Finite Group Databasebeta

← #10732514

Subgroups — #10732514

Order 768.

2878 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C22×#947C211yesmaximal, characteristic, complemented
3C22×#930C211yesmaximal, characteristic
4C2×#5229C211yesmaximal, characteristic, complemented
5C2×C4×#217C211yesmaximal, characteristic, complemented
6C2×#4988C211yesmaximal, characteristic, complemented
7#71570C214yesmaximal, complemented
8#71563C211yesmaximal, characteristic, complemented
9#71550C214yesmaximal, complemented
10#15215—31nomaximal, Sylow
11C23×C3×Q8C2211yescharacteristic
12C24×C3×C4C2211yescharacteristic
13C23×#67C2212yes—
14C23×D12C2211yescharacteristic
15C2×C3×C22⋊Q8—24no—
16C2×C3×C22⋊Q8—24no—
17C2×C3×C22⋊Q8—24no—
18C22×C3×C4⋊C4C2212yes—
19C22×C3×C4⋊C4C2211yescharacteristic
20C22×C3×C22⋊C4C2212yes—
21C22×#217C2212yes—
22C2×#947—24no—
23C2×#947—24no—
24C2×#947—24no—
25C2×#930—24no—
26C2×#930—24no—
27C2×#930—24no—
28C22×(C2×D3)⋊C4C2214yes—
29C22×(C2×D3)⋊C4C2212yes—
30C22×(C2×D3)⋊C4C2214yes—
31C22×C4⋊Dic3C2211yescharacteristic
32C22×C4×Dic3C2211yescharacteristic
33C22×C4×Dic3C2211yescharacteristic
34#5229—24no—
35C4×#217—24no—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2214yes—
38C2×C3⋊#95C2214yes—
39#4988—24no—
40C22×#124—31no—
41C22×C22⋊Q8D311yescharacteristic, complemented
42C22×#121—31no—
43C2×#391—31no—
44C2×#390—31no—
45C2×C4×C22⋊C4—31no—
46#1439—34no—
47#1438—34no—
48C4⋊#95—31no—
49C25×C3C2311yescharacteristic
50C24×D3C2312yes—
51C22×C3×Q8—22no—
52C22×C3×Q8—22no—
53C22×C3×Q8—22no—
54C22×C3×Q8—22no—
55C22×C3×Q8—22no—
56C22×C3×Q8—22no—
57C22×C3×Q8D414yescomplemented
58C23×C3×C4—22no—
59C23×C3×C4—22no—
60C23×C3×C4—22no—
61C23×C3×C4—22no—
62C23×C3×C4—22no—
63C23×C3×C4—22no—
64C23×C3×C4D414yes—
65C23×C3×C4C2311yescharacteristic
66C23×C3×C4C2312yes—
67C23×C3×C4C2312yes—
68C23×C3×C4C2311yescharacteristic
69C22×#67—24no—
70C22×#67—24no—
71C22×#67—28no—
72C22×#67—24no—
73C22×#67—44no—
74C23×Dic3C2312yes—
75C23×Dic3C2312yes—
76C23×Dic3C2312yes—
77C22×D12—22no—
78C22×D12—22no—
79C22×D12—22no—
80C22×D12—22no—
81C22×D12—22no—
82C22×D12—22no—
83C22×D12D414yes—
84C3×C22⋊Q8—232no—
85C2×C3×C4⋊C4—24no—
86C2×C3×C4⋊C4—24no—
87C2×C3×C4⋊C4—24no—
88C2×C3×C4⋊C4—22no—
89C2×C3×C4⋊C4—22no—
90C2×C3×C4⋊C4D414yescomplemented
91C2×C3×C22⋊C4—24no—
92C2×C3×C22⋊C4—24no—
93C2×C3×C22⋊C4—24no—
94C2×#217—24no—
95C2×#217—24no—
96C2×#217—24no—
97#947—232no—
98#930—232no—
99C2×(C2×D3)⋊C4—24no—
100C2×(C2×D3)⋊C4—28no—
101C2×(C2×D3)⋊C4—24no—
102C2×(C2×D3)⋊C4—28no—
103C2×(C2×D3)⋊C4—24no—
104C2×(C2×D3)⋊C4—28no—
105C2×(C2×D3)⋊C4—28no—
