Finite Group Databasebeta

← #10764121

Subgroups — #10764121

Order 768.

1112 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86243C211yesmaximal, characteristic
2#79340C211yesmaximal, characteristic, complemented
3#79015C211yesmaximal, characteristic, complemented
4C3×#1551C211yesmaximal, characteristic, complemented
5#71807C211yesmaximal, characteristic, complemented
6#70824C211yesmaximal, characteristic, complemented
7C2×#4481C211yesmaximal, characteristic, complemented
8#68487C211yesmaximal, characteristic, complemented
9#68483C211yesmaximal, characteristic, complemented
10#68483C211yesmaximal, characteristic, complemented
11D3×#333C211yesmaximal, characteristic, complemented
12#68389C211yesmaximal, characteristic, complemented
13#68385C211yesmaximal, characteristic, complemented
14#68385C211yesmaximal, characteristic, complemented
15#68382C211yesmaximal, characteristic, complemented
16#17779—31nomaximal, Sylow
17C2×#1010C412yes—
18C3×#532C2211yescharacteristic
19#5825C412yes—
20D3×C4⋊Q8C2211yescharacteristic
21D3×C4⋊Q8C2211yescharacteristic
22#5716C2211yescharacteristic
23#5716C2211yescharacteristic
24#5675C412yes—
25#5675C412yes—
26#5611—21no—
27#5611—21no—
28#5611—21no—
29#5611—21no—
30#5551—21no—
31#5551—21no—
32D4×Dic6—21no—
33D4×Dic6—21no—
34C4×#235C2211yescharacteristic
35C2×#869C2211yescharacteristic
36C3×#432C2211yescharacteristic
37C2×C3×C4⋊C8C2211yescharacteristic
38#5111—21no—
39C8×#67—21no—
40#4926C2211yescharacteristic
41C2×C4⋊(C3⋊C8)C2211yescharacteristic
42#4837C2211yescharacteristic
43#4837C2211yescharacteristic
44#4836—21no—
45#4835C2211yescharacteristic
46#4835C2211yescharacteristic
47#4833C2211yescharacteristic
48#4833C2211yescharacteristic
49D3×C4⋊C8C2211yescharacteristic
50D3×C4⋊C8C2211yescharacteristic
51#4828—21no—
52#4730—21no—
53#67⋊C8—21no—
54#4706—21no—
55#4701—21no—
56C3×#333C2211yescharacteristic
57C3×#333C2211yescharacteristic
58C3×#331C2211yescharacteristic
59C3×#331C2211yescharacteristic
60#4546C2211yescharacteristic
61#4546C2211yescharacteristic
62#4544C2211yescharacteristic
63#4544C2211yescharacteristic
64#4481C2211yescharacteristic
65#4481C2211yescharacteristic
66#4481C2211yescharacteristic
67#4481C2211yescharacteristic
68#4481C2211yescharacteristic
69#4481C2211yescharacteristic
70#4481C2211yescharacteristic
71#4481C2211yescharacteristic
72#3499—31no—
73#2990—31no—
74#2990—31no—
75#1560—31no—
76#1558—31no—
77#1558—31no—
78#1551—31no—
79#1551—31no—
80#1551—31no—
81#1551D311yescharacteristic, complemented
82#1548—31no—
83#1548—31no—
84#1543—31no—
85C2×#333—31no—
86C2×#333—31no—
87C2×C3×#41C2×C412yes—
88#1010—48no—
89C2×D3×Q8C2×C412yes—
90C2×D3×Q8C2×C412yes—
91C2×#237—22no—
