Finite Group Databasebeta

← #11058587

Subgroups — #11058587

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×#5555C211yesmaximal, characteristic
2C22×#870C211yesmaximal, characteristic, complemented
3C3×C4×#123C211yesmaximal, characteristic, complemented
4#82841C212yesmaximal, complemented
5#82374C211yesmaximal, characteristic, complemented
6#82080C211yesmaximal, characteristic, complemented
7#75675C214yesmaximal, complemented
8#75149C214yesmaximal, complemented
9#74662C212yesmaximal, complemented
10#74620C212yesmaximal, complemented
11#74064C212yesmaximal, complemented
12#73713C212yesmaximal, complemented
13#73677C212yesmaximal, complemented
14#73519C211yesmaximal, characteristic, complemented
15#73506C212yesmaximal, complemented
16#73495C212yesmaximal, complemented
17#73456C211yesmaximal, characteristic, complemented
18#38907—31nomaximal, Sylow
19C22×#237C2212yes—
20C2×C3×#123C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C22×C3×C42C2211yescharacteristic
23C2×#930C2211yescharacteristic
24C2×#930C2211yescharacteristic
25C2×#929C2212yes—
26C22×C4⋊Dic3C2211yescharacteristic
27C22×C4⋊Dic3C2211yescharacteristic
28C22×C4⋊Dic3C2211yescharacteristic
29C22×Dic3⋊C4C2212yes—
30C22×Dic3⋊C4C2212yes—
31#5555—28no—
32C2×#897C2212yes—
33C2×#886C2212yes—
34C2×#886C2212yes—
35C2×#877C2212yes—
36C2×C4×D12C2211yescharacteristic
37C2×#870—28no—
38C2×#870C2212yes—
39C2×#870C2212yes—
40C2×#870C2214yes—
41C2×#869C2211yescharacteristic
42C3×#388C2212yes—
43C3×#387C2212yes—
44C3×#386C2211yescharacteristic
45C3×#385C2211yescharacteristic
46C3×#381C2211yescharacteristic
47C3×C4×C4⋊C4C2212yes—
48C3×C4×C22⋊C4C2212yes—
49C3×C4×C22⋊C4C2211yescharacteristic
50#5220C2212yes—
51#5213C2212yes—
52#5212C2212yes—
53#5212C2211yescharacteristic
54#4993C2214yes—
55#4989C2214yes—
56#4986C2212yes—
57#4982C2214yes—
58#4979C2214yes—
59#4959C2214yes—
60#4958C2212yes—
61#4958C2212yes—
62#4957C2214yes—
63#4949C2212yes—
64#4946C2214yes—
65#4946C2212yes—
66#4943C2212yes—
67#4942C2214yes—
68#4940C2214yes—
69#4939C2212yes—
70#4939C2212yes—
71#4936C2212yes—
72C4×C4⋊Dic3C2212yes—
73#4928C2212yes—
74#4928C2212yes—
75#4928C2212yes—
76#4676C2214yes—
77#4675C2214yes—
78#4674C2214yes—
79#4669C2214yes—
80#4667C2214yes—
81#4660C2214yes—
82#4657C2214yes—
83#4653C2214yes—
84#4647C2214yes—
85#4646C2214yes—
86C2×#547—31no—
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×#123D311yescharacteristic, complemented
103C22×C3×D4C2311yescharacteristic
104C23×C3×C4C2311yescharacteristic
105C23×C3×C4C2311yescharacteristic
106C23×C3×C4C2311yescharacteristic
107C23×C3×C4C2311yescharacteristic
108C22×#67C2312yes—
109C22×#67C2312yes—
110C23×Dic3C2312yes—
111C23×Dic3C2312yes—
112C23×Dic3C2312yes—
113C2×#237—28no—
114C2×#237—28no—
115C2×#237—44no—
116C22×D12C2311yescharacteristic
117C22×C4×D3C2312yes—
118C22×Dic6C2312yes—
119C3×#123—24no—
120C3×C4×D4—24no—
121C2×C3×C4⋊C4C2312yes—
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2312yes—
124C2×C3×C22⋊C4C2311yescharacteristic
