Finite Group Databasebeta

← C2×#22564724 #31024952

Subgroups — C2×#22564724 #31024952

Order 17152.

2358 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524033C211yesmaximal, characteristic
2#22564724C2116yesmaximal, direct product factor
3C2×#16863335C211yesmaximal, characteristic
4C2×#16863334C211yesmaximal, characteristic
5C2×#16863329C211yesmaximal, characteristic
6C2×#16863329C211yesmaximal, characteristic
7C2×#16863291C211yesmaximal, characteristic
8C2×#16863291C211yesmaximal, characteristic
9C2×#16863291C211yesmaximal, characteristic
10C2×#16863291C211yesmaximal, characteristic
11C2×#16863280C211yesmaximal, characteristic
12C2×#16863277C211yesmaximal, characteristic
13C2×#16863265C211yesmaximal, characteristic
14C2×C4⋊C4×Dic67C211yesmaximal, characteristic
15C2×C4×Dic67⋊C4C211yesmaximal, characteristic
16C22×#125×C67C211yesmaximal, characteristic
17C2×#14524033—28no—
18C2×#14524033C2218yes—
19C22×C4⋊Dic67C2211yescharacteristic
20C22×C4⋊Dic67C2211yescharacteristic
21C22×Dic67⋊C4C2211yescharacteristic
22C22×Dic67⋊C4C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2211yescharacteristic
27C22×Dic67⋊C4C2211yescharacteristic
28C22×Dic67⋊C4C2211yescharacteristic
29C22×Dic67⋊C4C2211yescharacteristic
30C22×Dic67⋊C4C2211yescharacteristic
31C22×C4×Dic67C2211yescharacteristic
32C22×C4×Dic67C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34C22×C4×Dic67C2211yescharacteristic
35#16863335C2218yes—
36#16863334C2218yes—
37#16863329C2218yes—
38#16863329C2218yes—
39#16863291C2218yes—
40#16863291C2218yes—
41#16863291C2218yes—
42#16863291C2218yes—
43#16863280C2218yes—
44#16863277C2218yes—
45#16863265C2218yes—
46C4⋊C4×Dic67C2218yes—
47C4×Dic67⋊C4C2218yes—
48C2×C67⋊#95C2211yescharacteristic
49C2×C67⋊#95C2211yescharacteristic
50C2×C67⋊#95C2211yescharacteristic
51C2×C67⋊#95C2211yescharacteristic
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C2×#125×C67—28no—
61C2×#125×C67C2218yes—
62C22×C4⋊C4×C67C2211yescharacteristic
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C4⋊C4×C67C2211yescharacteristic
65C22×C4⋊C4×C67C2211yescharacteristic
66C22×C4⋊C4×C67C2211yescharacteristic
67C22×C4⋊C4×C67C2211yescharacteristic
68C22×C42×C67C2211yescharacteristic
69C23×Dic67C2311yescharacteristic
70C23×Dic67C2311yescharacteristic
71C23×Dic67C2311yescharacteristic
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77#14524033—232no—
78C2×C4⋊Dic67—24no—
79C2×C4⋊Dic67—24no—
80C2×C4⋊Dic67C2314yes—
81C2×C4⋊Dic67C2314yes—