92C2×#237—22no—
93C2×#237C2×C412yes—
94C2×#237C2×C412yes—
95C2×#235—22no—
96C2×#235C2×C411yescharacteristic
97C22×Dic6—22no—
98C22×Dic6C2×C412yes—
99C22×C3×C8—21no—
100C3×C4⋊Q8C2311yescharacteristic
101C3×#127C2311yescharacteristic
102C3×#124C2×C412yes—
103C3×#121—21no—
104C3×#121—21no—
105C3×C4×D4—21no—
106C3×C4×D4—21no—
107C2×C3×C42C2311yescharacteristic
108#944C2×C412yes—
109#944C2×C412yes—
110#938—21no—
111#938—21no—
112#938—21no—
113#938—21no—
114#936C2×C412yes—
115#936C2×C412yes—
116#935—22no—
117#935—22no—
118D4×Dic3—21no—
119D4×Dic3—21no—
120D4×Dic3—21no—
121D4×Dic3—21no—
122C4×#67D411yescharacteristic
123C4×#67D411yescharacteristic
124C4×#67D411yescharacteristic
125C4×#67D411yescharacteristic
126#926C2×C411yescharacteristic
127C2×C4⋊Dic3—21no—
128C2×C4⋊Dic3—21no—
129#924—22no—
130#924—22no—
131C22×C3⋊C8—21no—
132C2×ΓL(1,𝔽25)—21no—
133C2×ΓL(1,𝔽25)—21no—
134C2×D3×C8—21no—
135C2×D3×C8—21no—
136D3×C4⋊C4—21no—
137D3×C4⋊C4—21no—
138D3×C4⋊C4—21no—
139D3×C4⋊C4—21no—
140#888—21no—
141#888—21no—
142#888—21no—
143#888—21no—
144#883—22no—
145#883—22no—
146#883—22no—
147#883—22no—
148#878—22no—
149#878—22no—
150#878—22no—
151#878—22no—
152C4×D12D411yescharacteristic
153C4×D12D411yescharacteristic
154#872C2×C411yescharacteristic
155#872C2×C411yescharacteristic
156C42×D3C2311yescharacteristic
157C42×D3C2311yescharacteristic
158#869—21no—
159#869—21no—
160#869C2×C412yes—
161#869C2311yescharacteristic
162#869C2311yescharacteristic
163C4×Dic6D411yescharacteristic
164C4×Dic6D411yescharacteristic
165C3×C4⋊C8—21no—
166C3×C4⋊C8C2311yescharacteristic
167C3×C4⋊C8C2311yescharacteristic
168C3×C4⋊C8C2311yescharacteristic
169C3×C4⋊C8C2311yescharacteristic
170C3×C22⋊C8—21no—
171C3×#97—21no—
172#830—21no—
173(C2×D3)⋊C8—21no—
174(C2×D3)⋊C8—21no—
175(C2×D3)⋊C8—21no—
176(C2×D3)⋊C8—21no—
177#815—21no—
178#815—21no—
179Dic3⋊C8—21no—
180Dic3⋊C8—21no—
181Dic3⋊C8—21no—
182Dic3⋊C8—21no—
183C8×Dic3—21no—
184C8×Dic3—21no—
185C4⋊(C3⋊C8)—21no—
186C4⋊(C3⋊C8)C2311yescharacteristic
187C4⋊(C3⋊C8)C2311yescharacteristic
188C4⋊(C3⋊C8)C2311yescharacteristic
189C4⋊(C3⋊C8)C2311yescharacteristic
190#803—21no—
191C2×2−1+4—32no—
192D4×Q8—61no—
193D4×Q8—61no—
194#547—61no—
195#547—61no—
196#547—61no—
197#547—61no—
198#547—61no—
199#547—61no—
200#536—32no—
201#536—32no—
202#536—32no—
203#532—31no—
204#532—31no—
205#532C2×D311yescharacteristic
206C2×C4⋊Q8—31no—
207C2×C4⋊Q8—31no—
208C2×C4⋊Q8—31no—
209C4×#41—31no—
210#446—61no—
211#446—61no—
212#435—61no—
213#435—61no—
214#435—61no—
215#435—61no—
216C8×D4—61no—
217C8×D4—61no—
218#432—31no—
219#432—31no—
220#432—31no—
221#432C2×D311yescharacteristic
222#431—31no—
223#431—31no—
224#423—31no—
225#423—31no—
226C2×C4⋊C8—31no—
