Finite Group Databasebeta

← #10828549

Subgroups — #10828549

Order 768.

1130 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5562C211yesmaximal, characteristic
2C2×#4882C211yesmaximal, characteristic, complemented
3C2×#4777C211yesmaximal, characteristic, complemented
4#75968C211yesmaximal, characteristic, complemented
5C3×#1862C211yesmaximal, characteristic, complemented
6#71606C211yesmaximal, characteristic, complemented
7#70618C211yesmaximal, characteristic, complemented
8#70211C211yesmaximal, characteristic, complemented
9#70201C211yesmaximal, characteristic, complemented
10#70177C211yesmaximal, characteristic, complemented
11#69626C211yesmaximal, characteristic, complemented
12#68881C211yesmaximal, characteristic, complemented
13#68828C211yesmaximal, characteristic, complemented
14#68671C211yesmaximal, characteristic, complemented
15#68665C211yesmaximal, characteristic, complemented
16#24069—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×#940C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C2×#930—21no—
21C2×#929—21no—
22#5562—24no—
23#5562—24no—
24C2×#895C2211yescharacteristic
25C2×#892C2211yescharacteristic
26C2×D3×C4⋊C4C2211yescharacteristic
27C2×#890C2211yescharacteristic
28C2×#884—21no—
29C2×#883—21no—
30C2×C4×D12C2211yescharacteristic
31C2×#872C2211yescharacteristic
32C2×C3×#107C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×#821C2211yescharacteristic
39C2×#821C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×(C2×D3)⋊C8C2211yescharacteristic
42C2×#817C2211yescharacteristic
43#4989—21no—
44#4984C2211yescharacteristic
45#4975—21no—
46#4972C2211yescharacteristic
47C2×#809C2211yescharacteristic
48C2×#809C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4928C2211yescharacteristic
52#4882—24no—
53#4777—24no—
54#4668—21no—
55#4650—21no—
56C3×#340C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#540—31no—
65C2×#481—31no—
66C2×#480—31no—
67#2317—31no—
68#2059—31no—
69#2059—31no—
70#2041—31no—
71#2041—31no—
72#1875—31no—
73#1875—31no—
74#1864—31no—
75#1864—31no—
76#1862—31no—
77#1862D311yescharacteristic, complemented
78#1818—31no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×#67—21no—
84C22×D12—21no—
85C22×D12C2311yescharacteristic
86C22×C4×D3—21no—
87C22×C4×D3—21no—
88C22×C4×D3C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×C4×D4—22no—
92C3×C4×D4—22no—
93C2×C3×C4⋊C4—21no—
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C4⋊C4C2311yescharacteristic
96C2×C3×C4⋊C4C2311yescharacteristic
97C2×C3×C22⋊C4—21no—
98C2×C3×C42C2311yescharacteristic
99C2×#217—21no—
100#940—22no—
101#940—22no—
102#938—22no—
103#938D414yes—
104#930—28no—
105#929—28no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4D411yescharacteristic
110C2×(C2×D3)⋊C4D411yescharacteristic
111C2×C4⋊Dic3—21no—
112C2×C4⋊Dic3—21no—
113C2×C4⋊Dic3C2311yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C2×C4⋊Dic3C2311yescharacteristic
116C2×Dic3⋊C4—21no—
117C2×Dic3⋊C4—21no—
118C2×Dic3⋊C4—21no—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4D411yescharacteristic
121C2×Dic3⋊C4D411yescharacteristic
122C2×C4×Dic3—21no—
123C2×C4×Dic3C2311yescharacteristic
124C22×C3⋊C8C2311yescharacteristic
125C22×C3⋊C8C2311yescharacteristic
126#895—22no—
127#895D414yes—
128#892—22no—
129#892—22no—
130D3×C4⋊C4—22no—
131D3×C4⋊C4—22no—
132#890—22no—
133#890—22no—
134#884—28no—
135#883—28no—
136C4×D12—22no—
137C4×D12—22no—
138#872—22no—
139#872—22no—
140C3×#107—22no—
141C3×#102—22no—
142C3×#102—22no—
143C3×#95—21no—
144#832—22no—
