Finite Group Databasebeta

← #10823394

Subgroups — #10823394

Order 768.

1188 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×#5680C211yesmaximal, characteristic
2C2×Dic3×Q16C211yesmaximal, characteristic, complemented
3C2×Dic3×SD16C211yesmaximal, characteristic, complemented
4#76479C211yesmaximal, characteristic, complemented
5C3×#2015C211yesmaximal, characteristic, complemented
6#72071C211yesmaximal, characteristic, complemented
7#72054C211yesmaximal, characteristic
8#71722C211yesmaximal, characteristic, complemented
9#70243C211yesmaximal, characteristic, complemented
10Dic3×#103C211yesmaximal, characteristic, complemented
11#70175C211yesmaximal, characteristic
12Dic3×#102C211yesmaximal, characteristic, complemented
13#69669C211yesmaximal, characteristic, complemented
14#68634C211yesmaximal, characteristic, complemented
15#68599C211yesmaximal, characteristic, complemented
16#23572—31nomaximal, Sylow
17C22×C3×Q16C2211yescharacteristic
18C22×C3×SD16C2211yescharacteristic
19C2×C3×#124C2211yescharacteristic
20C2×#946C2211yescharacteristic
21C2×#946C2211yescharacteristic
22C2×Q8×Dic3C2211yescharacteristic
23C2×Q8×Dic3C2211yescharacteristic
24C2×#938C2211yescharacteristic
25C2×D4×Dic3C2211yescharacteristic
26#5680—24no—
27#5680—24no—
28C2×#883—21no—
29C2×#67⋊C4—21no—
30C2×#879—21no—
31C2×#877—21no—
32C2×C42×D3C2211yescharacteristic
33C2×#870C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C3×#391C2211yescharacteristic
37C2×#835C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×#832C2211yescharacteristic
43Dic3×Q16—24no—
44Dic3×SD16—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×#818C2211yescharacteristic
48C2×#817C2211yescharacteristic
49C2×C8×Dic3C2211yescharacteristic
50C2×C8×Dic3C2211yescharacteristic
51#4987C2211yescharacteristic
52Dic3×C4⋊C4C2211yescharacteristic
53#4928C2211yescharacteristic
54#4668—21no—
55#4666—21no—
56#4655—21no—
57#4649—21no—
58C3×#336C2211yescharacteristic
59#4551C2211yescharacteristic
60#4551C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×C4×Q16—31no—
66C2×C4×SD16—31no—
67C4×C22⋊Q8—31no—
68#2059—31no—
69#2042—31no—
70#2035—31no—
71#2033—31no—
72#2026—31no—
73#2015D311yescharacteristic, complemented
74#2001—31no—
75#2000—31no—
76C4×#103—31no—
77C4×#102—31no—
78C4×C22⋊C8—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C3×D4C2311yescharacteristic
82C22×#67—21no—
83C23×Dic3—21no—
84C22×C4×D3D411yescharacteristic
85C22×C4×D3D411yescharacteristic
86C22×C4×D3C2311yescharacteristic
87C2×C3×Q16—22no—
88C2×C3×Q16—22no—
89C2×C3×Q16—22no—
90C2×C3×SD16—22no—
91C2×C3×SD16—22no—
92C2×C3×SD16—22no—
93C22×C3×C8C2311yescharacteristic
94C22×C3×C8C2311yescharacteristic
95C3×#124—22no—
96C3×#124—22no—
97C2×C3×C4⋊C4C2311yescharacteristic
98C2×C3×C22⋊C4—21no—
99C2×C3×C22⋊C4—21no—
100C2×C3×C42C2311yescharacteristic
101C2×#217—21no—
102C2×#217—21no—
103#946—22no—
104#946—22no—
105#946—22no—
106#946—22no—
107Q8×Dic3—22no—
108Q8×Dic3—22no—
109Q8×Dic3—22no—
110Q8×Dic3D414yes—
