Finite Group Databasebeta

← C67×#26135 #30705386

Subgroups — C67×#26135 #30705386

Order 17152.

844 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#485×C67C211yesmaximal, characteristic, complemented
2C2×#427×C67C211yesmaximal, characteristic, complemented
3C67×#2415C211yesmaximal, characteristic
4C67×#2354C211yesmaximal, characteristic
5C67×#2096C211yesmaximal, characteristic, complemented
6C67×#2083C211yesmaximal, characteristic, complemented
7C67×#2077C211yesmaximal, characteristic, complemented
8C67×#2036C211yesmaximal, characteristic, complemented
9C67×#1928C211yesmaximal, characteristic, complemented
10C67×#1919C211yesmaximal, characteristic, complemented
11C67×#1892C211yesmaximal, characteristic, complemented
12C67×#1873C211yesmaximal, characteristic, complemented
13C67×#1869C211yesmaximal, characteristic
14C67×#1854C211yesmaximal, characteristic, complemented
15C67×#1854C211yesmaximal, characteristic, complemented
16C23×C8×C67C2211yescharacteristic
17C2×C22⋊Q8×C67C2211yescharacteristic
18C2×C22⋊Q8×C67C2211yescharacteristic
19C2×C4×D4×C67C2211yescharacteristic
20C2×#117×C67C2211yescharacteristic
21C2×#117×C67C2211yescharacteristic
22C2×#117×C67C2211yescharacteristic
23#485×C67—24no—
24#427×C67—24no—
25C2×#107×C67C2211yescharacteristic
26C2×#107×C67C2211yescharacteristic
27C2×#107×C67C2211yescharacteristic
28C2×#106×C67C2211yescharacteristic
29C2×#106×C67C2211yescharacteristic
30C2×#106×C67C2211yescharacteristic
31C2×#103×C67C2211yescharacteristic
32C2×#103×C67C2211yescharacteristic
33C2×#103×C67C2211yescharacteristic
34C2×#103×C67C2211yescharacteristic
35C2×C22⋊C8×C67C2211yescharacteristic
36C2×C22⋊C8×C67C2211yescharacteristic
37C2×C22⋊C8×C67C2211yescharacteristic
38#397×C67—21no—
39#394×C67—21no—
40#391×C67C2211yescharacteristic
41#390×C67—21no—
42#389×C67—21no—
43#389×C67C2211yescharacteristic
44#388×C67—21no—
45#388×C67—21no—
46#388×C67—21no—
47#384×C67C2211yescharacteristic
48#380×C67C2211yescharacteristic
49#380×C67C2211yescharacteristic
50#380×C67C2211yescharacteristic
51C4×C4⋊C4×C67—21no—
52C4×C4⋊C4×C67C2211yescharacteristic
53#340×C67C2211yescharacteristic
54#340×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#336×C67C2211yescharacteristic
60#336×C67C2211yescharacteristic
61C22×Q8×C67C2311yescharacteristic
62C22×D4×C67D411yescharacteristic
63C23×C4×C67C2311yescharacteristic
64C23×C4×C67C2311yescharacteristic
65C22×C8×C67—22no—
66C22×C8×C67—22no—
67C22×C8×C67—22no—
68C22×C8×C67C2311yescharacteristic
69C22×C8×C67C2311yescharacteristic
70C22×C8×C67C2311yescharacteristic
71C22×C8×C67C2311yescharacteristic
72C22⋊Q8×C67—22no—
73C22⋊Q8×C67—22no—
74C22⋊Q8×C67—22no—
75C22⋊Q8×C67—41no—
76C4×D4×C67—22no—
77C4×D4×C67—22no—
78#117×C67—22no—
79#117×C67—22no—
80#117×C67—22no—
81#117×C67—41no—
82#117×C67—41no—
83#117×C67—41no—
84C2×C4⋊C4×C67—21no—
85C2×C4⋊C4×C67—21no—
86C2×C4⋊C4×C67—21no—
87C2×C4⋊C4×C67—21no—
88C2×C4⋊C4×C67—21no—
89C2×C4⋊C4×C67D411yescharacteristic
90C2×C4⋊C4×C67C2311yescharacteristic
91C2×C4⋊C4×C67C2311yescharacteristic
92C2×C4⋊C4×C67C2311yescharacteristic
93C2×C4⋊C4×C67C2311yescharacteristic
