Finite Group Databasebeta

← C2×#22622502 #33964674

Subgroups — C2×#22622502 #33964674

Order 18688.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989276C211yesmaximal, characteristic
2C2×#17989272C211yesmaximal, characteristic
3#22622502C2116yesmaximal, direct product factor
4C2×#17988987C211yesmaximal, characteristic, complemented
5C2×#17988924C211yesmaximal, characteristic, complemented
6C2×#17988922C211yesmaximal, characteristic, complemented
7C2×#17988931C211yesmaximal, characteristic, complemented
8C2×#17988928C211yesmaximal, characteristic, complemented
9C2×#17988897C211yesmaximal, characteristic, complemented
10C2×#17988893C211yesmaximal, characteristic, complemented
11C2×#17988846C211yesmaximal, characteristic, complemented
12C2×#17988845C211yesmaximal, characteristic, complemented
13C2×#17988681C211yesmaximal, characteristic, complemented
14C2×#17988663C211yesmaximal, characteristic
15C2×#17988628C211yesmaximal, characteristic, complemented
16C2×#428×C73C211yesmaximal, characteristic, complemented
17C22×Dic292C2211yescharacteristic
18C22×#11924011C2211yescharacteristic
19#17989276—24no—
20#17989276C2218yes—
21#17989272—24no—
22#17989272C2218yes—
23C2×#14556586—21no—
24C2×#14556584—21no—
25C2×#14556583—21no—
26C2×#14556582C2211yescharacteristic
27C2×#14556582C2211yescharacteristic
28C2×#14556581—21no—
29C2×#14556574—21no—
30C2×#14556573—21no—
31C2×#14556571C2211yescharacteristic
32C2×#14556571C2211yescharacteristic
33C2×#14556570C2211yescharacteristic
34C2×#14556570C2211yescharacteristic
35C2×#14556556C2211yescharacteristic
36C2×#14556556C2211yescharacteristic
37C2×C4×C22⋊D73C2211yescharacteristic
38C2×#14556550—21no—
39C2×#14556549C2211yescharacteristic
40C2×#14556548—21no—
41C2×C4⋊C4×D73C2211yescharacteristic
42#17988987C2218yescomplemented
43#17988931C2218yescomplemented
44#17988928C2218yescomplemented
45#17988924C2218yescomplemented
46#17988922C2218yescomplemented
47#17988897C2218yescomplemented
48#17988893C2218yescomplemented
49#17988846C2218yescomplemented
50#17988845C2218yescomplemented
51#17988681C2218yescomplemented
52#17988663C2218yes—
53#17988628C2218yescomplemented
54C2×#14556524C2211yescharacteristic
55C2×#14556524C2211yescharacteristic
56C2×#14556524C2211yescharacteristic
57C2×#14556523C2211yescharacteristic
58C2×#14556522C2211yescharacteristic
59C2×#14556520C2211yescharacteristic
60C2×#14556516C2211yescharacteristic
61C2×#14556516C2211yescharacteristic
62C2×#14556514C2211yescharacteristic
63C2×#14556514C2211yescharacteristic
64C2×#14556514C2211yescharacteristic
65C2×#14556514C2211yescharacteristic
66C2×C22⋊#10596831C2211yescharacteristic
67C2×#14556503C2211yescharacteristic
68C2×C8×Dic73C2211yescharacteristic
69C22×M16×C73C2211yescharacteristic
70C2×#117×C73C2211yescharacteristic
71C22×C4⋊C4×C73C2211yescharacteristic
72#428×C73C2218yescomplemented
