Finite Group Databasebeta

← C3×#10594762 #13174359

Subgroups — C3×#10594762 #13174359

Order 1728.

1248 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×D3×#239C212yesmaximal, complemented
2C3×#64128C211yesmaximal, characteristic, complemented
3C32×#918C212yesmaximal, complemented
4C3×#63950C212yesmaximal, complemented
5C3×#63948C212yesmaximal, complemented
6C3×#63939C212yesmaximal, complemented
7C3×#63809C211yesmaximal, characteristic, complemented
8C3×#63794C212yesmaximal, complemented
9C3×#63791C211yesmaximal, characteristic, complemented
10C3×#5777—32nomaximal
11#10594762C311yesmaximal, characteristic, direct product factor
12C3×#3832C2212yescomplemented
13C32×#239C2212yes—
14C32×D3×Q8C2212yescomplemented
15C3×D3×D12—22no—
16C3×D3×D12C2212yescomplemented
17C3×C4×D32—22no—
18C3×C4×D32C2211yescharacteristic
19C3×#3799—22no—
20C3×#3799C2212yes—
21C3×#3796—22no—
22C3×#3796C2212yescomplemented
23C33×Q16C2211yescharacteristic, complemented
24C3×#3755C2212yescomplemented
25C3×#3745C2211yescharacteristic, complemented
26C3×C8×C3⋊D3C2211yescharacteristic, complemented
27C32×#216C2212yescomplemented
28C32×#215C2212yescomplemented
29C32×#204C2212yescomplemented
30C32×ΓL(1,𝔽25)C2212yescomplemented
31C3×#3718C2211yescharacteristic, complemented
32C3×#3717C2212yescomplemented
33C3×#3714C2212yescomplemented
34C3×#3713C2211yescharacteristic, complemented
35C3×#3711C2212yescomplemented
36C3×#3710C2211yescharacteristic, complemented
37C3×D3×#41—32no—
38C2×C3×#239—32no—
39D3×#239C2×C312yescomplemented
40C32×#137—32no—
41#64128C2×C311yescharacteristic, complemented
42C3×#949—32no—
43C3×#942—32no—
44C3×#919—32no—
45C3×#919—32no—
46C3×#919—61no—
47C3×#918—22no—
48C3×#918—32no—
49C3×#918D312yescomplemented
50C3×#918C2×C312yescomplemented
51C3×#916—32no—
52C3×#916—32no—
53C3×#914—32no—
54C3×#914—32no—
55C3×#908—32no—
56C3×D3×M16—32no—
57#63950C2×C312yescomplemented
58#63948C2×C312yescomplemented
59#63939C2×C312yescomplemented
60#63809C2×C311yescharacteristic, complemented
61#63794C2×C312yescomplemented
62#63791C2×C311yescharacteristic, complemented
63C2×C3×D32—22no—
64C2×C3×D32D411yescharacteristic
65C33×Q8C2312yes—
66C3×C4⋊(C3⋊D3)—22no—
67C3×C4⋊(C3⋊D3)C2312yes—
68C3×C4×C3⋊D3—22no—
69C3×C4×C3⋊D3C2311yescharacteristic
70C32×D12—22no—
71C32×D12C2312yes—
72C32×C4×D3—22no—
73C32×C4×D3—22no—
74C32×C4×D3C2312yes—
75C32×Dic6—22no—
76C32×Dic6C2312yes—
77C3×#626—22no—
78C3×#626—22no—
79C3×#626—22no—
80C3×#624—22no—
81C3×#624D411yescharacteristic
82C3×D3×Dic3—22no—
83C3×D3×Dic3D412yes—
84C33×C8C2311yescharacteristic
85C3×C3⋊(C3⋊C8)C2311yescharacteristic
86C32×C3⋊C8C2312yes—
87C3×#575—91no—
88#5777—32no—
89C32×#41—32no—
90C2×C32×Q8—32no—