94C2×C4⋊C4×C67C2311yescharacteristic
95C2×C4⋊C4×C67C2311yescharacteristic
96C2×C4⋊C4×C67C2311yescharacteristic
97C2×C22⋊C4×C67—21no—
98C2×C22⋊C4×C67—21no—
99C2×C22⋊C4×C67—21no—
100C2×C22⋊C4×C67—21no—
101C2×C22⋊C4×C67—21no—
102C2×C22⋊C4×C67—21no—
103C2×C22⋊C4×C67—21no—
104C2×C22⋊C4×C67—21no—
105C2×C22⋊C4×C67D411yescharacteristic
106C2×C22⋊C4×C67D411yescharacteristic
107C2×C42×C67—21no—
108C2×C42×C67—21no—
109C2×C42×C67—21no—
110C2×C42×C67—21no—
111C2×C42×C67C2311yescharacteristic
112#107×C67—22no—
113#107×C67—22no—
114#107×C67—22no—
115#106×C67—22no—
116#106×C67—41no—
117#106×C67D414yescomplemented
118#103×C67—22no—
119#103×C67—22no—
120#103×C67—22no—
121#103×C67—41no—
122C22⋊C8×C67—22no—
123C22⋊C8×C67—22no—
124C22⋊C8×C67—22no—
125#95×C67—21no—
126#95×C67—21no—
127#95×C67—21no—
128#95×C67—21no—
129#95×C67—21no—
130#95×C67—21no—
131#95×C67—21no—
132C24×C67C2×D411yescharacteristic
133C24×C67C2×D411yescharacteristic
134C2×Q8×C67—21no—
135C2×Q8×C67—21no—
136C2×Q8×C67—21no—
137C2×Q8×C67—21no—
138C2×Q8×C67—21no—
139C2×Q8×C67—21no—
140C2×D4×C67—22no—
141C2×D4×C67—22no—
142C2×D4×C67—41no—
143C22×C4×C67—21no—
144C22×C4×C67—21no—
145C22×C4×C67—21no—
146C22×C4×C67—21no—
147C22×C4×C67—21no—
148C22×C4×C67—21no—
149C22×C4×C67—21no—
150C22×C4×C67—21no—
151C22×C4×C67—21no—
152C22×C4×C67—21no—
153C22×C4×C67—21no—
154C22×C4×C67—21no—
155C22×C4×C67—21no—
156C22×C4×C67—21no—
157C22×C4×C67—21no—
158C22×C4×C67—21no—
159C22×C4×C67—21no—
160C22×C4×C67—21no—
161C22×C4×C67C2×D411yescharacteristic
162C22×C4×C67C2×D411yescharacteristic
163C22×C4×C67C2×D411yescharacteristic
164C22×C4×C67C2×D411yescharacteristic
165C22×C4×C67#4112yes—
166C22×C4×C67#4112yes—
167C22×C4×C67C2411yescharacteristic
168C2×C8×C67—28no—
169C2×C8×C67—21no—
170C2×C8×C67—21no—
171C2×C8×C67—21no—
172C2×C8×C67—21no—
173C2×C8×C67—21no—
174C2×C8×C67—21no—
175C2×C8×C67—21no—
176C2×C8×C67—21no—
177C2×C8×C67—21no—
178C2×C8×C67—21no—
179C2×C8×C67C2×D412yes—
180C2×C8×C67#4112yes—
181C4⋊C4×C67—22no—
182C4⋊C4×C67—21no—
183C4⋊C4×C67—21no—
184C4⋊C4×C67—21no—
185C4⋊C4×C67—21no—
186C4⋊C4×C67—21no—
187C4⋊C4×C67—21no—
188C4⋊C4×C67—21no—
189C4⋊C4×C67—21no—
190C4⋊C4×C67—21no—
191C4⋊C4×C67—21no—
192C4⋊C4×C67—21no—
193C4⋊C4×C67—21no—
194C4⋊C4×C67—42no—
195C4⋊C4×C67—42no—
196C4⋊C4×C67—42no—
197C4⋊C4×C67—42no—
198C4⋊C4×C67—81no—
199C4⋊C4×C67C2×D412yes—
200C4⋊C4×C67C2×D412yes—
201C22⋊C4×C67—22no—
202C22⋊C4×C67—22no—
203C22⋊C4×C67—42no—
204C22⋊C4×C67—42no—
205C22⋊C4×C67—42no—
206C22⋊C4×C67—42no—
207C22⋊C4×C67—42no—
208C22⋊C4×C67—42no—
209C22⋊C4×C67—81no—
210C22⋊C4×C67—81no—
211C42×C67—21no—
212C42×C67—21no—
213C42×C67—42no—
214C42×C67—42no—
215C42×C67—42no—
216C42×C67—42no—
217C23×C67—21no—
218C23×C67—21no—
219C23×C67—21no—
220C23×C67—21no—
221C23×C67—21no—
222C23×C67—21no—
223C23×C67—21no—
224C23×C67—21no—
225C23×C67—21no—
226C23×C67—21no—
227C23×C67—21no—
228C23×C67—21no—
229C23×C67—21no—
230C23×C67#12312yes—
231C23×C67C22×D411yescharacteristic
232Q8×C67—41no—
233Q8×C67—41no—
234Q8×C67—41no—
235Q8×C67—41no—
236D4×C67—44no—
237C2×C4×C67—21no—
238C2×C4×C67—21no—
239C2×C4×C67—21no—
240C2×C4×C67—21no—
