Finite Group Databasebeta

← C67×#33054 #30712305

Subgroups — C67×#33054 #30712305

Order 17152.

872 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#489×C67C211yesmaximal, characteristic, complemented
2C2×#405×C67C211yesmaximal, characteristic, complemented
3C67×#2628C211yesmaximal, characteristic, complemented
4C67×#2620C211yesmaximal, characteristic
5C67×#1990C211yesmaximal, characteristic, complemented
6C67×#1958C211yesmaximal, characteristic, complemented
7C67×#1936C211yesmaximal, characteristic, complemented
8C67×#1935C211yesmaximal, characteristic, complemented
9C67×#1934C211yesmaximal, characteristic, complemented
10C67×#1933C211yesmaximal, characteristic, complemented
11C67×#1895C211yesmaximal, characteristic
12C67×#1894C211yesmaximal, characteristic, complemented
13C67×#1893C211yesmaximal, characteristic
14C67×#1892C211yesmaximal, characteristic, complemented
15C67×#1836C211yesmaximal, characteristic, complemented
16C22×M16×C67C2211yescharacteristic
17C23×C8×C67C2211yescharacteristic
18C2×C4⋊Q8×C67C2211yescharacteristic
19C2×#124×C67C2211yescharacteristic
20C2×C22⋊Q8×C67C2211yescharacteristic
21C2×#121×C67C2211yescharacteristic
22C2×#117×C67C2211yescharacteristic
23#489×C67—24no—
24C2×#103×C67C2211yescharacteristic
25C2×#103×C67C2211yescharacteristic
26C2×#103×C67C2211yescharacteristic
27C2×#103×C67C2211yescharacteristic
28C2×#102×C67C2211yescharacteristic
29C2×#102×C67C2211yescharacteristic
30C2×#102×C67C2211yescharacteristic
31C2×#102×C67C2211yescharacteristic
32#405×C67—24no—
33C2×#97×C67C2211yescharacteristic
34C2×#97×C67C2211yescharacteristic
35C2×C4×C8×C67C2211yescharacteristic
36C2×C4×C8×C67C2211yescharacteristic
37#400×C67—21no—
38#399×C67—21no—
39#396×C67—21no—
40#396×C67—21no—
41#395×C67—21no—
42#394×C67—21no—
43#394×C67—21no—
44#393×C67—21no—
45#391×C67C2211yescharacteristic
46#390×C67C2211yescharacteristic
47#389×C67C2211yescharacteristic
48#389×C67C2211yescharacteristic
49#384×C67C2211yescharacteristic
50#382×C67C2211yescharacteristic
51#380×C67C2211yescharacteristic
52#380×C67C2211yescharacteristic
53#340×C67C2211yescharacteristic
54#340×C67C2211yescharacteristic
55#340×C67C2211yescharacteristic
56#340×C67C2211yescharacteristic
57#340×C67C2211yescharacteristic
58#340×C67C2211yescharacteristic
59#340×C67C2211yescharacteristic
60#340×C67C2211yescharacteristic
61C22×Q8×C67—21no—
62C22×Q8×C67C2311yescharacteristic
63C22×D4×C67—21no—
64C22×D4×C67C2311yescharacteristic
65C23×C4×C67C2311yescharacteristic
66C2×M16×C67—22no—
67C2×M16×C67—22no—
68C2×M16×C67—22no—
69C22×C8×C67—22no—
70C22×C8×C67—22no—
71C22×C8×C67—22no—
72C22×C8×C67C2311yescharacteristic
73C22×C8×C67C2311yescharacteristic
74C22×C8×C67C2311yescharacteristic
75C22×C8×C67C2311yescharacteristic
76C4⋊Q8×C67—22no—
77C4⋊Q8×C67—22no—
78#124×C67—22no—
79#124×C67—22no—
80C22⋊Q8×C67—22no—
81C22⋊Q8×C67—22no—
82#121×C67—22no—
83#121×C67—22no—
84#117×C67—22no—
85#117×C67—22no—
86C2×C4⋊C4×C67—21no—
87C2×C4⋊C4×C67—21no—
88C2×C4⋊C4×C67—21no—
89C2×C4⋊C4×C67—21no—
90C2×C4⋊C4×C67—21no—
91C2×C4⋊C4×C67—21no—