91#3832C22×C312yescomplemented
92C3×#239—22no—
93C3×#239—32no—
94C3×#239—32no—
95C3×#239—32no—
96C3×#239—32no—
97C3×#239—62no—
98C3×#239—62no—
99C3×#239—62no—
100C3×#239C2×D312yes—
101C3×#239C22×C312yes—
102C3×D3×Q8—22no—
103C3×D3×Q8C2×D312yescomplemented
104C3×D3×Q8C22×C312yescomplemented
105C3×#237—32no—
106C3×#237—62no—
107C3×D3×D4—32no—
108C3×D3×D4—62no—
109C3×#235—32no—
110C3×#235—62no—
111C2×C3×D12—32no—
112C2×C3×D12—62no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—62no—
115C2×C3×C4×D3—62no—
116D3×D12—22no—
117D3×D12C22×C312yescomplemented
118C4×D32—22no—
119C4×D32C22×C311yescharacteristic
120#3799—22no—
121#3799C22×C312yes—
122#3796—22no—
123#3796C22×C312yescomplemented
124C32×Q16—21no—
125C32×Q16—22no—
126C32×Q16—32no—
127C32×Q16—41no—
128C32×Q16C2×D312yescomplemented
129C32×Q16C22×C311yescharacteristic, complemented
130C32×SD16—32no—
131C32×SD16—32no—
132C32×M16—32no—
133#3755C22×C312yescomplemented
134#3745C22×C311yescharacteristic, complemented
135C8×C3⋊D3C22×C311yescharacteristic, complemented
136C3×#216—22no—
137C3×#216—32no—
138C3×#216C2×D312yescomplemented
139C3×#216C22×C312yescomplemented
140C3×#215—22no—
141C3×#215—32no—
142C3×#215—32no—
143C3×#215—32no—
144C3×#215—62no—
145C3×#215C2×D312yescomplemented
146C3×#215C22×C312yescomplemented
147C3×#213—32no—
148C3×#213—32no—
149C3×#208—32no—
150C3×D24—32no—
151C3×D24—32no—
152C3×D24—61no—
153C3×#204—22no—
154C3×#204—32no—
155C3×#204C2×D312yescomplemented
156C3×#204C22×C312yescomplemented
157C3×ΓL(1,𝔽25)—22no—
158C3×ΓL(1,𝔽25)—32no—
159C3×ΓL(1,𝔽25)C2×D312yescomplemented
160C3×ΓL(1,𝔽25)C22×C312yescomplemented
161C3×D3×C8—32no—
162C3×D3×C8—32no—
163C3×D3×C8—61no—
164#3718C22×C311yescharacteristic, complemented
165#3717C22×C312yescomplemented
166#3714C22×C312yescomplemented
167#3713C22×C311yescharacteristic, complemented
168#3711C22×C312yescomplemented
169#3710C22×C311yescharacteristic, complemented
170C2×C3×C3⋊D3—22no—
171C2×C3×C3⋊D3C2×D411yescharacteristic
172C2×C32×D3—22no—
173C2×C32×D3C2×D412yes—
174C3×D32—41no—
175C3×D32—44no—
176C33×C4—22no—
177C33×C4C2411yescharacteristic
178C3×C3⋊Dic3C2×D411yescharacteristic
179C32×Dic3—22no—
180C32×Dic3C2×D412yes—
181C2×C3×#41—92no—
182D3×#41—32no—
183C2×#239—32no—
184C3×#137—32no—
185C3×#137—32no—
186C3×#137—62no—
187C3×#137—92no—
188C3×AGL(1,ℤ/8)—92no—
189C3×AGL(1,ℤ/8)—92no—
190C3×#135—91no—
191C3×#135—92no—
192C3×#135—91no—
193C2×C3×M16—91no—
194#949—32no—
195#942—32no—
196#919—32no—
197#919—32no—
198#919—61no—
199#918—32no—
200#918C3×D312yescomplemented
201#916—32no—
202#916—32no—
203#914—32no—
204#914—32no—
205#908—32no—
206D3×M16—32no—
207C22×C3×D3—32no—
208C22×C3×D3—62no—
209C22×C3×D3—62no—
210C2×D32—22no—
