Finite Group Databasebeta

← #1736×D67 #30853232

Subgroups — #1736×D67 #30853232

Order 17152.

2574 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×M16×D67C211yesmaximal, characteristic
2C2×#117×D67C211yesmaximal, characteristic
3C22×C4⋊C4×D67C211yesmaximal, characteristic
4#22559930C211yesmaximal, characteristic, complemented
5#22559929C211yesmaximal, characteristic, complemented
6#22559928C211yesmaximal, characteristic, complemented
7#22559927C214yesmaximal, complemented
8#340×D67C214yesmaximal, complemented
9C67×#1736C211yesmaximal, characteristic, complemented
10C23×C4×D67—21no—
11C23×C4×D67C2211yescharacteristic
12C22×#11761612C2211yescharacteristic
13C22×#11761611C2212yes—
14C2×M16×D67—24no—
15C2×M16×D67—24no—
16C2×M16×D67C418yescomplemented
17C22×C8×D67C2212yes—
18C2×#14524002C2211yescharacteristic
19C2×#14524001C2212yes—
20C2×#14524000—21no—
21C2×#14523999—21no—
22#117×D67—24no—
23#117×D67C418yescomplemented
24C22×C4⋊Dic67C2211yescharacteristic
25C22×Dic67⋊C4—21no—
26C2×C4⋊C4×D67—21no—
27C2×C4⋊C4×D67—21no—
28C2×C4⋊C4×D67—24no—
29C2×C4⋊C4×D67C418yescomplemented
30C2×C4⋊C4×D67C2212yes—
31C2×C4⋊C4×D67C2212yes—
32C2×C4⋊C4×D67C2212yes—
33C2×C22⋊C4×D67—21no—
34C2×C42×D67—21no—
35#16863159C2214yescomplemented
36#16863158C2214yescomplemented
37#16863158C2214yescomplemented
38C22×M16×C67C2211yescharacteristic
39C2×#117×C67C2211yescharacteristic
40C22×C4⋊C4×C67C2211yescharacteristic
41#340×C67C2214yescomplemented
42C24×D67D411yescharacteristic
43C23×Dic67—21no—
44C23×Dic67D411yescharacteristic
45C22×C4×D67—28no—
46C22×C4×D67—22no—
47C22×C4×D67—22no—
48C22×C4×D67—22no—
49C22×C4×D67—48no—
50C22×C4×D67C2×C414yes—
51C22×C4×D67C2×C414yes—
52C22×C4×D67C2×C414yes—
53C22×C4×D67D411yescharacteristic
54C22×C4×D67D411yescharacteristic
55C22×C4×D67D414yes—
56C22×C4×D67D414yes—
57C22×C4×D67Q814yes—
58C22×C4×D67C2311yescharacteristic
59C22×C4×D67C2311yescharacteristic
60C2×#11761612—22no—
61C2×#11761612—22no—
62C2×#11761612C2×C414yescomplemented
63C2×#11761611—24no—
64C2×#11761611—24no—
65C2×#11761611C2×C418yescomplemented
66M16×D67—232no—
67C22×C67⋊C8C2312yes—
68C2×C8×D67—24no—
69C2×C8×D67—24no—
70C2×C8×D67C2×C418yescomplemented
71#14524002—22no—
72#14524002C2×C414yescomplemented
73#14524001—24no—
74#14524001C2×C418yescomplemented
75#14524000—28no—
76#14523999—28no—
77C2×C4⋊Dic67—21no—
78C2×C4⋊Dic67—22no—
79C2×C4⋊Dic67C2×C414yescomplemented
80C2×C4⋊Dic67C2312yes—
81C2×C4⋊Dic67C2312yes—
82C2×Dic67⋊C4—28no—
83C2×Dic67⋊C4—22no—
84C2×Dic67⋊C4—22no—
85C2×Dic67⋊C4—22no—
86C4⋊C4×D67—28no—
87C4⋊C4×D67—28no—
88C4⋊C4×D67—24no—
89C4⋊C4×D67—24no—
