Finite Group Databasebeta

← #32014323

Subgroups — #32014323

Order 18176.

1054 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×#17986130C211yesmaximal, characteristic, complemented
2#22591297C211yesmaximal, characteristic, complemented
3#22589273C211yesmaximal, characteristic
4#22589273C211yesmaximal, characteristic
5#22589264C211yesmaximal, characteristic, complemented
6#22589161C211yesmaximal, characteristic, complemented
7#22589157C211yesmaximal, characteristic
8#22589152C211yesmaximal, characteristic
9#22588355C211yesmaximal, characteristic, complemented
10#22588350C211yesmaximal, characteristic
11#22588345C211yesmaximal, characteristic, complemented
12#22588170C211yesmaximal, characteristic, complemented
13#22588165C211yesmaximal, characteristic
14C4×#14556052C211yesmaximal, characteristic, complemented
15C2×#556×C71C211yesmaximal, characteristic
16#17986130—24no—
17C2×C4⋊(C71⋊C8)C2211yescharacteristic
18C2×C4⋊(C71⋊C8)C2211yescharacteristic
19C2×C4⋊(C71⋊C8)C2211yescharacteristic
20C2×#14556052C2211yescharacteristic
21C2×#14556052C2211yescharacteristic
22C2×#14556052C2211yescharacteristic
23C2×#14556052C2211yescharacteristic
24C2×#14556052C2211yescharacteristic
25C2×#14556052C2211yescharacteristic
26C2×#14556052C2211yescharacteristic
27C2×#14556052C2211yescharacteristic
28C2×#14556049C2211yescharacteristic
29C2×#14556049C2211yescharacteristic
30C2×#14556049C2211yescharacteristic
31C2×#14556049C2211yescharacteristic
32C2×#14556039C2211yescharacteristic
33C2×#14556039C2211yescharacteristic
34C2×C4×C71⋊C8C2211yescharacteristic
35#17985906—21no—
36#17985885—21no—
37#17985885—21no—
38#17985869C2211yescharacteristic
39#17985865C2211yescharacteristic
40#17985865C2211yescharacteristic
41C4⋊C4×Dic71—21no—
42C4×C4⋊Dic71C2211yescharacteristic
43C4×C4⋊Dic71C2211yescharacteristic
44C4×C4⋊Dic71C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49#556×C71—24no—
50#556×C71C418yescomplemented
51C2×C4⋊Q8×C71C2211yescharacteristic
52C2×#126×C71—21no—
53C2×#126×C71—21no—
54C2×#124×C71C2211yescharacteristic
55C2×#124×C71C2211yescharacteristic
56C2×C22⋊Q8×C71—21no—
57C2×C4×Q8×C71C2211yescharacteristic
58C2×C4×Q8×C71C2211yescharacteristic
59C2×C4×Q8×C71C2211yescharacteristic
60C2×C4×D4×C71C2211yescharacteristic
61C2×#117×C71—21no—
62C22×C71⋊C8C2311yescharacteristic
63C22×C71⋊C8C2311yescharacteristic
64C22×C71⋊C8C2311yescharacteristic
65C22×C71⋊C8C2311yescharacteristic
66C2×C4⋊Dic71—21no—
67C2×C4⋊Dic71—21no—
68C2×C4⋊Dic71C2311yescharacteristic
69C2×C4⋊Dic71C2311yescharacteristic
70C2×C4⋊Dic71C2311yescharacteristic
71C2×C4⋊Dic71C2311yescharacteristic
72C2×C4×Dic71—21no—
73C2×C4×Dic71—21no—
74C2×C4×Dic71—21no—
75C4⋊(C71⋊C8)—22no—
76C4⋊(C71⋊C8)—22no—
77C4⋊(C71⋊C8)—22no—
78#14556052—22no—
79#14556052—22no—
80#14556052—22no—
81#14556052—22no—
82#14556052—41no—
83#14556052—41no—
84#14556052—41no—
85#14556052—41no—
86#14556049—22no—
87#14556049—22no—
88#14556049—41no—
89#14556049—41no—
90#14556039—22no—
91#14556039—22no—
92C4×C71⋊C8—22no—
93C71⋊#95—21no—
94C71⋊#95—21no—
95C71⋊#95—21no—