111#938—22no—
112#938—22no—
113D4×Dic3—22no—
114D4×Dic3D414yes—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—21no—
117C2×(C2×D3)⋊C4—21no—
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3C2311yescharacteristic
121C2×C4⋊Dic3C2311yescharacteristic
122C2×C4⋊Dic3C2311yescharacteristic
123C2×C4⋊Dic3C2311yescharacteristic
124C2×Dic3⋊C4—21no—
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3—21no—
132C2×C4×Dic3D411yescharacteristic
133C2×C4×Dic3D411yescharacteristic
134C2×C4×Dic3C2311yescharacteristic
135C22×C3⋊C8C2311yescharacteristic
136C22×C3⋊C8C2311yescharacteristic
137#883—28no—
138#67⋊C4—28no—
139#879—28no—
140#877—28no—
141C42×D3—22no—
142C42×D3—22no—
143#870—22no—
144#870—22no—
145C3×#103—22no—
146C3×#102—22no—
147C3×#95—21no—
148C3×#95—21no—
149#835—22no—
150#835—22no—
151#835—22no—
152#835—22no—
153#832—22no—
154#832—22no—
155C3⋊#95—21no—
156C3⋊#95—21no—
157C3⋊#95—21no—
158(C2×D3)⋊C8—22no—
159(C2×D3)⋊C8—22no—
160#818—22no—
161#817—22no—
162C8×Dic3—22no—
163C8×Dic3—22no—
164C22×Q16C2×D311yescharacteristic
165C22×SD16C2×D311yescharacteristic
166#529—64no—
167#529—64no—
168C2×#126—61no—
169C2×#125—31no—
170C2×#124C2×D311yescharacteristic
171C2×#123—61no—
172C2×C22⋊Q8—31no—
173C2×C22⋊Q8—31no—
174C2×#121—31no—
175C2×C4×Q8—31no—
176C2×C4×Q8—31no—
177C2×C4×D4—31no—
178C2×C4×D4—61no—
179C2×#117—61no—
180C22×C42—31no—
181C4×Q16—64no—
182C4×SD16—64no—
183C2×#107—31no—
184C2×#106—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#102—31no—
191C2×#102—31no—
192C2×#102C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C22⋊C8—31no—
195C2×C4×C8—31no—
196C2×C4×C8—31no—
197#391C2×D311yescharacteristic
198#389—31no—
199#387—61no—
200#385—61no—
201#380—31no—
202C4×C4⋊C4—31no—
203C4×C4⋊C4—61no—
204C4×C22⋊C4—61no—
205#340—31no—
206#340—31no—
207#340—31no—
208#340—31no—
209#336—31no—
210#336C2×D311yescharacteristic
211C24×C3—21no—
212C23×D3C2×D411yescharacteristic
213C2×C3×Q8—21no—
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8C2×D412yes—
224C2×C3×Q8#4112yes—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—21no—
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4C2×D412yes—
231C22×C3×C4—21no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D411yescharacteristic
236C22×C3×C4C2411yescharacteristic
237C2×#67—24no—
238C2×#67—42no—
239C2×#67—42no—
240C22×Dic3—21no—
241C22×Dic3—21no—
242C22×Dic3—21no—
243C22×Dic3—24no—
244C22×Dic3—21no—
245C22×Dic3—42no—
246C22×Dic3—42no—
247C22×Dic3C2×D411yescharacteristic
248C22×Dic3C2×D411yescharacteristic
249C22×Dic3C2×D411yescharacteristic
250C2×C4×D3—22no—
251C2×C4×D3—21no—
252C2×C4×D3—21no—
253C2×C4×D3—21no—
254C2×C4×D3—21no—
255C2×C4×D3—21no—
256C2×C4×D3—21no—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3—22no—
261C2×C4×D3—41no—
262C3×Q16—28no—
263C3×SD16—28no—
264C2×C3×C8—21no—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—21no—
268C2×C3×C8#4112yes—
269C2×C3×C8#4112yes—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—24no—