106C2×(C2×D3)⋊C4—28no—
107C2×(C2×D3)⋊C4—44no—
108C2×C4⋊Dic3—22no—
109C2×C4⋊Dic3—22no—
110C2×C4⋊Dic3D414yes—
111C2×C4×Dic3—22no—
112C2×C4×Dic3—22no—
113C2×C4×Dic3—22no—
114C2×C4×Dic3—22no—
115C2×C4×Dic3—22no—
116C2×C4×Dic3D414yescomplemented
117C3⋊#95—24no—
118C3⋊#95—28no—
119C3⋊#95—44no—
120C23×Q8C2×D311yescharacteristic
121C23×D4—32no—
122C23×D4—31no—
123C24×C4C2×D311yescharacteristic
124C2×#124—64no—
125C2×#124—64no—
126C2×#124—64no—
127C2×C22⋊Q8—24no—
128C2×C22⋊Q8—24no—
129C2×C22⋊Q8—24no—
130C2×#121—64no—
131C2×#121—64no—
132C2×#121—64no—
133C22×C4⋊C4—31no—
134C22×C4⋊C4C2×D312yes—
135C22×C4⋊C4C2×D311yescharacteristic
136C22×C22⋊C4—32no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—34no—
139C22×C22⋊C4—34no—
140C22×C22⋊C4C2×D312yes—
141C22×C42—31no—
142C22×C42—31no—
143#391—64no—
144#390—64no—
145C4×C22⋊C4—64no—
146C2×#95—34no—
147C2×#95—32no—
148C2×#95—34no—
149C24×C3—21no—
150C24×C3—21no—
151C24×C3—21no—
152C24×C3—21no—
153C24×C3—21no—
154C24×C3—22no—
155C24×C3—21no—
156C24×C3—22no—
157C24×C3—22no—
158C24×C3C2×D412yes—
159C24×C3#4114yes—
160C24×C3C2411yescharacteristic
161C23×D3—22no—
162C23×D3—22no—
163C23×D3—22no—
164C23×D3—22no—
165C23×D3—22no—
166C23×D3—24no—
167C23×D3—22no—
168C23×D3—24no—
169C23×D3—24no—
170C23×D3—24no—
171C23×D3C2×D414yes—
172C2×C3×Q8—28no—
173C2×C3×Q8—28no—
174C2×C3×Q8—28no—
175C2×C3×Q8—44no—
176C2×C3×Q8—44no—
177C2×C3×Q8—44no—
178C2×C3×Q8—44no—
179C22×C3×C4—21no—
180C22×C3×C4—22no—
181C22×C3×C4—21no—
182C22×C3×C4—21no—
183C22×C3×C4—22no—
184C22×C3×C4—22no—
185C22×C3×C4—22no—
186C22×C3×C4—22no—
187C22×C3×C4—22no—
188C22×C3×C4—22no—
189C22×C3×C4—21no—
190C22×C3×C4—21no—
191C22×C3×C4—24no—
192C22×C3×C4—21no—
193C22×C3×C4—22no—
194C22×C3×C4—24no—
195C22×C3×C4—28no—
196C22×C3×C4—28no—
197C22×C3×C4—28no—
198C22×C3×C4—44no—
199C22×C3×C4—44no—
200C22×C3×C4—44no—
201C22×C3×C4—44no—
202C22×C3×C4C2×D412yes—
203C22×C3×C4C2×D412yes—
204C22×C3×C4C2×D412yes—
205C22×C3×C4C2×D414yes—
206C22×C3×C4C2×D414yes—
207C22×C3×C4C2×D412yes—
208C22×C3×C4C2×D412yes—
209C22×C3×C4C2×D412yes—
210C22×C3×C4C2×D412yes—
211C22×C3×C4#4112yes—
212C2×#67—216no—
213C2×#67—416no—
214C2×#67—416no—
215C2×#67—48no—
216C2×#67—48no—
217C22×Dic3—22no—
218C22×Dic3—22no—
219C22×Dic3—22no—
220C22×Dic3—22no—
221C22×Dic3—22no—
222C22×Dic3—22no—
223C22×Dic3—22no—
224C22×Dic3—22no—
225C22×Dic3—22no—
226C22×Dic3—22no—
227C22×Dic3—24no—
228C22×Dic3—22no—
229C22×Dic3—24no—
230C22×Dic3—22no—
231C22×Dic3—22no—
232C22×Dic3—22no—
233C22×Dic3C2×D414yes—
234C22×Dic3C2×D414yes—
235C22×Dic3#4114yes—
236C2×D12—28no—
237C2×D12—28no—
238C2×D12—28no—