211C2×D32C3×D411yescharacteristic
212C32×Q8—22no—
213C32×Q8—22no—
214C32×Q8—22no—
215C32×Q8—32no—
216C32×Q8—42no—
217C32×Q8—62no—
218C32×Q8C22×D312yes—
219C32×Q8C22×D312yes—
220C32×Q8C23×C312yes—
221C32×D4—32no—
222C32×D4—62no—
223C2×C32×C4—32no—
224C2×C32×C4—62no—
225C2×C32×C4—62no—
226C4⋊(C3⋊D3)—22no—
227C4⋊(C3⋊D3)C23×C312yes—
228C4×C3⋊D3—22no—
229C4×C3⋊D3C23×C311yescharacteristic
230C3×#67—62no—
231C3×#67—62no—
232C3×#67—62no—
233C2×C3×Dic3—32no—
234C2×C3×Dic3—62no—
235C3×D12—22no—
236C3×D12—22no—
237C3×D12—22no—
238C3×D12—32no—
239C3×D12—32no—
240C3×D12—42no—
241C3×D12—62no—
242C3×D12—62no—
243C3×D12—62no—
244C3×D12—62no—
245C3×D12—62no—
246C3×D12—62no—
247C3×D12—122no—
248C3×D12C22×D312yes—
249C3×D12C23×C312yes—
250C3×C4×D3—22no—
251C3×C4×D3—22no—
252C3×C4×D3—22no—
253C3×C4×D3—22no—
254C3×C4×D3—22no—
255C3×C4×D3—32no—
256C3×C4×D3—32no—
257C3×C4×D3—32no—
258C3×C4×D3—42no—
259C3×C4×D3—42no—
260C3×C4×D3—61no—
261C3×C4×D3—62no—
262C3×C4×D3—62no—
263C3×C4×D3—62no—
264C3×C4×D3—62no—
265C3×C4×D3—62no—
266C3×C4×D3—122no—
267C3×C4×D3C22×D312yes—
268C3×C4×D3C23×C312yes—
269C3×Dic6—22no—
270C3×Dic6—22no—
271C3×Dic6—22no—
272C3×Dic6—42no—
273C3×Dic6C22×D312yes—
274C3×Dic6C23×C312yes—
275#626—22no—
276#626—22no—
277#626—22no—
278#624—22no—
279#624C3×D411yescharacteristic
280D3×Dic3—22no—
281D3×Dic3C3×D412yes—
282C32×C8—21no—
283C32×C8—22no—
284C32×C8—32no—
285C32×C8—41no—
286C32×C8C22×D312yes—
287C32×C8C23×C311yescharacteristic
288C3⋊(C3⋊C8)C23×C311yescharacteristic
289C3×C3⋊C8—22no—
290C3×C3⋊C8—32no—
291C3×C3⋊C8—61no—
292C3×C3⋊C8C22×D312yes—
293C3×C3⋊C8C23×C312yes—
294#575—91noSylow
295C2×C33C22×D411yescharacteristic
296C3×C3⋊D3—21no—
297C3×C3⋊D3—42no—
298C32×D3—22no—
299C32×D3—42no—
300C3×#41—32no—
301C3×#41—32no—
302C3×#41—62no—
303C3×#41—92no—
304C3×#41—92no—
305C3×#41—92no—
306C3×#41—182no—
307C3×#41—182no—
308C2×C3×Q8—32no—
309C2×C3×Q8—32no—
310C2×C3×Q8—62no—
311C2×C3×D4—92no—
312C2×C3×D4—182no—
313C22×C3×C4—91no—
314C22×C3×C4—182no—
315#239—32no—
316#239—32no—
317#239—32no—
318#239—32no—
319#239—62no—
320#239—62no—
321#239—62no—
322#239C2×C3×D312yes—
323D3×Q8C2×C3×D312yescomplemented
324#237—32no—
325#237—62no—
326D3×D4—32no—
327D3×D4—62no—
328#235—32no—
329#235—62no—
330C2×D12—32no—
331C2×D12—62no—
332C2×C4×D3—32no—
333C2×C4×D3—62no—
334C2×C4×D3—62no—
335C3×Q16—21no—
336C3×Q16—22no—
337C3×Q16—32no—
338C3×Q16—32no—
339C3×Q16—41no—
340C3×Q16—62no—
341C3×Q16—91no—
342C3×Q16D3211yescharacteristic, complemented
343C3×Q16C2×C3×D312yescomplemented
344C3×SD16—32no—
345C3×SD16—32no—
346C3×SD16—32no—
347C3×SD16—32no—
348C3×SD16—62no—
349C3×SD16—62no—
350C3×SD16—92no—
351C3×SD16—92no—
352C3×D8—92no—
353C3×D8—91no—
354C3×D8—91no—
