
138C22×C3⋊C8C2311yescharacteristic
139#890—28no—
140#890—22no—
141#890—22no—
142#889—28no—
143#887—22no—
144#887D414yescomplemented
145#879—28no—
146#879—28no—
147C3×#103—22no—
148C3×#102—22no—
149C3×C22⋊C8—22no—
150#835—22no—
151#835—22no—
152#832—22no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95—21no—
156#830—22no—
157#817—22no—
158#816—22no—
159#816—22no—
160#815—22no—
161C8×Dic3—22no—
162#810—22no—
163#807—22no—
164C22×SD16—31no—
165C22×SD16C2×D311yescharacteristic
166#541—64no—
167#541—64no—
168C2×C4⋊Q8—31no—
169C2×#126—61no—
170C2×#126—61no—
171C2×#125—31no—
172C2×#125—61no—
173C2×#125—61no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8C2×D311yescharacteristic
176C2×#121C2×D311yescharacteristic
177C2×C4×Q8—31no—
178C2×C4×Q8—31no—
179C2×C4×D4—31no—
180C2×#117—31no—
181#440—64no—
182C4×SD16—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103—31no—
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C22⋊C8C2×D311yescharacteristic
195C2×#97—31no—
196C2×C4×C8—31no—
197#390—31no—
198#390—61no—
199#389—31no—
200#388—61no—
201#386—61no—
202#385—61no—
203#380—31no—
204C4×C4⋊C4—31no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340C2×D311yescharacteristic
209#336—31no—
210#336—31no—
211C24×C3—21no—
212C24×C3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8C2×D412yes—
219C2×C3×D4—24no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—21no—
223C2×C3×D4—21no—
224C2×C3×D4—21no—
225C2×C3×D4—81no—
226C2×C3×D4—81no—
227C2×C3×D4#4112yes—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—21no—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—21no—
235C22×C3×C4—21no—
236C22×C3×C4—21no—
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2411yescharacteristic
239C22×Dic3—21no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—42no—
244C22×Dic3—81no—
245C22×Dic3—81no—
246C22×Dic3C2×D411yescharacteristic
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6C2×D412yes—
256C3×SD16—28no—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8#4112yes—
263C3×C4⋊C4—24no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4C2×D412yes—
267C3×C4⋊C4#4112yes—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—24no—
270#217—24no—
271#217—22no—
272#217—22no—
273#217—42no—
274#217—81no—
275#217—81no—
276#217—81no—
277#214—28no—
278C4⋊Dic3—24no—
279C4⋊Dic3—21no—
280C4⋊Dic3—24no—
281C4⋊Dic3—22no—
282C4⋊Dic3—22no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—81no—
288C4⋊Dic3C2×D412yes—
289Dic3⋊C4—24no—
290Dic3⋊C4—24no—
291Dic3⋊C4—24no—
292Dic3⋊C4—24no—
293Dic3⋊C4—24no—
294C4×Dic3—21no—
295C4×Dic3—21no—
296C4×Dic3—24no—
297C4×Dic3—24no—
298C4×Dic3—81no—
299C4×Dic3C2×D412yes—
300C4×Dic3C2×D412yes—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8#4112yes—
307C22×Q8—31no—
308C22×Q8C22×D311yescharacteristic
309C22×D4—21no—
310C22×D4C22×D311yescharacteristic
311C23×C4—61no—
312C23×C4C22×D311yescharacteristic
313C2×SD16—22no—
314C2×SD16—22no—
315C2×SD16—22no—
316C2×SD16—62no—
317C2×SD16—62no—
318C2×SD16—62no—
319C22×C8—31no—
320C22×C8—31no—
321C22×C8C22×D311yescharacteristic
322C22×C8C22×D311yescharacteristic
323C4⋊Q8—62no—
324C4⋊Q8—62no—
325#126—68no—
326#126—68no—
327#125—62no—
328#125—68no—
329#125—68no—
330#125—62no—
331C22⋊Q8—22no—
332C22⋊Q8—22no—
333C22⋊Q8—62no—
334C22⋊Q8—62no—
335#121—22no—
336#121—22no—
337C4×Q8—34no—
338C4×Q8—34no—
339C4×Q8—62no—
340C4×Q8—62no—
341C4×D4—62no—
342C4×D4—62no—
343#117—62no—
