Finite Group Databasebeta

← C67×#18418 #30697669

Subgroups — C67×#18418 #30697669

Order 17152.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C67×#3537C211yesmaximal, characteristic, complemented
2C67×#3192C211yesmaximal, characteristic, complemented
3C67×#3188C211yesmaximal, characteristic, complemented
4C67×#2656C211yesmaximal, characteristic, complemented
5C67×#1618C212yesmaximal, complemented
6C67×#1613C212yesmaximal, complemented
7C67×#1600C212yesmaximal, complemented
8C67×#1595C212yesmaximal, complemented
9C67×#1504C211yesmaximal, characteristic, complemented
10C2×#327×C67C211yesmaximal, characteristic, complemented
11C67×#1471C211yesmaximal, characteristic, complemented
12#560×C67—22no—
13#553×C67—21no—
14#553×C67—21no—
15D42×C67—22no—
16D42×C67—21no—
17D42×C67—21no—
18#540×C67—21no—
19#538×C67—21no—
20#538×C67C2212yes—
21#535×C67—21no—
22#534×C67—21no—
23#534×C67C2212yes—
24#525×C67C2211yescharacteristic
25C2×#121×C67—22no—
26C2×#121×C67C2211yescharacteristic
27C2×#121×C67C2211yescharacteristic
28C2×#121×C67C2211yescharacteristic, complemented
29#484×C67C2211yescharacteristic, complemented
30#482×C67—21no—
31#481×C67—21no—
32#481×C67C2211yescharacteristic, complemented
33#481×C67C2212yescomplemented
34#469×C67—22no—
35#466×C67—21no—
36#465×C67—21no—
37#450×C67C2211yescharacteristic, complemented
38#449×C67—21no—
39#447×C67—21no—
40#447×C67C2211yescharacteristic, complemented
41#447×C67C2212yescomplemented
42#407×C67C2211yescharacteristic, complemented
43C2×C22⋊C8×C67C2211yescharacteristic, complemented
44#399×C67—21no—
45#399×C67C2212yescomplemented
46#392×C67—21no—
47#392×C67C2212yescomplemented
48C2×#95×C67C2211yescharacteristic, complemented
49#328×C67C2212yescomplemented
50#327×C67C2212yescomplemented
51#327×C67C2212yescomplemented
52#327×C67C2212yescomplemented
53#323×C67C2212yescomplemented
54#323×C67C2212yescomplemented
55C2×#41×C67D411yescharacteristic, complemented
56C22×D4×C67—22no—
57C22×D4×C67—21no—
58C22×D4×C67—21no—
59C22×D4×C67—22no—
60C22×D4×C67—21no—
61C22×D4×C67—22no—
62C22×D4×C67D412yes—
63C22×D4×C67D411yescharacteristic
64C22×D4×C67D411yescharacteristic, complemented
65C22×D4×C67C2311yescharacteristic
66C23×C4×C67—21no—
67C23×C4×C67C2311yescharacteristic
68C2×SD16×C67—21no—
69C2×D8×C67—21no—
70C2×D8×C67—22no—
71C2×M16×C67—21no—
72C22×C8×C67—21no—
73#127×C67—22no—
74#127×C67—21no—
75#126×C67—22no—
76#126×C67—22no—
77#125×C67—21no—
78#124×C67—22no—
79#123×C67—22no—
80#123×C67—21no—
81#123×C67—22no—
82#123×C67—22no—
83#123×C67—22no—
84C22⋊Q8×C67D411yescharacteristic, complemented
85C22⋊Q8×C67C2311yescharacteristic
86#121×C67—22no—
87#121×C67—21no—
88#121×C67—21no—
89#121×C67—22no—
90#121×C67—22no—
91#121×C67—22no—
92#121×C67—22no—
93#121×C67—21no—
94#121×C67—21no—
95#121×C67—21no—
96#121×C67—21no—
97#121×C67—21no—
98#121×C67—21no—
99#121×C67—22no—
100#121×C67—21no—
101#121×C67—21no—
102#121×C67—21no—
103#121×C67—21no—
104#121×C67—48no—
105#121×C67D411yescharacteristic, complemented
106#121×C67D412yescomplemented