92C2×C4⋊C4×C67D411yescharacteristic
93C2×C4⋊C4×C67D411yescharacteristic
94C2×C4⋊C4×C67C2311yescharacteristic
95C2×C4⋊C4×C67C2311yescharacteristic
96C2×C4⋊C4×C67C2311yescharacteristic
97C2×C4⋊C4×C67C2311yescharacteristic
98C2×C4⋊C4×C67C2311yescharacteristic
99C2×C4⋊C4×C67C2311yescharacteristic
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×C67—21no—
106C2×C22⋊C4×C67—21no—
107C2×C22⋊C4×C67—21no—
108C2×C22⋊C4×C67D411yescharacteristic
109C2×C22⋊C4×C67D411yescharacteristic
110C2×C42×C67C2311yescharacteristic
111C2×C42×C67C2311yescharacteristic
112#103×C67—22no—
113#103×C67—22no—
114#103×C67—22no—
115#103×C67—22no—
116#102×C67—22no—
117#102×C67—22no—
118#102×C67—22no—
119#102×C67—22no—
120#97×C67—22no—
121#97×C67D414yescomplemented
122C4×C8×C67—22no—
123C4×C8×C67—22no—
124#95×C67—21no—
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×C67—21no—
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×Q8×C67—42no—
141C2×Q8×C67—81no—
142C2×Q8×C67—81no—
143C2×D4×C67—21no—
144C2×D4×C67—21no—
145C2×D4×C67—21no—
146C2×D4×C67—21no—
147C2×D4×C67—21no—
148C2×D4×C67—21no—
149C2×D4×C67—42no—
150C2×D4×C67—81no—
151C2×D4×C67—81no—
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×C67—21no—
162C22×C4×C67—21no—
163C22×C4×C67C2×D411yescharacteristic
164C22×C4×C67C2×D411yescharacteristic
165C22×C4×C67C2×D411yescharacteristic
166C22×C4×C67C2×D411yescharacteristic
167C22×C4×C67C2×D411yescharacteristic
168C22×C4×C67#4112yes—
169C22×C4×C67#4112yes—
170C22×C4×C67C2411yescharacteristic
171M16×C67—28no—
172C2×C8×C67—28no—
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×C67—21no—
180C2×C8×C67—21no—
181C2×C8×C67C2×D412yes—
182C2×C8×C67C2×D412yes—
183C2×C8×C67#4112yes—
184C2×C8×C67#4112yes—
185C4⋊C4×C67—22no—
186C4⋊C4×C67—22no—
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—21no—
195C4⋊C4×C67—21no—
196C4⋊C4×C67—21no—
197C4⋊C4×C67—21no—
198C4⋊C4×C67—21no—
199C4⋊C4×C67—42no—
200C4⋊C4×C67—42no—
201C4⋊C4×C67—81no—
202C4⋊C4×C67—81no—
203C4⋊C4×C67—81no—
204C4⋊C4×C67—81no—
205C22⋊C4×C67—22no—
206C22⋊C4×C67—22no—
207C22⋊C4×C67—42no—
208C22⋊C4×C67—42no—
209C22⋊C4×C67—42no—
210C22⋊C4×C67—42no—
211C22⋊C4×C67—81no—
212C22⋊C4×C67—81no—
213C22⋊C4×C67—81no—
214C22⋊C4×C67—81no—
215C42×C67—21no—
216C42×C67—21no—
217C42×C67C2×D412yes—
218C42×C67#4112yes—
219C23×C67—21no—
220C23×C67—21no—
221C23×C67—21no—
222C23×C67—21no—
223C23×C67—21no—
224C23×C67—21no—
225C23×C67—41no—
226C23×C67—41no—
227C23×C67—41no—
228C23×C67—41no—
229C23×C67—41no—
230C23×C67—41no—
231C23×C67—41no—
232C23×C67#12412yes—
233C23×C67C22×D411yescharacteristic
234Q8×C67—41no—
235Q8×C67—41no—
236Q8×C67—41no—
237Q8×C67—41no—
238Q8×C67—84no—
239D4×C67—41no—
240D4×C67—41no—
241D4×C67—41no—
242D4×C67—41no—
243D4×C67—84no—
244C2×C4×C67—21no—
245C2×C4×C67—21no—
246C2×C4×C67—21no—
247C2×C4×C67—21no—
248C2×C4×C67—21no—
249C2×C4×C67—21no—
250C2×C4×C67—22no—
251C2×C4×C67—22no—
252C2×C4×C67—22no—
253C2×C4×C67—22no—
254C2×C4×C67—21no—
255C2×C4×C67—21no—
256C2×C4×C67—21no—
257C2×C4×C67—21no—
258C2×C4×C67—21no—
259C2×C4×C67—21no—
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—41no—