125C2×C3×C22⋊C4C2312yes—
126C2×C3×C22⋊C4C2311yescharacteristic
127C2×C3×C22⋊C4C2311yescharacteristic
128C2×C3×C22⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4C2312yes—
130C2×C3×C42—24no—
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2312yes—
133C2×C3×C42C2312yes—
134C2×C3×C42C2312yes—
135C2×#217C2312yes—
136C2×#217C2314yes—
137#930—24no—
138#930—24no—
139#929—44no—
140C2×(C2×D3)⋊C4C2312yes—
141C2×(C2×D3)⋊C4C2312yes—
142C2×(C2×D3)⋊C4C2312yes—
143C2×(C2×D3)⋊C4C2314yes—
144C2×(C2×D3)⋊C4C2314yes—
145C2×(C2×D3)⋊C4C2314yes—
146C2×(C2×D3)⋊C4C2314yes—
147C2×C4⋊Dic3—24no—
148C2×C4⋊Dic3—24no—
149C2×C4⋊Dic3D418yes—
150C2×C4⋊Dic3C2312yes—
151C2×C4⋊Dic3C2312yes—
152C2×C4⋊Dic3C2312yes—
153C2×C4⋊Dic3C2311yescharacteristic
154C2×C4⋊Dic3C2312yes—
155C2×C4⋊Dic3C2312yes—
156C2×C4⋊Dic3C2312yes—
157C2×C4⋊Dic3C2311yescharacteristic
158C2×C4⋊Dic3C2311yescharacteristic
159C2×Dic3⋊C4—28no—
160C2×Dic3⋊C4—28no—
161C2×Dic3⋊C4C2314yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2314yes—
164C2×Dic3⋊C4C2314yes—
165C2×Dic3⋊C4C2314yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×C4×Dic3C2314yes—
169#897—28no—
170#886—28no—
171#886—28no—
172#877—44no—
173C4×D12—24no—
174#870—28no—
175#870—28no—
176#870—216no—
177#869—24no—
178C3×#95C2312yes—
179C3×#95C2312yes—
180C3×#95C2312yes—
181C3×#95C2312yes—
182C3×#95C2312yes—
183C3⋊#95C2314yes—
184C3⋊#95C2314yes—
185C3⋊#95C2314yes—
186C3⋊#95C2312yes—
187C3⋊#95C2314yes—
188C3⋊#95C2314yes—
189C3⋊#95C2314yes—
190C3⋊#95C2314yes—
191C22×#41—32no—
192#547—68no—
193C2×C4⋊Q8—31no—
194C2×#125—34no—
195C2×#125—32no—
196C2×#125—32no—
197C2×#125—68no—
198C2×#123—32no—
199C2×#123—32no—
200C2×#123—32no—
201C2×#123C2×D311yescharacteristic
202C2×C22⋊Q8—32no—
203C2×#121—31no—
204C2×#121—31no—
205C2×C4×D4—31no—
206C2×C4×D4C2×D311yescharacteristic
207C2×#117—32no—
208C22×C4⋊C4—31no—
209C22×C4⋊C4—32no—
210C22×C4⋊C4—32no—
211C22×C4⋊C4—31no—
212C22×C4⋊C4—31no—
213C22×C42C2×D311yescharacteristic
214#400—32no—
215#400—34no—
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—32no—
232#389—34no—
233#388—34no—
234#388—34no—
235#388C2×D312yes—
236#387—34no—
237#387C2×D312yes—
238#386—32no—
239#386—32no—
240#386—32no—
241#386—32no—
242#386C2×D311yescharacteristic
243#385—34no—
244#385—32no—
245#385—34no—
246#385C2×D311yescharacteristic
247#382—32no—
248#381—32no—
249#381C2×D311yescharacteristic
250#380—31no—
251#380—32no—
252#380—34no—
253#380—34no—
254C4×C4⋊C4—32no—
255C4×C4⋊C4C2×D312yes—
256C4×C22⋊C4C2×D311yescharacteristic
257C4×C22⋊C4C2×D312yes—
258C24×C3C2411yescharacteristic
259C24×C3C2411yescharacteristic
260C23×D3C2412yes—
261C2×C3×D4—22no—
262C2×C3×D4—22no—
263C2×C3×D4#4114yes—
264C22×C3×C4—24no—
265C22×C3×C4—22no—
266C22×C3×C4—22no—
267C22×C3×C4—22no—
268C22×C3×C4—22no—
269C22×C3×C4—22no—
270C22×C3×C4—24no—
271C22×C3×C4—42no—
272C22×C3×C4C2×D414yes—
273C22×C3×C4C2412yes—
274C22×C3×C4C2411yescharacteristic
275C22×C3×C4C2412yes—
276C22×C3×C4C2412yes—
277C22×C3×C4C2412yes—
278C22×C3×C4C2411yescharacteristic