107#121×C67C2312yes—
108#121×C67C2311yescharacteristic
109#120×C67—22no—
110#120×C67—22no—
111#120×C67—22no—
112#120×C67—21no—
113#120×C67—22no—
114#120×C67—22no—
115#120×C67—22no—
116C4×D4×C67—22no—
117C4×D4×C67—21no—
118C4×D4×C67—21no—
119C4×D4×C67—21no—
120C4×D4×C67—21no—
121C4×D4×C67—22no—
122#117×C67—21no—
123#117×C67D411yescharacteristic, complemented
124C2×C4⋊C4×C67—22no—
125C2×C4⋊C4×C67D411yescharacteristic
126C2×C4⋊C4×C67D411yescharacteristic, complemented
127C2×C4⋊C4×C67C2311yescharacteristic
128C2×C22⋊C4×C67—21no—
129C2×C22⋊C4×C67—22no—
130C2×C22⋊C4×C67—22no—
131C2×C22⋊C4×C67—21no—
132C2×C22⋊C4×C67C2312yes—
133#107×C67—21no—
134#106×C67—21no—
135#106×C67—22no—
136#103×C67—21no—
137#102×C67—21no—
138#102×C67—22no—
139#102×C67—21no—
140#102×C67—21no—
141#102×C67—22no—
142C22⋊C8×C67—21no—
143C22⋊C8×C67—21no—
144C22⋊C8×C67C2311yescharacteristic
145C22⋊C8×C67C2312yes—
146C22⋊C8×C67C2311yescharacteristic
147#95×C67—21no—
148#95×C67C2312yes—
149C24×C67—22no—
150C24×C67—21no—
151C24×C67—21no—
152C24×C67C2×D411yescharacteristic
153C24×C67C2×D412yes—
154#41×C67—81no—
155C2×Q8×C67C2×D411yescharacteristic
156C2×D4×C67—22no—
157C2×D4×C67—21no—
158C2×D4×C67—21no—
159C2×D4×C67—22no—
160C2×D4×C67—22no—
161C2×D4×C67—22no—
162C2×D4×C67—22no—
163C2×D4×C67—22no—
164C2×D4×C67—22no—
165C2×D4×C67—21no—
166C2×D4×C67—22no—
167C2×D4×C67—22no—
168C2×D4×C67—21no—
169C2×D4×C67—21no—
170C2×D4×C67—21no—
171C2×D4×C67—21no—
172C2×D4×C67—21no—
173C2×D4×C67—44no—
174C2×D4×C67—44no—
175C2×D4×C67—44no—
176C2×D4×C67—41no—
177C2×D4×C67—41no—
178C2×D4×C67—81no—
179C2×D4×C67—81no—
180C2×D4×C67—82no—
181C2×D4×C67—81no—
182C2×D4×C67—82no—
183C2×D4×C67—82no—
184C2×D4×C67—81no—
185C2×D4×C67—81no—
186C2×D4×C67—82no—
187C2×D4×C67—82no—
188C2×D4×C67—84no—
189C2×D4×C67C2×D411yescharacteristic
190C2×D4×C67C2×D412yes—
191C22×C4×C67—22no—
192C22×C4×C67—22no—
193C22×C4×C67—22no—
194C22×C4×C67—24no—
195C22×C4×C67—21no—
196C22×C4×C67—21no—
197C22×C4×C67—21no—
198C22×C4×C67—81no—
199C22×C4×C67—81no—
200C22×C4×C67—81no—
201C22×C4×C67C2×D412yes—
202C22×C4×C67C2×D411yescharacteristic
203C22×C4×C67C2×D411yescharacteristic
204C22×C4×C67C2×D411yescharacteristic
205C22×C4×C67C2×D411yescharacteristic
206C22×C4×C67C2×D411yescharacteristic
207C22×C4×C67C2411yescharacteristic
208SD16×C67—81no—
209D8×C67—81no—
210D8×C67—82no—
211M16×C67—81no—
212C2×C8×C67—21no—
213C2×C8×C67—22no—
214C2×C8×C67—21no—
215C2×C8×C67—81no—
216C4⋊C4×C67—22no—
217C4⋊C4×C67—22no—
218C4⋊C4×C67—21no—
219C4⋊C4×C67—21no—
220C4⋊C4×C67—21no—
221C4⋊C4×C67—21no—
222C4⋊C4×C67—21no—
223C4⋊C4×C67—21no—
224C4⋊C4×C67—21no—
225C4⋊C4×C67—44no—
226C4⋊C4×C67C2×D412yes—
227C4⋊C4×C67C2×D411yescharacteristic
228C4⋊C4×C67C2×D411yescharacteristic
229C22⋊C4×C67—22no—
230C22⋊C4×C67—22no—
231C22⋊C4×C67—22no—
232C22⋊C4×C67—22no—
233C22⋊C4×C67—22no—
234C22⋊C4×C67—21no—
235C22⋊C4×C67—21no—
236C22⋊C4×C67—21no—
237C22⋊C4×C67—22no—
238C22⋊C4×C67—21no—
239C22⋊C4×C67—22no—
240C22⋊C4×C67—22no—
241C22⋊C4×C67—22no—
242C22⋊C4×C67—21no—
243C22⋊C4×C67—44no—