82C2×Dic67⋊C4—24no—
83C2×Dic67⋊C4—24no—
84C2×Dic67⋊C4—24no—
85C2×Dic67⋊C4—24no—
86C2×Dic67⋊C4—24no—
87C2×Dic67⋊C4—24no—
88C2×Dic67⋊C4—24no—
89C2×Dic67⋊C4—24no—
90C2×Dic67⋊C4—24no—
91C2×Dic67⋊C4Q818yes—
92C2×Dic67⋊C4C2314yes—
93C2×Dic67⋊C4C2314yes—
94C2×Dic67⋊C4C2314yes—
95C2×Dic67⋊C4C2314yes—
96C2×Dic67⋊C4C2314yes—
97C2×Dic67⋊C4C2314yes—
98C2×Dic67⋊C4C2314yes—
99C2×Dic67⋊C4C2314yes—
100C2×Dic67⋊C4C2314yes—
101C2×Dic67⋊C4C2314yes—
102C2×C4×Dic67—24no—
103C2×C4×Dic67—24no—
104C2×C4×Dic67—24no—
105C2×C4×Dic67—24no—
106C2×C4×Dic67C2314yes—
107C2×C4×Dic67C2314yes—
108C2×C4×Dic67C2314yes—
109C2×C4×Dic67C2314yes—
110C67⋊#95C2314yes—
111C67⋊#95C2314yes—
112C67⋊#95C2314yes—
113C67⋊#95C2314yes—
114C67⋊#95C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C23×C4×C67C2311yescharacteristic
123C23×C4×C67C2311yescharacteristic
124C23×C4×C67C2311yescharacteristic
125C23×C4×C67C2311yescharacteristic
126C23×C4×C67C2311yescharacteristic
127C23×C4×C67C2311yescharacteristic
128C23×C4×C67C2311yescharacteristic
129#125×C67—232no—
130C2×C4⋊C4×C67—24no—
131C2×C4⋊C4×C67—24no—
132C2×C4⋊C4×C67—24no—
133C2×C4⋊C4×C67—24no—
134C2×C4⋊C4×C67—24no—
135C2×C4⋊C4×C67D418yes—
136C2×C4⋊C4×C67C2314yes—
137C2×C4⋊C4×C67C2314yes—
138C2×C4⋊C4×C67C2314yes—
139C2×C4⋊C4×C67C2314yes—
140C2×C4⋊C4×C67C2314yes—
141C2×C4⋊C4×C67C2314yes—
142C2×C42×C67—24no—
143C2×C42×C67C2314yes—
144C22×Dic67—22no—
145C22×Dic67—22no—
146C22×Dic67—22no—
147C22×Dic67—22no—
148C22×Dic67—22no—
149C22×Dic67—22no—
150C22×Dic67—22no—
151C22×Dic67—22no—
152C22×Dic67—22no—
153C22×Dic67—22no—
154C22×Dic67—22no—
155C22×Dic67—22no—
156C22×Dic67—22no—
157C22×Dic67—22no—
158C22×Dic67—22no—
159C22×Dic67—22no—
160C22×Dic67—22no—
161C22×Dic67—22no—
162C22×Dic67—22no—
163C22×Dic67C2×Q814yes—
164C22×Dic67C2×Q814yes—
165C22×Dic67#4114yes—
166C22×Dic67#4114yes—
167C22×Dic67#4114yes—
168C22×Dic67C2412yes—
169C22×Dic67C2412yes—
170C22×Dic67C2412yes—
171C22×Dic67C2412yes—
172C22×Dic67C2412yes—
173C22×Dic67C2412yes—
174C22×Dic67C2412yes—
175C22×Dic67C2412yes—
176C4⋊Dic67—28no—
177C4⋊Dic67—28no—
178Dic67⋊C4—28no—
179Dic67⋊C4—28no—
180Dic67⋊C4—28no—
181Dic67⋊C4—28no—
182Dic67⋊C4—28no—
183Dic67⋊C4—28no—
184Dic67⋊C4—28no—
185Dic67⋊C4—28no—
186Dic67⋊C4—28no—
187Dic67⋊C4C2×Q8116yes—
188C4×Dic67—28no—
189C4×Dic67—28no—
190C4×Dic67—28no—
191C4×Dic67—28no—
192C24×C67C2411yescharacteristic
193C22×C4×C67—22no—
194C22×C4×C67—22no—
195C22×C4×C67—22no—
196C22×C4×C67—22no—
197C22×C4×C67—22no—