96C71⋊#95—21no—
97C71⋊#95—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C22×Q8×C71D411yescharacteristic
101C22×Q8×C71C2311yescharacteristic
102C22×Q8×C71C2311yescharacteristic
103C22×D4×C71C2311yescharacteristic
104C23×C4×C71—21no—
105C4⋊Q8×C71—22no—
106C4⋊Q8×C71C2×C414yes—
107#126×C71—28no—
108#126×C71—28no—
109#124×C71—22no—
110#124×C71—22no—
111#124×C71C2×C414yes—
112#124×C71C2×C414yes—
113C22⋊Q8×C71—28no—
114C4×Q8×C71—22no—
115C4×Q8×C71—22no—
116C4×Q8×C71C2×C414yes—
117C4×Q8×C71C2×C414yes—
118C4×Q8×C71C2×C414yes—
119C4×Q8×C71D414yes—
120C4×D4×C71—22no—
121C4×D4×C71C2×C414yes—
122#117×C71—28no—
123C2×C4⋊C4×C71—21no—
124C2×C4⋊C4×C71—21no—
125C2×C4⋊C4×C71—21no—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71D411yescharacteristic
128C2×C4⋊C4×C71D411yescharacteristic
129C2×C4⋊C4×C71D411yescharacteristic
130C2×C4⋊C4×C71C2311yescharacteristic
131C2×C22⋊C4×C71—21no—
132C2×C22⋊C4×C71—21no—
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71—21no—
136C2×C42×C71—21no—
137C2×C42×C71—21no—
138C2×C42×C71C2311yescharacteristic
139C2×C42×C71C2311yescharacteristic
140C2×C42×C71C2311yescharacteristic
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C2×C71⋊C8—21no—
146C2×C71⋊C8—21no—
147C2×C71⋊C8—21no—
148C2×C71⋊C8—21no—
149C2×C71⋊C8—21no—
150C2×C71⋊C8—21no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8#4112yes—
157C4⋊Dic71—21no—
158C4⋊Dic71—21no—
159C4⋊Dic71—21no—
160C4⋊Dic71—21no—
161C4⋊Dic71—21no—
162C4⋊Dic71—21no—
163C4⋊Dic71—21no—
164C4⋊Dic71—42no—
165C4⋊Dic71—81no—
166C4⋊Dic71#4112yes—
167C4×Dic71—42no—
168C4×Dic71—81no—
169C4×Dic71—81no—
170C24×C71—21no—
171C2×Q8×C71—21no—
172C2×Q8×C71—21no—
173C2×Q8×C71—21no—
174C2×Q8×C71—21no—
175C2×Q8×C71—21no—
176C2×Q8×C71—21no—
177C2×Q8×C71—21no—
178C2×Q8×C71—21no—
179C2×Q8×C71—21no—
180C2×Q8×C71—21no—
181C2×Q8×C71—41no—
182C2×Q8×C71—41no—
183C2×Q8×C71C22⋊C414yes—
184C2×Q8×C71C22×C412yes—
185C2×Q8×C71C22×C412yes—
186C2×D4×C71—21no—
187C2×D4×C71—21no—
188C2×D4×C71—21no—
189C2×D4×C71—21no—
190C2×D4×C71—21no—
191C2×D4×C71C22×C412yes—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—24no—
196C22×C4×C71—42no—
197C22×C4×C71—42no—
198C22×C4×C71C2×D411yescharacteristic
199C22×C4×C71C2×D411yescharacteristic
200C22×C4×C71C2×D411yescharacteristic
201C22×C4×C71C2×D411yescharacteristic
202C22×C4×C71C2×D411yescharacteristic
203C22×C4×C71C2×D411yescharacteristic
204C22×C4×C71C2411yescharacteristic
205C4⋊C4×C71—24no—
206C4⋊C4×C71—24no—
207C4⋊C4×C71—24no—
208C4⋊C4×C71—24no—
209C4⋊C4×C71—21no—
210C4⋊C4×C71C22⋊C414yes—
211C4⋊C4×C71C22⋊C414yes—
212C4⋊C4×C71C22⋊C414yes—
213C4⋊C4×C71C22×C412yes—
214C22⋊C4×C71—24no—
215C22⋊C4×C71—24no—
216C22⋊C4×C71—24no—
217C22⋊C4×C71—24no—
218C22⋊C4×C71—24no—
219C42×C71—24no—
220C42×C71—24no—
221C42×C71C22×C412yes—
222C42×C71C22×C412yes—
223C42×C71C22×C412yes—
224C42×C71C2×D412yes—
225C42×C71C2×D412yes—
226C42×C71C2×D412yes—
227C23×C71—22no—
228C23×C71—41no—
229C23×C71—41no—
230C23×C71—41no—
231C23×C71—41no—
232C23×C71—41no—
233C23×C71—41no—
234C23×C71C22×D411yescharacteristic
235Q8×C71—22no—
