Finite Group Databasebeta

← #10729017

Subgroups — #10729017

Order 768.

4146 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×#937C211yesmaximal, characteristic
3C23×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
4C2×#5220C211yesmaximal, characteristic, complemented
5C2×#5211C211yesmaximal, characteristic, complemented
6C2×#4955C211yesmaximal, characteristic, complemented
7#71570C214yesmaximal, complemented
8#71550C214yesmaximal, complemented
9#71544C211yesmaximal, characteristic, complemented
10#14911—31nomaximal, Sylow
11C25×D3C2211yescharacteristic
12C23×C3×D4C2211yescharacteristic
13C24×C3×C4C2211yescharacteristic
14C23×#67C2212yes—
15C24×Dic3C2211yescharacteristic
16C2×C3×#123—24no—
17C2×C3×#123—24no—
18C2×C3×#123—24no—
19C22×C3×C4⋊C4C2212yescomplemented
20C22×C3×C22⋊C4C2211yescharacteristic
21C22×C3×C22⋊C4C2212yescomplemented
22C22×#217C2211yescharacteristic
23C22×#217C2211yescharacteristic
24C22×#217C2212yescomplemented
25C2×#937—24no—
26C2×#937—24no—
27C2×#937—24no—
28C22×(C2×D3)⋊C4—24no—
29C22×(C2×D3)⋊C4—24no—
30C22×(C2×D3)⋊C4—24no—
31C22×(C2×D3)⋊C4C2214yes—
32C22×(C2×D3)⋊C4C2212yes—
33C22×(C2×D3)⋊C4C2214yes—
34#5220—24no—
35#5211—24no—
36C2×C3⋊#95C2214yescomplemented
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2214yescomplemented
39#4955—24no—
40C22×#123D311yescharacteristic, complemented
41C22×#120—31no—
42C23×C22⋊C4—31no—
43C2×#386—31no—
44C2×#381—31no—
45C2×#379—31no—
46#1439—34no—
47#1438—34no—
48C22⋊#95—31no—
49C25×C3C2311yescharacteristic
50C25×C3C2311yescharacteristic
51C24×D3—22no—
52C24×D3—22no—
53C24×D3—28no—
54C24×D3—22no—
55C24×D3—22no—
56C24×D3—22no—
57C24×D3—22no—
58C24×D3—44no—
59C24×D3D414yes—
60C24×D3C2312yes—
61C22×C3×D4—22no—
62C22×C3×D4—22no—
63C22×C3×D4—22no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—22no—
67C22×C3×D4D414yes—
68C23×C3×C4—22no—
69C23×C3×C4—22no—
70C23×C3×C4—22no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—22no—
74C23×C3×C4D414yescomplemented
75C23×C3×C4C2312yes—
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2312yes—
78C22×#67—24no—
79C22×#67—24no—
80C22×#67—28no—
81C22×#67—24no—
82C22×#67—44no—
83C23×Dic3—22no—
84C23×Dic3—22no—
85C23×Dic3—44no—
86C23×Dic3D414yescomplemented
87C23×Dic3C2312yes—
88C23×Dic3C2312yes—
89C23×Dic3C2312yes—
90C3×#123—232no—
91C2×C3×C4⋊C4—24no—
92C2×C3×C4⋊C4—24no—
93C2×C3×C4⋊C4—24no—
94C2×C3×C22⋊C4—22no—
95C2×C3×C22⋊C4—22no—
96C2×C3×C22⋊C4—24no—
97C2×C3×C22⋊C4—24no—
98C2×C3×C22⋊C4—24no—
99C2×C3×C22⋊C4D414yescomplemented
100C2×#217—22no—
101C2×#217—22no—
102C2×#217—22no—
103C2×#217—22no—
104C2×#217—22no—
105C2×#217—24no—
106C2×#217—44no—