145#832—22no—
146C3⋊#95—21no—
147C3⋊#95—21no—
148C3⋊#95—21no—
149#821—22no—
150#821—22no—
151(C2×D3)⋊C8—22no—
152(C2×D3)⋊C8—22no—
153#817—22no—
154#809—22no—
155#809—22no—
156#808—22no—
157#807—22no—
158#540—64no—
159#540—64no—
160C2×#127—31no—
161C2×#125—31no—
162C2×#123—61no—
163C2×#123—61no—
164C2×#121—31no—
165C2×#121—31no—
166C2×#121—61no—
167C2×#121—61no—
168C2×C4×D4—31no—
169C2×C4×D4C2×D311yescharacteristic
170C2×#117—31no—
171C2×#117—31no—
172C22×C4⋊C4—31no—
173#481—64no—
174#480—64no—
175C2×#107—31no—
176C2×#107C2×D311yescharacteristic
177C2×#106—31no—
178C2×#106—31no—
179C2×#102—31no—
180C2×#102—31no—
181C2×#102—31no—
182C2×#102—31no—
183C2×#102—31no—
184C2×#102—31no—
185C2×#102C2×D311yescharacteristic
186C2×#102C2×D311yescharacteristic
187C2×C22⋊C8—31no—
188C2×C22⋊C8—31no—
189#389—31no—
190#389—31no—
191#389—31no—
192#389C2×D311yescharacteristic
193#385—61no—
194#385—61no—
195#384—61no—
196#382—61no—
197#340—31no—
198#340—31no—
199#340—31no—
200#340C2×D311yescharacteristic
201#336—31no—
202#336—31no—
203#336—31no—
204#336C2×D311yescharacteristic
205C24×C3—21no—
206C23×D3—21no—
207C23×D3C2×D411yescharacteristic
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4C2×D412yes—
214C22×C3×C4—21no—
215C22×C3×C4—21no—
216C22×C3×C4—24no—
217C22×C3×C4—21no—
218C22×C3×C4—81no—
219C22×C3×C4—81no—
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2411yescharacteristic
223C2×#67—24no—
224C2×#67—24no—
225C2×#67—24no—
226C2×#67—81no—
227C2×#67—81no—
228C2×#67—81no—
229C2×#67—81no—
230C2×#67—81no—
231C2×#67—81no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3C2×D411yescharacteristic
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238C2×D12—21no—
239C2×D12—21no—
240C2×D12—21no—
241C2×D12—21no—
242C2×D12—21no—
243C2×D12—24no—
244C2×D12—81no—
245C2×D12—81no—
246C2×D12C2×D412yes—
247C2×C4×D3—21no—
248C2×C4×D3—21no—
249C2×C4×D3—21no—
250C2×C4×D3—21no—
251C2×C4×D3—24no—
252C2×C4×D3—42no—
253C2×C4×D3—81no—
254C2×C4×D3—81no—
255C2×C4×D3—81no—
256C2×C4×D3—81no—
257C2×C4×D3C2×D412yes—
258C2×C4×D3C2×D412yes—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C2×C3×C8—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—81no—
270C3×C4⋊C4C2×D412yes—
271C3×C4⋊C4#4112yes—
272C3×C22⋊C4—24no—
273C3×C42—21no—
274C3×C42—21no—
275#217—24no—
276(C2×D3)⋊C4—24no—
277(C2×D3)⋊C4—24no—
278(C2×D3)⋊C4—22no—
279(C2×D3)⋊C4—22no—
280(C2×D3)⋊C4—24no—
281C4⋊Dic3—24no—
282C4⋊Dic3—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—81no—
287C4⋊Dic3C2×D412yes—
288C4⋊Dic3#4112yes—
289Dic3⋊C4—24no—
290Dic3⋊C4—22no—
291Dic3⋊C4—22no—
292Dic3⋊C4—42no—
293Dic3⋊C4—81no—
294Dic3⋊C4—81no—
295C4×Dic3—24no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—21no—
304C22×D4—31no—
305C22×D4—61no—
306C22×D4—61no—
307C22×D4—61no—
308C22×D4—61no—
309C22×D4C22×D311yescharacteristic
310C23×C4—21no—
311C23×C4—31no—
312C23×C4—61no—
313C23×C4—61no—
314C22×C8—31no—
315C22×C8—31no—
316C22×C8C22×D311yescharacteristic
317C22×C8C22×D311yescharacteristic
318#127—62no—
319#127—62no—
320#125—62no—
321#125—62no—
322#123—68no—
323#123—68no—
324#121—34no—
325#121—34no—
326#121—68no—
327#121—62no—
328#121—68no—
329#121—62no—
330C4×D4—22no—
331C4×D4—22no—
332C4×D4—62no—
333C4×D4—62no—
334#117—62no—
335#117—62no—
336#117—62no—
337#117—62no—
338C2×C4⋊C4—21no—
339C2×C4⋊C4—31no—
340C2×C4⋊C4—31no—
341C2×C4⋊C4—31no—
342C2×C4⋊C4—31no—
343C2×C4⋊C4—31no—
344C2×C4⋊C4—62no—
345C2×C4⋊C4—62no—
346C2×C4⋊C4—61no—