236Q8×C71—22no—
237Q8×C71—22no—
238Q8×C71—22no—
239Q8×C71—44no—
240Q8×C71—41no—
241Q8×C71—41no—
242Q8×C71—41no—
243Q8×C71—41no—
244D4×C71—22no—
245D4×C71—22no—
246D4×C71—41no—
247D4×C71—41no—
248C2×C4×C71—21no—
249C2×C4×C71—21no—
250C2×C4×C71—21no—
251C2×C4×C71—21no—
252C2×C4×C71—21no—
253C2×C4×C71—21no—
254C2×C4×C71—21no—
255C2×C4×C71—21no—
256C2×C4×C71—21no—
257C2×C4×C71—21no—
258C2×C4×C71—21no—
259C2×C4×C71—21no—
260C2×C4×C71—22no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71—48no—
264C2×C4×C71—41no—
265C2×C4×C71—41no—
266C2×C4×C71—41no—
267C2×C4×C71—41no—
268C2×C4×C71—41no—
269C2×C4×C71—41no—
270C2×C4×C71C2×C22⋊C412yes—
271C2×C4×C71C2×C22⋊C412yes—
272C2×C4×C71C2×C22⋊C412yes—
273C2×C4×C71C2×C22⋊C412yes—
274C2×C4×C71C2×C22⋊C412yes—
275C2×C4×C71C2×C22⋊C412yes—
276C2×C4×C71C23×C411yescharacteristic
277C2×C4×C71C22×D411yescharacteristic
278C2×C4×C71C2×#4111yescharacteristic
279C2×C4×C71C2×#4111yescharacteristic
280C2×C4×C71H(5,𝔽2)11yescharacteristic
281C2×C4×C712−1+411yescharacteristic
282C2×Dic71—22no—
283C2×Dic71—41no—
284C2×Dic71—41no—
285C2×Dic71—41no—
286C2×Dic71—41no—
287C2×Dic71—41no—
288C2×Dic71—41no—
289C2×Dic71—41no—
290C2×Dic71—41no—
291C2×Dic71—41no—
292C2×Dic71—41no—
293C2×Dic71—41no—
294C71⋊C8—22no—
295C71⋊C8—41no—
296C71⋊C8—41no—
297C71⋊C8—41no—
298C22×C71—42no—
299C22×C71—42no—
300C22×C71—42no—
301C22×C71—81no—
302C22×C71—81no—
303C22×C71—81no—
304C22×C71—81no—
305C22×C71C22×C22⋊C411yescharacteristic
306C22×C71#54811yescharacteristic
307C22×C71#55011yescharacteristic
308C22×C71#57511yescharacteristic
309C22×C71#57511yescharacteristic
310C22×C71#57711yescharacteristic
311C22×C71#57811yescharacteristic
312C4×C71—22no—
313C4×C71—22no—
314C4×C71—22no—
315C4×C71—22no—
316C4×C71—22no—
317C4×C71—22no—
318C4×C71—42no—
319C4×C71—42no—
320C4×C71—42no—
321C4×C71C4×#4111yescharacteristic
322C4×C71#52011yescharacteristic
323C4×C71#54811yescharacteristic
324C4×C71#55011yescharacteristic
325Dic71—42no—
326Dic71—81no—
327Dic71—81no—
328Dic71—81no—
329#22548—711nomaximal, Sylow
330C2×C71—82no—
331C2×C71#234111yescharacteristic
332C2×C71#289611yescharacteristic
333C2×C71#289811yescharacteristic
334C2×C71#337611yescharacteristic
335C2×C71#337711yescharacteristic
336C2×C71#340111yescharacteristic
337C2×C71#340211yescharacteristic
338C2×#556D7111yescharacteristic
339C2×#446—711no—
340#2355—711no—
341#1983—711no—
342#1983—711no—
343#1981—711no—
344#1960—711no—
345#1959—711no—
346#1958—711no—
347#1805—711no—
348#1804—711no—
349#1803—711no—
350#1763—711no—
351#1762—711no—
352C4×#103—711no—
353C71#2254811yescharacteristic, complemented, Sylow
354#556—24no—
355#556Dic7118yescomplemented
356C2×C4⋊Q8C2×D7111yescharacteristic
357C2×#126—21no—
358C2×#126—21no—
359C2×#124C2×D7111yescharacteristic
360C2×#124C2×D7111yescharacteristic
361C2×C22⋊Q8—21no—
362C2×C4×Q8C2×D7111yescharacteristic
363C2×C4×Q8C2×D7111yescharacteristic
364C2×C4×Q8C2×D7111yescharacteristic
365C2×C4×D4C2×D7111yescharacteristic
366C2×#117—21no—
367#446—1424no—
368C2×C4⋊C8—711no—
369C2×C4⋊C8—711no—