239C2×D12—44no—
240C2×D12—44no—
241C2×D12—44no—
242C2×D12—44no—
243C3×C4⋊C4—216no—
244C3×C4⋊C4—28no—
245C3×C22⋊C4—216no—
246#217—216no—
247(C2×D3)⋊C4—216no—
248(C2×D3)⋊C4—232no—
249(C2×D3)⋊C4—416no—
250C4⋊Dic3—28no—
251C4×Dic3—28no—
252C4×Dic3—44no—
253C25—32no—
254C25C22×D311yescharacteristic
255C22×Q8—22no—
256C22×Q8—22no—
257C22×Q8—22no—
258C22×Q8—22no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8#6714yescomplemented
262C22×D4—34no—
263C22×D4—64no—
264C22×D4—64no—
265C22×D4—64no—
266C22×D4—68no—
267C22×D4—62no—
268C22×D4—62no—
269C22×D4—62no—
270C22×D4—62no—
271C22×D4—62no—
272C22×D4—62no—
273C22×D4—124no—
274C23×C4—22no—
275C23×C4—22no—
276C23×C4—22no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—22no—
280C23×C4—32no—
281C23×C4—32no—
282C23×C4—32no—
283C23×C4#6714yes—
284C23×C4C22×D312yes—
285C23×C4C22×D312yes—
286C23×C4C22×D311yescharacteristic
287C23×C4C22×D311yescharacteristic
288#124—632no—
289C22⋊Q8—232no—
290#121—632no—
291C2×C4⋊C4—24no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—24no—
294C2×C4⋊C4—22no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—34no—
297C2×C4⋊C4—62no—
298C2×C4⋊C4—62no—
299C2×C4⋊C4#6714yescomplemented
300C2×C22⋊C4—24no—
301C2×C22⋊C4—24no—
302C2×C22⋊C4—24no—
303C2×C22⋊C4—64no—
304C2×C22⋊C4—68no—
305C2×C22⋊C4—64no—
306C2×C22⋊C4—68no—
307C2×C22⋊C4—64no—
308C2×C22⋊C4—64no—
309C2×C22⋊C4—64no—
310C2×C22⋊C4—64no—
311C2×C22⋊C4—68no—
312C2×C22⋊C4—68no—
313C2×C22⋊C4—68no—
314C2×C22⋊C4—124no—
315C2×C42—34no—
316C2×C42—62no—
317C2×C42—62no—
318C2×C42—62no—
319C2×C42—62no—
320C2×C42—62no—
321#95—64no—
322#95—68no—
323#95—124no—
324C23×C3—22no—
325C23×C3—22no—
326C23×C3—22no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—22no—
330C23×C3—22no—
331C23×C3—22no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—24no—
336C23×C3—41no—
337C23×C3—41no—
338C23×C3—41no—
339C23×C3—41no—
340C23×C3—42no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—42no—
346C23×C3#12414yescomplemented
347C23×C3C22×D411yescharacteristic
348C23×C3C22×D411yescharacteristic
349C23×C3C22×D411yescharacteristic
350C23×C3C22×D411yescharacteristic
351C23×C3C22×D411yescharacteristic
352C23×C3C22×D411yescharacteristic
353C23×C3C2×#4111yescharacteristic
354C23×C3C2×#4112yes—
355C23×C3C2×#4112yes—
356C23×C3H(5,𝔽2)12yes—
357C23×C32−1+412yes—
358C22×D3—24no—
359C22×D3—24no—
360C22×D3—24no—
361C22×D3—28no—
362C22×D3—28no—
363C22×D3—42no—
364C22×D3—42no—
365C22×D3—42no—
366C22×D3—44no—
367C22×D3—42no—
368C22×D3—44no—
369C22×D3—42no—
370C22×D3—42no—
371C22×D3—42no—
372C22×D3—42no—
373C22×D3—44no—