198C22×C4×C67—22no—
199C22×C4×C67—22no—
200C22×C4×C67—22no—
201C22×C4×C67—22no—
202C22×C4×C67—22no—
203C22×C4×C67—22no—
204C22×C4×C67—22no—
205C22×C4×C67—22no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
208C22×C4×C67—22no—
209C22×C4×C67—22no—
210C22×C4×C67C2×D414yes—
211C22×C4×C67C2×D414yes—
212C22×C4×C67C2×D414yes—
213C22×C4×C67C2×Q814yes—
214C22×C4×C67C2412yes—
215C22×C4×C67C2412yes—
216C22×C4×C67C2412yes—
217C22×C4×C67C2412yes—
218C22×C4×C67C2412yes—
219C22×C4×C67C2412yes—
220C22×C4×C67C2412yes—
221C4⋊C4×C67—28no—
222C4⋊C4×C67—28no—
223C4⋊C4×C67—28no—
224C4⋊C4×C67—28no—
225C4⋊C4×C67—28no—
226C4⋊C4×C67C2×D4116yes—
227C42×C67—28no—
228C23×C67C22×D412yes—
229C23×C67C22×Q812yes—
230C23×C67C2×#4112yes—
231C23×C67C2×#4112yes—
232C23×C67C2×#4112yes—
233C23×C672−1+412yes—
234C23×C672−1+412yes—
235C23×C67C2511yescharacteristic
236C2×C4×C67—28no—
237C2×C4×C67—28no—
238C2×C4×C67—28no—
239C2×C4×C67—28no—
240C2×C4×C67—22no—
241C2×C4×C67—22no—
242C2×C4×C67—22no—
243C2×C4×C67—22no—
244C2×C4×C67—22no—
245C2×C4×C67—22no—
246C2×C4×C67—22no—
247C2×C4×C67—22no—
248C2×C4×C67—22no—
249C2×C4×C67—22no—
250C2×C4×C67—22no—
251C2×C4×C67—22no—
252C2×C4×C67—22no—
253C2×C4×C67—22no—
254C2×C4×C67—22no—
255C2×C4×C67—22no—
256C2×C4×C67—22no—
257C2×C4×C67—44no—
258C2×C4×C67—44no—
259C2×C4×C67—44no—
260C2×C4×C67C22×D414yes—
261C2×C4×C67C22×D414yes—
262C2×C4×C67C22×D414yes—
263C2×C4×C67C22×Q814yes—
264C2×Dic67—28no—
265C2×Dic67—28no—
266C2×Dic67—22no—
267C2×Dic67—22no—
268C2×Dic67—22no—
269C2×Dic67—22no—
270C2×Dic67—22no—
271C2×Dic67—22no—
272C2×Dic67—22no—
273C2×Dic67—22no—
274C2×Dic67—22no—
275C2×Dic67—22no—
276C2×Dic67—22no—
277C2×Dic67—22no—
278C2×Dic67—22no—
279C2×Dic67—22no—
280C2×Dic67—22no—
281C2×Dic67—22no—
282C2×Dic67—22no—
283C2×Dic67—22no—
284C2×Dic67—22no—
285C2×Dic67—44no—
286C2×Dic67—44no—
287C2×Dic67—44no—
288C2×Dic67—44no—
289C2×Dic67—44no—
290C2×Dic67#125116yescomplemented
291C2×Dic67C22×Q814yes—
292C2×Dic67C22×Q814yes—
293C2×Dic67C2×#4114yes—
294C2×Dic67C2×#4114yes—
295C2×Dic67C2×#4114yes—
296C22×C67C2×#12514yes—
297C22×C67#53214yes—
298C22×C67#54114yes—
299C22×C67#54714yes—
300C22×C67D4×Q814yes—
301C22×C67#55214yes—
302C22×C67#55714yes—
303C22×C67C23×D411yescharacteristic
304C22×C67C23×Q811yescharacteristic
305C22×C67C22×#4111yescharacteristic
306C22×C67C22×#4111yescharacteristic
307C22×C67C22×#4111yescharacteristic
308C22×C67C2×2−1+411yescharacteristic
309C22×C67C2×2−1+411yescharacteristic
310C4×C67—24no—
