Finite Group Databasebeta

← #10972900

Subgroups — #10972900

Order 768.

2654 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5832C211yesmaximal, characteristic
2C22×#887C211yesmaximal, characteristic, complemented
3C3×#2406C211yesmaximal, characteristic, complemented
4#84090C211yesmaximal, characteristic, complemented
5#82891C212yesmaximal, complemented
6#82859C212yesmaximal, complemented
7#82192C211yesmaximal, characteristic, complemented
8#77203C212yesmaximal, complemented
9#77189C212yesmaximal, complemented
10#76977C212yesmaximal, complemented
11#76946C212yesmaximal, complemented
12#74872C212yesmaximal, complemented
13#74701C212yesmaximal, complemented
14#74487C214yesmaximal, complemented
15#74386C214yesmaximal, complemented
16#74063C211yesmaximal, characteristic, complemented
17#74051C211yesmaximal, characteristic, complemented
18#35249—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C22×#235C2211yescharacteristic
21C23×Dic6C2211yescharacteristic
22C2×C3×#123C2212yes—
23C22×C3×C4⋊C4C2211yescharacteristic
24#5832—28no—
25C2×#947C2211yescharacteristic
26C2×#944C2211yescharacteristic
27C2×#940C2211yescharacteristic
28C2×#939C2212yes—
29C2×#939C2212yes—
30C2×#936C2211yescharacteristic
31C2×#935C2212yes—
32C2×#929C2212yes—
33C2×C4×#67C2212yes—
34C2×C4×#67C2212yes—
35C22×Dic3⋊C4C2211yescharacteristic
36C22×Dic3⋊C4C2211yescharacteristic
37C22×C4×Dic3C2211yescharacteristic
38C22×C4×Dic3C2211yescharacteristic
39C22×C4×Dic3C2211yescharacteristic
40C2×#887—28no—
41C2×#887C2212yes—
42C2×#887C2212yes—
43C2×#887C2212yes—
44C2×#887C2212yes—
45C2×#886C2212yes—
46C2×#885C2214yes—
47C3×#395C2212yes—
48C3×#394C2212yes—
49C3×#386C2212yes—
50C3×#385C2214yes—
51C3×#381C2211yescharacteristic
52#5230C2212yes—
53#5222C2212yes—
54#5220C2212yes—
55#5213C2212yes—
56#5211C2211yescharacteristic
57#5210C2214yes—
58#4993C2214yes—
59#4991C2212yes—
60#4990C2214yes—
61#4989C2214yes—
62#4979C2212yes—
63#4976C2214yes—
64#4975C2214yes—
65#4958C2212yes—
66#4957C2214yes—
67#4957C2214yes—
68#4957C2214yes—
69#4951C2214yes—
70#4949C2214yes—
71#4947C2214yes—
72#4945C2214yes—
73#4942C2212yes—
74Dic3×C22⋊C4C2212yes—
75#4673C2214yes—
76#4672C2212yes—
77#4669C2214yes—
78#4668C2214yes—
79#4656C2212yes—
80#4651C2212yes—
81#4650C2212yes—
82#4649C2212yes—
83#4648C2212yes—
84#4647C2214yes—
85#4646C2214yes—
86C2×#532—31no—
87C22×C4×Q8—31no—
88#2854—32no—
89#2854—32no—
90#2632—32no—
91#2632—32no—
92#2580—34no—
93#2567—32no—
94#2548—32no—
95#2501—32no—
96#2436—32no—
97#2406—31no—
98#2406—31no—
99#2406—31no—
100#2406D311yescharacteristic, complemented