374C22×D3—44no—
375C22×D3—44no—
376C22×D3—44no—
377C22×D3—44no—
378C22×D3—44no—
379C22×D3—44no—
380C22×D3—44no—
381C3×Q8—416no—
382C2×C3×C4—22no—
383C2×C3×C4—24no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—24no—
389C2×C3×C4—28no—
390C2×C3×C4—41no—
391C2×C3×C4—42no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—42no—
395C2×C3×C4—42no—
396C2×C3×C4—41no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—44no—
401C2×C3×C4—416no—
402C2×C3×C4#12014yes—
403C2×C3×C4#12014yes—
404C2×C3×C4#12014yes—
405C2×C3×C4#12114yes—
406C2×C3×C4#12114yes—
407C2×C3×C4#12114yes—
408C2×C3×C4#12714yes—
409#67—432no—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—24no—
413C2×Dic3—24no—
414C2×Dic3—24no—
415C2×Dic3—24no—
416C2×Dic3—28no—
417C2×Dic3—24no—
418C2×Dic3—42no—
419C2×Dic3—42no—
420C2×Dic3—42no—
421C2×Dic3—42no—
422C2×Dic3—42no—
423C2×Dic3—42no—
424C2×Dic3—44no—
425C2×Dic3—42no—
426C2×Dic3—42no—
427C2×Dic3—42no—
428C2×Dic3—42no—
429D12—416no—
430C24—21no—
431C24—21no—
432C24—21no—
433C24—21no—
434C24—22no—
435C24—22no—
436C24—22no—
437C24—21no—
438C24—21no—
439C24—34no—
440C24—62no—
441C24—62no—
442C24—62no—
443C24—64no—
444C24—64no—
445C24—64no—
446C24—64no—
447C24—62no—
448C24—62no—
449C24—62no—
450C24#23914yes—
451C24C2×#6712yes—
452C24C23×D311yescharacteristic
453C2×Q8—28no—
454C2×Q8—28no—
455C2×Q8—28no—
456C2×Q8—44no—
457C2×Q8—44no—
458C2×Q8—44no—
459C2×Q8—44no—
460C2×D4—616no—
461C2×D4—68no—
462C2×D4—68no—
463C2×D4—68no—
464C2×D4—1216no—
465C2×D4—1216no—
466C2×D4—128no—
467C2×D4—128no—
468C2×D4—124no—
469C2×D4—124no—
470C2×D4—124no—
471C2×D4—124no—
472C22×C4—21no—
473C22×C4—22no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—22no—
478C22×C4—21no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—24no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—28no—
489C22×C4—28no—
490C22×C4—28no—
491C22×C4—34no—
492C22×C4—34no—
493C22×C4—34no—
494C22×C4—44no—
495C22×C4—44no—
496C22×C4—44no—
497C22×C4—44no—
498C22×C4—62no—
499C22×C4—62no—
500C22×C4—62no—
501C22×C4—62no—
502C22×C4—62no—
503C22×C4—62no—
504C22×C4—64no—
505C22×C4—62no—
506C22×C4—62no—
507C22×C4—62no—
508C22×C4—62no—
509C22×C4—64no—
510C22×C4—62no—
511C22×C4—62no—
512C22×C4—62no—
513C22×C4—62no—
514C22×C4D3×D412yes—
515C22×C4D3×D412yes—
516C22×C4D3×D412yes—
517C22×C4#23712yes—
518C22×C4C2×#6714yes—
519C22×C4C2×#6714yes—
520C22×C4C2×#6712yes—
521C22×C4C2×#6712yes—
522C22×C4C2×#6712yes—
523C22×C4C2×#6712yes—
524C4⋊C4—216no—
525C4⋊C4—28no—
526C4⋊C4—68no—
527C22⋊C4—216no—
528C22⋊C4—616no—
529C22⋊C4—632no—
530C22⋊C4—616no—
531C22⋊C4—1216no—