355C3×M16—32no—
356C3×M16—32no—
357C3×M16—62no—
358C3×M16—92no—
359C2×C3×C8—91no—
360C2×C3×C8—91no—
361#216—32no—
362#216C2×C3×D312yescomplemented
363#215—32no—
364#215—32no—
365#215—32no—
366#215—62no—
367#215C2×C3×D312yescomplemented
368#213—32no—
369#213—32no—
370#208—32no—
371D24—32no—
372D24—32no—
373D24—61no—
374#204—32no—
375#204C2×C3×D312yescomplemented
376ΓL(1,𝔽25)—32no—
377ΓL(1,𝔽25)C2×C3×D312yescomplemented
378D3×C8—32no—
379D3×C8—32no—
380D3×C8—61no—
381C22×C32—32no—
382C22×C32—62no—
383C2×C3⋊D3—22no—
384C2×C3⋊D3C2×C3×D411yescharacteristic
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—32no—
389C2×C3×D3—42no—
390C2×C3×D3—61no—
391C2×C3×D3—62no—
392C2×C3×D3—62no—
393C2×C3×D3—122no—
394C2×C3×D3—122no—
395C2×C3×D3—124no—
396C2×C3×D3—124no—
397C2×C3×D3D3×D412yes—
398C2×C3×D3C2×C3×D412yes—
399D32—41no—
400D32—44no—
401C32×C4—22no—
402C32×C4—22no—
403C32×C4—22no—
404C32×C4—21no—
405C32×C4—22no—
406C32×C4—32no—
407C32×C4—41no—
408C32×C4—42no—
409C32×C4—42no—
410C32×C4—42no—
411C32×C4—62no—
412C32×C4—82no—
413C32×C4C23×D312yes—
414C32×C4C24×C311yescharacteristic
415C3⋊Dic3C2×C3×D411yescharacteristic
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—32no—
420C3×Dic3—42no—
421C3×Dic3—61no—
422C3×Dic3D3×D412yes—
423C3×Dic3C2×C3×D412yes—
424C2×#41—92no—
425#137—32no—
426#137—92no—
427AGL(1,ℤ/8)—92no—
428AGL(1,ℤ/8)—92no—
429#135—91no—
430#135—92no—
431#135—91no—
432C2×M16—91no—
433C33#57511yescharacteristic, complemented, Sylow
434C23×C3—91no—
435C23×C3—182no—
436C22×D3—32no—
437C22×D3—62no—
438C22×D3—62no—
439C3×Q8—22no—
440C3×Q8—22no—
441C3×Q8—22no—
442C3×Q8—32no—
443C3×Q8—32no—
444C3×Q8—42no—
445C3×Q8—62no—
446C3×Q8—62no—
447C3×Q8—62no—
448C3×Q8—122no—
449C3×Q8C2×D3212yes—
450C3×Q8C22×C3×D312yes—
451C3×Q8C22×C3×D312yes—
452C3×D4—32no—
453C3×D4—32no—
454C3×D4—62no—
455C3×D4—62no—
456C3×D4—62no—
457C3×D4—92no—
458C3×D4—122no—
459C3×D4—182no—
460C3×D4—182no—
461C3×D4—182no—
462C3×D4—182no—
463C2×C3×C4—32no—
464C2×C3×C4—32no—
465C2×C3×C4—62no—
466C2×C3×C4—62no—
467C2×C3×C4—62no—
468C2×C3×C4—62no—
469C2×C3×C4—62no—
470C2×C3×C4—91no—
471C2×C3×C4—92no—
472C2×C3×C4—91no—
473C2×C3×C4—122no—
474C2×C3×C4—122no—
475C2×C3×C4—182no—
476C2×C3×C4—182no—
477C2×C3×C4—182no—
478#67—62no—
479#67—62no—
480#67—62no—
481C2×Dic3—32no—
482C2×Dic3—62no—
483D12—22no—
484D12—32no—
485D12—32no—
486D12—62no—
487D12—62no—
488D12—62no—
489D12—62no—
490D12—62no—
491D12—62no—
492D12—122no—
493D12C22×C3×D312yes—
494C4×D3—22no—
495C4×D3—22no—
496C4×D3—32no—
497C4×D3—32no—
498C4×D3—32no—
499C4×D3—61no—
500C4×D3—62no—
501C4×D3—62no—
502C4×D3—62no—
503C4×D3—62no—
504C4×D3—62no—
505C4×D3—122no—
506C4×D3C22×C3×D312yes—
507Dic6—22no—
508Dic6C22×C3×D312yes—