347C2×C4⋊C4—61no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4—61no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4C22×D311yescharacteristic
353C2×C4⋊C4C22×D311yescharacteristic
354C2×C4⋊C4C22×D311yescharacteristic
355C2×C22⋊C4—21no—
356C2×C22⋊C4—31no—
357C2×C22⋊C4—31no—
358C2×C22⋊C4—61no—
359C2×C22⋊C4—61no—
360C2×C22⋊C4—61no—
361C2×C22⋊C4—61no—
362C2×C42—31no—
363C2×C42—61no—
364C2×C42C22×D311yescharacteristic
365#107—22no—
366#107—62no—
367#106—62no—
368#106—62no—
369#102—22no—
370#102—22no—
371#102—62no—
372#102—62no—
373#102—62no—
374#102—62no—
375#102—62no—
376#102—62no—
377C22⋊C8—62no—
378C22⋊C8—62no—
379#95—21no—
380#95—61no—
381#95—61no—
382#95—61no—
383C23×C3—22no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3C22×D411yescharacteristic
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—22no—
398C22×D3—41no—
399C22×D3—41no—
400C22×D3—41no—
401C22×D3—41no—
402C22×D3—41no—
403C22×D3—41no—
404C22×D3#12012yes—
405C3×D4—22no—
406C3×D4—22no—
407C3×D4—41no—
408C3×D4—41no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—84no—
425C2×C3×C4C22×D411yescharacteristic
426C2×C3×C4C22×D411yescharacteristic
427C2×C3×C4C2×#4111yescharacteristic
428C2×C3×C4C2×#4111yescharacteristic
429C2×C3×C42−1+411yescharacteristic
430C2×C3×C42−1+411yescharacteristic
431#67—84no—
432#67—84no—
433#67—84no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—21no—
441C2×Dic3—21no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3#12012yes—
452D12—22no—
453D12—22no—
454D12—41no—
455D12—41no—
456D12—84no—
457C4×D3—22no—
458C4×D3—22no—
459C4×D3—22no—
460C4×D3—22no—
461C4×D3—84no—
462C4×D3—84no—
463C3×C8—41no—
464C3×C8—41no—
465C3⋊C8—41no—
466C3⋊C8—41no—
467C24—21no—
468C24—31no—
469C24—61no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—32no—
476C2×D4—64no—
477C2×D4—64no—
478C2×D4—64no—
479C2×D4—64no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4—241no—
486C2×D4—241no—
487C2×D4—241no—
488C2×D4—241no—
489C2×D4—241no—
490C2×D4—241no—
491C2×D4—241no—
492C2×D4—241no—
493C2×D4D3×D412yes—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—31no—
499C22×C4—32no—
500C22×C4—32no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—64no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—81no—
512C22×C4—81no—
513C22×C4—122no—
514C22×C4—241no—
515C22×C4—241no—
516C22×C4—241no—
517C22×C4—241no—
518C22×C4D3×D411yescharacteristic
519C22×C4D3×D411yescharacteristic
520C22×C4C23×D311yescharacteristic
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—61no—
528C2×C8—61no—
529C2×C8—61no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—61no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—32no—
538C4⋊C4—32no—
539C4⋊C4—62no—
540C4⋊C4—62no—
541C4⋊C4—64no—
542C4⋊C4—64no—
543C4⋊C4—61no—
544C4⋊C4—61no—
545C4⋊C4—61no—
546C4⋊C4—61no—
547C4⋊C4—81no—
548C4⋊C4—122no—
549C4⋊C4—241no—
550C4⋊C4—241no—
551C4⋊C4—241no—
552C4⋊C4#23512yes—
553C4⋊C4D3×D412yes—
554C22⋊C4—24no—
555C22⋊C4—64no—
556C22⋊C4—62no—
557C22⋊C4—62no—
558C22⋊C4—64no—
559C22⋊C4—64no—
560C22⋊C4—64no—
561C42—21no—
562C42—21no—
563C42—64no—
564C42—61no—
565C42—61no—
566C22×C3—42no—
567C22×C3—42no—
568C22×C3—42no—
569C22×C3—81no—
570C22×C3—81no—
571C22×C3—81no—
572C22×C3—81no—
573C22×C3C2×#12011yescharacteristic
574C22×C3#52511yescharacteristic
575C22×C3#53611yescharacteristic
576C22×C3#57611yescharacteristic
577C22×C3#57611yescharacteristic
578C22×C3#57711yescharacteristic
579C22×C3#57711yescharacteristic
580C2×D3—22no—
581C2×D3—22no—
582C2×D3—22no—
583C2×D3—41no—
584C2×D3—41no—
585C2×D3—41no—
586C2×D3—41no—
587C2×D3—42no—
588C2×D3—42no—