370C2×C4⋊C8—711no—
371C2×#103—711no—
372C2×#103—711no—
373C2×#103—711no—
374C2×#103—711no—
375C2×#103—711no—
376C2×#103—711no—
377C2×#103—711no—
378C2×#103—711no—
379C2×#102—711no—
380C2×#102—711no—
381C2×#102—711no—
382C2×#102—711no—
383C2×#97—711no—
384C2×#97—711no—
385C2×C4×C8—711no—
386#391—1421no—
387#387—1421no—
388#387—1421no—
389#384—711no—
390#382—711no—
391#382—711no—
392C4×C4⋊C4—711no—
393C4×C4⋊C4—711no—
394C4×C4⋊C4—711no—
395C4×C4⋊C4—1421no—
396#340—711no—
397#340—711no—
398#340—711no—
399#340—711no—
400C22×Q8C22⋊D7111yescharacteristic
401C22×Q8C22×D7111yescharacteristic
402C22×Q8C22×D7111yescharacteristic
403C22×D4C22×D7111yescharacteristic
404C23×C4—21no—
405C22×C8—711no—
406C22×C8—711no—
407C22×C8—711no—
408C22×C8—711no—
409C4⋊Q8—22no—
410C4⋊Q8C2×Dic7114yes—
411#126—28no—
412#126—28no—
413#124—22no—
414#124—22no—
415#124C2×Dic7114yes—
416#124C2×Dic7114yes—
417C22⋊Q8—28no—
418C4×Q8—22no—
419C4×Q8—22no—
420C4×Q8C2×Dic7114yes—
421C4×Q8C2×Dic7114yes—
422C4×Q8C2×Dic7114yes—
423C4×Q8C22⋊D7114yes—
424C4×D4—22no—
425C4×D4C2×Dic7114yes—
426#117—28no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—711no—
432C2×C4⋊C4—711no—
433C2×C4⋊C4—711no—
434C2×C4⋊C4—711no—
435C2×C4⋊C4—1421no—
436C2×C4⋊C4—1421no—
437C2×C4⋊C4C22⋊D7111yescharacteristic
438C2×C4⋊C4C22⋊D7111yescharacteristic
439C2×C4⋊C4C22⋊D7111yescharacteristic
440C2×C4⋊C4C22×D7111yescharacteristic
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C42—21no—
447C2×C42—21no—
448C2×C42—1421no—
449C2×C42—1421no—
450C2×C42—1421no—
451C2×C42C22×D7111yescharacteristic
452C2×C42C22×D7111yescharacteristic
453C2×C42C22×D7111yescharacteristic
454C4⋊C8—1422no—
455C4⋊C8—1422no—
456C4⋊C8—1422no—
457#103—2841no—
458#103—2841no—
459#103—2841no—
460#103—2841no—
461#103—1422no—
462#103—1422no—
463#103—1422no—
464#103—1422no—
465#102—2841no—
466#102—2841no—
467#102—1422no—
468#102—1422no—
469#97—1422no—
470#97—1422no—
471C4×C8—1422no—
472#95—1421no—
473#95—1421no—
474#95—1421no—
475#95—1421no—
476#95—1421no—
477#95—1421no—
478#95—1421no—
479C24—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—41no—
491C2×Q8—41no—
492C2×Q8C22⋊Dic7114yes—
493C2×Q8C22×Dic7112yes—
494C2×Q8C22×Dic7112yes—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—21no—
500C2×D4C22×Dic7112yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—24no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—1421no—
508C22×C4—1421no—
509C22×C4—1421no—
510C22×C4—1421no—
511C22×C4C2×C22⋊D7111yescharacteristic
512C22×C4C2×C22⋊D7111yescharacteristic
513C22×C4C2×C22⋊D7111yescharacteristic
514C22×C4C2×C22⋊D7111yescharacteristic
515C22×C4C2×C22⋊D7111yescharacteristic
516C22×C4C2×C22⋊D7111yescharacteristic
517C22×C4C23×D7111yescharacteristic
518C2×C8—712no—
519C2×C8—1421no—
520C2×C8—1421no—
521C2×C8—1421no—
522C2×C8—1421no—
523C2×C8—1421no—
524C2×C8—1421no—
525C2×C8—1421no—
526C2×C8—1421no—
527C2×C8—1421no—
528C2×C8—1421no—
529C2×C8—1421no—
530C4⋊C4—21no—
531C4⋊C4—24no—
532C4⋊C4—24no—
533C4⋊C4—24no—
534C4⋊C4—24no—
535C4⋊C4—2842no—
536C4⋊C4—5681no—
537C4⋊C4—712no—
538C4⋊C4—1421no—