344#117—62no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—31no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4C22×D311yescharacteristic
360C2×C4⋊C4C22×D311yescharacteristic
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—31no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—61no—
366C2×C22⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C22⋊C4—61no—
370C2×C42—31no—
371C2×C42—31no—
372C2×C42—61no—
373C2×C42—61no—
374C2×C42—61no—
375#107—62no—
376#106—62no—
377#103—22no—
378#103—62no—
379#103—62no—
380#103—62no—
381#103—62no—
382#103—62no—
383#102—22no—
384#102—62no—
385C22⋊C8—22no—
386C22⋊C8—62no—
387#97—62no—
388C4×C8—62no—
389#95—61no—
390#95—61no—
391#95—61no—
392C23×C3—21no—
393C23×C3—22no—
394C23×C3—21no—
395C23×C3—21no—
396C23×C3—21no—
397C23×C3—21no—
398C23×C3—21no—
399C23×C3—21no—
400C23×C3—41no—
401C23×C3—41no—
402C23×C3—41no—
403C23×C3—41no—
404C23×C3—41no—
405C23×C3—41no—
406C23×C3C22×D411yescharacteristic
407C3×Q8—22no—
408C3×Q8—22no—
409C3×Q8—41no—
410C3×Q8—41no—
411C3×D4—22no—
412C3×D4—22no—
413C3×D4—41no—
414C3×D4—41no—
415C3×D4—84no—
416C2×C3×C4—22no—
417C2×C3×C4—22no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—22no—
421C2×C3×C4—21no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4C22×D411yescharacteristic
433C2×C3×C4C22×D411yescharacteristic
434C2×C3×C4C2×#4111yescharacteristic
435C2×C3×C4C2×#4111yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—22no—
444C2×Dic3—21no—
445C2×Dic3—22no—
446C2×Dic3—21no—
447C2×Dic3—21no—
448C2×Dic3—21no—
449C2×Dic3—21no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—41no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—84no—
461C2×Dic3#12012yes—
462C2×Dic3#12012yes—
463Dic6—22no—
464Dic6—22no—
465Dic6—41no—
466Dic6—41no—
467C3×C8—22no—
468C3×C8—41no—
469C3⋊C8—22no—
470C3⋊C8—41no—
471C24—21no—
472C24D3×D411yescharacteristic
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—32no—
479C2×Q8—61no—
480C2×Q8—61no—
481C2×Q8—61no—
482C2×Q8—61no—
483C2×Q8—61no—
484C2×Q8D3×D412yes—
485C2×D4—24no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—81no—
492C2×D4—81no—
493C2×D4#23712yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—31no—
504C22×C4—31no—
505C22×C4—31no—
506C22×C4—31no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—122no—
512C22×C4—241no—
513C22×C4—241no—
514C22×C4D3×D411yescharacteristic
515C22×C4C23×D311yescharacteristic
516SD16—28no—
517SD16—68no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—32no—
524C2×C8—61no—
525C2×C8—61no—
526C2×C8—61no—
527C2×C8—61no—
528C2×C8—61no—
529C2×C8#23712yes—
530C4⋊C4—24no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—32no—
534C4⋊C4—62no—
535C4⋊C4—62no—
536C4⋊C4—64no—
537C4⋊C4—64no—
538C4⋊C4—64no—
539C4⋊C4—64no—
540C4⋊C4—64no—
541C4⋊C4—64no—
542C4⋊C4—64no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—61no—
548C4⋊C4—241no—
549C4⋊C4D3×D412yes—
550C4⋊C4#23712yes—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—62no—
554C22⋊C4—62no—
555C22⋊C4—64no—
556C22⋊C4—122no—
557C22⋊C4—241no—
558C22⋊C4—241no—
559C22⋊C4—241no—
560C42—32no—
561C42—32no—
562C42—64no—
563C42—64no—
564C42—61no—
565C42—61no—
566C42—241no—
567C22×C3—41no—
568C22×C3—42no—
569C22×C3—41no—
570C22×C3—42no—
571C22×C3—41no—
572C22×C3—42no—
573C22×C3—41no—
574C22×C3—41no—
575C22×C3—41no—
576C22×C3—41no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3—81no—
581C22×C3C2×#12011yescharacteristic
582C22×C3#52511yescharacteristic
583C22×C3#53211yescharacteristic
584C22×C3#57711yescharacteristic
585C22×C3#57711yescharacteristic