589C2×D3—42no—
590C2×D3—81no—
591C2×D3—81no—
592C2×D3—81no—
593C2×D3—81no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—81no—
599C3×C4#54711yescharacteristic
600C3×C4#54711yescharacteristic
601C3×C4#54711yescharacteristic
602C3×C4#54711yescharacteristic
603Dic3—22no—
604Dic3—42no—
605Dic3—41no—
606Dic3—42no—
607Dic3—41no—
608Dic3—81no—
609C23—22no—
610C23—32no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—62no—
624C23—121no—
625C23—121no—
626C23—121no—
627C23—121no—
628C23—121no—
629C23—121no—
630C23C2×D3×D411yescharacteristic
631D4—22no—
632D4—22no—
633D4—41no—
634D4—41no—
635D4—62no—
636D4—62no—
637D4—121no—
638D4—121no—
639D4—244no—
640D4—244no—
641D4—244no—
642D4—244no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—32no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—62no—
665C2×C4—61no—
666C2×C4—61no—
667C2×C4—61no—
668C2×C4—61no—
669C2×C4—62no—
670C2×C4—61no—
671C2×C4—61no—
672C2×C4—62no—
673C2×C4—84no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4—244no—
682C2×C4—244no—
683C2×C4C2×#23511yescharacteristic
684C2×C4C2×D3×D411yescharacteristic
685C2×C4C2×D3×D411yescharacteristic
686C2×C4#100711yescharacteristic
687C2×C4D3×#4111yescharacteristic
688C2×C4#101011yescharacteristic
689C8—41no—
690C8—41no—
691C8—121no—
692C8—121no—
693C2×C3—82no—
694C2×C3#240611yescharacteristic
695C2×C3#300811yescharacteristic
696C2×C3#300911yescharacteristic
697C2×C3#311911yescharacteristic
698C2×C3#311911yescharacteristic
699C2×C3#324111yescharacteristic
700C2×C3#324111yescharacteristic
701D3—42no—
702D3—82no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—62no—
707C22—62no—
708C22—62no—
709C22—81no—
710C22—81no—
711C22—81no—
712C22—81no—
713C22—121no—
714C22—121no—
715C22—121no—
716C22—121no—
717C22—122no—
718C22—122no—
719C22—122no—
720C22—241no—
721C22—241no—
722C22—241no—
723C22—241no—
724C22#554711yescharacteristic
725C22D3×#12011yescharacteristic
726C22#562811yescharacteristic
727C22#575711yescharacteristic
728C22#577011yescharacteristic
729C22#577411yescharacteristic
730C22#577811yescharacteristic
731C4—41no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—62no—
736C4—81no—
737C4—121no—
738C4—122no—
739C4—121no—
740C4—122no—
741C4—241no—
742C4#550711yescharacteristic
743C4#555111yescharacteristic
744C4#563111yescharacteristic
745C4#565511yescharacteristic
746C3#2406911yescharacteristic, complemented, Sylow
747C2—82no—
748C2—122no—
749C2—242no—
750C2#7460011yescharacteristic
751C2#7959511yescharacteristic
752C2#7981211yescharacteristic
753C2#8000411yescharacteristic
754C2#8022911yescharacteristic
755C2#8097311yescharacteristic
756C2#8117711yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1862C2
socleC23×C3C22×D4
prime radicalC2×#5562C2
hypercenter#1862D3
hypocenterC3#24069
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1862

Complements

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

NH ≅ G/Ntype
2. C2×#4882C2semidirect
3. C2×#4777C2semidirect
4. #75968C2semidirect
5. C3×#1862C2semidirect
6. #71606C2semidirect
7. #70618C2semidirect
8. #70211C2semidirect
9. #70201C2semidirect
10. #70177C2semidirect
11. #69626C2semidirect
12. #68881C2semidirect
13. #68828C2semidirect
14. #68671C2semidirect
15. #68665C2semidirect
77. #1862D3semidirect
746. C3#24069semidirect

Maximal subgroups

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

subgroupindex
C2×#55622
C2×#48822
C2×#47772
#759682
C3×#18622
#716062
#706182
#702112
#702012
#701772
#696262
#688812
#688282
#686712
#686652
#240693