311C4×C67—24no—
312C4×C67—24no—
313C4×C67—24no—
314C4×C67—42no—
315C4×C67—42no—
316C4×C67—42no—
317Dic67—24no—
318Dic67—24no—
319Dic67—42no—
320Dic67—42no—
321Dic67—42no—
322Dic67—42no—
323Dic67—42no—
324Dic67C2×#12518yescomplemented
325C2×#2506—671nomaximal, Sylow
326C2×C67#250618yescomplemented
327C2×C67C22×#12511yescharacteristic
328C2×C67C2×#53211yescharacteristic
329C2×C67C2×#54111yescharacteristic
330C2×C67C2×#54711yescharacteristic
331C2×C67C2×D4×Q811yescharacteristic
332C2×C67C2×#55211yescharacteristic
333C2×C67C2×#55711yescharacteristic
334C22×#125—671no—
335C22×#125D6711yescharacteristic
336#2506—6716no—
337C2×#400—671no—
338C2×#400—671no—
339C2×#398—671no—
340C2×#398—671no—
341C2×#389—671no—
342C2×#389—671no—
343C2×#389—671no—
344C2×#389—671no—
345C2×#387—671no—
346C2×#387—671no—
347C2×#384—671no—
348C2×C4×C4⋊C4—671no—
349C2×C4×C4⋊C4—671no—
350C67C2×#250611yescharacteristic, complemented, Sylow
351C2×#125—28no—
352C2×#125—678no—
353C2×#125—1348no—
354C2×#125C2×D6718yes—
355C22×C4⋊C4—671no—
356C22×C4⋊C4—671no—
357C22×C4⋊C4—671no—
358C22×C4⋊C4—671no—
359C22×C4⋊C4—671no—
360C22×C4⋊C4—671no—
361C22×C4⋊C4—671no—
362C22×C4⋊C4—671no—
363C22×C4⋊C4—671no—
364C22×C4⋊C4—671no—
365C22×C4⋊C4—671no—
366C22×C4⋊C4—671no—
367C22×C4⋊C4C2×D6711yescharacteristic
368C22×C4⋊C4C2×D6711yescharacteristic
369C22×C4⋊C4C2×D6711yescharacteristic
370C22×C4⋊C4C2×D6711yescharacteristic
371C22×C4⋊C4C2×D6711yescharacteristic
372C22×C4⋊C4C2×D6711yescharacteristic
373C22×C42—671no—
374C22×C42—671no—
375C22×C42—671no—
376C22×C42—671no—
377C22×C42C2×D6711yescharacteristic
378#400—678no—
379#400—678no—
380#398—678no—
381#398—678no—
382#389—678no—
383#389—678no—
384#389—678no—
385#389—678no—
386#387—678no—
387#387—678no—
388#384—678no—
389C4×C4⋊C4—678no—
390C4×C4⋊C4—678no—
391C2×#95—671no—
392C2×#95—671no—
393C2×#95—671no—
394C2×#95—671no—
395C2×#95—671no—
396C2×#95—671no—
397C2×#95—671no—
398C2×#95—671no—
399C2×#95—671no—
400C2×#95—671no—
401C2×#95—671no—
402C2×#95—671no—
403C23×C4—671no—
404C23×C4—671no—
405C23×C4—671no—
406C23×C4—671no—
407C23×C4—671no—
408C23×C4—671no—
409C23×C4—671no—
410C23×C4—671no—
411C23×C4C22×D6711yescharacteristic
412C23×C4C22×D6711yescharacteristic
413C23×C4C22×D6711yescharacteristic
414C23×C4C22×D6711yescharacteristic
415C23×C4C22×D6711yescharacteristic
416C23×C4C22×D6711yescharacteristic
417C23×C4C22×D6711yescharacteristic
418#125—232no—
419#125—13432no—
420C2×C4⋊C4—24no—
421C2×C4⋊C4—24no—
422C2×C4⋊C4—24no—
