Finite Group Databasebeta

← #11058585

Subgroups — #11058585

Order 768.

2310 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#547C211yesmaximal, characteristic
2C22×#890C211yesmaximal, characteristic, complemented
3#84090C212yesmaximal, complemented
4#84087C212yesmaximal, complemented
5#83241C212yesmaximal, complemented
6#82876C214yesmaximal, complemented
7#82866C212yesmaximal, complemented
8#82843C212yesmaximal, complemented
9#82796C214yesmaximal, complemented
10#82699C211yesmaximal, characteristic, complemented
11#82665C211yesmaximal, characteristic, complemented
12#82661C212yesmaximal, complemented
13#82374C211yesmaximal, characteristic, complemented
14#82363C212yesmaximal, complemented
15C4×#935C211yesmaximal, characteristic, complemented
16#82172C212yesmaximal, complemented
17#82159C211yesmaximal, characteristic, complemented
18#38907—31nomaximal, Sylow
19C22×C3×#41C2212yes—
20C3×#547—28no—
21C2×C3×C4⋊Q8C2211yescharacteristic
22C2×C3×#123C2212yes—
23C2×C3×#123C2212yes—
24C2×C3×C22⋊Q8C2212yes—
25C2×C3×#121C2211yescharacteristic
26C2×C3×#121C2211yescharacteristic
27C2×C3×C4×D4C2211yescharacteristic
28C2×C3×C4×D4C2211yescharacteristic
29C22×C3×C4⋊C4C2211yescharacteristic
30C22×C3×C4⋊C4C2211yescharacteristic
31C2×#935C2211yescharacteristic
32C2×#935C2212yes—
33C2×#926C2212yes—
34C22×C4⋊Dic3C2212yes—
35C22×C4⋊Dic3C2211yescharacteristic
36C22×Dic3⋊C4C2212yes—
37C22×C4×Dic3C2211yescharacteristic
38C2×#890—28no—
39C2×#890C2212yes—
40C2×#890C2214yes—
41C2×#890C2212yes—
42#5230C2214yes—
43#5229C2214yes—
44#5222C2214yes—
45#5221C2212yes—
46#5221C2214yes—
47#5221C2212yes—
48#5220C2212yes—
49#5220C2211yescharacteristic
50#5220C2212yes—
51#5220C2212yes—
52#5220C2212yes—
53#5212C2211yescharacteristic
54#5212C2214yes—
55#5212C2214yes—
56#5212C2212yes—
57#5211C2212yes—
58#5210C2214yes—
59#5210C2214yes—
60C4×#217C2212yes—
61C4×#217C2211yescharacteristic
62#4986C2212yes—
63#4986C2214yes—
64#4984C2212yes—
65#4982C2214yes—
66#4981C2214yes—
67#4980C2214yes—
68#4978C2212yes—
69#4977C2212yes—
70#4976C2214yes—
71Dic3×C4⋊C4C2212yes—
72#4972C2212yes—
73#4953C2214yes—
74#4953C2214yes—
75#4949C2214yes—
76#4949C2212yes—
77#4948C2214yes—
78#4946C2211yescharacteristic
79#4946C2212yes—
80#4945C2214yes—
81#4944C2214yes—
82#4944C2212yes—
83#4943C2211yescharacteristic
84C4×Dic3⋊C4C2212yes—
85#4928C2212yes—
86C2×#547D311yescharacteristic
87C22×#125—31no—
88#2854—31no—
89#2694—34no—
90#2690—34no—
91#2623—32no—
92#2550—32no—
93#2504—31no—
94#2490—32no—
95#2487—31no—
96#2454—32no—
97#2442—32no—
98#2413—32no—
99#2406—32no—
100#2344—31no—
101#2311—32no—
102C4×#123—31no—
103C2×C3×#41—28no—
104C2×C3×#41—28no—
105C2×C3×#41—44no—
106C22×C3×Q8C2312yes—
107C22×C3×D4C2312yes—
108C22×C3×D4C2311yescharacteristic
109C22×C3×D4C2312yes—
110C22×C3×D4C2311yescharacteristic
111C23×C3×C4C2311yescharacteristic
112C23×C3×C4C2312yes—
113C23×C3×C4C2312yes—
114C23×C3×C4C2312yes—
115C23×C3×C4C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2312yes—
119C3×C4⋊Q8—24no—
120C3×#123—28no—
121C3×#123—28no—
122C3×C22⋊Q8—28no—
