Finite Group Databasebeta

← #10828771

Subgroups — #10828771

Order 768.

1122 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5558C211yesmaximal, characteristic
2C2×#4860C211yesmaximal, characteristic, complemented
3C2×#4784C211yesmaximal, characteristic, complemented
4#76229C211yesmaximal, characteristic, complemented
5C3×#1864C211yesmaximal, characteristic, complemented
6#71606C211yesmaximal, characteristic, complemented
7#70579C211yesmaximal, characteristic, complemented
8#70206C211yesmaximal, characteristic, complemented
9#70202C211yesmaximal, characteristic, complemented
10#70176C211yesmaximal, characteristic, complemented
11#69606C211yesmaximal, characteristic, complemented
12#68874C211yesmaximal, characteristic, complemented
13#68813C211yesmaximal, characteristic, complemented
14#68668C211yesmaximal, characteristic, complemented
15#68634C211yesmaximal, characteristic, complemented
16#24090—31nomaximal, Sylow
17C2×C3×C4×D4C2211yescharacteristic
18C2×#938C2211yescharacteristic
19C2×#938C2211yescharacteristic
20C2×#929—21no—
21C2×C4×#67—21no—
22C22×D3×C8C2211yescharacteristic
23#5558—24no—
24#5558—24no—
25C2×#892C2211yescharacteristic
26C2×#892C2211yescharacteristic
27C2×D3×C4⋊C4C2211yescharacteristic
28C2×#884—21no—
29C2×#879—21no—
30C2×C4×D12C2211yescharacteristic
31C2×#870C2211yescharacteristic
32C2×C3×#106C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C3×#389C2211yescharacteristic
36C2×#832C2211yescharacteristic
37C2×#832C2211yescharacteristic
38C2×(C2×D3)⋊C8C2211yescharacteristic
39C2×(C2×D3)⋊C8C2211yescharacteristic
40C2×(C2×D3)⋊C8C2211yescharacteristic
41C2×#818C2211yescharacteristic
42C2×#817C2211yescharacteristic
43#4991—21no—
44#4987C2211yescharacteristic
45#4987C2211yescharacteristic
46#4987C2211yescharacteristic
47#4980—21no—
48C2×#808C2211yescharacteristic
49C2×#807C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4928C2211yescharacteristic
52#4860—24no—
53#4784—24no—
54#4675—21no—
55#4669—21no—
56C3×#340C2211yescharacteristic
57C3×#336C2211yescharacteristic
58#4551C2211yescharacteristic
59#4551C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#553—31no—
65C2×#482—31no—
66C2×#427—31no—
67#2485—31no—
68#2059—31no—
69#2059—31no—
70#2034—31no—
71#2033—31no—
72#1893—31no—
73#1869—31no—
74#1864D311yescharacteristic, complemented
75#1862—31no—
76#1853—31no—
77#1852—31no—
78#1825—31no—
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C22×#67—21no—
82C22×#67—21no—
83C22×D12D411yescharacteristic
84C22×C4×D3—21no—
85C22×C4×D3C2311yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C3×C4×D4—22no—
90C3×C4×D4—22no—
91C2×C3×C4⋊C4—21no—
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C22⋊C4—21no—
96C2×C3×C42C2311yescharacteristic
97C2×#217—21no—
98C2×#217—21no—
99#938—22no—
100#938—22no—
101#938—22no—
102#938D414yes—
103#929—28no—
104C4×#67—28no—
105C2×(C2×D3)⋊C4—21no—
106C2×(C2×D3)⋊C4—21no—
107C2×(C2×D3)⋊C4—21no—
108C2×(C2×D3)⋊C4—21no—
109C2×(C2×D3)⋊C4—21no—
110C2×(C2×D3)⋊C4D411yescharacteristic
111C2×(C2×D3)⋊C4D411yescharacteristic
112C2×C4⋊Dic3D411yescharacteristic
113C2×C4⋊Dic3C2311yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C2×C4⋊Dic3C2311yescharacteristic
116C2×C4⋊Dic3C2311yescharacteristic
117C2×Dic3⋊C4—21no—
118C2×Dic3⋊C4—21no—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C2×C4×Dic3—21no—
122C2×C4×Dic3—21no—
123C22×C3⋊C8C2311yescharacteristic
124C22×C3⋊C8C2311yescharacteristic
125C2×D3×C8—22no—
126C2×D3×C8—22no—
127C2×D3×C8—22no—
128#892—22no—
129#892—22no—
130#892—22no—
131#892D414yes—
132D3×C4⋊C4—22no—
133D3×C4⋊C4—22no—
134#884—28no—