423C2×C4⋊C4—24no—
424C2×C4⋊C4—24no—
425C2×C4⋊C4—678no—
426C2×C4⋊C4—674no—
427C2×C4⋊C4—674no—
428C2×C4⋊C4—674no—
429C2×C4⋊C4—674no—
430C2×C4⋊C4—674no—
431C2×C4⋊C4—674no—
432C2×C4⋊C4—674no—
433C2×C4⋊C4—674no—
434C2×C4⋊C4—674no—
435C2×C4⋊C4—674no—
436C2×C4⋊C4—674no—
437C2×C4⋊C4—674no—
438C2×C4⋊C4—1344no—
439C2×C4⋊C4—1344no—
440C2×C4⋊C4—1344no—
441C2×C4⋊C4—1344no—
442C2×C4⋊C4—1344no—
443C2×C4⋊C4—1344no—
444C2×C4⋊C4—1344no—
445C2×C4⋊C4—1344no—
446C2×C4⋊C4—1344no—
447C2×C4⋊C4—1344no—
448C2×C4⋊C4—1344no—
449C2×C4⋊C4C22⋊D6718yes—
450C2×C4⋊C4C22×D6714yes—
451C2×C4⋊C4C22×D6714yes—
452C2×C4⋊C4C22×D6714yes—
453C2×C4⋊C4C22×D6714yes—
454C2×C4⋊C4C22×D6714yes—
455C2×C4⋊C4C22×D6714yes—
456C2×C42—24no—
457C2×C42—674no—
458C2×C42—674no—
459C2×C42—674no—
460C2×C42—674no—
461C2×C42—1344no—
462C2×C42—1344no—
463C2×C42—1344no—
464C2×C42—1344no—
465C2×C42C22×D6714yes—
466#95—674no—
467#95—674no—
468#95—674no—
469#95—674no—
470#95—674no—
471#95—674no—
472#95—674no—
473#95—674no—
474#95—674no—
475#95—674no—
476#95—674no—
477#95—674no—
478C24C23×D6711yescharacteristic
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—22no—
488C22×C4—22no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—674no—
497C22×C4—674no—
498C22×C4—674no—
499C22×C4—672no—
500C22×C4—674no—
501C22×C4—674no—
502C22×C4—672no—
503C22×C4—672no—
504C22×C4—672no—
505C22×C4—672no—
506C22×C4—672no—
507C22×C4—672no—
508C22×C4—672no—
509C22×C4—1342no—
510C22×C4—1342no—
511C22×C4—1342no—
512C22×C4—1342no—
513C22×C4—1342no—
514C22×C4—1342no—
515C22×C4—1342no—
516C22×C4—1342no—
517C22×C4—1342no—
518C22×C4—1342no—
519C22×C4—1342no—
520C22×C4—1342no—
521C22×C4—1342no—
522C22×C4—1342no—
523C22×C4—1342no—
524C22×C4—1342no—
525C22×C4—1342no—
526C22×C4—1342no—
527C22×C4—1342no—
528C22×C4C2×C22⋊D6714yes—
529C22×C4C2×C22⋊D6714yes—
530C22×C4C2×C22⋊D6714yes—
531C22×C4Q8×D6714yes—
532C22×C4C23×D6712yes—
533C22×C4C23×D6712yes—
534C22×C4C23×D6712yes—
535C22×C4C23×D6712yes—
536C22×C4C23×D6712yes—
537C22×C4C23×D6712yes—
538C22×C4C23×D6712yes—
539C4⋊C4—28no—
540C4⋊C4—28no—
541C4⋊C4—28no—
542C4⋊C4—28no—
543C4⋊C4—28no—
544C4⋊C4—6716no—
545C4⋊C4—1348no—
546C4⋊C4—1348no—
547C4⋊C4—1348no—
548C4⋊C4—1348no—
549C4⋊C4—1348no—
550C4⋊C4—1348no—
551C4⋊C4—1348no—
552C4⋊C4—1348no—
553C4⋊C4—1348no—
554C4⋊C4—1348no—
555C4⋊C4—1348no—
556C4⋊C4C2×C22⋊D67116yes—
557C42—28no—
558C42—1348no—
559C42—1348no—
560C42—1348no—
561C42—1348no—
562C23C22×C22⋊D6712yes—
563C23C2×Q8×D6712yes—
564C23#41×D6712yes—