107C2×#217D414yes—
108#937—232no—
109C2×(C2×D3)⋊C4—232no—
110C2×(C2×D3)⋊C4—28no—
111C2×(C2×D3)⋊C4—24no—
112C2×(C2×D3)⋊C4—28no—
113C2×(C2×D3)⋊C4—24no—
114C2×(C2×D3)⋊C4—28no—
115C2×(C2×D3)⋊C4—24no—
116C2×(C2×D3)⋊C4—28no—
117C2×(C2×D3)⋊C4—28no—
118C2×(C2×D3)⋊C4—44no—
119C3⋊#95—28no—
120C3⋊#95—24no—
121C3⋊#95—44no—
122C26—31no—
123C23×D4—32no—
124C23×D4C2×D311yescharacteristic
125C24×C4—31no—
126C24×C4C2×D311yescharacteristic
127C2×#123—24no—
128C2×#123—24no—
129C2×#123—24no—
130C2×#120—64no—
131C2×#120—64no—
132C2×#120—64no—
133C22×C4⋊C4C2×D312yescomplemented
134C22×C22⋊C4—31no—
135C22×C22⋊C4—31no—
136C22×C22⋊C4—34no—
137C22×C22⋊C4—32no—
138C22×C22⋊C4—34no—
139C22×C22⋊C4—32no—
140C22×C22⋊C4—64no—
141C22×C22⋊C4—64no—
142C22×C22⋊C4—64no—
143C22×C22⋊C4C2×D311yescharacteristic
144C22×C22⋊C4C2×D312yescomplemented
145#386—64no—
146#381—64no—
147#379—64no—
148C2×#95—34no—
149C2×#95—32no—
150C2×#95—34no—
151C24×C3—24no—
152C24×C3—24no—
153C24×C3—21no—
154C24×C3—21no—
155C24×C3—21no—
156C24×C3—21no—
157C24×C3—21no—
158C24×C3—24no—
159C24×C3—21no—
160C24×C3—24no—
161C24×C3C2×D412yes—
162C24×C3C2×D412yes—
163C24×C3C2×D412yes—
164C24×C3C2×D412yes—
165C24×C3C2×D412yes—
166C24×C3C2×D412yes—
167C24×C3C2×D412yes—
168C24×C3#4112yes—
169C24×C3C2411yescharacteristic
170C23×D3—216no—
171C23×D3—216no—
172C23×D3—28no—
173C23×D3—22no—
174C23×D3—22no—
175C23×D3—22no—
176C23×D3—22no—
177C23×D3—22no—
178C23×D3—22no—
179C23×D3—24no—
180C23×D3—24no—
181C23×D3—24no—
182C23×D3—216no—
183C23×D3—28no—
184C23×D3—28no—
185C23×D3—48no—
186C23×D3—416no—
187C23×D3—416no—
188C23×D3—416no—
189C23×D3—416no—
190C23×D3—48no—
191C23×D3—48no—
192C23×D3—44no—
193C23×D3—44no—
194C23×D3—44no—
195C23×D3—44no—
196C23×D3C2×D414yes—
197C23×D3#4118yes—
198C2×C3×D4—28no—
199C2×C3×D4—28no—
200C2×C3×D4—28no—
201C2×C3×D4—44no—
202C2×C3×D4—44no—
203C2×C3×D4—44no—
204C2×C3×D4—44no—
205C22×C3×C4—28no—
206C22×C3×C4—28no—
207C22×C3×C4—28no—
208C22×C3×C4—22no—
209C22×C3×C4—21no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—21no—
213C22×C3×C4—21no—
214C22×C3×C4—22no—
215C22×C3×C4—22no—
216C22×C3×C4—22no—
217C22×C3×C4—22no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—24no—
221C22×C3×C4—22no—
222C22×C3×C4—21no—
223C22×C3×C4—24no—
224C22×C3×C4—44no—
225C22×C3×C4—44no—
226C22×C3×C4—44no—
227C22×C3×C4—44no—
228C22×C3×C4C2×D414yes—
229C22×C3×C4C2×D414yes—
230C22×C3×C4C2×D412yes—
231C2×#67—216no—
232C2×#67—416no—
233C2×#67—416no—
234C2×#67—48no—
235C2×#67—48no—
236C22×Dic3—28no—
237C22×Dic3—22no—
238C22×Dic3—22no—
239C22×Dic3—22no—
240C22×Dic3—22no—
241C22×Dic3—24no—
242C22×Dic3—24no—
243C22×Dic3—24no—
244C22×Dic3—24no—