279C22×C3×C4C2411yescharacteristic
280C22×C3×C4C2411yescharacteristic
281C22×C3×C4C2411yescharacteristic
282C2×#67—24no—
283C2×#67—24no—
284C2×#67—24no—
285C2×#67—24no—
286C2×#67—24no—
287C2×#67—42no—
288C22×Dic3—24no—
289C22×Dic3—24no—
290C22×Dic3—24no—
291C22×Dic3—24no—
292C22×Dic3—24no—
293C22×Dic3—42no—
294C22×Dic3—44no—
295C22×Dic3C2×D418yes—
296C22×Dic3C2414yes—
297C22×Dic3C2412yes—
298C22×Dic3C2414yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301#237—432no—
302C2×D12—22no—
303C2×D12—24no—
304C2×C4×D3—24no—
305C2×C4×D3—24no—
306C2×C4×D3—42no—
307C2×Dic6—24no—
308C2×Dic6—24no—
309C2×Dic6—42no—
310C3×C4⋊C4—22no—
311C3×C4⋊C4—24no—
312C3×C4⋊C4—42no—
313C3×C22⋊C4—22no—
314C3×C22⋊C4—22no—
315C3×C22⋊C4—24no—
316C3×C22⋊C4—22no—
317C3×C22⋊C4—22no—
318C3×C22⋊C4—42no—
319C3×C42—22no—
320C3×C42—24no—
321C3×C42—24no—
322C3×C42—24no—
323#217—24no—
324#217—44no—
325(C2×D3)⋊C4—24no—
326(C2×D3)⋊C4—24no—
327(C2×D3)⋊C4—24no—
328(C2×D3)⋊C4—44no—
329(C2×D3)⋊C4—44no—
330(C2×D3)⋊C4—44no—
331(C2×D3)⋊C4—44no—
332C4⋊Dic3—22no—
333C4⋊Dic3—24no—
334C4⋊Dic3—24no—
335C4⋊Dic3—24no—
336C4⋊Dic3—24no—
337C4⋊Dic3—24no—
338C4⋊Dic3C2×D414yes—
339C4⋊Dic3C2×D414yes—
340C4⋊Dic3C2×D418yes—
341Dic3⋊C4—28no—
342Dic3⋊C4—28no—
343Dic3⋊C4—28no—
344Dic3⋊C4—28no—
345Dic3⋊C4—44no—
346Dic3⋊C4—44no—
347Dic3⋊C4—44no—
348C4×Dic3—44no—
349C2×#41—68no—
350C2×#41—68no—
351C2×#41—124no—
352C22×Q8—32no—
353C22×D4—32no—
354C22×D4—32no—
355C22×D4—31no—
356C22×D4C22×D311yescharacteristic
357C23×C4—32no—
358C23×C4—32no—
359C23×C4—32no—
360C23×C4—32no—
361C23×C4C22×D311yescharacteristic
362C23×C4C22×D311yescharacteristic
363C23×C4C22×D311yescharacteristic
364C23×C4C22×D311yescharacteristic
365C4⋊Q8—64no—
366#125—68no—
367#125—68no—
368#125—616no—
369#123—24no—
370#123—68no—
371#123—68no—
372#123—124no—
373C22⋊Q8—68no—
374#121—64no—
375#121—64no—
376C4×D4—24no—
377C4×D4—64no—
378#117—124no—
379C2×C4⋊C4—38no—
380C2×C4⋊C4—31no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—32no—
383C2×C4⋊C4—31no—
384C2×C4⋊C4—32no—
385C2×C4⋊C4—34no—
386C2×C4⋊C4—32no—
387C2×C4⋊C4—34no—
388C2×C4⋊C4—34no—
389C2×C4⋊C4—34no—
390C2×C4⋊C4—32no—
391C2×C4⋊C4—32no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—34no—
394C2×C4⋊C4—34no—
395C2×C4⋊C4—34no—
396C2×C4⋊C4—64no—
397C2×C4⋊C4—68no—
398C2×C4⋊C4—68no—
399C2×C4⋊C4—64no—
400C2×C4⋊C4C22×D311yescharacteristic
401C2×C4⋊C4C22×D312yes—
402C2×C4⋊C4C22×D312yes—
403C2×C22⋊C4—32no—
404C2×C22⋊C4—32no—
405C2×C22⋊C4—32no—
406C2×C22⋊C4—32no—
407C2×C22⋊C4—34no—
408C2×C22⋊C4—34no—
409C2×C22⋊C4—34no—
410C2×C22⋊C4—34no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4C22×D311yescharacteristic
413C2×C22⋊C4C22×D311yescharacteristic
414C2×C22⋊C4C22×D311yescharacteristic
415C2×C22⋊C4C22×D311yescharacteristic
416C2×C22⋊C4C22×D312yes—
417C2×C22⋊C4C22×D312yes—
418C2×C42—24no—
419C2×C42—34no—
420C2×C42C22×D311yescharacteristic
421C2×C42C22×D312yes—
422C2×C42C22×D312yes—
423C2×C42C22×D312yes—
424#95—34no—
425#95—34no—
426#95—34no—
427#95—34no—
428#95—34no—
429#95—32no—