532C42—68no—
533C42—124no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—24no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—44no—
542C22×C3—42no—
543C22×C3—42no—
544C22×C3—44no—
545C22×C3C2×#12011yescharacteristic
546C22×C3C2×#12011yescharacteristic
547C22×C3C2×#12011yescharacteristic
548C22×C3C2×#12111yescharacteristic
549C22×C3C2×#12111yescharacteristic
550C22×C3C2×#12111yescharacteristic
551C22×C3#52512yes—
552C22×C3C2×#12411yescharacteristic
553C22×C3#52912yes—
554C22×C3C2×#12711yescharacteristic
555C22×C3#53211yescharacteristic
556C22×C3#53511yescharacteristic
557C22×C3#53611yescharacteristic
558C22×C3#53712yes—
559C22×C3#54212yes—
560C22×C3#54612yes—
561C22×C3#54612yes—
562C22×C3#54612yes—
563C22×C3#54712yes—
564C22×C3#54812yes—
565C22×C3#54812yes—
566C22×C3#54812yes—
567C22×C3#55012yes—
568C2×D3—44no—
569C2×D3—48no—
570C2×D3—48no—
571C2×D3—44no—
572C2×D3—44no—
573C2×D3—82no—
574C2×D3—82no—
575C2×D3—84no—
576C2×D3—82no—
577C2×D3—82no—
578C2×D3—84no—
579C3×C4—42no—
580C3×C4—44no—
581C3×C4—44no—
582C3×C4#39218yes—
583Dic3—44no—
584Dic3—44no—
585Dic3—44no—
586C23—22no—
587C23—22no—
588C23—22no—
589C23—24no—
590C23—24no—
591C23—22no—
592C23—22no—
593C23—22no—
594C23—24no—
595C23—24no—
596C23—24no—
597C23—24no—
598C23—42no—
599C23—42no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—64no—
609C23—64no—
610C23—64no—
611C23—68no—
612C23—68no—
613C23—124no—
614C23—124no—
615C23—122no—
616C23—122no—
617C23—122no—
618C23—122no—
619C23—122no—
620C23—124no—
621C23—124no—
622C23—124no—
623C23—122no—
624C23—122no—
625C23—124no—
626C23—122no—
627C23—124no—
628C23—124no—
629C23—124no—
630C23—124no—
631C23#94714yescomplemented
632C23C2×D3×D411yescharacteristic
633C23C2×D3×D411yescharacteristic
634C23C2×D3×D411yescharacteristic
635C23C2×#23711yescharacteristic
636C23C2×#23912yes—
637C23#100712yes—
638C23D3×#4112yes—
639C23#100912yes—
640C23C22×#6711yescharacteristic
641C23C22×#6711yescharacteristic
642C23C22×#6711yescharacteristic
643Q8—416no—
644D4—1232no—
645D4—1216no—
646C2×C4—22no—
647C2×C4—24no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—28no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—41no—
655C2×C4—42no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—42no—
660C2×C4—41no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—44no—
665C2×C4—416no—
666C2×C4—64no—
667C2×C4—64no—
668C2×C4—64no—
669C2×C4—64no—
670C2×C4—64no—
671C2×C4—64no—
672C2×C4—64no—
673C2×C4—68no—
674C2×C4—122no—
675C2×C4—122no—
676C2×C4—122no—
677C2×C4—122no—
678C2×C4—122no—
679C2×C4—122no—
680C2×C4—122no—
681C2×C4—124no—