227C2×C4⋊C8—31no—
228C2×C4⋊C8—31no—
229C2×C4⋊C8C2×D311yescharacteristic
230#333—31no—
231#333—31no—
232#333—31no—
233#333—31no—
234#333—31no—
235#333—31no—
236#333—31no—
237#333—31no—
238#333—31no—
239#333—31no—
240#333C2×D311yescharacteristic
241#333C2×D311yescharacteristic
242#331—31no—
243#331—31no—
244#331C2×D311yescharacteristic
245#331C2×D311yescharacteristic
246C3×#41—44no—
247C2×C3×Q8C22×C412yes—
248C2×C3×D4—22no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4C22×C412yes—
252C22×C3×C4—22no—
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C2×D411yescharacteristic
255C22×C3×C4C2×D411yescharacteristic
256C2×#67—22no—
257C2×#67—22no—
258C2×#67C22⋊C411yescharacteristic
259C2×#67C22⋊C411yescharacteristic
260C22×Dic3—22no—
261C22×Dic3—22no—
262C22×Dic3—22no—
263D3×Q8—44no—
264D3×Q8—44no—
265#237—44no—
266#237—44no—
267#237—48no—
268#237—48no—
269#235—24no—
270#235—48no—
271C2×D12C22⋊C411yescharacteristic
272C2×C4×D3—22no—
273C2×C4×D3—22no—
274C2×C4×D3C22×C411yescharacteristic
275C2×C4×D3C22×C411yescharacteristic
276C2×C4×D3C2×D411yescharacteristic
277C2×C4×D3C2×D411yescharacteristic
278C2×C4×D3C2×D411yescharacteristic
279C2×C4×D3C2×D411yescharacteristic
280C2×Dic6—22no—
281C2×Dic6—22no—
282C2×Dic6—22no—
283C2×Dic6—48no—
284C2×Dic6—44no—
285C2×Dic6C22⋊C411yescharacteristic
286C2×Dic6C22×C412yes—
287C2×Dic6C22×C412yes—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—81no—
293C3×C4⋊C4—21no—
294C3×C4⋊C4—21no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—22no—
297C3×C42C22×C411yescharacteristic
298C3×C42C2×D411yescharacteristic
299C3×C42C2×D411yescharacteristic
300C3×C42C2411yescharacteristic
301#217—22no—
302#217—22no—
303#217—22no—
304#217—22no—
305#217C22⋊C411yescharacteristic
306#217C22⋊C411yescharacteristic
307(C2×D3)⋊C4C22⋊C411yescharacteristic
308(C2×D3)⋊C4C22⋊C411yescharacteristic
309(C2×D3)⋊C4C22⋊C411yescharacteristic
310(C2×D3)⋊C4C22⋊C411yescharacteristic
311C4⋊Dic3—22no—
312C4⋊Dic3—22no—
313C4⋊Dic3—21no—
314C4⋊Dic3—21no—
315C4⋊Dic3—21no—
316C4⋊Dic3—21no—
317C4⋊Dic3C22⋊C411yescharacteristic
318C4⋊Dic3C22⋊C411yescharacteristic
319Dic3⋊C4—22no—
320Dic3⋊C4—22no—
321Dic3⋊C4—22no—
322Dic3⋊C4—22no—
323Dic3⋊C4C22⋊C411yescharacteristic
324Dic3⋊C4C22⋊C411yescharacteristic
325Dic3⋊C4C22⋊C411yescharacteristic
326Dic3⋊C4C22⋊C411yescharacteristic
327C4×Dic3C22×C411yescharacteristic
328C4×Dic3C22×C411yescharacteristic
329C4×Dic3C2×D411yescharacteristic
330C4×Dic3C2×D411yescharacteristic
331C4×Dic3C2×D411yescharacteristic
332C4×Dic3C2×D411yescharacteristic
333C2×C3⋊C8—21no—
334C2×C3⋊C8—21no—
335C2×C3⋊C8—21no—
336C2×C3⋊C8—21no—
337C2×C3⋊C8—81no—
338ΓL(1,𝔽25)—81no—
339ΓL(1,𝔽25)—81no—
340D3×C8—81no—