241C2×C4×C67—22no—
242C2×C4×C67—22no—
243C2×C4×C67—22no—
244C2×C4×C67—22no—
245C2×C4×C67—21no—
246C2×C4×C67—21no—
247C2×C4×C67—22no—
248C2×C4×C67—21no—
249C2×C4×C67—22no—
250C2×C4×C67—21no—
251C2×C4×C67—21no—
252C2×C4×C67—21no—
253C2×C4×C67—41no—
254C2×C4×C67—41no—
255C2×C4×C67—41no—
256C2×C4×C67—41no—
257C2×C4×C67—41no—
258C2×C4×C67—41no—
259C2×C4×C67—41no—
260C2×C4×C67—41no—
261C2×C4×C67—41no—
262C2×C4×C67—41no—
263C2×C4×C67—41no—
264C2×C4×C67—41no—
265C2×C4×C67—41no—
266C2×C4×C67—41no—
267C2×C4×C67—41no—
268C2×C4×C67—41no—
269C2×C4×C67—41no—
270C2×C4×C67—41no—
271C2×C4×C67—41no—
272C2×C4×C67—41no—
273C2×C4×C67—41no—
274C2×C4×C67—41no—
275C2×C4×C67—41no—
276C2×C4×C67—41no—
277C2×C4×C67—41no—
278C2×C4×C67—41no—
279C2×C4×C67#12312yes—
280C2×C4×C67#13512yes—
281C2×C4×C67C22×D411yescharacteristic
282C2×C4×C67C2×#4111yescharacteristic
283C2×C4×C67C2×#4111yescharacteristic
284C2×C4×C67C2×#4111yescharacteristic
285C2×C4×C67H(5,𝔽2)11yescharacteristic
286C2×C4×C672−1+411yescharacteristic
287C8×C67—22no—
288C8×C67—22no—
289C8×C67—41no—
290C8×C67—41no—
291C22×C67—22no—
292C22×C67—22no—
293C22×C67—22no—
294C22×C67—41no—
295C22×C67—41no—
296C22×C67—41no—
297C22×C67—41no—
298C22×C67—41no—
299C22×C67—41no—
300C22×C67—41no—
301C22×C67—41no—
302C22×C67—41no—
303C22×C67—41no—
304C22×C67—41no—
305C22×C67C2×#12311yescharacteristic
306C22×C67D4211yescharacteristic
307C22×C67#54711yescharacteristic
308C22×C67C2×#13511yescharacteristic
309C22×C67#57511yescharacteristic
310C22×C67#57711yescharacteristic
311C22×C67#57811yescharacteristic
312C4×C67—22no—
313C4×C67—22no—
314C4×C67—41no—
315C4×C67—41no—
316C4×C67—42no—
317C4×C67—42no—
318C4×C67—81no—
319C4×C67—81no—
320C4×C67—81no—
321C4×C67—81no—
322C4×C67—81no—
323C4×C67—81no—
324C4×C67#52511yescharacteristic
325C4×C67#53911yescharacteristic
326C4×C67#54811yescharacteristic
327C4×C67#55311yescharacteristic
328#26135C6711yesmaximal, characteristic, direct product factor, Sylow
329C2×C67—42no—
330C2×C67—81no—
331C2×C67#244311yescharacteristic
332C2×C67#309111yescharacteristic
333C2×C67#309711yescharacteristic
334C2×C67#326911yescharacteristic
335C2×C67#328411yescharacteristic
336C2×C67#334211yescharacteristic
337C2×C67#334811yescharacteristic
338C2×#485C2×C6711yescharacteristic, complemented
339C2×#427C2×C6711yescharacteristic, complemented
340#2415C2×C6711yescharacteristic
341#2354C2×C6711yescharacteristic
342#2096C2×C6711yescharacteristic, complemented
343#2083C2×C6711yescharacteristic, complemented
344#2077C2×C6711yescharacteristic, complemented
345#2036C2×C6711yescharacteristic, complemented
346#1928C2×C6711yescharacteristic, complemented
347#1919C2×C6711yescharacteristic, complemented
348#1892C2×C6711yescharacteristic, complemented
349#1873C2×C6711yescharacteristic, complemented
350#1869C2×C6711yescharacteristic
351#1854C2×C6711yescharacteristic, complemented
352#1854C2×C6711yescharacteristic, complemented
353C67#2613511yescharacteristic, direct product factor, Sylow
354C23×C8C22×C6711yescharacteristic
355C2×C22⋊Q8C22×C6711yescharacteristic
356C2×C22⋊Q8C22×C6711yescharacteristic
357C2×C4×D4C22×C6711yescharacteristic