73C2×#107×C73C2211yescharacteristic
74C2×#107×C73C2211yescharacteristic
75C2×#106×C73C2211yescharacteristic
76C2×#106×C73C2211yescharacteristic
77C22×Dic146C2311yescharacteristic
78C22×Dic146C2311yescharacteristic
79C22×C22⋊D73D411yescharacteristic
80C22×C4×D73—21no—
81C22×C4×D73C2311yescharacteristic
82C2×Dic292—24no—
83C2×Dic292C2314yes—
84C2×#11924011—24no—
85C2×#11924011C2314yes—
86C22×#10596831C2311yescharacteristic
87C22×#10596831C2311yescharacteristic
88#14556586—28no—
89#14556584—28no—
90#14556583—28no—
91#14556582—22no—
92#14556582—22no—
93#14556582C2314yes—
94#14556582C2314yes—
95#14556581—28no—
96#14556574—28no—
97#14556573—28no—
98#14556571—22no—
99#14556571—22no—
100#14556571C2314yes—
101#14556571C2314yes—
102#14556570—22no—
103#14556570—22no—
104#14556570C2314yes—
105#14556570C2314yes—
106#14556556—22no—
107#14556556—22no—
108#14556556C2314yes—
109#14556556C2314yes—
110C4×C22⋊D73D414yes—
111C4×C22⋊D73C2314yes—
112#14556550—28no—
113#14556549—22no—
114#14556549C2314yes—
115#14556548—28no—
116C2×C4⋊Dic73—21no—
117C2×C4⋊Dic73—21no—
118C2×C4⋊Dic73—21no—
119C2×C4⋊Dic73—21no—
120C2×C4⋊Dic73C2311yescharacteristic
121C2×C4⋊Dic73C2311yescharacteristic
122C2×#11924007—21no—
123C2×#11924007—21no—
124C2×#11924007—21no—
125C2×#11924007—21no—
126C2×#11924007—21no—
127C2×#11924007—21no—
128C2×#11924007—21no—
129C2×#11924007D411yescharacteristic
130C4⋊C4×D73—22no—
131C4⋊C4×D73C2314yes—
132C2×C22⋊Dic73—21no—
133C2×C22⋊Dic73—21no—
134C2×C22⋊Dic73D411yescharacteristic
135C2×#11924005—21no—
136C2×#11924005—21no—
137C2×#11924005—21no—
138C2×#11924005D411yescharacteristic
139C2×C4×Dic73—21no—
140C2×C4×Dic73—21no—
141C2×C4×Dic73—21no—
142C2×C4×Dic73C2311yescharacteristic
143#14556524C2314yes—
144#14556524C2314yes—
145#14556524C2314yes—
146#14556523C2314yes—
147#14556522C2314yes—
148#14556520C2314yes—
149#14556516C2314yes—
150#14556516C2314yes—
151#14556514C2314yes—
152#14556514C2314yes—
153#14556514C2314yes—
154#14556514C2314yes—
155C22⋊#10596831C2314yes—
156#14556503C2314yes—
157C8×Dic73C2314yes—
158C23×C4×C73—21no—
159C23×C4×C73C2311yescharacteristic
160C2×M16×C73—24no—
161C2×M16×C73C2314yes—
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164#117×C73—22no—
165#117×C73C2314yes—
166C2×C4⋊C4×C73—22no—
167C2×C4⋊C4×C73—21no—
168C2×C4⋊C4×C73C2311yescharacteristic
169C2×C4⋊C4×C73C2311yescharacteristic
170C2×C4⋊C4×C73C2311yescharacteristic
171C2×C4⋊C4×C73C2311yescharacteristic
172C2×C4⋊C4×C73C2314yes—
173C2×C22⋊C4×C73—21no—
174C2×C42×C73—21no—
175#107×C73C2314yes—
176#107×C73C2314yes—
177#106×C73C2314yes—
178#106×C73C2314yes—
179C23×D73C2×D411yescharacteristic
180C2×Dic146—22no—
181C2×Dic146—22no—
182C2×Dic146—22no—
183C2×Dic146—22no—
184C2×Dic146—21no—
185C2×Dic146—21no—
186C2×Dic146C2412yes—
187C2×Dic146C2412yes—
188C2×C22⋊D73—42no—
189C2×C22⋊D73C2×D414yes—
190C22×Dic73—21no—