280C2×C4×C67—41no—
281C2×C4×C67#12112yes—
282C2×C4×C67#12112yes—
283C2×C4×C67#12412yes—
284C2×C4×C67C22×D411yescharacteristic
285C2×C4×C67C2×#4111yescharacteristic
286C2×C4×C67C2×#4111yescharacteristic
287C2×C4×C67C2×#4111yescharacteristic
288C2×C4×C67C2×#4111yescharacteristic
289C2×C4×C67C2×#4111yescharacteristic
290C8×C67—22no—
291C8×C67—22no—
292C8×C67—22no—
293C8×C67—22no—
294C22×C67—22no—
295C22×C67—22no—
296C22×C67—22no—
297C22×C67—41no—
298C22×C67—41no—
299C22×C67—41no—
300C22×C67—41no—
301C22×C67—81no—
302C22×C67—81no—
303C22×C67—81no—
304C22×C67—81no—
305C22×C67—81no—
306C22×C67—81no—
307C22×C67—81no—
308C22×C67C2×#12111yescharacteristic
309C22×C67C2×#12411yescharacteristic
310C22×C67#53211yescharacteristic
311C22×C67#57611yescharacteristic
312C22×C67#57711yescharacteristic
313C22×C67#57711yescharacteristic
314C22×C67#57811yescharacteristic
315C4×C67—22no—
316C4×C67—22no—
317C4×C67—22no—
318C4×C67—41no—
319C4×C67—41no—
320C4×C67—81no—
321C4×C67—81no—
322C4×C67—81no—
323C4×C67—81no—
324C4×C67—81no—
325C4×C67—81no—
326C4×C67—81no—
327C4×C67#52511yescharacteristic
328C4×C67#52511yescharacteristic
329C4×C67#52911yescharacteristic
330C4×C67#52911yescharacteristic
331#33054C6711yesmaximal, characteristic, direct product factor, Sylow
332C2×C67—42no—
333C2×C67—161no—
334C2×C67#285011yescharacteristic
335C2×C67#306211yescharacteristic
336C2×C67#306311yescharacteristic
337C2×C67#313611yescharacteristic
338C2×C67#313711yescharacteristic
339C2×C67#317311yescharacteristic
340C2×C67#317511yescharacteristic
341C2×#489C2×C6711yescharacteristic, complemented
342C2×#405C2×C6711yescharacteristic, complemented
343#2628C2×C6711yescharacteristic, complemented
344#2620C2×C6711yescharacteristic
345#1990C2×C6711yescharacteristic, complemented
346#1958C2×C6711yescharacteristic, complemented
347#1936C2×C6711yescharacteristic, complemented
348#1935C2×C6711yescharacteristic, complemented
349#1934C2×C6711yescharacteristic, complemented
350#1933C2×C6711yescharacteristic, complemented
351#1895C2×C6711yescharacteristic
352#1894C2×C6711yescharacteristic, complemented
353#1893C2×C6711yescharacteristic
354#1892C2×C6711yescharacteristic, complemented
355#1836C2×C6711yescharacteristic, complemented
356C67#3305411yescharacteristic, direct product factor, Sylow
357C22×M16C22×C6711yescharacteristic
358C23×C8C22×C6711yescharacteristic
359C2×C4⋊Q8C22×C6711yescharacteristic
360C2×#124C22×C6711yescharacteristic
361C2×C22⋊Q8C22×C6711yescharacteristic
362C2×#121C22×C6711yescharacteristic
363C2×#117C22×C6711yescharacteristic
364#489—24no—
365C2×#103C22×C6711yescharacteristic
366C2×#103C22×C6711yescharacteristic
367C2×#103C22×C6711yescharacteristic
368C2×#103C22×C6711yescharacteristic
369C2×#102C22×C6711yescharacteristic
370C2×#102C22×C6711yescharacteristic
371C2×#102C22×C6711yescharacteristic
372C2×#102C22×C6711yescharacteristic
373#405—24no—
374C2×#97C22×C6711yescharacteristic
375C2×#97C22×C6711yescharacteristic
376C2×C4×C8C22×C6711yescharacteristic
377C2×C4×C8C22×C6711yescharacteristic
378#400—21no—
379#399—21no—