509C3×C8—22no—
510C3×C8—21no—
511C3×C8—32no—
512C3×C8—32no—
513C3×C8—41no—
514C3×C8—62no—
515C3×C8—91no—
516C3×C8C2×D3211yescharacteristic
517C3×C8C22×C3×D312yes—
518C3⋊C8—32no—
519C3⋊C8—61no—
520C3⋊C8C22×C3×D312yes—
521C2×C32—21no—
522C2×C32—22no—
523C2×C32—41no—
524C2×C32—62no—
525C2×C32—122no—
526C2×C32C2×D3×D412yes—
527C2×C32C22×C3×D411yescharacteristic
528C3⋊D3—21no—
529C3⋊D3—42no—
530C3×D3—22no—
531C3×D3—22no—
532C3×D3—42no—
533C3×D3—42no—
534C3×D3—42no—
535C3×D3—62no—
536C3×D3—82no—
537C3×D3—121no—
538C3×D3—122no—
539C3×D3—122no—
540C3×D3—242no—
541#41—32no—
542#41—92no—
543#41—92no—
544#41—92no—
545#41—182no—
546#41—182no—
547C2×Q8—32no—
548C2×D4—92no—
549C2×D4—182no—
550C22×C4—91no—
551C22×C4—182no—
552Q16—32no—
553Q16—91no—
554Q16C3×D3211yescharacteristic, complemented
555SD16—32no—
556SD16—32no—
557SD16—92no—
558SD16—92no—
559D8—92no—
560D8—91no—
561D8—91no—
562M16—32no—
563M16—92no—
564C2×C8—91no—
565C2×C8—91no—
566C22×C3—32no—
567C22×C3—32no—
568C22×C3—62no—
569C22×C3—62no—
570C22×C3—62no—
571C22×C3—91no—
572C22×C3—122no—
573C22×C3—182no—
574C22×C3—361no—
575C22×C3—364no—
576C2×D3—22no—
577C2×D3—32no—
578C2×D3—61no—
579C2×D3—62no—
580C2×D3—62no—
581C2×D3—122no—
582C2×D3—122no—
583C2×D3—124no—
584C2×D3—124no—
585C2×D3C3×D3×D412yes—
586C3×C4—22no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—21no—
590C3×C4—22no—
591C3×C4—32no—
592C3×C4—32no—
593C3×C4—42no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—41no—
597C3×C4—62no—
598C3×C4—62no—
599C3×C4—62no—
600C3×C4—82no—
601C3×C4—91no—
602C3×C4—122no—
603C3×C4C22×D3211yescharacteristic
604C3×C4C23×C3×D312yes—
605Dic3—22no—
606Dic3—32no—
607Dic3—61no—
608Dic3C3×D3×D412yes—
609C32—22no—
610C32—21no—
611C32—41no—
612C32#577712yescomplemented
613C32C3×#57511yescharacteristic, complemented
614C23—91no—
615C23—182no—
616Q8—32no—
617Q8—62no—
618Q8C2×C3×D3212yes—
619D4—32no—
620D4—62no—
621D4—92no—
622D4—182no—
623D4—182no—
624D4—182no—
625D4—182no—
626C2×C4—32no—
627C2×C4—62no—
628C2×C4—62no—
629C2×C4—91no—
630C2×C4—92no—
631C2×C4—91no—
632C2×C4—182no—
633C2×C4—182no—
634C2×C4—182no—
635C8—32no—
636C8—91no—
637C8C2×C3×D3211yescharacteristic
638C2×C3—21no—
639C2×C3—22no—
640C2×C3—41no—
641C2×C3—62no—
642C2×C3—62no—
643C2×C3—122no—
644C2×C3—122no—
645C2×C3—122no—
646C2×C3—181no—
647C2×C3—242no—
648C2×C3—362no—
649C2×C3D32×D411yescharacteristic
650C2×C3C2×C3×D3×D412yes—
651D3—22no—
652D3—42no—
653D3—62no—
654D3—121no—
655D3—122no—
656D3—122no—
657D3—242no—
658C22—32no—
659C22—62no—
660C22—91no—
661C22—182no—
662C22—361no—
663C22—364no—
664C4—22no—
665C4—32no—
666C4—62no—
667C4—91no—
668C4C22×C3×D3211yescharacteristic
669C3—21no—
670C3—22no—
671C3—41no—