565C23#41×D6712yes—
566C23#41×D6712yes—
567C23#1452409012yes—
568C23#1452409112yes—
569C23C24×D6711yescharacteristic
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—28no—
573C2×C4—28no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4—2684no—
595C2×C4—2684no—
596C2×C4—2684no—
597C2×C4—2684no—
598C2×C4—2684no—
599C2×C4—6716no—
600C2×C4—674no—
601C2×C4—674no—
602C2×C4—674no—
603C2×C4—674no—
604C2×C4—674no—
605C2×C4—1342no—
606C2×C4—1342no—
607C2×C4—1342no—
608C2×C4—1342no—
609C2×C4—1342no—
610C2×C4—1342no—
611C2×C4—1342no—
612C2×C4—1342no—
613C2×C4—1342no—
614C2×C4—1342no—
615C2×C4—1342no—
616C2×C4—1342no—
617C2×C4—1342no—
618C2×C4—1342no—
619C2×C4—1342no—
620C2×C4—1348no—
621C2×C4—1348no—
622C2×C4—1342no—
623C2×C4—1342no—
624C2×C4—1342no—
625C2×C4—1342no—
626C2×C4C22×C22⋊D6714yes—
627C2×C4C22×C22⋊D6714yes—
628C2×C4C22×C22⋊D6714yes—
629C2×C4C2×Q8×D6714yes—
630C22#125×D6714yes—
631C22#1686394214yes—
632C22#1686400514yes—
633C22#1686404514yes—
634C22Q8×C22⋊D6714yes—
635C22#1686407814yes—
636C22#1686412314yes—
637C22C23×C22⋊D6711yescharacteristic
638C22C22×Q8×D6711yescharacteristic
639C22C2×#41×D6711yescharacteristic
640C22C2×#41×D6711yescharacteristic
641C22C2×#41×D6711yescharacteristic
642C22C2×#1452409011yescharacteristic
643C22C2×#1452409111yescharacteristic
644C4—24no—
645C4—24no—
646C4—24no—
647C4—24no—
648C4—42no—
649C4—42no—
650C4—42no—
651C4—2682no—
652C4—2682no—
653C4—2682no—
654C4—2682no—
655C4—2682no—
656C4—678no—
657C4—1344no—
658C4—1344no—
659C2#2256472418yesdirect product factor
660C2C2×#125×D6711yescharacteristic
661C2C2×#1686394211yescharacteristic
662C2C2×#1686400511yescharacteristic
663C2C2×#1686404511yescharacteristic
664C2C2×Q8×C22⋊D6711yescharacteristic
665C2C2×#1686407811yescharacteristic
666C2C2×#1686412311yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC22×#125×C67C2
socle, prime radicalC24×C67C24
hypercenterC22×#125D67
hypocenterC67C2×#2506
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×#125

Complements

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

NH ≅ G/Ntype
2. #22564724C2direct (N × H)
290. C2×Dic67#125semidirect
324. Dic67C2×#125semidirect
326. C2×C67#2506semidirect
350. C67C2×#2506semidirect
659. C2#22564724direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240332
#225647242
C2×#168633352
C2×#168633342
C2×#168633292
C2×#168632912
C2×#168632802
C2×#168632772
C2×#168632652
C2×C4⋊C4×Dic672
C2×C4×Dic67⋊C42
C22×#125×C672
C2×#250667