244C22⋊C4×C67—44no—
245C22⋊C4×C67—41no—
246C22⋊C4×C67—41no—
247C42×C67—22no—
248C42×C67—21no—
249C23×C67—21no—
250C23×C67—21no—
251C23×C67—22no—
252C23×C67—22no—
253C23×C67—22no—
254C23×C67—21no—
255C23×C67—22no—
256C23×C67—22no—
257C23×C67—41no—
258C23×C67—42no—
259C23×C67—42no—
260C23×C67—42no—
261C23×C67—42no—
262C23×C67—42no—
263C23×C67—41no—
264C23×C67—41no—
265C23×C67—41no—
266C23×C67—81no—
267C23×C67—81no—
268C23×C67—82no—
269C23×C67—82no—
270C23×C67—82no—
271C23×C67#12011yescharacteristic
272C23×C67#12011yescharacteristic
273C23×C67C22×D411yescharacteristic
274Q8×C67—41no—
275D4×C67—42no—
276D4×C67—41no—
277D4×C67—42no—
278D4×C67—42no—
279D4×C67—42no—
280D4×C67—41no—
281D4×C67—41no—
282D4×C67—42no—
283D4×C67—41no—
284D4×C67—42no—
285D4×C67—41no—
286D4×C67—44no—
287D4×C67—42no—
288D4×C67—81no—
289D4×C67—82no—
290D4×C67—82no—
291D4×C67—81no—
292D4×C67—82no—
293D4×C67—82no—
294D4×C67—82no—
295D4×C67—82no—
296D4×C67—82no—
297D4×C67—88no—
298D4×C67—82no—
299D4×C67—82no—
300C2×C4×C67—24no—
301C2×C4×C67—21no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—21no—
305C2×C4×C67—21no—
306C2×C4×C67—41no—
307C2×C4×C67—41no—
308C2×C4×C67—41no—
309C2×C4×C67—41no—
310C2×C4×C67—41no—
311C2×C4×C67—41no—
312C2×C4×C67—42no—
313C2×C4×C67—42no—
314C2×C4×C67—42no—
315C2×C4×C67—42no—
316C2×C4×C67—42no—
317C2×C4×C67—41no—
318C2×C4×C67—81no—
319C2×C4×C67—84no—
320C2×C4×C67—82no—
321C2×C4×C67—82no—
322C2×C4×C67#12011yescharacteristic
323C2×C4×C67#12011yescharacteristic
324C2×C4×C67C22×D411yescharacteristic
325C2×C4×C67C22×D411yescharacteristic
326C8×C67—41no—
327C8×C67—41no—
328C8×C67—42no—
329C22×C67—21no—
330C22×C67—21no—
331C22×C67—21no—
332C22×C67—21no—
333C22×C67—21no—
334C22×C67—21no—
335C22×C67—21no—
336C22×C67—42no—
337C22×C67—42no—
338C22×C67—42no—
339C22×C67—42no—
340C22×C67—41no—
341C22×C67—42no—
342C22×C67—42no—
343C22×C67—41no—
344C22×C67—41no—
345C22×C67—42no—
346C22×C67—42no—
347C22×C67—82no—
348C22×C67—82no—
349C22×C67—82no—
350C22×C67—82no—
351C22×C67—81no—
352C22×C67—81no—
353C22×C67—81no—
354C22×C67—162no—
355C22×C67—164no—
356C22×C67#45312yes—
357C22×C67C2×#12011yescharacteristic
358C22×C67#57611yescharacteristic
359C22×C67#57711yescharacteristic
360C4×C67—21no—
361C4×C67—21no—
362C4×C67—21no—
363C4×C67—21no—
364C4×C67—44no—
365C4×C67—42no—
366C4×C67—41no—
367C4×C67—42no—
368C4×C67—41no—
369C4×C67—41no—
370C4×C67—81no—
371#18418C6711yesmaximal, characteristic, direct product factor, Sylow
372C2×C67—21no—
373C2×C67—21no—
374C2×C67—22no—
375C2×C67—41no—
376C2×C67—82no—
377C2×C67—82no—
378C2×C67—81no—
379C2×C67—161no—
380C2×C67#301211yescharacteristic
381C2×C67C2×#45311yescharacteristic
382C2×C67#302611yescharacteristic
383#3537C2×C6711yescharacteristic, complemented
384#3192C2×C6711yescharacteristic, complemented
385#3188C2×C6711yescharacteristic, complemented
386#2656C2×C6711yescharacteristic, complemented
387#1618C2×C6712yescomplemented
388#1613C2×C6712yescomplemented
389#1600C2×C6712yescomplemented
390#1595C2×C6712yescomplemented