672C3#1059476211yescharacteristic, direct product factor
673C3C3×#577712yescomplemented
674C2—62no—
675C2—122no—
676C2—181no—
677C2—362no—
678C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×Q16C22
socleC2×C33C22×D4
hypercenterC3×Q16D32
hypocenterC32C3×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×Q16

Complements

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

NH ≅ G/Ntype
1. C3×D3×#239C2semidirect
2. C3×#64128C2semidirect
3. C32×#918C2semidirect
4. C3×#63950C2semidirect
5. C3×#63948C2semidirect
6. C3×#63939C2semidirect
7. C3×#63809C2semidirect
8. C3×#63794C2semidirect
9. C3×#63791C2semidirect
11. #10594762C3direct (N × H)
12. C3×#3832C22semidirect
14. C32×D3×Q8C22semidirect
16. C3×D3×D12C22semidirect
22. C3×#3796C22semidirect
23. C33×Q16C22semidirect
24. C3×#3755C22semidirect
25. C3×#3745C22semidirect
26. C3×C8×C3⋊D3C22semidirect
27. C32×#216C22semidirect
28. C32×#215C22semidirect
29. C32×#204C22semidirect
30. C32×ΓL(1,𝔽25)C22semidirect
31. C3×#3718C22semidirect
32. C3×#3717C22semidirect
33. C3×#3714C22semidirect
34. C3×#3713C22semidirect
35. C3×#3711C22semidirect
36. C3×#3710C22semidirect
39. D3×#239C2×C3semidirect
41. #64128C2×C3semidirect
49. C3×#918D3semidirect
50. C3×#918C2×C3semidirect
57. #63950C2×C3semidirect
58. #63948C2×C3semidirect
59. #63939C2×C3semidirect
60. #63809C2×C3semidirect
61. #63794C2×C3semidirect
62. #63791C2×C3semidirect
91. #3832C22×C3semidirect
103. C3×D3×Q8C2×D3semidirect
104. C3×D3×Q8C22×C3semidirect
117. D3×D12C22×C3semidirect
123. #3796C22×C3semidirect
128. C32×Q16C2×D3semidirect
129. C32×Q16C22×C3semidirect
133. #3755C22×C3semidirect
134. #3745C22×C3semidirect
135. C8×C3⋊D3C22×C3semidirect
138. C3×#216C2×D3semidirect
139. C3×#216C22×C3semidirect
145. C3×#215C2×D3semidirect
146. C3×#215C22×C3semidirect
155. C3×#204C2×D3semidirect
156. C3×#204C22×C3semidirect
159. C3×ΓL(1,𝔽25)C2×D3semidirect
160. C3×ΓL(1,𝔽25)C22×C3semidirect
164. #3718C22×C3semidirect
165. #3717C22×C3semidirect
166. #3714C22×C3semidirect
167. #3713C22×C3semidirect
168. #3711C22×C3semidirect
169. #3710C22×C3semidirect
200. #918C3×D3semidirect
323. D3×Q8C2×C3×D3semidirect
342. C3×Q16D32semidirect
343. C3×Q16C2×C3×D3semidirect
362. #216C2×C3×D3semidirect
367. #215C2×C3×D3semidirect
375. #204C2×C3×D3semidirect
377. ΓL(1,𝔽25)C2×C3×D3semidirect
433. C33#575semidirect
554. Q16C3×D32semidirect
612. C32#5777semidirect
613. C32C3×#575semidirect
672. C3#10594762direct (N × H)
673. C3C3×#5777semidirect

Maximal subgroups

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

subgroupindex
C3×D3×#2392
C3×#641282
C32×#9182
C3×#639502
C3×#639482
C3×#639392
C3×#638092
C3×#637942
C3×#637912
C3×#57773
#105947623