135#879—28no—
136C4×D12—22no—
137C4×D12—22no—
138#870—22no—
139#870—22no—
140C3×#106—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—
149C3⋊#95—21no—
150(C2×D3)⋊C8—22no—
151(C2×D3)⋊C8—22no—
152(C2×D3)⋊C8—22no—
153#818—22no—
154#817—22no—
155#808—22no—
156#807—22no—
157#807—22no—
158C23×C8—31no—
159#553—64no—
160#553—64no—
161C2×#126—61no—
162C2×#125—31no—
163C2×#123—61no—
164C2×#121—31no—
165C2×#121—31no—
166C2×#121—61no—
167C2×C4×D4—31no—
168C2×C4×D4—61no—
169C2×C4×D4C2×D311yescharacteristic
170C2×#117—31no—
171C2×#117—31no—
172C22×C4⋊C4—31no—
173#482—64no—
174#427—64no—
175C2×#107—31no—
176C2×#107—31no—
177C2×#107—31no—
178C2×#106—31no—
179C2×#106—31no—
180C2×#106C2×D311yescharacteristic
181C2×#102—31no—
182C2×#102—31no—
183C2×#102C2×D311yescharacteristic
184C2×#102C2×D311yescharacteristic
185C2×C22⋊C8—31no—
186C2×C22⋊C8—31no—
187C2×C22⋊C8—31no—
188#397—61no—
189#394—61no—
190#389—31no—
191#389C2×D311yescharacteristic
192#388—61no—
193#387—61no—
194#380—31no—
195#380—31no—
196#380—31no—
197#340—31no—
198#340—31no—
199#340—31no—
200#340—31no—
201#340—31no—
202#340C2×D311yescharacteristic
203#336—31no—
204#336C2×D311yescharacteristic
205C24×C3—21no—
206C23×D3C2×D411yescharacteristic
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—24no—
216C22×C3×C4—21no—
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—42no—
226C2×#67—42no—
227C2×#67—81no—
228C2×#67—81no—
229C22×Dic3—21no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3C2×D411yescharacteristic
234C22×Dic3C2×D411yescharacteristic
235C2×D12—22no—
236C2×D12—22no—
237C2×D12—41no—
238C2×C4×D3—21no—
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×C4×D3—21no—
247C2×C4×D3—21no—
248C2×C4×D3—24no—
249C2×C4×D3—81no—
250C2×C4×D3—81no—
251C2×C4×D3C2×D412yes—
252C2×C4×D3C2×D412yes—
253C2×C3×C8—21no—
254C2×C3×C8—21no—
255C2×C3×C8—21no—
256C2×C3×C8—21no—
257C2×C3×C8—21no—
258C2×C3×C8#4112yes—
259C3×C4⋊C4—21no—
260C3×C4⋊C4—21no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—42no—
265C3×C4⋊C4C2×D412yes—
266C3×C22⋊C4—24no—
267C3×C42—21no—
268C3×C42—21no—
269#217—24no—
270#217—24no—
271(C2×D3)⋊C4—22no—
272(C2×D3)⋊C4—24no—
273(C2×D3)⋊C4—22no—
274(C2×D3)⋊C4—42no—
275(C2×D3)⋊C4—42no—
276(C2×D3)⋊C4—81no—
277(C2×D3)⋊C4—81no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—22no—
281C4⋊Dic3—21no—
282C4⋊Dic3—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3C2×D412yes—
286C4⋊Dic3C2×D412yes—
287Dic3⋊C4—24no—
288Dic3⋊C4—24no—
289Dic3⋊C4—24no—
290Dic3⋊C4—81no—
291C4×Dic3—24no—
292C4×Dic3—42no—
293C2×C3⋊C8—21no—
294C2×C3⋊C8—21no—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—21no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8#4112yes—
299D3×C8—28no—
300C22×D4—31no—
301C22×D4—61no—
302C22×D4—61no—
303C22×D4C22×D311yescharacteristic
304C23×C4—21no—
305C23×C4—31no—
306C23×C4—31no—
307C23×C4—61no—
308C22×C8—31no—
309C22×C8—31no—
310C22×C8—62no—
311C22×C8—62no—
312C22×C8—62no—
313C22×C8C22×D311yescharacteristic
314C22×C8C22×D311yescharacteristic
315#126—68no—
316#125—62no—
317#125—62no—
318#123—68no—
319#121—34no—
320#121—68no—
321#121—62no—
322#121—62no—
323#121—62no—
324C4×D4—22no—
325C4×D4—22no—
326C4×D4—62no—
327C4×D4—62no—
328C4×D4—68no—
329#117—34no—
330#117—62no—
331#117—62no—
332#117—62no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—31no—
338C2×C4⋊C4—31no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—61no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4—61no—
343C2×C4⋊C4—62no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4C22×D311yescharacteristic
346C2×C4⋊C4C22×D311yescharacteristic