358C2×#117C22×C6711yescharacteristic
359C2×#117C22×C6711yescharacteristic
360C2×#117C22×C6711yescharacteristic
361#485—24no—
362#427—24no—
363C2×#107C22×C6711yescharacteristic
364C2×#107C22×C6711yescharacteristic
365C2×#107C22×C6711yescharacteristic
366C2×#106C22×C6711yescharacteristic
367C2×#106C22×C6711yescharacteristic
368C2×#106C22×C6711yescharacteristic
369C2×#103C22×C6711yescharacteristic
370C2×#103C22×C6711yescharacteristic
371C2×#103C22×C6711yescharacteristic
372C2×#103C22×C6711yescharacteristic
373C2×C22⋊C8C22×C6711yescharacteristic
374C2×C22⋊C8C22×C6711yescharacteristic
375C2×C22⋊C8C22×C6711yescharacteristic
376#397—21no—
377#394—21no—
378#391C22×C6711yescharacteristic
379#390—21no—
380#389—21no—
381#389C22×C6711yescharacteristic
382#388—21no—
383#388—21no—
384#388—21no—
385#384C22×C6711yescharacteristic
386#380C22×C6711yescharacteristic
387#380C22×C6711yescharacteristic
388#380C22×C6711yescharacteristic
389C4×C4⋊C4—21no—
390C4×C4⋊C4C22×C6711yescharacteristic
391#340C22×C6711yescharacteristic
392#340C22×C6711yescharacteristic
393#340C22×C6711yescharacteristic
394#340C22×C6711yescharacteristic
395#340C22×C6711yescharacteristic
396#340C22×C6711yescharacteristic
397#336C22×C6711yescharacteristic
398#336C22×C6711yescharacteristic
399C22×Q8C23×C6711yescharacteristic
400C22×D4D4×C6711yescharacteristic
401C23×C4C23×C6711yescharacteristic
402C23×C4C23×C6711yescharacteristic
403C22×C8—22no—
404C22×C8—22no—
405C22×C8—22no—
406C22×C8C23×C6711yescharacteristic
407C22×C8C23×C6711yescharacteristic
408C22×C8C23×C6711yescharacteristic
409C22×C8C23×C6711yescharacteristic
410C22⋊Q8—22no—
411C22⋊Q8—22no—
412C22⋊Q8—22no—
413C22⋊Q8—41no—
414C4×D4—22no—
415C4×D4—22no—
416#117—22no—
417#117—22no—
418#117—22no—
419#117—41no—
420#117—41no—
421#117—41no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4D4×C6711yescharacteristic
428C2×C4⋊C4C23×C6711yescharacteristic
429C2×C4⋊C4C23×C6711yescharacteristic
430C2×C4⋊C4C23×C6711yescharacteristic
431C2×C4⋊C4C23×C6711yescharacteristic
432C2×C4⋊C4C23×C6711yescharacteristic
433C2×C4⋊C4C23×C6711yescharacteristic
434C2×C4⋊C4C23×C6711yescharacteristic
435C2×C22⋊C4—21no—
436C2×C22⋊C4—21no—
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4D4×C6711yescharacteristic
444C2×C22⋊C4D4×C6711yescharacteristic
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—21no—
449C2×C42C23×C6711yescharacteristic
450#107—22no—
451#107—22no—
452#107—22no—
453#106—22no—
454#106—41no—
455#106D4×C6714yescomplemented
456#103—22no—
457#103—22no—
458#103—22no—
459#103—41no—
460C22⋊C8—22no—
461C22⋊C8—22no—
462C22⋊C8—22no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470C24C2×D4×C6711yescharacteristic
471C24C2×D4×C6711yescharacteristic
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×D4—22no—
479C2×D4—22no—
480C2×D4—41no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4C2×D4×C6711yescharacteristic
500C22×C4C2×D4×C6711yescharacteristic
501C22×C4C2×D4×C6711yescharacteristic
502C22×C4C2×D4×C6711yescharacteristic
503C22×C4#41×C6712yes—
504C22×C4#41×C6712yes—
505C22×C4C24×C6711yescharacteristic