191C22×Dic73—21no—
192C22×Dic73—21no—
193C22×Dic73—21no—
194C22×Dic73C2×D411yescharacteristic
195C22×Dic73C2×D411yescharacteristic
196C22×Dic73C2×D411yescharacteristic
197C2×C4×D73—22no—
198C2×C4×D73—22no—
199C2×C4×D73—24no—
200C2×C4×D73—44no—
201C2×C4×D73C2×D412yes—
202C2×C4×D73C2412yes—
203Dic292—28no—
204#11924011—28no—
205C2×#10596831—22no—
206C2×#10596831—22no—
207C2×#10596831C2412yes—
208C2×#10596831C2412yes—
209C4⋊Dic73—21no—
210C4⋊Dic73—21no—
211C4⋊Dic73—24no—
212C4⋊Dic73—24no—
213C4⋊Dic73—24no—
214C4⋊Dic73—24no—
215C4⋊Dic73C2412yes—
216C4⋊Dic73C2412yes—
217#11924007—24no—
218#11924007—24no—
219#11924007—24no—
220#11924007—24no—
221#11924007—24no—
222#11924007—24no—
223#11924007—24no—
224#11924007C2×D414yes—
225C22⋊Dic73—24no—
226C22⋊Dic73—24no—
227C22⋊Dic73C2×D414yes—
228#11924005—24no—
229#11924005—24no—
230#11924005—24no—
231#11924005C2×D414yes—
232C4×Dic73—24no—
233C4×Dic73—24no—
234C4×Dic73—24no—
235C4×Dic73C2×D412yes—
236C4×Dic73C2412yes—
237C24×C73C2×D411yescharacteristic
238C22×C4×C73—22no—
239C22×C4×C73—22no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—24no—
245C22×C4×C73—44no—
246C22×C4×C73C2×D411yescharacteristic
247C22×C4×C73C2×D412yes—
248C22×C4×C73C2412yes—
249C22×C4×C73C2411yescharacteristic
250M16×C73—28no—
251C2×C8×C73—22no—
252C2×C8×C73#4114yes—
253C2×C8×C73C2412yes—
254C2×C8×C73C2412yes—
255C4⋊C4×C73—21no—
256C4⋊C4×C73—21no—
257C4⋊C4×C73—24no—
258C4⋊C4×C73—21no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73C2412yes—
261C4⋊C4×C73C2412yes—
262C4⋊C4×C73C2412yes—
263C4⋊C4×C73C2412yes—
264C22⋊C4×C73—24no—
265C42×C73—24no—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—22no—
269C23×C73C22×D412yes—
270C23×C73C22×D411yescharacteristic
271C22×D73—22no—
272C22×D73—22no—
273C22×D73—22no—
274C22×D73C22×D412yes—
275C2×C4×C73—22no—
276C2×C4×C73—24no—
277C2×C4×C73—22no—
278C2×C4×C73—22no—
279C2×C4×C73—22no—
280C2×C4×C73—22no—
281C2×C4×C73—22no—
282C2×C4×C73—22no—
283C2×C4×C73—48no—
284C2×C4×C73—42no—
285C2×C4×C73—42no—
286C2×C4×C73—42no—
287C2×C4×C73—42no—
288C2×C4×C73C22×D412yes—
289C2×C4×C73C22×D411yescharacteristic
290C2×C4×C73C2×#4112yes—
291C2×C4×C732−1+412yes—
292C2×C4×C73C2511yescharacteristic
293C22⋊D73—44no—
294C2×Dic73—22no—
295C2×Dic73—22no—
296C2×Dic73—22no—
297C2×Dic73—22no—
298C2×Dic73—22no—
299C2×Dic73—22no—
300C2×Dic73—22no—
301C2×Dic73—42no—
302C2×Dic73—42no—
303C2×Dic73—42no—
304C2×Dic73—42no—
305C2×Dic73C22×D412yes—
306C2×Dic73C22×D412yes—
307C2×Dic73C22×D412yes—
308C4×D73—24no—
309C4×D73—22no—
310C4×D73—22no—
311C4×D73—48no—
312Dic146—22no—
313Dic146—22no—
314Dic146—22no—
315Dic146—22no—
316Dic146—42no—
317Dic146—42no—
318C8×C73—22no—
319C8×C73C2×#4114yes—
320#10596831—22no—
321#10596831—22no—
322C22×C73—22no—
323C22×C73—22no—
324C22×C73—22no—
325C22×C73—44no—
326C22×C73#54712yes—
327C22×C73#57512yes—
328C22×C73#57812yes—