90C4⋊C4×D67—24no—
91C4⋊C4×D67C2×C418yes—
92C4⋊C4×D67C2×C418yescomplemented
93C4⋊C4×D67C2×C418yescomplemented
94C2×C22⋊Dic67—21no—
95C2×(C2×D67)⋊C4—22no—
96C22⋊C4×D67—28no—
97C2×C4×Dic67—22no—
98C2×C4×Dic67—21no—
99C42×D67—28no—
100C23×C4×C67—21no—
101C23×C4×C67C2311yescharacteristic
102C2×M16×C67—22no—
103C2×M16×C67—22no—
104C2×M16×C67C2×C414yescomplemented
105C22×C8×C67C2312yes—
106#117×C67—22no—
107#117×C67C2×C414yescomplemented
108C2×C4⋊C4×C67—21no—
109C2×C4⋊C4×C67—22no—
110C2×C4⋊C4×C67C2×C414yescomplemented
111C2×C4⋊C4×C67C2312yes—
112C2×C4⋊C4×C67C2312yes—
113C2×C22⋊C4×C67—21no—
114C2×C42×C67—21no—
115C23×D67—24no—
116C23×D67—24no—
117C23×D67C22⋊C414yes—
118C23×D67C22⋊C414yes—
119C23×D67C4⋊C414yes—
120C23×D67C2×D411yescharacteristic
121C23×D67C2×D411yescharacteristic
122C22×Dic67—24no—
123C22×Dic67—22no—
124C22×Dic67—22no—
125C22×Dic67—44no—
126C22×Dic67C22⋊C414yes—
127C22×Dic67C22⋊C414yes—
128C22×Dic67C4⋊C414yes—
129C22×Dic67C2×D411yescharacteristic
130C22×Dic67C2×D411yescharacteristic
131C2×C4×D67—28no—
132C2×C4×D67—28no—
133C2×C4×D67—28no—
134C2×C4×D67—48no—
135C2×C4×D67—432no—
136C2×C4×D67—44no—
137C2×C4×D67—48no—
138C2×C4×D67—44no—
139C2×C4×D67C42116yes—
140C2×C4×D67C22⋊C414yes—
141C2×C4×D67C22⋊C414yes—
142C2×C4×D67C22⋊C414yes—
143C2×C4×D67C22⋊C414yes—
144C2×C4×D67C22⋊C4116yes—
145C2×C4×D67C4⋊C414yes—
146C2×C4×D67C4⋊C414yes—
147C2×C4×D67C4⋊C4116yes—
148C2×C4×D67C4⋊C4116yes—
149C2×C4×D67C22×C412yes—
150C2×C4×D67C22×C412yes—
151C2×C4×D67C22×C412yes—
152C2×C4×D67C22×C412yes—
153C2×C4×D67C22×C412yes—
154C2×C4×D67C22×C412yes—
155C2×C4×D67C2×D412yes—
156C2×C4×D67C2×D412yes—
157C2×C4×D67C2×D412yes—
158C2×C4×D67C2×D412yes—
159C2×C4×D67C2×Q812yes—
160C2×C4×D67C2×Q812yes—
161#11761612—28no—
162#11761611—216no—
163C2×C67⋊C8—22no—
164C2×C67⋊C8—22no—
165C2×C67⋊C8C22×C414yescomplemented
166C8×D67—216no—
167C4⋊Dic67—24no—
168C4⋊Dic67—22no—
169C4⋊Dic67—22no—
170C4⋊Dic67C22×C414yes—
171C4⋊Dic67C22×C414yescomplemented
172Dic67⋊C4—28no—
173Dic67⋊C4—28no—
174Dic67⋊C4—28no—
175C22⋊Dic67—24no—
176(C2×D67)⋊C4—28no—
177C4×Dic67—24no—
178C4×Dic67—28no—
179C24×C67C2×D411yescharacteristic
180C22×C4×C67—24no—
181C22×C4×C67—22no—
182C22×C4×C67—22no—
183C22×C4×C67—44no—
184C22×C4×C67C22×C412yes—
185C22×C4×C67C22×C412yes—
186C22×C4×C67C22×C412yes—
187C22×C4×C67C2×D411yescharacteristic
188C22×C4×C67C2×D412yes—
189C22×C4×C67C2×D412yes—
190C22×C4×C67C2×Q812yes—
191C22×C4×C67C2411yescharacteristic
192M16×C67—28no—
193C2×C8×C67—22no—
194C2×C8×C67—22no—
195C2×C8×C67C22×C414yescomplemented
196C4⋊C4×C67—24no—
197C4⋊C4×C67—22no—
198C4⋊C4×C67—22no—