123C3×#121—24no—
124C3×#121—24no—
125C3×C4×D4—24no—
126C3×C4×D4—24no—
127C2×C3×C4⋊C4—24no—
128C2×C3×C4⋊C4D418yes—
129C2×C3×C4⋊C4C2311yescharacteristic
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2312yes—
133C2×C3×C4⋊C4C2311yescharacteristic
134C2×C3×C4⋊C4C2312yes—
135C2×C3×C4⋊C4C2311yescharacteristic
136C2×C3×C22⋊C4C2311yescharacteristic
137C2×C3×C22⋊C4C2311yescharacteristic
138C2×C3×C22⋊C4C2312yes—
139C2×C3×C22⋊C4C2312yes—
140C2×C3×C22⋊C4C2312yes—
141C2×C3×C42C2311yescharacteristic
142C2×#217C2311yescharacteristic
143C2×#217C2312yes—
144C2×#217C2311yescharacteristic
145C2×#217C2312yes—
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2312yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152#935—24no—
153#935—44no—
154#926—44no—
155C2×C4⋊Dic3—28no—
156C2×C4⋊Dic3—24no—
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2312yes—
159C2×C4⋊Dic3C2312yes—
160C2×C4⋊Dic3C2314yes—
161C2×C4⋊Dic3C2314yes—
162C2×C4⋊Dic3C2314yes—
163C2×Dic3⋊C4—28no—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2314yes—
170C2×C4×Dic3—24no—
171C2×C4×Dic3C2312yes—
172C2×C4×Dic3C2312yes—
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2314yes—
175#890—28no—
176#890—28no—
177#890—216no—
178C3⋊#95C2314yes—
179C3⋊#95C2312yes—
180C3⋊#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C22×#41C2×D312yes—
192#547—28no—
193C2×C4⋊Q8C2×D311yescharacteristic
194C2×#125—34no—
195C2×#125—32no—
196C2×#125—32no—
197C2×#125—68no—
198C2×#123—31no—
199C2×#123—32no—
200C2×#123C2×D312yes—
201C2×#123C2×D312yes—
202C2×C22⋊Q8C2×D312yes—
203C2×#121C2×D311yescharacteristic
204C2×#121C2×D311yescharacteristic
205C2×C4×D4C2×D311yescharacteristic
206C2×C4×D4C2×D311yescharacteristic
207C2×#117—32no—
208C22×C4⋊C4—32no—
209C22×C4⋊C4—32no—
210C22×C4⋊C4—31no—
211C22×C4⋊C4C2×D311yescharacteristic
212C22×C4⋊C4C2×D311yescharacteristic
213C22×C42—31no—
214#400—34no—
215#400—32no—
216#399—34no—
217#399—32no—
218#398—34no—
219#398—34no—
220#397—34no—
221#397—34no—
222#396—34no—
223#395—34no—
224#394—34no—
225#391—34no—
226#390—34no—
227#390—32no—
228#390—32no—
229#389—32no—
230#389—32no—
231#389—34no—
232#389—32no—
233#388—34no—
234#388—32no—
235#388—34no—
236#387—34no—
237#387—32no—
238#386—31no—
239#386—32no—
240#386—32no—
241#386—32no—
242#386—32no—
243#385—34no—
244#385—34no—
245#385—31no—
246#385—32no—
247#382—32no—
248#381—32no—
249#381—31no—
250#380—34no—
251#380—34no—
252#380—31no—
253#380—32no—
254C4×C4⋊C4—32no—
255C4×C4⋊C4—32no—
256C4×C22⋊C4—31no—
257C4×C22⋊C4—32no—
258C24×C3C2412yes—
259C24×C3C2411yescharacteristic
260C24×C3C2411yescharacteristic
261C3×#41—432no—
262C2×C3×Q8—24no—
263C2×C3×Q8—24no—
264C2×C3×Q8—42no—
265C2×C3×D4—22no—
266C2×C3×D4—22no—
267C2×C3×D4—24no—
268C2×C3×D4—24no—
269C2×C3×D4—24no—
270C2×C3×D4—24no—
271C2×C3×D4—22no—
272C2×C3×D4—24no—
273C2×C3×D4—24no—
274C2×C3×D4—42no—
275C2×C3×D4#4114yes—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—24no—
279C22×C3×C4—24no—
280C22×C3×C4—22no—
281C22×C3×C4—24no—
282C22×C3×C4—24no—
283C22×C3×C4—24no—
284C22×C3×C4—24no—