245C22×Dic3—22no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—24no—
249C22×Dic3—24no—
250C22×Dic3—48no—
251C22×Dic3—48no—
252C22×Dic3—48no—
253C22×Dic3C2×D414yes—
254C22×Dic3C2×D414yes—
255C3×C4⋊C4—216no—
256C3×C22⋊C4—216no—
257C3×C22⋊C4—28no—
258#217—28no—
259#217—48no—
260#217—44no—
261(C2×D3)⋊C4—232no—
262(C2×D3)⋊C4—216no—
263(C2×D3)⋊C4—416no—
264C25—32no—
265C25—34no—
266C25—68no—
267C25—62no—
268C25—62no—
269C25—62no—
270C25—62no—
271C25—62no—
272C25—62no—
273C25—124no—
274C25C22×D311yescharacteristic
275C25C22×D311yescharacteristic
276C22×D4—22no—
277C22×D4—22no—
278C22×D4—22no—
279C22×D4—22no—
280C22×D4—22no—
281C22×D4—22no—
282C22×D4—64no—
283C22×D4—64no—
284C22×D4—64no—
285C22×D4—68no—
286C22×D4—124no—
287C22×D4#6714yes—
288C23×C4—22no—
289C23×C4—22no—
290C23×C4—22no—
291C23×C4—22no—
292C23×C4—22no—
293C23×C4—22no—
294C23×C4—32no—
295C23×C4—32no—
296C23×C4—34no—
297C23×C4—32no—
298C23×C4—62no—
299C23×C4—62no—
300C23×C4—124no—
301C23×C4#6714yescomplemented
302C23×C4C22×D312yes—
303C23×C4C22×D312yes—
304C23×C4C22×D311yescharacteristic
305#123—232no—
306#120—632no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—24no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—24no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—24no—
315C2×C22⋊C4—34no—
316C2×C22⋊C4—68no—
317C2×C22⋊C4—64no—
318C2×C22⋊C4—68no—
319C2×C22⋊C4—64no—
320C2×C22⋊C4—632no—
321C2×C22⋊C4—62no—
322C2×C22⋊C4—62no—
323C2×C22⋊C4—68no—
324C2×C22⋊C4—64no—
325C2×C22⋊C4—68no—
326C2×C22⋊C4—64no—
327C2×C22⋊C4—62no—
328C2×C22⋊C4—62no—
329C2×C22⋊C4—62no—
330C2×C22⋊C4—68no—
331C2×C22⋊C4—124no—
332C2×C22⋊C4—124no—
333C2×C22⋊C4#6714yescomplemented
334#95—68no—
335#95—64no—
336#95—124no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—24no—
341C23×C3—24no—
342C23×C3—24no—
343C23×C3—28no—
344C23×C3—28no—
345C23×C3—28no—
346C23×C3—28no—
347C23×C3—22no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—28no—
351C23×C3—41no—
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—42no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—41no—
358C23×C3—42no—
359C23×C3—42no—
360C23×C3—42no—
361C23×C3—44no—
362C23×C3—44no—
363C23×C3—44no—
364C23×C3#12014yes—
365C23×C3#12014yes—
366C23×C3#12014yes—
367C23×C3#12114yes—
368C23×C3#12114yes—
369C23×C3#12114yes—
370C23×C3#12714yes—
371C23×C3C22×D411yescharacteristic
372C23×C3C22×D411yescharacteristic
373C23×C3C22×D411yescharacteristic
374C23×C3C22×D411yescharacteristic
375C23×C3C22×D411yescharacteristic
376C23×C3C22×D411yescharacteristic
377C23×C3C2×#4111yescharacteristic
378C23×C3C2×#4114yes—
379C23×C3H(5,𝔽2)14yes—
380C22×D3—232no—
381C22×D3—24no—