199C4⋊C4×C67C22×C414yes—
200C4⋊C4×C67C22×C414yescomplemented
201C22⋊C4×C67—24no—
202C42×C67—24no—
203C23×C67—22no—
204C23×C67—22no—
205C23×C67C2×C22⋊C412yes—
206C23×C67C2×C22⋊C412yes—
207C23×C67C2×C4⋊C412yes—
208C23×C67C22×D411yescharacteristic
209C22×D67—22no—
210C22×D67—22no—
211C22×D67—216no—
212C22×D67—28no—
213C22×D67—28no—
214C22×D67—216no—
215C22×D67#95116yes—
216C22×D67C2×C22⋊C412yes—
217C22×D67C2×C22⋊C412yes—
218C22×D67C2×C22⋊C412yes—
219C22×D67C2×C22⋊C412yes—
220C22×D67C2×C4⋊C412yes—
221C22×D67C2×C4⋊C412yes—
222C22×D67AGL(1,ℤ/8)14yes—
223C22×D67#13714yes—
224C2×C4×C67—24no—
225C2×C4×C67—24no—
226C2×C4×C67—48no—
227C2×C4×C67—44no—
228C2×C4×C67—42no—
229C2×C4×C67—42no—
230C2×C4×C67C2×C4214yes—
231C2×C4×C67C2×C22⋊C414yes—
232C2×C4×C67C2×C22⋊C412yes—
233C2×C4×C67C2×C22⋊C412yes—
234C2×C4×C67C2×C4⋊C414yes—
235C2×C4×C67C2×C4⋊C414yes—
236C2×C4×C67C2×C4⋊C412yes—
237C2×C4×C67C23×C411yescharacteristic
238C2×C4×C67C23×C411yescharacteristic
239C2×C4×C67C23×C411yescharacteristic
240C2×C4×C67C22×D411yescharacteristic
241C2×C4×C67C22×D411yescharacteristic
242C2×C4×C67C22×Q811yescharacteristic
243C2×Dic67—24no—
244C2×Dic67—24no—
245C2×Dic67—48no—
246C2×Dic67—44no—
247C2×Dic67—42no—
248C2×Dic67—42no—
249C2×Dic67#95116yes—
250C2×Dic67C2×C22⋊C412yes—
251C2×Dic67C2×C22⋊C412yes—
252C2×Dic67C2×C22⋊C412yes—
253C2×Dic67C2×C22⋊C412yes—
254C2×Dic67C2×C4⋊C412yes—
255C2×Dic67C2×C4⋊C412yes—
256C4×D67—416no—
257C4×D67—416no—
258C4×D67—416no—
259C4×D67#95116yes—
260C4×D67#95116yes—
261C4×D67C2×C4214yes—
262C4×D67C2×C4214yes—
263C4×D67C2×C22⋊C414yes—
264C4×D67C2×C22⋊C414yes—
265C4×D67C2×C4⋊C414yes—
266C4×D67C2×C4⋊C414yes—
267C4×D67C2×C4⋊C414yes—
268C4×D67C2×C4⋊C414yes—
269C8×C67—24no—
270C67⋊C8—24no—
271C22×C67—22no—
272C22×C67—22no—
273C22×C67—24no—
274C22×C67—24no—
275C22×C67C2×#9514yes—
276C22×C67C22×C22⋊C411yescharacteristic
277C22×C67C22×C22⋊C411yescharacteristic
278C22×C67C22×C4⋊C411yescharacteristic
279C22×C67C2×AGL(1,ℤ/8)12yes—
280C22×C67C2×#13712yes—
281C2×D67—22no—
282C2×D67—22no—
283C2×D67—24no—
284C2×D67—24no—
285C2×D67—232no—
286C2×D67C2×#9514yes—
287C2×D67C2×#9514yes—
288C2×D67#41718yes—
289C2×D67#41814yes—
290C2×D67#41914yes—
291C2×D67#42818yes—
292C4×C67—44no—
293C4×C67—44no—
294C4×C67C2×#9514yes—
295C4×C67C22×C4211yescharacteristic
296C4×C67C22×C22⋊C411yescharacteristic
297C4×C67C22×C4⋊C411yescharacteristic
298C4×C67C22×C4⋊C411yescharacteristic
299Dic67—44no—
300Dic67—44no—
301Dic67C2×#9514yes—
302Dic67C2×#9514yes—
303C2×#1736—671nomaximal, Sylow
304C2×C67—24no—
305C2×C67C22×#9511yescharacteristic
306C2×C67C2×#41811yescharacteristic