341D3×C8—81no—
3422−1+4—128no—
343C2×#41—31no—
344C2×#41—32no—
345C2×#41—32no—
346C2×#41—62no—
347C2×#41—62no—
348C2×#41—62no—
349C2×#41C4×D312yes—
350C22×Q8—32no—
351C22×Q8—32no—
352C22×Q8—32no—
353C22×Q8—62no—
354C2×M16—61no—
355C2×M16—61no—
356C22×C8—21no—
357C22×C8—61no—
358C22×C8—61no—
359C22×C8—61no—
360C4⋊Q8—32no—
361C4⋊Q8—32no—
362C4⋊Q8—32no—
363C4⋊Q8—31no—
364C4⋊Q8—31no—
365C4⋊Q8—61no—
366C4⋊Q8—61no—
367C4⋊Q8—61no—
368C4⋊Q8—61no—
369C4⋊Q8—61no—
370C4⋊Q8—61no—
371C4⋊Q8C22×D311yescharacteristic
372#127C22×D311yescharacteristic
373#124—32no—
374#124—32no—
375#124C4×D312yes—
376#123—62no—
377#123—62no—
378#123—62no—
379#123—62no—
380#123—62no—
381#123—62no—
382C22⋊Q8—62no—
383C22⋊Q8—62no—
384C22⋊Q8—62no—
385C22⋊Q8—62no—
386C22⋊Q8—62no—
387C22⋊Q8—62no—
388#121—21no—
389#121—21no—
390#121—61no—
391#121—61no—
392#121—61no—
393#121—61no—
394C4×Q8—31no—
395C4×Q8—31no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4—31no—
399C4×D4—31no—
400C4×D4—31no—
401C4×D4—31no—
402C4×D4—31no—
403C4×D4—31no—
404C4×D4—61no—
405C4×D4—61no—
406C4×D4—61no—
407C4×D4—61no—
408#117—31no—
409#117—31no—
410#117—31no—
411C2×C4⋊C4—61no—
412C2×C4⋊C4—61no—
413C2×C4⋊C4—61no—
414C2×C4⋊C4—61no—
415C2×C4⋊C4—61no—
416C2×C4⋊C4—61no—
417C2×C42—31no—
418C2×C42—31no—
419C2×C42C22×D311yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—31no—
422C4⋊C8—31no—
423C4⋊C8—31no—
424C4⋊C8—31no—
425C4⋊C8—61no—
426C4⋊C8—61no—
427C4⋊C8—61no—
428C4⋊C8—61no—
429C4⋊C8—61no—
430C4⋊C8C22×D311yescharacteristic
431C4⋊C8C22×D311yescharacteristic
432C4⋊C8C22×D311yescharacteristic
433C4⋊C8C22×D311yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—61no—
436C22⋊C8—61no—
437C22⋊C8—61no—
438C22⋊C8—61no—
439C22⋊C8—61no—
440#97—21no—
441#97—61no—
442#97—61no—
443#97—61no—
444C4×C8—61no—
445C4×C8—61no—
446C23×C3—22no—
447C23×C3C2×C22⋊C411yescharacteristic
448C22×D3C2×C22⋊C411yescharacteristic
449C22×D3C2×C22⋊C411yescharacteristic
450C3×Q8—42no—
451C3×D4—42no—
452C3×D4—44no—
453C3×D4—41no—
454C3×D4—41no—
455C3×D4—41no—
456C3×D4—41no—
457C2×C3×C4—22no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—22no—
463C2×C3×C4—44no—
464C2×C3×C4C2×C22⋊C411yescharacteristic
465C2×C3×C4C2×C22⋊C411yescharacteristic
466C2×C3×C4C2×C22⋊C411yescharacteristic
467C2×C3×C4C23×C411yescharacteristic
468C2×C3×C4C22×D411yescharacteristic
469C2×C3×C4C22×D411yescharacteristic
470#67—22no—
471#67—44no—
472#67—44no—
473#67#10014yes—
474C2×Dic3—22no—
475C2×Dic3—22no—
476C2×Dic3—44no—
477C2×Dic3—44no—
478C2×Dic3—44no—
479C2×Dic3C2×C22⋊C411yescharacteristic
480C2×Dic3C2×C22⋊C411yescharacteristic
481C2×Dic3C2×C22⋊C411yescharacteristic
482C2×Dic3C2×C22⋊C411yescharacteristic
483C2×Dic3C2×C22⋊C411yescharacteristic