506C2×C8—28no—
507C2×C8—21no—
508C2×C8—21no—
509C2×C8—21no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8C2×D4×C6712yes—
518C2×C8#41×C6712yes—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—81no—
537C4⋊C4C2×D4×C6712yes—
538C4⋊C4C2×D4×C6712yes—
539C22⋊C4—22no—
540C22⋊C4—22no—
541C22⋊C4—42no—
542C22⋊C4—42no—
543C22⋊C4—42no—
544C22⋊C4—42no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—81no—
548C22⋊C4—81no—
549C42—21no—
550C42—21no—
551C42—42no—
552C42—42no—
553C42—42no—
554C42—42no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—21no—
567C23—21no—
568C23#123×C6712yes—
569C23C22×D4×C6711yescharacteristic
570Q8—41no—
571Q8—41no—
572Q8—41no—
573Q8—41no—
574D4—44no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—22no—
586C2×C4—21no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4#123×C6712yes—
618C2×C4#135×C6712yes—
619C2×C4C22×D4×C6711yescharacteristic
620C2×C4C2×#41×C6711yescharacteristic
621C2×C4C2×#41×C6711yescharacteristic
622C2×C4C2×#41×C6711yescharacteristic
623C2×C4H(5,𝔽2)×C6711yescharacteristic
624C2×C42−1+4×C6711yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—41no—
637C22—41no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—41no—
643C22C2×#123×C6711yescharacteristic
644C22D42×C6711yescharacteristic
645C22#547×C6711yescharacteristic
646C22C2×#135×C6711yescharacteristic
647C22#575×C6711yescharacteristic
648C22#577×C6711yescharacteristic
649C22#578×C6711yescharacteristic
650C4—22no—
651C4—22no—
652C4—42no—
653C4—42no—
654C4—41no—
655C4—41no—
656C4—81no—
657C4—81no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4#525×C6711yescharacteristic
663C4#539×C6711yescharacteristic
664C4#548×C6711yescharacteristic
665C4#553×C6711yescharacteristic
666C2—42no—
667C2—81no—
668C2C67×#244311yescharacteristic
669C2C67×#309111yescharacteristic
670C2C67×#309711yescharacteristic
671C2C67×#326911yescharacteristic
672C2C67×#328411yescharacteristic
673C2C67×#334211yescharacteristic
674C2C67×#334811yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC22×D4×C67D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×C4×D4×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#485×C67C2semidirect
2. C2×#427×C67C2semidirect
5. C67×#2096C2semidirect
6. C67×#2083C2semidirect
7. C67×#2077C2semidirect
8. C67×#2036C2semidirect
9. C67×#1928C2semidirect
10. C67×#1919C2semidirect
11. C67×#1892C2semidirect
12. C67×#1873C2semidirect
14. C67×#1854C2semidirect
15. C67×#1854C2semidirect
117. #106×C67D4semidirect
328. #26135C67direct (N × H)
338. C2×#485C2×C67semidirect
339. C2×#427C2×C67semidirect
342. #2096C2×C67semidirect
343. #2083C2×C67semidirect
344. #2077C2×C67semidirect
345. #2036C2×C67semidirect
346. #1928C2×C67semidirect
347. #1919C2×C67semidirect
348. #1892C2×C67semidirect
349. #1873C2×C67semidirect
351. #1854C2×C67semidirect
352. #1854C2×C67semidirect
353. C67#26135direct (N × H)
455. #106D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#485×C672
C2×#427×C672
C67×#24152
C67×#23542
C67×#20962
C67×#20832
C67×#20772
C67×#20362
C67×#19282
C67×#19192
C67×#18922
C67×#18732
C67×#18692
C67×#18542
#2613567