307C2×C67C2×#41911yescharacteristic
308C2×C67C2×#41712yes—
309C2×C67C2×#42812yes—
310D67—24no—
311D67#173618yesdirect product factor
312C23×M16—671no—
313C22×#117—671no—
314C23×C4⋊C4—671no—
315#1736—674no—
316#1736—671no—
317#1736—671no—
318#1736—671no—
319#1736D6711yescharacteristic, direct product factor
320C2×#340—674no—
321C67C2×#173611yescharacteristic, complemented, Sylow
322C24×C4—671no—
323C24×C4—1341no—
324C22×M16—671no—
325C22×M16—678no—
326C22×M16—672no—
327C22×M16—1344no—
328C22×M16—1344no—
329C22×M16C2×D6711yescharacteristic
330C23×C8—672no—
331C2×#117—671no—
332C2×#117—678no—
333C2×#117—672no—
334C2×#117—1341no—
335C2×#117—1341no—
336C2×#117—1344no—
337C2×#117C2×D6711yescharacteristic
338C22×C4⋊C4—671no—
339C22×C4⋊C4—678no—
340C22×C4⋊C4—672no—
341C22×C4⋊C4—672no—
342C22×C4⋊C4—672no—
343C22×C4⋊C4—1341no—
344C22×C4⋊C4—1344no—
345C22×C4⋊C4—1341no—
346C22×C4⋊C4—1341no—
347C22×C4⋊C4C2×D6711yescharacteristic
348C22×C22⋊C4—1341no—
349C22×C42—1341no—
350#340—674no—
351#340—674no—
352#340—674no—
353#340C2×D6714yescomplemented
354C25—671no—
355C23×C4—21no—
356C23×C4—2688no—
357C23×C4—671no—
358C23×C4—674no—
359C23×C4—674no—
360C23×C4—674no—
361C23×C4—671no—
362C23×C4—674no—
363C23×C4—671no—
364C23×C4—674no—
365C23×C4—674no—
366C23×C4—671no—
367C23×C4—671no—
368C23×C4—1342no—
369C23×C4—1348no—
370C23×C4—1342no—
371C23×C4—1342no—
372C23×C4—1341no—
373C23×C4C22×D6711yescharacteristic
374C2×M16—22no—
375C2×M16—22no—
376C2×M16—674no—
377C2×M16—678no—
378C2×M16—1344no—
379C2×M16—1344no—
380C2×M16—13432no—
381C2×M16—1342no—
382C2×M16—1342no—
383C2×M16C4×D6714yescomplemented
384C22×C8—672no—
385C22×C8—678no—
386C22×C8—1344no—
387C22×C8—1344no—
388C22×C8C22×D6712yes—
389#117—22no—
390#117—674no—
391#117—678no—
392#117—1348no—
393#117—1348no—
394#117—1344no—
395#117—1342no—
396#117C4×D6714yescomplemented
397C2×C4⋊C4—21no—
398C2×C4⋊C4—22no—
399C2×C4⋊C4—674no—
400C2×C4⋊C4—672no—
401C2×C4⋊C4—672no—
402C2×C4⋊C4—678no—
403C2×C4⋊C4—678no—
404C2×C4⋊C4—678no—
405C2×C4⋊C4—1348no—
406C2×C4⋊C4—1348no—
407C2×C4⋊C4—1344no—
408C2×C4⋊C4—1344no—
409C2×C4⋊C4—1344no—
410C2×C4⋊C4—1348no—
411C2×C4⋊C4—1342no—
412C2×C4⋊C4—1342no—
413C2×C4⋊C4—1342no—
414C2×C4⋊C4—1341no—
415C2×C4⋊C4—1342no—
416C2×C4⋊C4C4×D6714yescomplemented
417C2×C4⋊C4C22×D6712yes—
418C2×C4⋊C4C22×D6712yes—
419C2×C22⋊C4—21no—
420C2×C22⋊C4—1348no—
421C2×C22⋊C4—1342no—
422C2×C22⋊C4—1341no—
423C2×C42—21no—
424C2×C42—1348no—
425C2×C42—1342no—
426C2×C42—1341no—
427C24—671no—
428C24—674no—
429C24—674no—
430C24—674no—
431C24—671no—
432C24—1344no—
433C24—1344no—