380#396—21no—
381#396—21no—
382#395—21no—
383#394—21no—
384#394—21no—
385#393—21no—
386#391C22×C6711yescharacteristic
387#390C22×C6711yescharacteristic
388#389C22×C6711yescharacteristic
389#389C22×C6711yescharacteristic
390#384C22×C6711yescharacteristic
391#382C22×C6711yescharacteristic
392#380C22×C6711yescharacteristic
393#380C22×C6711yescharacteristic
394#340C22×C6711yescharacteristic
395#340C22×C6711yescharacteristic
396#340C22×C6711yescharacteristic
397#340C22×C6711yescharacteristic
398#340C22×C6711yescharacteristic
399#340C22×C6711yescharacteristic
400#340C22×C6711yescharacteristic
401#340C22×C6711yescharacteristic
402C22×Q8—21no—
403C22×Q8C23×C6711yescharacteristic
404C22×D4—21no—
405C22×D4C23×C6711yescharacteristic
406C23×C4C23×C6711yescharacteristic
407C2×M16—22no—
408C2×M16—22no—
409C2×M16—22no—
410C22×C8—22no—
411C22×C8—22no—
412C22×C8—22no—
413C22×C8C23×C6711yescharacteristic
414C22×C8C23×C6711yescharacteristic
415C22×C8C23×C6711yescharacteristic
416C22×C8C23×C6711yescharacteristic
417C4⋊Q8—22no—
418C4⋊Q8—22no—
419#124—22no—
420#124—22no—
421C22⋊Q8—22no—
422C22⋊Q8—22no—
423#121—22no—
424#121—22no—
425#117—22no—
426#117—22no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—21no—
432C2×C4⋊C4—21no—
433C2×C4⋊C4D4×C6711yescharacteristic
434C2×C4⋊C4D4×C6711yescharacteristic
435C2×C4⋊C4C23×C6711yescharacteristic
436C2×C4⋊C4C23×C6711yescharacteristic
437C2×C4⋊C4C23×C6711yescharacteristic
438C2×C4⋊C4C23×C6711yescharacteristic
439C2×C4⋊C4C23×C6711yescharacteristic
440C2×C4⋊C4C23×C6711yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4D4×C6711yescharacteristic
450C2×C22⋊C4D4×C6711yescharacteristic
451C2×C42C23×C6711yescharacteristic
452C2×C42C23×C6711yescharacteristic
453#103—22no—
454#103—22no—
455#103—22no—
456#103—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—22no—
461#97—22no—
462#97D4×C6714yescomplemented
463C4×C8—22no—
464C4×C8—22no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473C24—21no—
474C24C2×D4×C6711yescharacteristic
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—42no—
482C2×Q8—81no—
483C2×Q8—81no—
484C2×D4—21no—
485C2×D4—21no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—42no—
491C2×D4—81no—
492C2×D4—81no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4C2×D4×C6711yescharacteristic
505C22×C4C2×D4×C6711yescharacteristic
506C22×C4C2×D4×C6711yescharacteristic
507C22×C4C2×D4×C6711yescharacteristic
508C22×C4C2×D4×C6711yescharacteristic
509C22×C4#41×C6712yes—
510C22×C4#41×C6712yes—
511C22×C4C24×C6711yescharacteristic
512M16—28no—
513C2×C8—28no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8C2×D4×C6712yes—
523C2×C8C2×D4×C6712yes—
524C2×C8#41×C6712yes—
525C2×C8#41×C6712yes—
526C4⋊C4—22no—
527C4⋊C4—22no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—21no—
537C4⋊C4—21no—
538C4⋊C4—21no—
539C4⋊C4—21no—
540C4⋊C4—42no—
541C4⋊C4—42no—
542C4⋊C4—81no—
543C4⋊C4—81no—
544C4⋊C4—81no—
545C4⋊C4—81no—
546C22⋊C4—22no—
547C22⋊C4—22no—
548C22⋊C4—42no—
549C22⋊C4—42no—
550C22⋊C4—42no—
551C22⋊C4—42no—
552C22⋊C4—81no—
553C22⋊C4—81no—
554C22⋊C4—81no—