329C22×C73C23×D411yescharacteristic
330C2×D73—22no—
331C2×D73—22no—
332C2×D73—22no—
333C2×D73—44no—
334C4×C73—22no—
335C4×C73—42no—
336C4×C73—42no—
337C4×C73—42no—
338C4×C73—42no—
339C4×C73#54712yes—
340C4×C73C22×#4111yescharacteristic
341C4×C73C2×2−1+411yescharacteristic
342Dic73—22no—
343Dic73—22no—
344Dic73—22no—
345Dic73—42no—
346Dic73—42no—
347Dic73—42no—
348Dic73—42no—
349C2×#3352—731nomaximal, Sylow
350C2×C73—42no—
351C2×C73#335214yescomplemented
352C2×C73C2×#54711yescharacteristic
353C2×C73C2×#57511yescharacteristic
354C2×C73C2×#57811yescharacteristic
355D73—42no—
356C2×#552—731no—
357C2×#552—731no—
358#3352—7316no—
359C2×#499—731no—
360C2×#484—731no—
361C2×#484—731no—
362C2×#485—731no—
363C2×#485—731no—
364C2×#479—731no—
365C2×#479—731no—
366C2×#470—731no—
367C2×#470—731no—
368C2×C4×Q16—731no—
369C2×#436—731no—
370C2×#428—731no—
371C2×#428D7311yescharacteristic, complemented
372C73C2×#335211yescharacteristic, complemented, Sylow
373C22×Q16—731no—
374C22×M16—731no—
375C22×M16C2×D7311yescharacteristic
376#552—738no—
377#552—738no—
378#552—1464no—
379#552—1464no—
380C2×#126—1461no—
381C2×#126—1461no—
382C2×#125—731no—
383C2×#125—731no—
384C2×#125—1461no—
385C2×#125—1461no—
386C2×#123—1461no—
387C2×#123—1461no—
388C2×C22⋊Q8—731no—
389C2×C22⋊Q8—731no—
390C2×C22⋊Q8—731no—
391C2×C22⋊Q8—731no—
392C2×C4×Q8—731no—
393C2×C4×Q8—731no—
394C2×C4×D4—731no—
395C2×#117—731no—
396C2×#117—1461no—
397C2×#117—1461no—
398C2×#117C2×D7311yescharacteristic
399C22×C4⋊C4—731no—
400C22×C4⋊C4C2×D7311yescharacteristic
401#499—738no—
402#485—738no—
403#485—738no—
404#484—738no—
405#484—738no—
406#479—738no—
407#479—738no—
408#470—738no—
409#470—738no—
410C4×Q16—738no—
411#436—738no—
412#428—738no—
413#428C2×D7318yescomplemented
414C2×#107—731no—
415C2×#107—731no—
416C2×#107—731no—
417C2×#107C2×D7311yescharacteristic
418C2×#107C2×D7311yescharacteristic
419C2×#106—731no—
420C2×#106—731no—
421C2×#106C2×D7311yescharacteristic
422C2×#106C2×D7311yescharacteristic
423C2×C4⋊C8—731no—
424C2×#103—731no—
425C2×#103—731no—
426C2×#103—731no—
427C2×#103—731no—
428C2×#103—731no—
429C2×#103—731no—
430C2×C22⋊C8—731no—
431C2×C22⋊C8—731no—
432C2×C4×C8—731no—
433C22×Q8—731no—
434C22×Q8—731no—
435C22×D4—731no—
436C23×C4—21no—
437C23×C4—731no—
438C23×C4—1461no—
439C23×C4C22×D7311yescharacteristic
440C2×Q16—734no—
441C2×Q16—1464no—
442C2×M16—24no—
443C2×M16—734no—
444C2×M16—1464no—
445C2×M16C22×D7314yes—
446C22×C8—731no—
447C22×C8—731no—
448C22×C8C22×D7311yescharacteristic
449C22×C8C22×D7311yescharacteristic
450#126—1468no—
451#126—1468no—
452#125—734no—
453#125—734no—
454#125—1468no—
455#125—1462no—
456#125—1462no—
457#125—1468no—
458#123—1468no—
459#123—1468no—
460C22⋊Q8—734no—
461C22⋊Q8—734no—
462C22⋊Q8—734no—
463C22⋊Q8—734no—
464C22⋊Q8—1462no—
465C22⋊Q8—1462no—
466C22⋊Q8—1462no—
467C22⋊Q8—1462no—
468C4×Q8—734no—