434C24D4×D6711yescharacteristic
435C22×C4—24no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—44no—
439C22×C4—2688no—
440C22×C4—2684no—
441C22×C4—2684no—
442C22×C4—26832no—
443C22×C4—2688no—
444C22×C4—2684no—
445C22×C4—674no—
446C22×C4—674no—
447C22×C4—674no—
448C22×C4—671no—
449C22×C4—671no—
450C22×C4—6716no—
451C22×C4—674no—
452C22×C4—674no—
453C22×C4—674no—
454C22×C4—674no—
455C22×C4—6716no—
456C22×C4—6716no—
457C22×C4—6716no—
458C22×C4—674no—
459C22×C4—674no—
460C22×C4—672no—
461C22×C4—672no—
462C22×C4—672no—
463C22×C4—672no—
464C22×C4—672no—
465C22×C4—672no—
466C22×C4—672no—
467C22×C4—672no—
468C22×C4—672no—
469C22×C4—672no—
470C22×C4—672no—
471C22×C4—672no—
472C22×C4—1348no—
473C22×C4—1348no—
474C22×C4—1348no—
475C22×C4—1344no—
476C22×C4—1342no—
477C22×C4—1342no—
478C22×C4C2×C4×D6712yes—
479C22×C4C2×C4×D6712yes—
480C22×C4C2×C4×D6712yes—
481C22×C4D4×D6711yescharacteristic
482C22×C4D4×D6712yes—
483C22×C4D4×D6712yes—
484C22×C4Q8×D6712yes—
485C22×C4C23×D6711yescharacteristic
486M16—28no—
487M16—13416no—
488M16—1348no—
489C2×C8—22no—
490C2×C8—22no—
491C2×C8—674no—
492C2×C8—13416no—
493C2×C8—1342no—
494C2×C8—1342no—
495C2×C8C2×C4×D6714yescomplemented
496C4⋊C4—24no—
497C4⋊C4—22no—
498C4⋊C4—22no—
499C4⋊C4—674no—
500C4⋊C4—674no—
501C4⋊C4—1348no—
502C4⋊C4—1348no—
503C4⋊C4—1348no—
504C4⋊C4—1344no—
505C4⋊C4—1342no—
506C4⋊C4—1342no—
507C4⋊C4C2×C4×D6714yes—
508C4⋊C4C2×C4×D6714yescomplemented
509C22⋊C4—24no—
510C22⋊C4—1348no—
511C22⋊C4—1344no—
512C42—24no—
513C42—1348no—
514C42—1344no—
515C23—22no—
516C23—22no—
517C23—672no—
518C23—672no—
519C23—672no—
520C23—674no—
521C23—674no—
522C23—6716no—
523C23—672no—
524C23—672no—
525C23—672no—
526C23—1348no—
527C23—1348no—
528C23—13416no—
529C23—13416no—
530C23—1342no—
531C23—1342no—
532C23C22⋊C4×D6712yes—
533C23C22⋊C4×D6712yes—
534C23C4⋊C4×D6712yes—
535C23C2×D4×D6711yescharacteristic
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—48no—
539C2×C4—44no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—26816no—
543C2×C4—26816no—
544C2×C4—26816no—
545C2×C4—2688no—
546C2×C4—2684no—
547C2×C4—2682no—
548C2×C4—2682no—
549C2×C4—6716no—
550C2×C4—672no—
551C2×C4—672no—
552C2×C4—672no—
553C2×C4—672no—
554C2×C4—672no—
555C2×C4—672no—
556C2×C4—6716no—
557C2×C4—6716no—
558C2×C4—674no—
559C2×C4—674no—
560C2×C4—674no—
561C2×C4—674no—
562C2×C4—674no—
563C2×C4—674no—
564C2×C4—674no—
565C2×C4—674no—
566C2×C4—1344no—
567C2×C4—1344no—
568C2×C4C42×D6714yes—
569C2×C4C22⋊C4×D6712yes—
570C2×C4C22⋊C4×D6712yes—
571C2×C4C22⋊C4×D6714yes—
572C2×C4C4⋊C4×D6712yes—
573C2×C4C4⋊C4×D6714yes—
574C2×C4C4⋊C4×D6714yes—