484C2×Dic3C2×C22⋊C411yescharacteristic
485D12—22no—
486C4×D3—22no—
487C4×D3—21no—
488C4×D3—21no—
489C4×D3—21no—
490C4×D3—21no—
491C4×D3—21no—
492C4×D3—21no—
493C4×D3—21no—
494C4×D3—21no—
495C4×D3—22no—
496C4×D3—44no—
497C4×D3—44no—
498Dic6—22no—
499Dic6—44no—
500Dic6—44no—
501Dic6—44no—
502Dic6—42no—
503Dic6—42no—
504C3×C8—41no—
505C3×C8—41no—
506C3×C8—41no—
507C3×C8—41no—
508C3⋊C8—41no—
509C3⋊C8—41no—
510C3⋊C8—41no—
511C3⋊C8—41no—
512#41—44no—
513#41—64no—
514#41—128no—
515#41—124no—
516#41—124no—
517#41—128no—
518#41—128no—
519C2×Q8—31no—
520C2×Q8—32no—
521C2×Q8—32no—
522C2×Q8—62no—
523C2×Q8—62no—
524C2×Q8—62no—
525C2×Q8—124no—
526C2×Q8—128no—
527C2×Q8—124no—
528C2×Q8—124no—
529C2×Q8C2×C4×D312yes—
530C2×D4—22no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—31no—
534C2×D4—31no—
535C2×D4—31no—
536C2×D4—62no—
537C2×D4—62no—
538C2×D4C2×C4×D312yes—
539C22×C4—22no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—31no—
544C22×C4—31no—
545C22×C4—31no—
546C22×C4—62no—
547C22×C4—62no—
548C22×C4—62no—
549C22×C4—62no—
550C22×C4—62no—
551C22×C4C2×C4×D311yescharacteristic
552C22×C4D3×D411yescharacteristic
553C22×C4D3×D411yescharacteristic
554M16—241no—
555M16—241no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—61no—
561C2×C8—61no—
562C2×C8—61no—
563C2×C8—61no—
564C2×C8—81no—
565C2×C8—241no—
566C2×C8—241no—
567C2×C8—241no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—31no—
571C4⋊C4—31no—
572C4⋊C4—31no—
573C4⋊C4—31no—
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—62no—
577C4⋊C4—62no—
578C4⋊C4—62no—
579C4⋊C4—62no—
580C4⋊C4—62no—
581C4⋊C4—62no—
582C4⋊C4—61no—
583C4⋊C4—61no—
584C4⋊C4—61no—
585C4⋊C4—61no—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—31no—
589C22⋊C4—31no—
590C22⋊C4—31no—
591C22⋊C4—31no—
592C22⋊C4—31no—
593C22⋊C4—31no—
594C22⋊C4—62no—
595C22⋊C4—62no—
596C22⋊C4—62no—
597C22⋊C4—62no—
598C42—31no—
599C42—31no—
600C42—31no—
601C42—31no—
602C42—31no—
603C42—31no—
604C42C2×C4×D311yescharacteristic
605C42D3×D411yescharacteristic
606C42D3×D411yescharacteristic
607C42C23×D311yescharacteristic
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3C2×#10012yes—
614C22×C3C22×C22⋊C411yescharacteristic
615C2×D3—21no—
616C2×D3—21no—
617C2×D3—21no—
618C2×D3—21no—
619C2×D3—21no—
620C2×D3C2×#10012yes—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—21no—
625C3×C4—42no—
626C3×C4#57711yescharacteristic
627C3×C4#57711yescharacteristic
628C3×C4#57811yescharacteristic
629C3×C4#57811yescharacteristic
630Dic3—21no—
631Dic3—21no—
632Dic3—21no—
633Dic3—21no—
634Dic3—21no—
635Dic3—42no—
636Dic3—42no—
637Dic3C2×#10012yes—
638C23—22no—
639C23—31no—
640C23—31no—
641C23D3×C22⋊C411yescharacteristic