469C4×Q8—734no—
470C4×Q8—1462no—
471C4×Q8—1462no—
472C4×D4—734no—
473C4×D4—734no—
474#117—22no—
475#117—734no—
476#117—1468no—
477#117—1468no—
478#117—1462no—
479#117C22×D7314yes—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—731no—
483C2×C4⋊C4—731no—
484C2×C4⋊C4—731no—
485C2×C4⋊C4—734no—
486C2×C4⋊C4—1462no—
487C2×C4⋊C4—1461no—
488C2×C4⋊C4—1461no—
489C2×C4⋊C4—1461no—
490C2×C4⋊C4—1461no—
491C2×C4⋊C4—1461no—
492C2×C4⋊C4—1461no—
493C2×C4⋊C4—1461no—
494C2×C4⋊C4—1461no—
495C2×C4⋊C4—1461no—
496C2×C4⋊C4—1461no—
497C2×C4⋊C4—1461no—
498C2×C4⋊C4C22×D7311yescharacteristic
499C2×C4⋊C4C22×D7311yescharacteristic
500C2×C4⋊C4C22×D7311yescharacteristic
501C2×C4⋊C4C22×D7314yes—
502C2×C4⋊C4C22×D7311yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—731no—
505C2×C22⋊C4—731no—
506C2×C22⋊C4—1461no—
507C2×C22⋊C4—1461no—
508C2×C22⋊C4—1461no—
509C2×C22⋊C4—1461no—
510C2×C22⋊C4—1461no—
511C2×C42—21no—
512C2×C42—731no—
513C2×C42—1461no—
514C2×C42—1461no—
515C2×C42—1461no—
516#107—734no—
517#107—734no—
518#107—734no—
519#107C22×D7314yes—
520#107C22×D7314yes—
521#106—734no—
522#106—734no—
523#106C22×D7314yes—
524#106C22×D7314yes—
525C4⋊C8—734no—
526#103—734no—
527#103—734no—
528#103—734no—
529#103—734no—
530#103—734no—
531#103—734no—
532C22⋊C8—734no—
533C22⋊C8—734no—
534C4×C8—734no—
535C24—731no—
536C24D4×D7311yescharacteristic
537C2×Q8—732no—
538C2×Q8—732no—
539C2×Q8—1462no—
540C2×Q8—1462no—
541C2×Q8—1462no—
542C2×Q8—1462no—
543C2×Q8—1461no—
544C2×Q8—1461no—
545C2×D4—2922no—
546C2×D4—734no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—44no—
555C22×C4—2924no—
556C22×C4—731no—
557C22×C4—731no—
558C22×C4—731no—
559C22×C4—732no—
560C22×C4—732no—
561C22×C4—1464no—
562C22×C4—1461no—
563C22×C4—1461no—
564C22×C4—1461no—
565C22×C4—1461no—
566C22×C4—1462no—
567C22×C4—1462no—
568C22×C4D4×D7312yes—
569C22×C4D4×D7311yescharacteristic
570C22×C4C23×D7312yes—
571C22×C4C23×D7311yescharacteristic
572Q16—1468no—
573M16—28no—
574M16—1468no—
575C2×C8—22no—
576C2×C8—732no—
577C2×C8—732no—
578C2×C8—1462no—
579C2×C8—1462no—
580C2×C8#1192402814yes—
581C2×C8C23×D7312yes—
582C2×C8C23×D7312yes—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—24no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—734no—
589C4⋊C4—732no—
590C4⋊C4—732no—
591C4⋊C4—1464no—
592C4⋊C4—1464no—
593C4⋊C4—1464no—
594C4⋊C4—1464no—
595C4⋊C4—1464no—
596C4⋊C4—1464no—
597C4⋊C4—1464no—
598C4⋊C4—1464no—
599C4⋊C4—1464no—
600C4⋊C4—1464no—
601C4⋊C4—1464no—
602C4⋊C4—1461no—
603C4⋊C4—1461no—
604C4⋊C4C23×D7312yes—
605C4⋊C4C23×D7312yes—
606C4⋊C4C23×D7312yes—
607C4⋊C4C23×D7312yes—
608C22⋊C4—24no—
609C22⋊C4—734no—
610C22⋊C4—734no—
611C22⋊C4—1464no—
612C22⋊C4—1464no—
613C22⋊C4—1464no—
614C22⋊C4—1464no—
615C22⋊C4—1464no—
616C42—24no—
617C42—732no—
618C42—732no—
619C42—1464no—
620C42—1464no—
621C42—1464no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—732no—