575C2×C4C22×C4×D6711yescharacteristic
576C2×C4C22×C4×D6711yescharacteristic
577C2×C4C22×C4×D6711yescharacteristic
578C2×C4C2×D4×D6711yescharacteristic
579C2×C4C2×D4×D6711yescharacteristic
580C2×C4C2×Q8×D6711yescharacteristic
581C8—24no—
582C8—1344no—
583C22—22no—
584C22—22no—
585C22—24no—
586C22—24no—
587C22—674no—
588C22—674no—
589C22—678no—
590C22—678no—
591C22—674no—
592C22—674no—
593C22—13432no—
594C22—1342no—
595C22—1342no—
596C22—1344no—
597C22—1344no—
598C22#95×D6714yes—
599C22C2×C22⋊C4×D6711yescharacteristic
600C22C2×C22⋊C4×D6711yescharacteristic
601C22C2×C4⋊C4×D6711yescharacteristic
602C22AGL(1,ℤ/8)×D6712yes—
603C22#137×D6712yes—
604C4—44no—
605C4—44no—
606C4—2684no—
607C4—2684no—
608C4—674no—
609C4—674no—
610C4#95×D6714yes—
611C4C2×C42×D6711yescharacteristic
612C4C2×C22⋊C4×D6711yescharacteristic
613C4C2×C4⋊C4×D6711yescharacteristic
614C4C2×C4⋊C4×D6711yescharacteristic
615C2—24no—
616C2—678no—
617C2—1344no—
618C2C2×#95×D6711yescharacteristic
619C2#418×D6711yescharacteristic
620C2#419×D6711yescharacteristic
621C2#417×D6712yes—
622C2#428×D6712yes—
subgroupG/H
centerC23C2×D4×D67
commutatorC4×C67C22×C42
FrattiniC22×C4C23×D67
FittingC67×#1736C2
socleC23×C67C22×D4
prime radicalC24×D67D4
cosocleC22×C4×C67C24
hypercenter#1736D67
hypocenterC67C2×#1736
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #22559930C2semidirect
5. #22559929C2semidirect
6. #22559928C2semidirect
7. #22559927C2semidirect
8. #340×D67C2semidirect
9. C67×#1736C2semidirect
16. C2×M16×D67C4semidirect
23. #117×D67C4semidirect
29. C2×C4⋊C4×D67C4semidirect
35. #16863159C22semidirect
36. #16863158C22semidirect
37. #16863158C22semidirect
41. #340×C67C22semidirect
62. C2×#11761612C2×C4semidirect
65. C2×#11761611C2×C4semidirect
70. C2×C8×D67C2×C4semidirect
72. #14524002C2×C4semidirect
74. #14524001C2×C4semidirect
79. C2×C4⋊Dic67C2×C4semidirect
92. C4⋊C4×D67C2×C4semidirect
93. C4⋊C4×D67C2×C4semidirect
104. C2×M16×C67C2×C4semidirect
107. #117×C67C2×C4semidirect
110. C2×C4⋊C4×C67C2×C4semidirect
165. C2×C67⋊C8C22×C4semidirect
171. C4⋊Dic67C22×C4semidirect
195. C2×C8×C67C22×C4semidirect
200. C4⋊C4×C67C22×C4semidirect
311. D67#1736direct (N × H)
319. #1736D67direct (N × H)
321. C67C2×#1736semidirect
353. #340C2×D67semidirect
383. C2×M16C4×D67semidirect
396. #117C4×D67semidirect
416. C2×C4⋊C4C4×D67semidirect
495. C2×C8C2×C4×D67semidirect
508. C4⋊C4C2×C4×D67semidirect

Maximal subgroups

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

subgroupindex
C22×M16×D672
C2×#117×D672
C22×C4⋊C4×D672
#225599302
#225599292
#225599282
#225599272
#340×D672
C67×#17362
C2×#173667