274C3×C42—21no—
275C3×C42—21no—
276#217—24no—
277#217—24no—
278(C2×D3)⋊C4—24no—
279(C2×D3)⋊C4—24no—
280(C2×D3)⋊C4—42no—
281C4⋊Dic3—21no—
282C4⋊Dic3—21no—
283C4⋊Dic3—21no—
284C4⋊Dic3—24no—
285C4⋊Dic3—21no—
286C4⋊Dic3—21no—
287C4⋊Dic3—42no—
288C4⋊Dic3C2×D412yes—
289C4⋊Dic3C2×D412yes—
290C4⋊Dic3#4112yes—
291Dic3⋊C4—24no—
292Dic3⋊C4—24no—
293Dic3⋊C4—24no—
294Dic3⋊C4—24no—
295Dic3⋊C4—42no—
296C4×Dic3—22no—
297C4×Dic3—22no—
298C4×Dic3—24no—
299C4×Dic3—42no—
300C4×Dic3—42no—
301C4×Dic3C2×D412yes—
302C4×Dic3C2×D412yes—
303C2×C3⋊C8—21no—
304C2×C3⋊C8—21no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—21no—
308C2×C3⋊C8—21no—
309C22×Q8C22×D311yescharacteristic
310C22×Q8C22×D311yescharacteristic
311C22×D4—61no—
312C22×D4C22×D311yescharacteristic
313C23×C4—31no—
314C23×C4—31no—
315C23×C4—31no—
316C23×C4—61no—
317C2×Q16—22no—
318C2×Q16—22no—
319C2×Q16—22no—
320C2×SD16—22no—
321C2×SD16—22no—
322C2×SD16—22no—
323C22×C8—31no—
324C22×C8—31no—
325C22×C8C22×D311yescharacteristic
326C22×C8C22×D311yescharacteristic
327#126—68no—
328#125—62no—
329#125—62no—
330#124—22no—
331#124—22no—
332#123—68no—
333C22⋊Q8—62no—
334C22⋊Q8—62no—
335C22⋊Q8—62no—
336C22⋊Q8—62no—
337#121—62no—
338#121—62no—
339C4×Q8—34no—
340C4×Q8—62no—
341C4×Q8—62no—
342C4×Q8—62no—
343C4×D4—34no—
344C4×D4—62no—
345C4×D4—68no—
346#117—68no—
347C2×C4⋊C4—31no—
348C2×C4⋊C4—31no—
349C2×C4⋊C4—31no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—61no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4C22×D311yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—61no—
362C2×C22⋊C4—61no—
363C2×C22⋊C4—61no—
364C2×C22⋊C4—61no—
365C2×C22⋊C4—61no—
366C2×C42—31no—
367C2×C42—31no—
368C2×C42—31no—
369C2×C42—62no—
370C2×C42—62no—
371C2×C42—61no—
372C2×C42—61no—
373C2×C42—61no—
374C2×C42C22×D311yescharacteristic
375#107—62no—
376#106—62no—
377#103—22no—
378#103—62no—
379#103—62no—
380#103—62no—
381#103—62no—
382#102—22no—
383#102—62no—
384#102—62no—
385C22⋊C8—62no—
386C22⋊C8—62no—
387C4×C8—62no—
388C4×C8—62no—
389#95—21no—
390#95—21no—
391#95—61no—
392#95—61no—
393#95—61no—
394C23×C3—22no—
395C23×C3—41no—
396C23×C3—41no—
397C23×C3—41no—
398C23×C3—41no—
399C23×C3—41no—
400C23×C3—41no—
401C23×C3C22×D411yescharacteristic
402C22×D3—21no—
403C22×D3—21no—
404C22×D3—21no—
405C22×D3—21no—
406C22×D3—21no—
407C22×D3—21no—
408C22×D3#13512yes—
409C3×Q8—22no—
410C3×Q8—22no—
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—41no—
414C3×Q8—41no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×D4—22no—
418C3×D4—22no—
419C3×D4—41no—
420C3×D4—41no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—22no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—41no—
430C2×C3×C4—41no—
431C2×C3×C4—41no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—41no—
435C2×C3×C4—41no—
436C2×C3×C4C22×D411yescharacteristic
437C2×C3×C4C22×D411yescharacteristic
438C2×C3×C4C2×#4111yescharacteristic
439C2×C3×C4C2×#4111yescharacteristic
440C2×C3×C4C2×#4111yescharacteristic
441C2×C3×C4C2×#4111yescharacteristic