382C22×D3—24no—
383C22×D3—24no—
384C22×D3—24no—
385C22×D3—28no—
386C22×D3—28no—
387C22×D3—24no—
388C22×D3—24no—
389C22×D3—28no—
390C22×D3—28no—
391C22×D3—28no—
392C22×D3—28no—
393C22×D3—432no—
394C22×D3—432no—
395C22×D3—416no—
396C22×D3—432no—
397C22×D3—432no—
398C22×D3—432no—
399C22×D3—432no—
400C22×D3—42no—
401C22×D3—42no—
402C22×D3—42no—
403C22×D3—42no—
404C22×D3—44no—
405C22×D3—44no—
406C22×D3—44no—
407C22×D3—44no—
408C22×D3—44no—
409C22×D3—44no—
410C22×D3—416no—
411C22×D3#12318yescomplemented
412C3×D4—416no—
413C2×C3×C4—24no—
414C2×C3×C4—22no—
415C2×C3×C4—24no—
416C2×C3×C4—24no—
417C2×C3×C4—22no—
418C2×C3×C4—24no—
419C2×C3×C4—22no—
420C2×C3×C4—28no—
421C2×C3×C4—42no—
422C2×C3×C4—41no—
423C2×C3×C4—42no—
424C2×C3×C4—42no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—44no—
432C2×C3×C4—416no—
433#67—432no—
434C2×Dic3—24no—
435C2×Dic3—24no—
436C2×Dic3—24no—
437C2×Dic3—24no—
438C2×Dic3—28no—
439C2×Dic3—416no—
440C2×Dic3—42no—
441C2×Dic3—44no—
442C2×Dic3—42no—
443C2×Dic3—44no—
444C2×Dic3—44no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3—42no—
448C2×Dic3—44no—
449C2×Dic3—44no—
450C24—24no—
451C24—24no—
452C24—21no—
453C24—21no—
454C24—21no—
455C24—21no—
456C24—24no—
457C24—24no—
458C24—21no—
459C24—21no—
460C24—34no—
461C24—38no—
462C24—616no—
463C24—616no—
464C24—616no—
465C24—68no—
466C24—62no—
467C24—62no—
468C24—62no—
469C24—64no—
470C24—64no—
471C24—64no—
472C24—62no—
473C24—62no—
474C24—62no—
475C24—68no—
476C24—68no—
477C24—128no—
478C24—1216no—
479C24—1216no—
480C24—1216no—
481C24—1216no—
482C24—128no—
483C24—128no—
484C24—124no—
485C24—124no—
486C24—124no—
487C24—124no—
488C24D3×D412yes—
489C24D3×D412yes—
490C24D3×D412yes—
491C24#23712yes—
492C24C2×#6712yes—
493C24C2×#6712yes—
494C24C2×#6712yes—
495C24C2×#6712yes—
496C24C23×D311yescharacteristic
497C2×D4—28no—
498C2×D4—28no—
499C2×D4—28no—
500C2×D4—44no—
501C2×D4—44no—
502C2×D4—44no—
503C2×D4—44no—
504C2×D4—616no—
505C2×D4—1216no—
506C2×D4—1216no—
507C2×D4—128no—
508C2×D4—128no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—22no—
513C22×C4—21no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—21no—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—34no—
529C22×C4—34no—
530C22×C4—44no—
531C22×C4—44no—
532C22×C4—44no—
533C22×C4—44no—
534C22×C4—68no—
535C22×C4—62no—
536C22×C4—62no—
537C22×C4—64no—
538C22×C4—64no—
539C22×C4—64no—
540C22×C4—64no—
541C22×C4—62no—
542C22×C4—62no—
543C22×C4—62no—
544C22×C4—62no—
545C22×C4—64no—
546C22×C4—64no—
547C22×C4—62no—
548C22×C4—128no—
549C22×C4—128no—
550C22×C4—128no—
551C22×C4C2×#6714yes—
552C22×C4C2×#6714yes—
553C22×C4C2×#6712yes—