391#1504C2×C6711yescharacteristic, complemented
392C2×#327C2×C6711yescharacteristic, complemented
393#1471C2×C6711yescharacteristic, complemented
394C67#1841811yescharacteristic, direct product factor, Sylow
395#560—22no—
396#553—21no—
397#553—21no—
398D42—22no—
399D42—21no—
400D42—21no—
401#540—21no—
402#538—21no—
403#538C22×C6712yes—
404#535—21no—
405#534—21no—
406#534C22×C6712yes—
407#525C22×C6711yescharacteristic
408C2×#121—22no—
409C2×#121C22×C6711yescharacteristic
410C2×#121C22×C6711yescharacteristic
411C2×#121C22×C6711yescharacteristic, complemented
412#484C22×C6711yescharacteristic, complemented
413#482—21no—
414#481—21no—
415#481C22×C6711yescharacteristic, complemented
416#481C22×C6712yescomplemented
417#469—22no—
418#466—21no—
419#465—21no—
420#450C22×C6711yescharacteristic, complemented
421#449—21no—
422#447—21no—
423#447C22×C6711yescharacteristic, complemented
424#447C22×C6712yescomplemented
425#407C22×C6711yescharacteristic, complemented
426C2×C22⋊C8C22×C6711yescharacteristic, complemented
427#399—21no—
428#399C22×C6712yescomplemented
429#392—21no—
430#392C22×C6712yescomplemented
431C2×#95C22×C6711yescharacteristic, complemented
432#328C22×C6712yescomplemented
433#327C22×C6712yescomplemented
434#327C22×C6712yescomplemented
435#327C22×C6712yescomplemented
436#323C22×C6712yescomplemented
437#323C22×C6712yescomplemented
438C2×#41D4×C6711yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C6712yes—
446C22×D4D4×C6711yescharacteristic
447C22×D4D4×C6711yescharacteristic, complemented
448C22×D4C23×C6711yescharacteristic
449C23×C4—21no—
450C23×C4C23×C6711yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C6711yescharacteristic, complemented
468C22⋊Q8C23×C6711yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C6712yescomplemented
489#121D4×C6711yescharacteristic, complemented
490#121C23×C6712yes—
491#121C23×C6711yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C6711yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C6711yescharacteristic
509C2×C4⋊C4D4×C6711yescharacteristic, complemented
510C2×C4⋊C4C23×C6711yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C6712yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C6711yescharacteristic
528C22⋊C8C23×C6711yescharacteristic
529C22⋊C8C23×C6712yes—
530#95—21no—
531#95C23×C6712yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C6711yescharacteristic
536C24C2×D4×C6712yes—
537#41—81no—
538C2×Q8C2×D4×C6711yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C6711yescharacteristic
573C2×D4C2×D4×C6712yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C6712yes—
585C22×C4C2×D4×C6711yescharacteristic
586C22×C4C2×D4×C6711yescharacteristic
587C22×C4C2×D4×C6711yescharacteristic
588C22×C4C2×D4×C6711yescharacteristic
589C22×C4C2×D4×C6711yescharacteristic
590C22×C4C24×C6711yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C6712yes—
610C4⋊C4C2×D4×C6711yescharacteristic
611C4⋊C4C2×D4×C6711yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C6711yescharacteristic
655C23#120×C6711yescharacteristic