442#67—48no—
443C2×Dic3—21no—
444C2×Dic3—21no—
445C2×Dic3—21no—
446C2×Dic3—22no—
447C2×Dic3—22no—
448C2×Dic3—21no—
449C2×Dic3—22no—
450C2×Dic3—21no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3—41no—
455C2×Dic3—41no—
456C2×Dic3—41no—
457C2×Dic3—48no—
458C2×Dic3—41no—
459C2×Dic3—41no—
460C2×Dic3—41no—
461C2×Dic3#12012yes—
462C2×Dic3#12012yes—
463C2×Dic3#13512yes—
464C2×Dic3#13712yes—
465C4×D3—44no—
466C4×D3—41no—
467C4×D3—41no—
468C4×D3—41no—
469C4×D3—41no—
470C4×D3—44no—
471C3×C8—22no—
472C3×C8—22no—
473C3⋊C8—41no—
474C3⋊C8—41no—
475C24—21no—
476C24—31no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8D3×D412yes—
488C2×Q8#23712yes—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—64no—
495C2×D4—122no—
496C2×D4—122no—
497C2×D4D3×D412yes—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—31no—
504C22×C4—62no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—64no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4—61no—
514C22×C4—61no—
515C22×C4—61no—
516C22×C4—61no—
517C22×C4—61no—
518C22×C4—61no—
519C22×C4—61no—
520C22×C4—121no—
521C22×C4—122no—
522C22×C4—122no—
523C22×C4D3×D411yescharacteristic
524C22×C4D3×D411yescharacteristic
525C22×C4C23×D311yescharacteristic
526Q16—28no—
527SD16—28no—
528C2×C8—21no—
529C2×C8—21no—
530C2×C8—21no—
531C2×C8—21no—
532C2×C8—61no—
533C2×C8—61no—
534C2×C8—61no—
535C2×C8—61no—
536C2×C8—61no—
537C2×C8—61no—
538C2×C8#23712yes—
539C2×C8#23712yes—
540C4⋊C4—21no—
541C4⋊C4—21no—
542C4⋊C4—32no—
543C4⋊C4—32no—
544C4⋊C4—32no—
545C4⋊C4—64no—
546C4⋊C4—64no—
547C4⋊C4—64no—
548C4⋊C4—64no—
549C4⋊C4—64no—
550C4⋊C4—61no—
551C4⋊C4—61no—
552C4⋊C4—61no—
553C4⋊C4—61no—
554C4⋊C4—61no—
555C4⋊C4—122no—
556C4⋊C4—122no—
557C22⋊C4—24no—
558C22⋊C4—24no—
559C22⋊C4—64no—
560C22⋊C4—64no—
561C22⋊C4—64no—
562C22⋊C4—64no—
563C22⋊C4—122no—
564C42—21no—
565C42—21no—
566C42—32no—
567C42—32no—
568C42—62no—
569C42—62no—
570C42—64no—
571C42—122no—
572C42—122no—
573C22×C3—42no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—81no—
577C22×C3—81no—
578C22×C3—81no—
579C22×C3—81no—
580C22×C3C2×#12011yescharacteristic
581C22×C3#52511yescharacteristic
582C22×C3#53211yescharacteristic
583C22×C3C2×#13511yescharacteristic
584C22×C3C2×#13511yescharacteristic
585C22×C3C2×#13711yescharacteristic
586C22×C3#57511yescharacteristic
587C2×D3—22no—
588C2×D3—22no—
589C2×D3—22no—
590C2×D3—41no—
591C2×D3—41no—
592C2×D3—41no—
593C2×D3—41no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—41no—
597C3×C4—41no—
598C3×C4—81no—
599C3×C4#52511yescharacteristic
600C3×C4#52511yescharacteristic
601C3×C4#53211yescharacteristic
602C3×C4#53211yescharacteristic
603Dic3—22no—
604Dic3—42no—
605Dic3—41no—
606Dic3—42no—
607Dic3—42no—
608Dic3—81no—
609Dic3#45214yes—
610C23—22no—
611C23—32no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—61no—
619C23—61no—
620C23—61no—
621C23—61no—
622C23—61no—
623C23—61no—
624C23C2×D3×D411yescharacteristic
625Q8—22no—
626Q8—22no—
627Q8—22no—
628Q8—22no—