101#2326—34no—
102#2283—31no—
103C2×C3×#41—24no—
104C2×C3×#41—44no—
105C22×C3×Q8C2311yescharacteristic
106C22×C3×D4C2312yes—
107C22×C3×D4C2311yescharacteristic
108C23×C3×C4C2311yescharacteristic
109C23×C3×C4C2311yescharacteristic
110C23×C3×C4C2311yescharacteristic
111C23×C3×C4C2312yes—
112C22×#67C2312yes—
113C22×#67C2312yes—
114C22×#67C2312yes—
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C2×#235—24no—
120C2×#235—44no—
121C22×D12C2311yescharacteristic
122C22×C4×D3C2312yes—
123C22×Dic6—24no—
124C22×Dic6—28no—
125C22×Dic6C2312yes—
126C22×Dic6C2312yes—
127C22×Dic6C2311yescharacteristic
128C3×#123—44no—
129C2×C3×C4⋊C4—24no—
130C2×C3×C4⋊C4C2312yes—
131C2×C3×C4⋊C4C2312yes—
132C2×C3×C4⋊C4C2314yes—
133C2×C3×C22⋊C4C2312yes—
134C2×C3×C22⋊C4C2314yes—
135C2×C3×C22⋊C4C2314yes—
136C2×#217C2312yes—
137C2×#217C2312yes—
138C2×#217C2314yes—
139C2×#217C2312yes—
140C2×#217C2314yes—
141#947—24no—
142#944—24no—
143#940—24no—
144#939—28no—
145#939—28no—
146#936—24no—
147#935—44no—
148#929—44no—
149C4×#67—28no—
150C4×#67—28no—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×C4⋊Dic3C2314yes—
158C2×Dic3⋊C4—24no—
159C2×Dic3⋊C4—24no—
160C2×Dic3⋊C4C2312yes—
161C2×Dic3⋊C4C2312yes—
162C2×Dic3⋊C4C2314yes—
163C2×Dic3⋊C4C2312yes—
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2312yes—
166C2×Dic3⋊C4C2312yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2314yes—
169C2×C4×Dic3—24no—
170C2×C4×Dic3—24no—
171C2×C4×Dic3D418yes—
172C2×C4×Dic3C2314yes—
173C2×C4×Dic3C2312yes—
174C2×C4×Dic3C2312yes—
175C2×C4×Dic3C2312yes—
176C2×C4×Dic3C2312yes—
177C2×C4×Dic3C2311yescharacteristic
178C2×C4×Dic3C2311yescharacteristic
179C2×C4×Dic3C2311yescharacteristic
180C2×C4×Dic3C2311yescharacteristic
181#887—28no—
182#887—28no—
183#887—28no—
184#887—28no—
185#886—44no—
186#885—216no—
187C3×#95C2314yes—
188C3×#95C2312yes—
189C3×#95C2312yes—
190C3⋊#95C2314yes—
191C3⋊#95C2314yes—
192C3⋊#95C2314yes—
193C3⋊#95C2312yes—
194C3⋊#95C2314yes—
195C3⋊#95C2312yes—
196C3⋊#95C2314yes—
197C22×#41—31no—
198C22×#41C2×D311yescharacteristic
199C23×Q8—31no—
200#532—68no—
201C2×C4⋊Q8—31no—
202C2×#127—31no—
203C2×#124—31no—
204C2×#124—31no—
205C2×#124—34no—
206C2×#123—32no—
207C2×#123—32no—
208C2×#123—32no—
209C2×#123C2×D312yes—
210C2×#121—32no—
211C2×#121—32no—
212C2×C4×Q8—32no—
213C2×C4×Q8—32no—
214C2×C4×Q8—32no—
215C2×C4×Q8—32no—
216C2×C4×Q8—68no—
217C2×C4×D4—32no—
218C2×C4×D4—32no—
219C22×C4⋊C4—31no—
220C22×C4⋊C4—31no—
221C22×C4⋊C4C2×D311yescharacteristic
222C22×C42—31no—
223C22×C42—31no—
224C22×C42—31no—
225#399—34no—
226#399—34no—
227#395—32no—
228#395—32no—