555C22⋊C4—81no—
556C42—21no—
557C42—21no—
558C42C2×D4×C6712yes—
559C42#41×C6712yes—
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23—21no—
565C23—21no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23—41no—
573C23#124×C6712yes—
574C23C22×D4×C6711yescharacteristic
575Q8—41no—
576Q8—41no—
577Q8—41no—
578Q8—41no—
579Q8—84no—
580D4—41no—
581D4—41no—
582D4—41no—
583D4—41no—
584D4—84no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
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—41no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4#121×C6712yes—
623C2×C4#121×C6712yes—
624C2×C4#124×C6712yes—
625C2×C4C22×D4×C6711yescharacteristic
626C2×C4C2×#41×C6711yescharacteristic
627C2×C4C2×#41×C6711yescharacteristic
628C2×C4C2×#41×C6711yescharacteristic
629C2×C4C2×#41×C6711yescharacteristic
630C2×C4C2×#41×C6711yescharacteristic
631C8—22no—
632C8—22no—
633C8—22no—
634C8—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—41no—
639C22—41no—
640C22—41no—
641C22—41no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22C2×#121×C6711yescharacteristic
650C22C2×#124×C6711yescharacteristic
651C22#532×C6711yescharacteristic
652C22#576×C6711yescharacteristic
653C22#577×C6711yescharacteristic
654C22#577×C6711yescharacteristic
655C22#578×C6711yescharacteristic
656C4—22no—
657C4—22no—
658C4—22no—
659C4—41no—
660C4—41no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4—81no—
667C4—81no—
668C4#525×C6711yescharacteristic
669C4#525×C6711yescharacteristic
670C4#529×C6711yescharacteristic
671C4#529×C6711yescharacteristic
672C2—42no—
673C2—161no—
674C2C67×#285011yescharacteristic
675C2C67×#306211yescharacteristic
676C2C67×#306311yescharacteristic
677C2C67×#313611yescharacteristic
678C2C67×#313711yescharacteristic
679C2C67×#317311yescharacteristic
680C2C67×#317511yescharacteristic
subgroupG/H
center, socleC23×C67C22×D4
commutator, Frattini, cosocleC22×C4C24×C67
prime radicalC2×#121×C67C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C67 ◁ C2×#117×C67 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#489×C67C2semidirect
2. C2×#405×C67C2semidirect
3. C67×#2628C2semidirect
5. C67×#1990C2semidirect
6. C67×#1958C2semidirect
7. C67×#1936C2semidirect
8. C67×#1935C2semidirect
9. C67×#1934C2semidirect
10. C67×#1933C2semidirect
12. C67×#1894C2semidirect
14. C67×#1892C2semidirect
15. C67×#1836C2semidirect
121. #97×C67D4semidirect
331. #33054C67direct (N × H)
341. C2×#489C2×C67semidirect
342. C2×#405C2×C67semidirect
343. #2628C2×C67semidirect
345. #1990C2×C67semidirect
346. #1958C2×C67semidirect
347. #1936C2×C67semidirect
348. #1935C2×C67semidirect
349. #1934C2×C67semidirect
350. #1933C2×C67semidirect
352. #1894C2×C67semidirect
354. #1892C2×C67semidirect
355. #1836C2×C67semidirect
356. C67#33054direct (N × H)
462. #97D4×C67semidirect

Maximal subgroups

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

subgroupindex
C2×#489×C672
C2×#405×C672
C67×#26282
C67×#26202
C67×#19902
C67×#19582
C67×#19362
C67×#19352
C67×#19342
C67×#19332
C67×#18952
C67×#18942
C67×#18932
C67×#18922
C67×#18362
#3305467