682C2×C4—122no—
683C2×C4—122no—
684C2×C4—122no—
685C2×C4#93714yes—
686C2×C4#93714yes—
687C2×C4#93814yes—
688C2×C4#93914yes—
689C2×C4#93914yes—
690C2×C4#94014yes—
691C2×C4#95314yes—
692C2×C3—44no—
693C2×C3C2×#39211yescharacteristic
694C2×C3#240712yes—
695C2×C3#242612yes—
696C2×C3#242712yes—
697C2×C3#243111yescharacteristic
698C2×C3#243211yescharacteristic
699C2×C3#243511yescharacteristic
700C2×C3#243611yescharacteristic
701C2×C3#254012yes—
702C2×C3#262011yescharacteristic
703C2×C3#285011yescharacteristic
704D3—84no—
705C22—24no—
706C22—24no—
707C22—24no—
708C22—44no—
709C22—44no—
710C22—42no—
711C22—42no—
712C22—44no—
713C22—44no—
714C22—42no—
715C22—42no—
716C22—128no—
717C22—124no—
718C22—124no—
719C22—124no—
720C22—128no—
721C22—244no—
722C22—244no—
723C22—242no—
724C22—242no—
725C22—242no—
726C22—242no—
727C22#562412yes—
728C22#562712yes—
729C22#562912yes—
730C22#563012yes—
731C22#563012yes—
732C22#563112yes—
733C22#563312yes—
734C22#564312yes—
735C22C2×#93711yescharacteristic
736C22C2×#93711yescharacteristic
737C22C2×#93811yescharacteristic
738C22C2×#93911yescharacteristic
739C22C2×#93911yescharacteristic
740C22C2×#94011yescharacteristic
741C22C2×#94711yescharacteristic
742C22#581611yescharacteristic
743C22#581712yes—
744C22#581712yes—
745C22#582912yes—
746C22#583011yescharacteristic
747C22#583211yescharacteristic
748C22#583412yes—
749C22C2×#95311yescharacteristic
750C4—42no—
751C4—44no—
752C4—44no—
753C4—124no—
754C4—124no—
755C4—124no—
756C4#522318yes—
757C3#1521511yescharacteristic, complemented, Sylow
758C2—44no—
759C2—244no—
760C2#8275512yes—
761C2#8275612yes—
762C2#8275911yescharacteristic
763C2#8276111yescharacteristic
764C2#8277912yes—
765C2#8280911yescharacteristic
766C2#8281212yes—
767C2#8282111yescharacteristic
768C2C2×#522311yescharacteristic
769C2#8406611yescharacteristic
770C2#8409211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×C22⋊Q8C2
prime radicalC22×#930C2
hypercenterC22×C22⋊Q8D3
hypocenterC3#15215
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C22×#947C2semidirect
4. C2×#5229C2semidirect
5. C2×C4×#217C2semidirect
6. C2×#4988C2semidirect
7. #71570C2semidirect
8. #71563C2semidirect
9. #71550C2semidirect
41. C22×C22⋊Q8D3semidirect
57. C22×C3×Q8D4semidirect
90. C2×C3×C4⋊C4D4semidirect
116. C2×C4×Dic3D4semidirect
261. C22×Q8#67semidirect
299. C2×C4⋊C4#67semidirect
346. C23×C3#124semidirect
631. C23#947semidirect
757. C3#15215semidirect

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C22×#9472
C22×#9302
C2×#52292
C2×C4×#2172
C2×#49882
#715702
#715632
#715502
#152153