285C22×C3×C4—42no—
286C22×C3×C4—42no—
287C22×C3×C4C2×D414yes—
288C22×C3×C4C2×D418yes—
289C22×C3×C4C2411yescharacteristic
290C22×C3×C4C2412yes—
291C22×C3×C4C2411yescharacteristic
292C22×C3×C4C2411yescharacteristic
293C22×C3×C4C2412yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2411yescharacteristic
296C22×C3×C4C2411yescharacteristic
297C22×Dic3—22no—
298C22×Dic3—22no—
299C22×Dic3—24no—
300C22×Dic3—22no—
301C22×Dic3—22no—
302C22×Dic3—42no—
303C22×Dic3—44no—
304C22×Dic3C2412yes—
305C22×Dic3C2412yes—
306C22×Dic3C2414yes—
307C22×Dic3C2412yes—
308C22×Dic3C2414yes—
309C22×Dic3C2412yes—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—22no—
313C3×C4⋊C4—24no—
314C3×C4⋊C4C2×D414yes—
315C3×C4⋊C4C2×D414yes—
316C3×C4⋊C4C2×D418yes—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—22no—
319C3×C22⋊C4—24no—
320C3×C22⋊C4—24no—
321C3×C22⋊C4—24no—
322C3×C42—22no—
323#217—22no—
324#217—24no—
325#217—22no—
326#217—24no—
327#217—44no—
328#217—44no—
329#217—44no—
330#217—44no—
331#217—42no—
332#217—44no—
333C4⋊Dic3—28no—
334C4⋊Dic3—28no—
335C4⋊Dic3—24no—
336C4⋊Dic3—24no—
337C4⋊Dic3—24no—
338C4⋊Dic3—44no—
339Dic3⋊C4—28no—
340Dic3⋊C4—28no—
341Dic3⋊C4—24no—
342Dic3⋊C4—44no—
343Dic3⋊C4—42no—
344Dic3⋊C4—44no—
345C4×Dic3—24no—
346C4×Dic3—24no—
347C4×Dic3—24no—
348C4×Dic3—44no—
349C2×#41—28no—
350C2×#41—28no—
351C2×#41—44no—
352C22×Q8C22×D312yes—
353C22×D4C22×D311yescharacteristic
354C22×D4C22×D312yes—
355C22×D4C22×D312yes—
356C22×D4C22×D311yescharacteristic
357C23×C4—31no—
358C23×C4—32no—
359C23×C4—31no—
360C23×C4C22×D311yescharacteristic
361C23×C4C22×D312yes—
362C23×C4C22×D312yes—
363C23×C4C22×D312yes—
364C23×C4C22×D311yescharacteristic
365C4⋊Q8—24no—
366#125—68no—
367#125—68no—
368#125—616no—
369#123—28no—
370#123—28no—
371#123—64no—
372#123—124no—
373C22⋊Q8—28no—
374#121—24no—
375#121—24no—
376C4×D4—24no—
377C4×D4—24no—
378#117—124no—
379C2×C4⋊C4—24no—
380C2×C4⋊C4—34no—
381C2×C4⋊C4—32no—
382C2×C4⋊C4—34no—
383C2×C4⋊C4—34no—
384C2×C4⋊C4—34no—
385C2×C4⋊C4—32no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—32no—
388C2×C4⋊C4—34no—
389C2×C4⋊C4—34no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—34no—
392C2×C4⋊C4—68no—
393C2×C4⋊C4—68no—
394C2×C4⋊C4—64no—
395C2×C4⋊C4#6718yes—
396C2×C4⋊C4C22×D311yescharacteristic
397C2×C4⋊C4C22×D312yes—
398C2×C4⋊C4C22×D311yescharacteristic
399C2×C4⋊C4C22×D312yes—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D311yescharacteristic
402C2×C4⋊C4C22×D312yes—
403C2×C22⋊C4—31no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—31no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—32no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4C22×D311yescharacteristic
414C2×C22⋊C4C22×D311yescharacteristic
415C2×C22⋊C4C22×D312yes—
416C2×C22⋊C4C22×D312yes—
417C2×C22⋊C4C22×D312yes—
418C2×C42—32no—
419C2×C42—32no—
420C2×C42—32no—
421C2×C42—34no—
422C2×C42—64no—
423C2×C42C22×D311yescharacteristic
424#95—32no—
425#95—32no—
426#95—32no—
427#95—32no—
428#95—34no—
429#95—32no—
430#95—34no—
431#95—34no—
432#95—34no—
433#95—34no—
434#95—32no—
435#95—34no—