430#95—34no—
431#95—34no—
432#95C22×D312yes—
433#95C22×D312yes—
434#95C22×D312yes—
435#95C22×D312yes—
436#95C22×D312yes—
437C23×C3—22no—
438C23×C3—22no—
439C23×C3—21no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3C22×D412yes—
444C23×C3C2×#4112yes—
445C23×C3C2×#4112yes—
446C23×C3H(5,𝔽2)12yes—
447C23×C3C2511yescharacteristic
448C22×D3—22no—
449C22×D3—22no—
450C22×D3—22no—
451C22×D3—24no—
452C22×D3—24no—
453C3×D4—28no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—22no—
457C2×C3×C4—28no—
458C2×C3×C4—22no—
459C2×C3×C4—22no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—22no—
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—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—44no—
475C2×C3×C4—44no—
476C2×C3×C4—44no—
477C2×C3×C4C22×D412yes—
478C2×C3×C4C22×D412yes—
479C2×C3×C4C2×#4112yes—
480C2×C3×C42−1+414yes—
481#67—48no—
482#67—48no—
483C2×Dic3—216no—
484C2×Dic3—22no—
485C2×Dic3—22no—
486C2×Dic3—22no—
487C2×Dic3—22no—
488C2×Dic3—24no—
489C2×Dic3—22no—
490C2×Dic3—22no—
491C2×Dic3—24no—
492C2×Dic3—22no—
493C2×Dic3—24no—
494C2×Dic3—24no—
495C2×Dic3—24no—
496C2×Dic3—24no—
497C2×Dic3—48no—
498C2×Dic3—48no—
499C2×Dic3C22×D414yes—
500C2×Dic3C22×D414yes—
501D12—44no—
502C4×D3—48no—
503Dic6—48no—
504C24—32no—
505C24C23×D311yescharacteristic
506C24C23×D311yescharacteristic
507#41—1232no—
508C2×Q8—64no—
509C2×Q8—64no—
510C2×Q8—122no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—64no—
514C2×D4—64no—
515C2×D4—64no—
516C2×D4—64no—
517C2×D4—64no—
518C2×D4—62no—
519C2×D4—64no—
520C2×D4—122no—
521C2×D4#23514yes—
522C22×C4—24no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—24no—
529C22×C4—38no—
530C22×C4—32no—
531C22×C4—32no—
532C22×C4—34no—
533C22×C4—32no—
534C22×C4—34no—
535C22×C4—42no—
536C22×C4—64no—
537C22×C4—64no—
538C22×C4—64no—
539C22×C4—64no—
540C22×C4—64no—
541C22×C4—64no—
542C22×C4—64no—
543C22×C4—122no—
544C22×C4—122no—
545C22×C4—124no—
546C22×C4D3×D414yes—
547C22×C4C23×D312yes—
548C22×C4C23×D311yescharacteristic
549C22×C4C23×D312yes—
550C22×C4C23×D312yes—
551C22×C4C23×D312yes—
552C22×C4C23×D311yescharacteristic
553C22×C4C23×D311yescharacteristic
554C22×C4C23×D311yescharacteristic
555C22×C4C23×D311yescharacteristic
556C4⋊C4—24no—
557C4⋊C4—22no—
558C4⋊C4—34no—
559C4⋊C4—34no—
560C4⋊C4—38no—
561C4⋊C4—42no—
562C4⋊C4—64no—
563C4⋊C4—68no—
564C4⋊C4—68no—
565C4⋊C4—68no—
566C4⋊C4—68no—
567C4⋊C4—64no—
568C4⋊C4—62no—
569C4⋊C4—64no—
570C4⋊C4—64no—
571C4⋊C4—64no—
572C4⋊C4—124no—
573C4⋊C4—124no—
574C4⋊C4—124no—
575C22⋊C4—22no—
576C22⋊C4—24no—
577C22⋊C4—22no—
578C22⋊C4—22no—
579C22⋊C4—22no—
580C22⋊C4—42no—
581C22⋊C4—64no—
582C22⋊C4—64no—
583C22⋊C4—64no—
584C22⋊C4—64no—
585C22⋊C4—124no—
586C22⋊C4—124no—
587C22⋊C4—124no—
588C22⋊C4—124no—
589C22⋊C4—124no—
590C42—24no—
591C42—24no—
592C42—22no—
593C42—24no—
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#54614yes—
605C22×C3C23×D411yescharacteristic
606C22×C3C22×#4111yescharacteristic
607C22×C3C2×H(5,𝔽2)11yescharacteristic
608C22×C3C2×2−1+412yes—