629Q8—41no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633D4—22no—
634D4—22no—
635D4—41no—
636D4—41no—
637D4—128no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—32no—
647C2×C4—32no—
648C2×C4—32no—
649C2×C4—32no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—61no—
658C2×C4—61no—
659C2×C4—61no—
660C2×C4—61no—
661C2×C4—62no—
662C2×C4—62no—
663C2×C4—62no—
664C2×C4—61no—
665C2×C4—124no—
666C2×C4—128no—
667C2×C4—124no—
668C2×C4—121no—
669C2×C4—121no—
670C2×C4—121no—
671C2×C4—121no—
672C2×C4—121no—
673C2×C4—121no—
674C2×C4—121no—
675C2×C4—121no—
676C2×C4—121no—
677C2×C4—121no—
678C2×C4—121no—
679C2×C4—121no—
680C2×C4—121no—
681C2×C4C2×D3×D411yescharacteristic
682C2×C4C2×D3×D411yescharacteristic
683C2×C4C2×#23711yescharacteristic
684C2×C4C2×#23711yescharacteristic
685C2×C4C2×#23711yescharacteristic
686C2×C4D3×#4111yescharacteristic
687C8—22no—
688C8—22no—
689C8—121no—
690C8—121no—
691C2×C3—82no—
692C2×C3#238811yescharacteristic
693C2×C3C2×#45211yescharacteristic
694C2×C3#300211yescharacteristic
695C2×C3#310211yescharacteristic
696C2×C3#310811yescharacteristic
697C2×C3#316811yescharacteristic
698C2×C3#317211yescharacteristic
699D3—42no—
700C22—42no—
701C22—42no—
702C22—42no—
703C22—62no—
704C22—62no—
705C22—62no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—121no—
711C22—121no—
712C22—121no—
713C22—121no—
714C22D3×#12011yescharacteristic
715C22#560611yescharacteristic
716C22#571611yescharacteristic
717C22D3×#13511yescharacteristic
718C22D3×#13511yescharacteristic
719C22D3×#13711yescharacteristic
720C22#577711yescharacteristic
721C4—34no—
722C4—41no—
723C4—41no—
724C4—42no—
725C4—42no—
726C4—62no—
727C4—81no—
728C4—122no—
729C4—122no—
730C4—121no—
731C4—122no—
732C4—241no—
733C4#558611yescharacteristic
734C4#558611yescharacteristic
735C4#559611yescharacteristic
736C4#559611yescharacteristic
737C3#2357211yescharacteristic, complemented, Sylow
738C2—82no—
739C2—122no—
740C2#7666511yescharacteristic
741C2D3×#45211yescharacteristic
742C2#8022611yescharacteristic
743C2#8056811yescharacteristic
744C2#8056911yescharacteristic
745C2#8180911yescharacteristic
746C2#8186111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2015C2
socleC23×C3C22×D4
prime radicalC2×#938C22
hypercenter#2015D3
hypocenterC3#23572
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2015

Complements

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

NH ≅ G/Ntype
2. C2×Dic3×Q16C2semidirect
3. C2×Dic3×SD16C2semidirect
4. #76479C2semidirect
5. C3×#2015C2semidirect
6. #72071C2semidirect
8. #71722C2semidirect
9. #70243C2semidirect
10. Dic3×#103C2semidirect
12. Dic3×#102C2semidirect
13. #69669C2semidirect
14. #68634C2semidirect
15. #68599C2semidirect
73. #2015D3semidirect
737. C3#23572semidirect

Maximal subgroups

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

subgroupindex
C2×#56802
C2×Dic3×Q162
C2×Dic3×SD162
#764792
C3×#20152
#720712
#720542
#717222
#702432
Dic3×#1032
#701752
Dic3×#1022
#696692
#686342
#685992
#235723