436#95—34no—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—24no—
447C23×C3—24no—
448C23×C3C22×D412yes—
449C23×C3C2×#4112yes—
450C23×C3C2×#4112yes—
451C23×C3H(5,𝔽2)12yes—
452C23×C3C2511yescharacteristic
453C3×Q8—48no—
454C3×D4—28no—
455C3×D4—48no—
456C3×D4—48no—
457C3×D4—44no—
458C2×C3×C4—216no—
459C2×C3×C4—21no—
460C2×C3×C4—22no—
461C2×C3×C4—22no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
464C2×C3×C4—21no—
465C2×C3×C4—22no—
466C2×C3×C4—28no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—22no—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—48no—
475C2×C3×C4—48no—
476C2×C3×C4—44no—
477C2×C3×C4C22×D412yes—
478C2×C3×C4C22×D414yes—
479C2×C3×C4C22×D414yes—
480C2×C3×C4C22×D412yes—
481C2×C3×C4C2×#4112yes—
482C2×C3×C42−1+414yes—
483C2×Dic3—22no—
484C2×Dic3—22no—
485C2×Dic3—24no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—22no—
489C2×Dic3—24no—
490C2×Dic3—22no—
491C2×Dic3—22no—
492C2×Dic3—22no—
493C2×Dic3—24no—
494C2×Dic3—22no—
495C2×Dic3—24no—
496C2×Dic3—22no—
497C2×Dic3—24no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—24no—
501C2×Dic3—44no—
502C2×Dic3—48no—
503C2×Dic3—44no—
504C24C23×D312yes—
505C24C23×D311yescharacteristic
506C24C23×D311yescharacteristic
507#41—432no—
508C2×Q8—24no—
509C2×Q8—24no—
510C2×Q8—42no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—24no—
514C2×D4—24no—
515C2×D4—24no—
516C2×D4—24no—
517C2×D4—24no—
518C2×D4—22no—
519C2×D4—24no—
520C2×D4—42no—
521C2×D4#23714yes—
522C22×C4—24no—
523C22×C4—24no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—24no—
527C22×C4—24no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—32no—
532C22×C4—32no—
533C22×C4—34no—
534C22×C4—32no—
535C22×C4—34no—
536C22×C4—32no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—62no—
540C22×C4—62no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—64no—
544C22×C4—124no—
545C22×C4—122no—
546C22×C4C2×#6714yes—
547C22×C4C2×#6718yes—
548C22×C4C23×D311yescharacteristic
549C22×C4C23×D312yes—
550C22×C4C23×D311yescharacteristic
551C22×C4C23×D311yescharacteristic
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D312yes—
554C22×C4C23×D312yes—
555C22×C4C23×D311yescharacteristic
556C4⋊C4—22no—
557C4⋊C4—24no—
558C4⋊C4—22no—
559C4⋊C4—24no—
560C4⋊C4—64no—
561C4⋊C4—64no—
562C4⋊C4—68no—
563C4⋊C4—68no—
564C4⋊C4—68no—
565C4⋊C4—68no—
566C4⋊C4—64no—
567C4⋊C4—64no—
568C4⋊C4—124no—
569C4⋊C4—124no—
570C4⋊C4—122no—
571C4⋊C4—124no—
572C4⋊C4C2×#6714yes—
573C4⋊C4C2×#6714yes—
574C4⋊C4C2×#6718yes—
575C22⋊C4—22no—
576C22⋊C4—22no—
577C22⋊C4—24no—
578C22⋊C4—24no—
579C22⋊C4—24no—
580C22⋊C4—62no—
581C22⋊C4—64no—
582C22⋊C4—62no—
583C22⋊C4—64no—
584C22⋊C4—124no—
585C22⋊C4—122no—
586C22⋊C4—124no—
587C22⋊C4—124no—
588C22⋊C4—124no—
589C22⋊C4—124no—
590C42—22no—
591C42—64no—
592C42—64no—
593C42—64no—
594C42—124no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—24no—
598C22×C3—24no—
599C22×C3—22no—
600C22×C3—24no—
601C22×C3—41no—
602C22×C3—41no—
603C22×C3—42no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—42no—
607C22×C3—44no—
608C22×C3—44no—