609C22×C3#58512yes—
610C2×D3—42no—
611C2×D3—42no—
612C2×D3—42no—
613C2×D3—44no—
614C2×D3—44no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—41no—
618C3×C4—42no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4—42no—
622C3×C4—42no—
623C3×C4#53614yes—
624Dic3—24no—
625Dic3—24no—
626Dic3—42no—
627Dic3—44no—
628Dic3—44no—
629C23—22no—
630C23—22no—
631C23—21no—
632C23—21no—
633C23—22no—
634C23—22no—
635C23—62no—
636C23—62no—
637C23—62no—
638C23—64no—
639C23—64no—
640C23C2×#23512yes—
641C23C2×#23512yes—
642C23C2×D3×D412yes—
643C23#100912yes—
644C23C24×D311yescharacteristic
645Q8—128no—
646D4—28no—
647D4—128no—
648D4—128no—
649D4—124no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—22no—
653C2×C4—28no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—34no—
671C2×C4—34no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—44no—
675C2×C4—62no—
676C2×C4—62no—
677C2×C4—62no—
678C2×C4—62no—
679C2×C4—616no—
680C2×C4—62no—
681C2×C4—62no—
682C2×C4—64no—
683C2×C4—64no—
684C2×C4—62no—
685C2×C4—64no—
686C2×C4—64no—
687C2×C4—64no—
688C2×C4—64no—
689C2×C4—128no—
690C2×C4—128no—
691C2×C4—128no—
692C2×C4C2×#23512yes—
693C2×C4C2×D3×D412yes—
694C2×C4C2×D3×D412yes—
695C2×C4#101014yes—
696C2×C3—24no—
697C2×C3—42no—
698C2×C3C2×#53611yescharacteristic
699C2×C3C2×#54611yescharacteristic
700C2×C3#348711yescharacteristic
701C2×C3#351512yes—
702C2×C3#355912yes—
703D3—82no—
704C22—22no—
705C22—24no—
706C22—24no—
707C22—22no—
708C22—22no—
709C22—24no—
710C22—41no—
711C22—42no—
712C22—41no—
713C22—122no—
714C22—122no—
715C22—124no—
716C22—124no—
717C22—122no—
718C22#555014yes—
719C22C22×#23511yescharacteristic
720C22C22×D3×D411yescharacteristic
721C22C2×#100911yescharacteristic
722C22C2×#101012yes—
723C22#596412yes—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—41no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—41no—
732C4—64no—
733C4—64no—
734C4—124no—
735C4—122no—
736C4—124no—
737C4#564814yes—
738C3#3890711yescharacteristic, complemented, Sylow
739C2—24no—
740C2—42no—
741C2—242no—
742C2C2×#555011yescharacteristic
743C2#8583112yes—
744C2C2×#564811yescharacteristic
745C2#8602311yescharacteristic
746C2#8614012yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×C4×#123C2
prime radicalC2×#5555C2
hypercenterC4×#123D3
hypocenterC3#38907
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
2. C22×#870C2semidirect
3. C3×C4×#123C2semidirect
4. #82841C2semidirect
5. #82374C2semidirect
6. #82080C2semidirect
7. #75675C2semidirect
8. #75149C2semidirect
9. #74662C2semidirect
10. #74620C2semidirect
11. #74064C2semidirect
12. #73713C2semidirect
13. #73677C2semidirect
14. #73519C2semidirect
15. #73506C2semidirect
16. #73495C2semidirect
17. #73456C2semidirect
102. C4×#123D3semidirect
738. C3#38907semidirect

Maximal subgroups

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

subgroupindex
C2×#55552
C22×#8702
C3×C4×#1232
#828412
#823742
#820802
#756752
#751492
#746622
#746202
#740642
#737132
#736772
#735192
#735062
#734952
#734562
#389073