586C22×C3#57711yescharacteristic
587C22×C3#57811yescharacteristic
588C3×C4—42no—
589C3×C4—41no—
590C3×C4—42no—
591C3×C4—42no—
592C3×C4#52511yescharacteristic
593C3×C4#52511yescharacteristic
594C3×C4#53211yescharacteristic
595C3×C4#53211yescharacteristic
596Dic3—22no—
597Dic3—22no—
598Dic3—42no—
599Dic3—41no—
600Dic3—41no—
601Dic3—42no—
602Dic3—81no—
603Dic3—81no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—22no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23C2×D3×D411yescharacteristic
619Q8—22no—
620Q8—22no—
621Q8—41no—
622Q8—41no—
623Q8—62no—
624Q8—62no—
625Q8—121no—
626Q8—121no—
627D4—22no—
628D4—22no—
629D4—41no—
630D4—41no—
631D4—84no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—32no—
639C2×C4—32no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—61no—
651C2×C4—61no—
652C2×C4—61no—
653C2×C4—61no—
654C2×C4—61no—
655C2×C4—61no—
656C2×C4—61no—
657C2×C4—61no—
658C2×C4—62no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—62no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—121no—
667C2×C4—121no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—244no—
673C2×C4C2×D3×D411yescharacteristic
674C2×C4C2×D3×D411yescharacteristic
675C2×C4C2×#23711yescharacteristic
676C2×C4C2×#23711yescharacteristic
677C2×C4C2×#23711yescharacteristic
678C2×C4D3×#4111yescharacteristic
679C8—22no—
680C8—41no—
681C8—62no—
682C8—121no—
683C2×C3—81no—
684C2×C3—82no—
685C2×C3#238811yescharacteristic
686C2×C3#301011yescharacteristic
687C2×C3#301311yescharacteristic
688C2×C3#312011yescharacteristic
689C2×C3#312311yescharacteristic
690C2×C3#317411yescharacteristic
691C2×C3#317811yescharacteristic
692C22—41no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—41no—
697C22—42no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—81no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22#558611yescharacteristic
707C22D3×#12011yescharacteristic
708C22#559611yescharacteristic
709C22#576211yescharacteristic
710C22#577011yescharacteristic
711C22#577511yescharacteristic
712C22#577911yescharacteristic
713C4—42no—
714C4—41no—
715C4—42no—
716C4—42no—
717C4—62no—
718C4—62no—
719C4—122no—
720C4—121no—
721C4—122no—
722C4—121no—
723C4—241no—
724C4—241no—
725C4#558611yescharacteristic
726C4#559611yescharacteristic
727C4#560611yescharacteristic
728C4#571611yescharacteristic
729C3#2358411yescharacteristic, complemented, Sylow
730C2—81no—
731C2—82no—
732C2#7666511yescharacteristic
733C2#8004211yescharacteristic
734C2#8008611yescharacteristic
735C2#8013711yescharacteristic
736C2#8021611yescharacteristic
737C2#8063511yescharacteristic
738C2#8078811yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2000C2
socleC23×C3C22×D4
prime radicalC2×C3×#121C22
hypercenter#2000D3
hypocenterC3#23584
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C23×C4 ◁ #2000

Complements

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

NH ≅ G/Ntype
1. C2×#5625C2semidirect
2. C2×Dic3×SD16C2semidirect
4. C2×#4757C2semidirect
6. #72057C2semidirect
7. #71695C2semidirect
9. #70246C2semidirect
10. #70220C2semidirect
11. #70164C2semidirect
12. #69936C2semidirect
13. #69907C2semidirect
14. #68828C2semidirect
15. #68781C2semidirect
107. Q8×Dic3D4semidirect
144. #887D4semidirect
729. C3#23584semidirect

Maximal subgroups

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

subgroupindex
C2×#56252
C2×Dic3×SD162
#826332
C2×#47572
C3×#20002
#720572
#716952
#716852
#702462
#702202
#701642
#699362
#699072
#688282
#687812
#235843