229#395—32no—
230#395C2×D312yes—
231#394—32no—
232#394—32no—
233#394—32no—
234#394C2×D312yes—
235#393—34no—
236#393—34no—
237#391—34no—
238#390—34no—
239#390—34no—
240#390—34no—
241#389—34no—
242#389—34no—
243#388—34no—
244#388—34no—
245#388—34no—
246#388—34no—
247#386—32no—
248#386—32no—
249#386—32no—
250#386C2×D312yes—
251#385—34no—
252#385—34no—
253#385—34no—
254#385C2×D314yes—
255#384—34no—
256#383—32no—
257#382—32no—
258#381—31no—
259#381C2×D311yescharacteristic
260#380—32no—
261C4×C4⋊C4—32no—
262C4×C22⋊C4—32no—
263#376—32no—
264C24×C3C2412yes—
265C24×C3C2411yescharacteristic
266C23×D3C2412yes—
267C3×#41—416no—
268C2×C3×Q8—22no—
269C2×C3×Q8—42no—
270C2×C3×D4—24no—
271C2×C3×D4—24no—
272C2×C3×D4—24no—
273C2×C3×D4—22no—
274C2×C3×D4—42no—
275C22×C3×C4—22no—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—22no—
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4—42no—
282C22×C3×C4—42no—
283C22×C3×C4C2×D414yes—
284C22×C3×C4C2414yes—
285C22×C3×C4C2412yes—
286C22×C3×C4C2412yes—
287C22×C3×C4C2411yescharacteristic
288C22×C3×C4C2411yescharacteristic
289C22×C3×C4C2412yes—
290C2×#67—24no—
291C2×#67—24no—
292C2×#67—24no—
293C2×#67—24no—
294C2×#67—24no—
295C2×#67—28no—
296C2×#67—28no—
297C22×Dic3—22no—
298C22×Dic3—24no—
299C22×Dic3—24no—
300C22×Dic3—24no—
301C22×Dic3—22no—
302C22×Dic3—24no—
303C22×Dic3C2×D414yes—
304C22×Dic3C2×D414yes—
305C22×Dic3C2414yes—
306C22×Dic3C2412yes—
307C22×Dic3C2412yes—
308C22×Dic3C2411yescharacteristic
309C22×Dic3C2411yescharacteristic
310C22×Dic3C2412yes—
311C22×Dic3C2411yescharacteristic
312C22×Dic3C2411yescharacteristic
313#235—416no—
314C2×D12—22no—
315C2×D12—42no—
316C2×C4×D3—24no—
317C2×C4×D3—42no—
318C2×C4×D3—42no—
319C2×Dic6—232no—
320C2×Dic6—24no—
321C2×Dic6—24no—
322C2×Dic6—24no—
323C2×Dic6—24no—
324C2×Dic6—24no—
325C2×Dic6—22no—
326C2×Dic6—42no—
327C2×Dic6#4118yescomplemented
328C3×C4⋊C4—24no—
329C3×C4⋊C4—24no—
330C3×C4⋊C4—44no—
331C3×C22⋊C4—24no—
332C3×C22⋊C4—28no—
333C3×C22⋊C4—44no—
334#217—24no—
335#217—24no—
336#217—24no—
337#217—28no—
338#217—44no—
339(C2×D3)⋊C4—28no—
340(C2×D3)⋊C4—24no—
341(C2×D3)⋊C4—24no—
342(C2×D3)⋊C4—28no—
343(C2×D3)⋊C4—44no—
344(C2×D3)⋊C4—44no—
345C4⋊Dic3—44no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—24no—
349Dic3⋊C4—24no—
350Dic3⋊C4—24no—
351Dic3⋊C4—24no—
352Dic3⋊C4—28no—
353Dic3⋊C4—44no—
354Dic3⋊C4—44no—
355C4×Dic3—24no—
356C4×Dic3—24no—
357C4×Dic3—24no—
358C4×Dic3—24no—
359C4×Dic3—28no—
360C4×Dic3C2×D414yes—
361C4×Dic3C2×D414yes—
362C4×Dic3C2×D414yes—
363C4×Dic3C2×D414yes—
364C2×#41—24no—
365C2×#41—44no—
366C2×#41—64no—
367C2×#41—124no—