554C4⋊C4—216no—
555C22⋊C4—216no—
556C22⋊C4—28no—
557C22⋊C4—632no—
558C22⋊C4—616no—
559C22⋊C4—68no—
560C22⋊C4—1216no—
561C22⋊C4—128no—
562C22⋊C4—124no—
563C22×C3—24no—
564C22×C3—24no—
565C22×C3—28no—
566C22×C3—28no—
567C22×C3—28no—
568C22×C3—28no—
569C22×C3—28no—
570C22×C3—28no—
571C22×C3—42no—
572C22×C3—44no—
573C22×C3—44no—
574C22×C3—44no—
575C22×C3—81no—
576C22×C3—81no—
577C22×C3—82no—
578C22×C3—82no—
579C22×C3—82no—
580C22×C3#39218yes—
581C22×C3C2×#12011yescharacteristic
582C22×C3C2×#12011yescharacteristic
583C22×C3C2×#12011yescharacteristic
584C22×C3C2×#12111yescharacteristic
585C22×C3C2×#12111yescharacteristic
586C22×C3C2×#12111yescharacteristic
587C22×C3C2×#12312yes—
588C22×C3#52512yes—
589C22×C3#52512yes—
590C22×C3C2×#12711yescharacteristic
591C22×C3#53412yes—
592C22×C3#53412yes—
593C22×C3#53512yes—
594C22×C3#54614yes—
595C22×C3#54614yes—
596C22×C3#54614yes—
597C22×C3#55114yes—
598C2×D3—28no—
599C2×D3—28no—
600C2×D3—28no—
601C2×D3—464no—
602C2×D3—44no—
603C2×D3—44no—
604C2×D3—48no—
605C2×D3—44no—
606C2×D3—48no—
607C2×D3—44no—
608C2×D3—48no—
609C2×D3—48no—
610C3×C4—44no—
611C3×C4—42no—
612C3×C4—44no—
613Dic3—44no—
614Dic3—44no—
615Dic3—82no—
616C23—24no—
617C23—24no—
618C23—24no—
619C23—28no—
620C23—24no—
621C23—28no—
622C23—24no—
623C23—28no—
624C23—28no—
625C23—24no—
626C23—22no—
627C23—22no—
628C23—28no—
629C23—22no—
630C23—38no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—44no—
635C23—42no—
636C23—44no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—44no—
643C23—42no—
644C23—632no—
645C23—64no—
646C23—64no—
647C23—64no—
648C23—68no—
649C23—68no—
650C23—68no—
651C23—64no—
652C23—64no—
653C23—64no—
654C23—68no—
655C23—68no—
656C23—68no—
657C23—1232no—
658C23—1232no—
659C23—1232no—
660C23—1232no—
661C23—1232no—
662C23—1232no—
663C23—1216no—
664C23—124no—
665C23—124no—
666C23—124no—
667C23—1216no—
668C23—122no—
669C23—122no—
670C23—122no—
671C23—124no—
672C23—124no—
673C23—124no—
674C23—122no—
675C23#93714yes—
676C23#93714yes—
677C23#93814yes—
678C23#93914yes—
679C23#93914yes—
680C23#94014yes—
681C23#95314yes—
682C23C2×D3×D411yescharacteristic
683C23C2×D3×D411yescharacteristic
684C23C2×D3×D411yescharacteristic
685C23C2×#23711yescharacteristic
686C23D3×#4114yes—
687C23#100914yes—
688C23C22×#6711yescharacteristic
689C23C22×#6711yescharacteristic
690C23C22×#6711yescharacteristic
691D4—416no—
692D4—1232no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—28no—
698C2×C4—24no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—416no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—41no—
710C2×C4—42no—
711C2×C4—44no—
712C2×C4—42no—
713C2×C4—64no—