539C4⋊C4—1421no—
540C4⋊C4—1421no—
541C4⋊C4—1421no—
542C4⋊C4—1421no—
543C4⋊C4—1421no—
544C4⋊C4—1421no—
545C4⋊C4C22⋊Dic7114yes—
546C4⋊C4C22⋊Dic7114yes—
547C4⋊C4C22⋊Dic7114yes—
548C4⋊C4C22×Dic7112yes—
549C22⋊C4—24no—
550C22⋊C4—24no—
551C22⋊C4—24no—
552C22⋊C4—24no—
553C22⋊C4—24no—
554C42—24no—
555C42—24no—
556C42—2842no—
557C42—5681no—
558C42—5681no—
559C42C22×Dic7112yes—
560C42C22×Dic7112yes—
561C42C22×Dic7112yes—
562C42C2×C22⋊D7112yes—
563C42C2×C22⋊D7112yes—
564C42C2×C22⋊D7112yes—
565C23—22no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×C22⋊D7111yescharacteristic
573Q8—22no—
574Q8—22no—
575Q8—22no—
576Q8—22no—
577Q8—44no—
578Q8—41no—
579Q8—41no—
580Q8—41no—
581Q8—41no—
582D4—22no—
583D4—22no—
584D4—41no—
585D4—41no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—48no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—2841no—
609C2×C4—2841no—
610C2×C4—2841no—
611C2×C4—2841no—
612C2×C4—2841no—
613C2×C4—2841no—
614C2×C4—2841no—
615C2×C4—2841no—
616C2×C4—2841no—
617C2×C4—2841no—
618C2×C4—2841no—
619C2×C4—1422no—
620C2×C4C2×C22⋊Dic7112yes—
621C2×C4C2×C22⋊Dic7112yes—
622C2×C4C2×C22⋊Dic7112yes—
623C2×C4C2×C22⋊Dic7112yes—
624C2×C4C2×C22⋊Dic7112yes—
625C2×C4C2×C22⋊Dic7112yes—
626C2×C4C23×Dic7111yescharacteristic
627C2×C4C22×C22⋊D7111yescharacteristic
628C2×C4#41×D7111yescharacteristic
629C2×C4#41×D7111yescharacteristic
630C2×C4#1455617411yescharacteristic
631C2×C4#1455617511yescharacteristic
632C8—2841no—
633C8—2841no—
634C8—2841no—
635C8—1422no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C22×C22⋊Dic7111yescharacteristic
644C22#1798665611yescharacteristic
645C22#1798666811yescharacteristic
646C22#1798679711yescharacteristic
647C22#1798679711yescharacteristic
648C22#1798680711yescharacteristic
649C22#1798681411yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—22no—
654C4—22no—
655C4—22no—
656C4—42no—
657C4—42no—
658C4—42no—
659C4—2842no—
660C4—5681no—
661C4—5681no—
662C4—5681no—
663C4#41×Dic7111yescharacteristic
664C4#1798648211yescharacteristic
665C4#1798665611yescharacteristic
666C4#1798666811yescharacteristic
667C2—82no—
668C2#2259118111yescharacteristic
669C2#2259685911yescharacteristic
670C2#2259687311yescharacteristic
671C2#2260116111yescharacteristic
672C2#2260117611yescharacteristic
673C2#2260140611yescharacteristic
674C2#2260141511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC2×#556×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×C71C23
cosocleC22×C4×C71C24
hypercenterC2×#556D71
hypocenterC71#22548
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#17986130C2semidirect
2. #22591297C2semidirect
5. #22589264C2semidirect
6. #22589161C2semidirect
9. #22588355C2semidirect
11. #22588345C2semidirect
12. #22588170C2semidirect
14. C4×#14556052C2semidirect
50. #556×C71C4semidirect
353. C71#22548semidirect
355. #556Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179861302
#225912972
#225892732
#225892642
#225891612
#225891572
#225891522
#225883552
#225883502
#225883452
#225881702
#225881652
C4×#145560522
C2×#556×C712
#2254871