368C22×Q8—32no—
369C22×Q8—32no—
370C22×Q8—31no—
371C22×Q8—64no—
372C22×Q8—68no—
373C22×Q8C22×D311yescharacteristic
374C22×D4—32no—
375C22×D4—32no—
376C22×D4—32no—
377C22×D4—31no—
378C22×D4C22×D312yes—
379C22×D4C22×D311yescharacteristic
380C23×C4—31no—
381C23×C4—31no—
382C23×C4—31no—
383C23×C4—31no—
384C23×C4—32no—
385C23×C4C22×D311yescharacteristic
386C23×C4C22×D311yescharacteristic
387C23×C4C22×D311yescharacteristic
388C23×C4C22×D312yes—
389C4⋊Q8—64no—
390#127—64no—
391#124—64no—
392#124—64no—
393#124—616no—
394#123—44no—
395#123—124no—
396#123—124no—
397#123—124no—
398#121—68no—
399#121—68no—
400C4×Q8—68no—
401C4×Q8—68no—
402C4×Q8—68no—
403C4×Q8—68no—
404C4×D4—68no—
405C4×D4—68no—
406C2×C4⋊C4—24no—
407C2×C4⋊C4—32no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—32no—
411C2×C4⋊C4—32no—
412C2×C4⋊C4—32no—
413C2×C4⋊C4—34no—
414C2×C4⋊C4—34no—
415C2×C4⋊C4—34no—
416C2×C4⋊C4—34no—
417C2×C4⋊C4—64no—
418C2×C4⋊C4—64no—
419C2×C4⋊C4C22×D312yes—
420C2×C4⋊C4C22×D312yes—
421C2×C4⋊C4C22×D314yes—
422C2×C22⋊C4—32no—
423C2×C22⋊C4—32no—
424C2×C22⋊C4—32no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—32no—
427C2×C22⋊C4—32no—
428C2×C22⋊C4—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—34no—
431C2×C22⋊C4—34no—
432C2×C22⋊C4—34no—
433C2×C22⋊C4C22×D312yes—
434C2×C22⋊C4C22×D314yes—
435C2×C22⋊C4C22×D314yes—
436C2×C42—38no—
437C2×C42—31no—
438C2×C42—31no—
439C2×C42—31no—
440C2×C42—31no—
441C2×C42—32no—
442C2×C42—32no—
443C2×C42—32no—
444C2×C42—32no—
445C2×C42—34no—
446C2×C42—64no—
447C2×C42—64no—
448#95—34no—
449#95—32no—
450#95—34no—
451#95—32no—
452#95—34no—
453#95—34no—
454#95—34no—
455#95C22×D312yes—
456#95C22×D312yes—
457#95C22×D314yes—
458C23×C3—22no—
459C23×C3—22no—
460C23×C3—22no—
461C23×C3—24no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—24no—
465C23×C3C22×D412yes—
466C23×C3H(5,𝔽2)14yes—
467C23×C3C2511yescharacteristic
468C22×D3—22no—
469C22×D3—24no—
470C22×D3—22no—
471C22×D3—22no—
472C22×D3—24no—
473C3×Q8—44no—
474C3×D4—44no—
475C3×D4—48no—
476C2×C3×C4—28no—
477C2×C3×C4—28no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—24no—
485C2×C3×C4—22no—
486C2×C3×C4—24no—
487C2×C3×C4—24no—
488C2×C3×C4—22no—
489C2×C3×C4—24no—
490C2×C3×C4—48no—
491C2×C3×C4—44no—
492C2×C3×C4C22×D412yes—
493C2×C3×C4C22×D412yes—
494C2×C3×C4C2×#4114yes—
495#67—48no—
496#67—48no—
497#67—48no—
498C2×Dic3—28no—
499C2×Dic3—22no—
500C2×Dic3—22no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3—28no—
504C2×Dic3—28no—
505C2×Dic3—22no—
506C2×Dic3—22no—
507C2×Dic3—24no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—24no—