714C2×C4—64no—
715C2×C4—68no—
716C2×C4—64no—
717C2×C4—64no—
718C2×C4—1216no—
719C2×C4—122no—
720C2×C4—124no—
721C2×C4—122no—
722C2×C4—124no—
723C2×C4—124no—
724C2×C4—122no—
725C2×C4—124no—
726C2×C4—122no—
727C2×C4—122no—
728C2×C4—124no—
729C2×C3—28no—
730C2×C3—82no—
731C2×C3C2×#39211yescharacteristic
732C2×C3#240412yes—
733C2×C3#240512yes—
734C2×C3#241112yes—
735C2×C3#241212yes—
736C2×C3#253412yes—
737C2×C3#253912yes—
738C2×C3#261311yescharacteristic
739C2×C3#284911yescharacteristic
740D3—48no—
741C22—28no—
742C22—28no—
743C22—28no—
744C22—28no—
745C22—28no—
746C22—28no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—68no—
754C22—68no—
755C22—68no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—81no—
760C22—81no—
761C22—1264no—
762C22—124no—
763C22—128no—
764C22—124no—
765C22—128no—
766C22—124no—
767C22—128no—
768C22—128no—
769C22—124no—
770C22#522318yes—
771C22D3×#12312yes—
772C22#565312yes—
773C22#565312yes—
774C22#565414yes—
775C22#565612yes—
776C22#565814yes—
777C22C2×#93711yescharacteristic
778C22C2×#93711yescharacteristic
779C22C2×#93811yescharacteristic
780C22C2×#93911yescharacteristic
781C22C2×#93911yescharacteristic
782C22C2×#94011yescharacteristic
783C22#582812yes—
784C22#582914yes—
785C22#582914yes—
786C22#583012yes—
787C22C2×#95311yescharacteristic
788C4—44no—
789C4—42no—
790C4—44no—
791C4—124no—
792C4—124no—
793C4—242no—
794C3#1491111yescharacteristic, complemented, Sylow
795C2—28no—
796C2—82no—
797C2—128no—
798C2#8289312yes—
799C2#8289412yes—
800C2#8289512yes—
801C2#8290012yes—
802C2#8290112yes—
803C2#8290311yescharacteristic
804C2#8291211yescharacteristic
805C2C2×#522311yescharacteristic
806C2#8409612yes—
subgroupG/H
center, FrattiniC24C23×D3
commutator, socle, cosocleC24×C3C24
FittingC22×C3×#123C2
prime radicalC22×#937C2
hypercenterC22×#123D3
hypocenterC3#14911
LCSG ▷ C24×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
3. C23×(C2×D3)⋊C4C2semidirect
4. C2×#5220C2semidirect
5. C2×#5211C2semidirect
6. C2×#4955C2semidirect
7. #71570C2semidirect
8. #71550C2semidirect
9. #71544C2semidirect
19. C22×C3×C4⋊C4C22semidirect
21. C22×C3×C22⋊C4C22semidirect
24. C22×#217C22semidirect
36. C2×C3⋊#95C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
40. C22×#123D3semidirect
74. C23×C3×C4D4semidirect
86. C23×Dic3D4semidirect
99. C2×C3×C22⋊C4D4semidirect
133. C22×C4⋊C4C2×D3semidirect
144. C22×C22⋊C4C2×D3semidirect
301. C23×C4#67semidirect
333. C2×C22⋊C4#67semidirect
411. C22×D3#123semidirect
794. C3#14911semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×#9372
C23×(C2×D3)⋊C42
C2×#52202
C2×#52112
C2×#49552
#715702
#715502
#715442
#149113