642Q8—42no—
643Q8—62no—
644Q8—122no—
645Q8—122no—
646Q8—124no—
647Q8—124no—
648Q8—124no—
649D4—34no—
650D4—42no—
651D4—44no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—41no—
656D4—62no—
657D4—62no—
658D4—124no—
659D4—124no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—31no—
667C2×C4—31no—
668C2×C4—31no—
669C2×C4—31no—
670C2×C4—31no—
671C2×C4—31no—
672C2×C4—44no—
673C2×C4—62no—
674C2×C4—62no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—62no—
684C2×C4—62no—
685C2×C4—124no—
686C2×C4—124no—
687C2×C4—124no—
688C2×C4—124no—
689C2×C4—124no—
690C2×C4D3×C22⋊C411yescharacteristic
691C2×C4D3×C22⋊C411yescharacteristic
692C2×C4D3×C22⋊C411yescharacteristic
693C2×C4C22×C4×D311yescharacteristic
694C2×C4C2×D3×D411yescharacteristic
695C2×C4C2×D3×D411yescharacteristic
696C8—41no—
697C8—41no—
698C8—41no—
699C8—41no—
700C8—121no—
701C8—121no—
702C8—121no—
703C8—121no—
704C2×C3—22no—
705C2×C3—82no—
706C2×C3C22×#10011yescharacteristic
707C2×C3#289811yescharacteristic
708C2×C3#289811yescharacteristic
709D3—22no—
710D3—41no—
711C22—21no—
712C22—21no—
713C22—32no—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—61no—
718C22—61no—
719C22—61no—
720C22—61no—
721C22—61no—
722C22D3×#10012yes—
723C22C2×D3×C22⋊C411yescharacteristic
724C4—21no—
725C4—21no—
726C4—21no—
727C4—21no—
728C4—32no—
729C4—42no—
730C4—61no—
731C4—61no—
732C4—61no—
733C4—61no—
734C4—61no—
735C4—122no—
736C4—122no—
737C4#577011yescharacteristic
738C4#577111yescharacteristic
739C4#577511yescharacteristic
740C4#577911yescharacteristic
741C3#1777911yescharacteristic, complemented, Sylow
742C2—22no—
743C2—62no—
744C2—82no—
745C2—121no—
746C2C2×D3×#10011yescharacteristic
747C2#7883211yescharacteristic
748C2#7888311yescharacteristic
subgroupG/H
centerC22C2×D3×C22⋊C4
commutatorC2×C3×C4C23×C4
FrattiniC42C23×D3
FittingC3×#1551C2
socleC22×C3C22×C22⋊C4
prime radical#86243C2
cosocleC3×C42C24
hypercenter#1551D3
hypocenterC3#17779
LCSG ▷ C2×C3×C4 ▷ C22×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1551

Complements

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

NH ≅ G/Ntype
2. #79340C2semidirect
3. #79015C2semidirect
4. C3×#1551C2semidirect
5. #71807C2semidirect
6. #70824C2semidirect
7. C2×#4481C2semidirect
8. #68487C2semidirect
9. #68483C2semidirect
10. #68483C2semidirect
11. D3×#333C2semidirect
12. #68389C2semidirect
13. #68385C2semidirect
14. #68385C2semidirect
15. #68382C2semidirect
81. #1551D3semidirect
741. C3#17779semidirect

Maximal subgroups

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

subgroupindex
#862432
#793402
#790152
C3×#15512
#718072
#708242
C2×#44812
#684872
#684832
D3×#3332
#683892
#683852
#683822
#177793