511C2×Dic3—22no—
512C2×Dic3—24no—
513C2×Dic3—44no—
514C2×Dic3C22×D412yes—
515C2×Dic3C22×D412yes—
516C2×Dic3C22×D412yes—
517C2×Dic3C22×D412yes—
518C2×Dic3C2×#4114yes—
519C2×Dic3C2×#4114yes—
520C2×Dic32−1+414yes—
521D12—44no—
522C4×D3—48no—
523Dic6—216no—
524Dic6—216no—
525Dic6—44no—
526C24—32no—
527C24C23×D312yes—
528C24C23×D311yescharacteristic
529#41—416no—
530#41—1216no—
531C2×Q8—22no—
532C2×Q8—38no—
533C2×Q8—42no—
534C2×Q8—64no—
535C2×Q8—64no—
536C2×Q8—64no—
537C2×Q8—64no—
538C2×Q8—632no—
539C2×Q8—62no—
540C2×Q8—64no—
541C2×Q8—122no—
542C2×D4—24no—
543C2×D4—24no—
544C2×D4—24no—
545C2×D4—22no—
546C2×D4—42no—
547C2×D4—64no—
548C2×D4—64no—
549C2×D4—68no—
550C2×D4—68no—
551C2×D4—64no—
552C2×D4—64no—
553C2×D4—64no—
554C2×D4—62no—
555C2×D4—122no—
556C22×C4—22no—
557C22×C4—24no—
558C22×C4—24no—
559C22×C4—22no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—34no—
565C22×C4—34no—
566C22×C4—31no—
567C22×C4—31no—
568C22×C4—32no—
569C22×C4—34no—
570C22×C4—32no—
571C22×C4—32no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—64no—
575C22×C4—64no—
576C22×C4—64no—
577C22×C4—62no—
578C22×C4—62no—
579C22×C4—64no—
580C22×C4—64no—
581C22×C4—122no—
582C22×C4—122no—
583C22×C4D3×D414yes—
584C22×C4C23×D314yes—
585C22×C4C23×D312yes—
586C22×C4C23×D312yes—
587C22×C4C23×D311yescharacteristic
588C22×C4C23×D311yescharacteristic
589C22×C4C23×D312yes—
590C4⋊C4—24no—
591C4⋊C4—24no—
592C4⋊C4—44no—
593C4⋊C4—64no—
594C4⋊C4—64no—
595C4⋊C4—64no—
596C4⋊C4—64no—
597C4⋊C4—68no—
598C4⋊C4—64no—
599C4⋊C4—64no—
600C4⋊C4—124no—
601C4⋊C4—124no—
602C4⋊C4—124no—
603C22⋊C4—24no—
604C22⋊C4—28no—
605C22⋊C4—44no—
606C22⋊C4—64no—
607C22⋊C4—64no—
608C22⋊C4—68no—
609C22⋊C4—64no—
610C22⋊C4—64no—
611C22⋊C4—68no—
612C22⋊C4—64no—
613C22⋊C4—68no—
614C22⋊C4—124no—
615C22⋊C4—124no—
616C22⋊C4—124no—
617C42—34no—
618C42—34no—
619C42—34no—
620C42—34no—
621C42—64no—
622C42—64no—
623C42—64no—
624C42—64no—
625C42—68no—
626C22×C3—22no—
627C22×C3—22no—
628C22×C3—28no—
629C22×C3—42no—
630C22×C3—42no—
631C22×C3—42no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3#53514yes—
635C22×C3C23×D411yescharacteristic
636C22×C3C22×#4112yes—
637C22×C3C2×H(5,𝔽2)12yes—
638C22×C3C2×2−1+412yes—
639C2×D3—42no—
640C2×D3—42no—
641C2×D3—42no—
642C2×D3—44no—
643C2×D3—44no—
644C3×C4—24no—
645C3×C4—22no—
646C3×C4—22no—
647C3×C4—42no—
648C3×C4—42no—
649C3×C4—44no—
650Dic3—22no—
651Dic3—24no—
652Dic3—22no—
653Dic3—42no—
654Dic3—42no—
655Dic3—44no—
656Dic3#52514yes—
657Dic3#53614yes—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—62no—
666C23—62no—
667C23—62no—
668C23—64no—
669C23—64no—