626C23—1462no—
627C23—1462no—
628C23—1462no—
629C23C2×D4×D7312yes—
630C23C2×D4×D7311yescharacteristic
631Q8—2922no—
632Q8—2922no—
633Q8—1462no—
634Q8—1462no—
635Q8—1462no—
636Q8—1462no—
637D4—2924no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—24no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—48no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—2928no—
652C2×C4—2922no—
653C2×C4—2922no—
654C2×C4—2922no—
655C2×C4—2922no—
656C2×C4—732no—
657C2×C4—732no—
658C2×C4—732no—
659C2×C4—1462no—
660C2×C4—1462no—
661C2×C4—1462no—
662C2×C4—1462no—
663C2×C4—1462no—
664C2×C4—1462no—
665C2×C4—1462no—
666C2×C4—1462no—
667C2×C4—1462no—
668C2×C4—1464no—
669C2×C4C2×D4×D7312yes—
670C2×C4C2×D4×D7311yescharacteristic
671C2×C4C2×#1192402812yes—
672C2×C4#1455663912yes—
673C2×C4C24×D7311yescharacteristic
674C8—22no—
675C8—1462no—
676C8—1462no—
677C8C2×#1192402814yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—2924no—
683C22—1462no—
684C22—1462no—
685C22—1462no—
686C22#1798923812yes—
687C22#1798938312yes—
688C22#1798940312yes—
689C22C22×D4×D7311yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—2922no—
696C4—2922no—
697C4—2922no—
698C4—2922no—
699C4—1462no—
700C4—1462no—
701C4—1462no—
702C4#1798923812yes—
703C4C22×#1192402811yescharacteristic
704C4C2×#1455663911yescharacteristic
705C2—42no—
706C2—2922no—
707C2#2262250214yesdirect product factor
708C2C2×#1798923811yescharacteristic
709C2C2×#1798938311yescharacteristic
710C2C2×#1798940311yescharacteristic
subgroupG/H
centerC23C2×D4×D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC2×#428×C73C2
socleC23×C73C22×D4
prime radicalC22×C22⋊D73D4
hypercenterC2×#428D73
hypocenterC73C2×#3352
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
3. #22622502C2direct (N × H)
4. C2×#17988987C2semidirect
5. C2×#17988924C2semidirect
6. C2×#17988922C2semidirect
7. C2×#17988931C2semidirect
8. C2×#17988928C2semidirect
9. C2×#17988897C2semidirect
10. C2×#17988893C2semidirect
11. C2×#17988846C2semidirect
12. C2×#17988845C2semidirect
13. C2×#17988681C2semidirect
15. C2×#17988628C2semidirect
16. C2×#428×C73C2semidirect
42. #17988987C22semidirect
43. #17988931C22semidirect
44. #17988928C22semidirect
45. #17988924C22semidirect
46. #17988922C22semidirect
47. #17988897C22semidirect
48. #17988893C22semidirect
49. #17988846C22semidirect
50. #17988845C22semidirect
51. #17988681C22semidirect
53. #17988628C22semidirect
72. #428×C73C22semidirect
351. C2×C73#3352semidirect
371. C2×#428D73semidirect
372. C73C2×#3352semidirect
413. #428C2×D73semidirect
707. C2#22622502direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179892762
C2×#179892722
#226225022
C2×#179889872
C2×#179889242
C2×#179889222
C2×#179889312
C2×#179889282
C2×#179888972
C2×#179888932
C2×#179888462
C2×#179888452
C2×#179886812
C2×#179886632
C2×#179886282
C2×#428×C732
C2×#335273