609C22×C3#54614yes—
610C22×C3C23×D411yescharacteristic
611C22×C3C22×#4111yescharacteristic
612C22×C3C2×H(5,𝔽2)11yescharacteristic
613C22×C3C2×2−1+412yes—
614C22×C3#58512yes—
615C3×C4—22no—
616C3×C4—24no—
617C3×C4—24no—
618C3×C4—22no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4#53614yes—
623Dic3—42no—
624Dic3—42no—
625Dic3—44no—
626Dic3—42no—
627Dic3—42no—
628Dic3—44no—
629C23—22no—
630C23—22no—
631C23—21no—
632C23—22no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—24no—
638C23—24no—
639C23—22no—
640C23C2×#23712yes—
641C23C2×#23712yes—
642C23#100412yes—
643C23C22×#6712yes—
644C23C24×D311yescharacteristic
645Q8—48no—
646D4—28no—
647D4—48no—
648D4—48no—
649D4—44no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—22no—
656C2×C4—21no—
657C2×C4—216no—
658C2×C4—28no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—48no—
667C2×C4—48no—
668C2×C4—44no—
669C2×C4—62no—
670C2×C4—62no—
671C2×C4—62no—
672C2×C4—64no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—62no—
676C2×C4—64no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—64no—
680C2×C4—62no—
681C2×C4—64no—
682C2×C4—62no—
683C2×C4—64no—
684C2×C4—62no—
685C2×C4—62no—
686C2×C4—64no—
687C2×C4—124no—
688C2×C4—128no—
689C2×C4—124no—
690C2×C4C2×#23712yes—
691C2×C4#101014yes—
692C2×C4C22×#6712yes—
693C2×C4C22×#6714yes—
694C2×C4C22×#6714yes—
695C2×C4C22×#6712yes—
696C2×C3—24no—
697C2×C3—42no—
698C2×C3—82no—
699C2×C3C2×#53611yescharacteristic
700C2×C3C2×#54611yescharacteristic
701C2×C3#348711yescharacteristic
702C2×C3#351512yes—
703C2×C3#355912yes—
704C22—24no—
705C22—24no—
706C22—22no—
707C22—22no—
708C22—24no—
709C22—22no—
710C22—42no—
711C22—41no—
712C22—41no—
713C22—44no—
714C22—44no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22#580614yes—
719C22C22×#23711yescharacteristic
720C22C2×#100411yescharacteristic
721C22C2×#101012yes—
722C22#596812yes—
723C22C23×#6711yescharacteristic
724C4—24no—
725C4—24no—
726C4—22no—
727C4—22no—
728C4—42no—
729C4—41no—
730C4—41no—
731C4—122no—
732C4—122no—
733C4—124no—
734C4—122no—
735C4—122no—
736C4—124no—
737C4#582514yes—
738C3#3890711yescharacteristic, complemented, Sylow
739C2—24no—
740C2—42no—
741C2—82no—
742C2#8668312yes—
743C2#8669612yes—
744C2C2×#580611yescharacteristic
745C2C2×#582511yescharacteristic
746C2#8729011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
Fitting, prime radicalC2×C3×#547C2
hypercenterC2×#547D3
hypocenterC3#38907
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
2. C22×#890C2semidirect
3. #84090C2semidirect
4. #84087C2semidirect
5. #83241C2semidirect
6. #82876C2semidirect
7. #82866C2semidirect
8. #82843C2semidirect
9. #82796C2semidirect
10. #82699C2semidirect
11. #82665C2semidirect
12. #82661C2semidirect
13. #82374C2semidirect
14. #82363C2semidirect
15. C4×#935C2semidirect
16. #82172C2semidirect
17. #82159C2semidirect
738. C3#38907semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#5472
C22×#8902
#840902
#840872
#832412
#828762
#828662
#828432
#827962
#826992
#826652
#826612
#823742
#823632
C4×#9352
#821722
#821592
#389073