670C23C2×D3×D412yes—
671C23#100414yes—
672C23C24×D311yescharacteristic
673Q8—44no—
674Q8—616no—
675Q8—616no—
676Q8—124no—
677D4—44no—
678D4—48no—
679D4—124no—
680D4—128no—
681D4—128no—
682D4—128no—
683C2×C4—28no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—28no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—32no—
698C2×C4—32no—
699C2×C4—34no—
700C2×C4—34no—
701C2×C4—32no—
702C2×C4—32no—
703C2×C4—34no—
704C2×C4—48no—
705C2×C4—44no—
706C2×C4—68no—
707C2×C4—68no—
708C2×C4—68no—
709C2×C4—62no—
710C2×C4—62no—
711C2×C4—62no—
712C2×C4—62no—
713C2×C4—62no—
714C2×C4—62no—
715C2×C4—64no—
716C2×C4—64no—
717C2×C4—62no—
718C2×C4—62no—
719C2×C4—64no—
720C2×C4—64no—
721C2×C4—128no—
722C2×C4—124no—
723C2×C4C2×D3×D412yes—
724C2×C4C2×D3×D412yes—
725C2×C4D3×#4114yes—
726C2×C3—24no—
727C2×C3—82no—
728C2×C3C2×#52511yescharacteristic
729C2×C3C2×#53511yescharacteristic
730C2×C3C2×#53611yescharacteristic
731C2×C3#352214yes—
732D3—82no—
733C22—22no—
734C22—22no—
735C22—28no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—44no—
740C22—44no—
741C22—122no—
742C22—122no—
743C22—122no—
744C22—124no—
745C22—124no—
746C22#559214yes—
747C22C22×D3×D411yescharacteristic
748C22C2×#100412yes—
749C22C2×D3×#4112yes—
750C22D3×2−1+412yes—
751C4—24no—
752C4—22no—
753C4—22no—
754C4—34no—
755C4—34no—
756C4—42no—
757C4—42no—
758C4—44no—
759C4—62no—
760C4—64no—
761C4—62no—
762C4—122no—
763C4—122no—
764C4—124no—
765C3#3524911yescharacteristic, complemented, Sylow
766C2—24no—
767C2—82no—
768C2—242no—
769C2C2×#559211yescharacteristic
770C2D3×#52511yescharacteristic
771C2D3×#53611yescharacteristic
772C2#8668814yes—
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2406C2
prime radicalC2×#5832C2
hypercenter#2406D3
hypocenterC3#35249
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2406

Complements

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

NH ≅ G/Ntype
2. C22×#887C2semidirect
3. C3×#2406C2semidirect
4. #84090C2semidirect
5. #82891C2semidirect
6. #82859C2semidirect
7. #82192C2semidirect
8. #77203C2semidirect
9. #77189C2semidirect
10. #76977C2semidirect
11. #76946C2semidirect
12. #74872C2semidirect
13. #74701C2semidirect
14. #74487C2semidirect
15. #74386C2semidirect
16. #74063C2semidirect
17. #74051C2semidirect
100. #2406D3semidirect
327. C2×Dic6#41semidirect
765. C3#35249semidirect

Maximal subgroups

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

subgroupindex
C2×#58322
C22×#8872
C3×#24062
#840902
#828912
#828592
#821922
#772032
#771892
#769772
#769462
#748722
#747012
#744872
#743862
#740632
#740512
#352493