347C2×C4⋊C4C22×D311yescharacteristic
348C2×C22⋊C4—21no—
349C2×C22⋊C4—31no—
350C2×C22⋊C4—31no—
351C2×C22⋊C4—61no—
352C2×C22⋊C4—61no—
353C2×C22⋊C4—61no—
354C2×C22⋊C4—61no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—61no—
358C2×C42—61no—
359C2×C42—61no—
360C2×C42C22×D311yescharacteristic
361#107—62no—
362#107—62no—
363#107—62no—
364#106—22no—
365#106—62no—
366#106—62no—
367#102—22no—
368#102—22no—
369#102—62no—
370#102—62no—
371C22⋊C8—62no—
372C22⋊C8—62no—
373C22⋊C8—62no—
374#95—21no—
375#95—61no—
376#95—61no—
377#95—61no—
378#95—61no—
379C23×C3—22no—
380C23×C3—41no—
381C23×C3—41no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3C22×D411yescharacteristic
387C22×D3—21no—
388C22×D3—21no—
389C22×D3—21no—
390C22×D3—21no—
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3#12012yes—
400C22×D3#13512yes—
401C3×D4—22no—
402C3×D4—22no—
403C3×D4—41no—
404C3×D4—41no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—84no—
421C2×C3×C4C22×D411yescharacteristic
422C2×C3×C4C22×D411yescharacteristic
423C2×C3×C4C2×#4111yescharacteristic
424C2×C3×C4C2×#4111yescharacteristic
425C2×C3×C42−1+411yescharacteristic
426C2×C3×C42−1+411yescharacteristic
427#67—48no—
428#67—84no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—21no—
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—41no—
437C2×Dic3—41no—
438C2×Dic3—41no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3#12012yes—
447D12—44no—
448C4×D3—22no—
449C4×D3—22no—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—41no—
453C4×D3—41no—
454C4×D3—41no—
455C4×D3—41no—
456C4×D3—84no—
457C3×C8—22no—
458C3×C8—41no—
459C3⋊C8—22no—
460C3⋊C8—41no—
461C24—21no—
462C24—31no—
463C24—31no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—62no—
470C2×D4—62no—
471C2×D4—64no—
472C2×D4—64no—
473C2×D4—121no—
474C2×D4—122no—
475C2×D4—122no—
476C2×D4—241no—
477C2×D4—241no—
478C2×D4D3×D412yes—
479C22×C4—21no—
480C22×C4—24no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—31no—
484C22×C4—32no—
485C22×C4—32no—
486C22×C4—31no—
487C22×C4—64no—
488C22×C4—61no—
489C22×C4—61no—
490C22×C4—61no—
491C22×C4—61no—
492C22×C4—61no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—61no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—81no—
503C22×C4—81no—
504C22×C4—241no—
505C22×C4—241no—
506C22×C4D3×D411yescharacteristic
507C22×C4D3×D411yescharacteristic
508C22×C4C23×D311yescharacteristic
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—32no—
515C2×C8—68no—
516C2×C8—61no—
517C2×C8—61no—
518C2×C8—61no—
519C2×C8—61no—
520C2×C8—61no—
521C2×C8#23512yes—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—32no—
528C4⋊C4—32no—
529C4⋊C4—42no—
530C4⋊C4—62no—
531C4⋊C4—64no—
532C4⋊C4—64no—
533C4⋊C4—64no—
534C4⋊C4—61no—
535C4⋊C4—61no—
536C4⋊C4—61no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—241no—
541C4⋊C4D3×D412yes—
542C22⋊C4—24no—
543C22⋊C4—62no—
544C22⋊C4—62no—
545C22⋊C4—64no—
546C22⋊C4—64no—
547C22⋊C4—64no—
548C22⋊C4—122no—
549C22⋊C4—122no—
550C22⋊C4—241no—
551C22⋊C4—241no—
552C42—21no—
553C42—21no—
554C42—64no—
555C42—122no—
556C22×C3—42no—
557C22×C3—42no—
558C22×C3—42no—
559C22×C3—81no—
560C22×C3—81no—
561C22×C3—81no—
562C22×C3—81no—
563C22×C3C2×#12011yescharacteristic
564C22×C3#54711yescharacteristic
565C22×C3#54711yescharacteristic
566C22×C3C2×#13511yescharacteristic
567C22×C3#57511yescharacteristic
568C22×C3#57611yescharacteristic
569C22×C3#57711yescharacteristic
570C2×D3—22no—
571C2×D3—22no—
572C2×D3—22no—
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C2×D3—41no—
580C2×D3—41no—
581C2×D3—41no—
582C2×D3—41no—
583C2×D3—41no—
584C3×C4—41no—