656C23C22×D4×C6711yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—42no—
670D4—41no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C6711yescharacteristic
706C2×C4#120×C6711yescharacteristic
707C2×C4C22×D4×C6711yescharacteristic
708C2×C4C22×D4×C6711yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22#453×C6712yes—
740C22C2×#120×C6711yescharacteristic
741C22#576×C6711yescharacteristic
742C22#577×C6711yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2C67×#301211yescharacteristic
763C2C2×#453×C6711yescharacteristic
764C2C67×#302611yescharacteristic
subgroupG/H
center, socleC22×C67C2×#120
commutator, Frattini, cosocleC22×C4C24×C67
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C67 ◁ C23×C4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C67×#3537C2semidirect
2. C67×#3192C2semidirect
3. C67×#3188C2semidirect
4. C67×#2656C2semidirect
5. C67×#1618C2semidirect
6. C67×#1613C2semidirect
7. C67×#1600C2semidirect
8. C67×#1595C2semidirect
9. C67×#1504C2semidirect
10. C2×#327×C67C2semidirect
11. C67×#1471C2semidirect
28. C2×#121×C67C22semidirect
29. #484×C67C22semidirect
32. #481×C67C22semidirect
33. #481×C67C22semidirect
37. #450×C67C22semidirect
40. #447×C67C22semidirect
41. #447×C67C22semidirect
42. #407×C67C22semidirect
43. C2×C22⋊C8×C67C22semidirect
45. #399×C67C22semidirect
47. #392×C67C22semidirect
48. C2×#95×C67C22semidirect
49. #328×C67C22semidirect
50. #327×C67C22semidirect
51. #327×C67C22semidirect
52. #327×C67C22semidirect
53. #323×C67C22semidirect
54. #323×C67C22semidirect
55. C2×#41×C67D4semidirect
64. C22×D4×C67D4semidirect
84. C22⋊Q8×C67D4semidirect
105. #121×C67D4semidirect
106. #121×C67D4semidirect
123. #117×C67D4semidirect
126. C2×C4⋊C4×C67D4semidirect
371. #18418C67direct (N × H)
383. #3537C2×C67semidirect
384. #3192C2×C67semidirect
385. #3188C2×C67semidirect
386. #2656C2×C67semidirect
387. #1618C2×C67semidirect
388. #1613C2×C67semidirect
389. #1600C2×C67semidirect
390. #1595C2×C67semidirect
391. #1504C2×C67semidirect
392. C2×#327C2×C67semidirect
393. #1471C2×C67semidirect
394. C67#18418direct (N × H)
411. C2×#121C22×C67semidirect
412. #484C22×C67semidirect
415. #481C22×C67semidirect
416. #481C22×C67semidirect
420. #450C22×C67semidirect
423. #447C22×C67semidirect
424. #447C22×C67semidirect
425. #407C22×C67semidirect
426. C2×C22⋊C8C22×C67semidirect
428. #399C22×C67semidirect
430. #392C22×C67semidirect
431. C2×#95C22×C67semidirect
432. #328C22×C67semidirect
433. #327C22×C67semidirect
434. #327C22×C67semidirect
435. #327C22×C67semidirect
436. #323C22×C67semidirect
437. #323C22×C67semidirect
438. C2×#41D4×C67semidirect
447. C22×D4D4×C67semidirect
467. C22⋊Q8D4×C67semidirect
488. #121D4×C67semidirect
489. #121D4×C67semidirect
506. #117D4×C67semidirect
509. C2×C4⋊C4D4×C67semidirect

Maximal subgroups

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

subgroupindex
C67×#35372
C67×#31922
C67×#31882
C67×#26562
C67×#16182
C67×#16132
C67×#16002
C67×#15952
C67×#15042
C2×#327×C672
C67×#14712
#1841867