585C3×C4—42no—
586C3×C4—41no—
587C3×C4—81no—
588C3×C4—81no—
589C3×C4#52511yescharacteristic
590C3×C4#53611yescharacteristic
591C3×C4#54711yescharacteristic
592C3×C4#54711yescharacteristic
593Dic3—22no—
594Dic3—41no—
595Dic3—42no—
596Dic3—42no—
597Dic3—81no—
598Dic3—81no—
599C23—22no—
600C23—32no—
601C23—32no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—61no—
609C23—61no—
610C23—61no—
611C23—61no—
612C23—61no—
613C23—61no—
614C23—61no—
615C23—61no—
616C23—61no—
617C23—61no—
618C23—61no—
619C23—61no—
620C23C2×D3×D411yescharacteristic
621D4—22no—
622D4—22no—
623D4—41no—
624D4—41no—
625D4—124no—
626D4—128no—
627D4—244no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
635C2×C4—32no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—61no—
645C2×C4—61no—
646C2×C4—62no—
647C2×C4—62no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—61no—
651C2×C4—62no—
652C2×C4—61no—
653C2×C4—62no—
654C2×C4—61no—
655C2×C4—84no—
656C2×C4—121no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—121no—
660C2×C4—121no—
661C2×C4—121no—
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—244no—
671C2×C4C2×#23511yescharacteristic
672C2×C4C2×D3×D411yescharacteristic
673C2×C4C2×D3×D411yescharacteristic
674C2×C4#100711yescharacteristic
675C2×C4D3×#4111yescharacteristic
676C2×C4#101011yescharacteristic
677C8—22no—
678C8—41no—
679C8—62no—
680C8—121no—
681C2×C3—82no—
682C2×C3#240611yescharacteristic
683C2×C3#300211yescharacteristic
684C2×C3#301211yescharacteristic
685C2×C3#333711yescharacteristic
686C2×C3#333911yescharacteristic
687C2×C3#334711yescharacteristic
688C2×C3#335011yescharacteristic
689D3—42no—
690D3—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—62no—
695C22—62no—
696C22—62no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—81no—
701C22—81no—
702C22—81no—
703C22—81no—
704C22—121no—
705C22—121no—
706C22—121no—
707C22—121no—
708C22—121no—
709C22—121no—
710C22—121no—
711C22—121no—
712C22#555111yescharacteristic
713C22D3×#12011yescharacteristic
714C22#563111yescharacteristic
715C22#576211yescharacteristic
716C22D3×#13511yescharacteristic
717C22#577311yescharacteristic
718C22#577411yescharacteristic
719C4—41no—
720C4—42no—
721C4—41no—
722C4—62no—
723C4—81no—
724C4—81no—
725C4—122no—
726C4—121no—
727C4—122no—
728C4—241no—
729C4—241no—
730C4#550711yescharacteristic
731C4#554711yescharacteristic
732C4#562811yescharacteristic
733C4#565511yescharacteristic
734C3#2409011yescharacteristic, complemented, Sylow
735C2—82no—
736C2—122no—
737C2—122no—
738C2#7460011yescharacteristic
739C2#7968911yescharacteristic
740C2#7988511yescharacteristic
741C2#8008211yescharacteristic
742C2#8014911yescharacteristic
743C2#8108411yescharacteristic
744C2#8119511yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#1864C2
socleC23×C3C22×D4
prime radicalC2×#5558C2
hypercenter#1864D3
hypocenterC3#24090
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1864

Complements

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

NH ≅ G/Ntype
2. C2×#4860C2semidirect
3. C2×#4784C2semidirect
4. #76229C2semidirect
5. C3×#1864C2semidirect
6. #71606C2semidirect
7. #70579C2semidirect
8. #70206C2semidirect
9. #70202C2semidirect
10. #70176C2semidirect
11. #69606C2semidirect
12. #68874C2semidirect
13. #68813C2semidirect
14. #68668C2semidirect
15. #68634C2semidirect
74. #1864D3semidirect
734. C3#24090semidirect

Maximal subgroups

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

subgroupindex
C2×#55582
C2×#48602
C2×#47842
#762292
C3×#18642
#716062
#705792
#702062
#702022
#701762
#696062
#688742
#688132
#686682
#686342
#240903