Finite Group Databasebeta

← C3×#10591664 #13158703

Subgroups — C3×#10591664 #13158703

Order 1728.

918 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#1009C211yesmaximal, characteristic
2C32×#951C211yesmaximal, characteristic, complemented
3C3×#63863C211yesmaximal, characteristic, complemented
4C3×#63827C211yesmaximal, characteristic, complemented
5C3×#63664C211yesmaximal, characteristic, complemented
6C3×#63568C211yesmaximal, characteristic, complemented
7C3×#63558C211yesmaximal, characteristic, complemented
8C3×#5242—31nomaximal
9C3×#5202—31nomaximal
10#10591664C311yesmaximal, characteristic, direct product factor
11C33×#41C2211yescharacteristic
12C32×#239—21no—
13C32×D3×D4—22no—
14C32×D3×D4—21no—
15C32×#235—21no—
16C32×#235C2211yescharacteristic
17C2×C32×D12—21no—
18C2×C32×D12C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic, complemented
20C3×C4×C3⋊Dic3C2211yescharacteristic, complemented
21C3×#3748C2211yescharacteristic, complemented
22C32×#216—21no—
23C32×#214—21no—
24C32×#208C2211yescharacteristic, complemented
25C3×(C2×D3)⋊Dic3—22no—
26C3×#3718—21no—
27C3×#3715—21no—
28C32×H(5,𝔽2)—31no—
29C3×#1009—21no—
30C3×#1009D311yescharacteristic
31C3×#1009C2×C311yescharacteristic
32C32×#137—31no—
33C3×#951—21no—
34C3×#951—31no—
35C3×#951D311yescharacteristic, complemented
36C3×#951C2×C311yescharacteristic, complemented
37C3×#947—31no—
38C3×#942—31no—
39C3×#936—31no—
40#63863C2×C311yescharacteristic, complemented
41#63827C2×C311yescharacteristic, complemented
42#63664C2×C311yescharacteristic, complemented
43C3×#837—31no—
44C3×#837—31no—
45C3×#837—31no—
46C3×#837—61no—
47C3×#833—31no—
48C3×#825—31no—
49C3×#823—31no—
50#63568C2×C311yescharacteristic, complemented
51#63558C2×C311yescharacteristic, complemented
52C22×C32×D3—22no—
53C22×C32×D3D412yes—
54C33×Q8D411yescharacteristic
55C33×D4—21no—
56C33×D4D411yescharacteristic
57C2×C33×C4—21no—
58C2×C33×C4C2311yescharacteristic
59C2×C3×C3⋊Dic3—21no—
60C32×#67—22no—
61C32×#67—21no—
62C2×C32×Dic3—21no—
63C32×D12—22no—
64C32×D12—21no—
65C32×D12—21no—
66C32×D12D411yescharacteristic
67C32×C4×D3—22no—
68C32×C4×D3—21no—
69C32×Dic6—21no—
70C32×Dic6—21no—
71C32×Dic6D411yescharacteristic
72C3×C3⋊(C3⋊C8)—21no—
73C32×C3⋊C8—21no—
74C3×#455—91no—
75#5242—31no—
76#5202—31no—
77C32×#41—21no—
78C32×#41—21no—
79C32×#41—21no—
80C32×#41—31no—
81C32×#41—41no—
82C32×#41—61no—
83C32×#41—61no—
84C32×#41C2×D311yescharacteristic
85C32×#41C2×D311yescharacteristic
86C32×#41C22×C311yescharacteristic
87C2×C32×Q8—31no—
88C2×C32×D4—31no—
89C2×C32×D4—61no—
90C2×C32×D4—62no—
91C2×C32×D4—61no—
92C3×#239—22no—
93C3×#239—21no—
94C3×#239—21no—
95C3×D3×D4—24no—
96C3×D3×D4—22no—
97C3×D3×D4—22no—
98C3×D3×D4—22no—
99C3×D3×D4—21no—
100C3×D3×D4—21no—
101C3×#235—22no—
102C3×#235—21no—
103C3×#235—21no—
104C3×#235—21no—
105C3×#235C2×D311yescharacteristic
106C3×#235C22×C311yescharacteristic
107C2×C3×D12—22no—
108C2×C3×D12—21no—
109C2×C3×D12—21no—
110C2×C3×D12—21no—
111C2×C3×D12C2×D311yescharacteristic
112C2×C3×D12C22×C311yescharacteristic
113C2×C3×Dic6—21no—
114C2×C3×Dic6C2×D311yescharacteristic, complemented
115C2×C3×Dic6C22×C311yescharacteristic, complemented
116C32×Q16—61no—
117C32×SD16—61no—
118C32×M16—31no—
119C4×C3⋊Dic3C22×C311yescharacteristic, complemented
120#3748C22×C311yescharacteristic, complemented
121C3×#217—62no—
122C3×#216—22no—
123C3×#216—21no—
124C3×#216—21no—
125C3×#216—61no—
126C3×#216—61no—
127C3×#215—61no—
128C3×#214—22no—
129C3×#214—21no—
130C3×#214—21no—
131C3×#214—61no—
132C3×(C2×D3)⋊C4—62no—
133C3×C4×Dic3—31no—
134C3×C4×Dic3—31no—
135C3×C4×Dic3—61no—
136C3×#208—21no—
137C3×#208—31no—
138C3×#208—31no—
139C3×#208—61no—
140C3×#208C2×D311yescharacteristic, complemented
141C3×#208C22×C311yescharacteristic, complemented
142(C2×D3)⋊Dic3—22no—
143#3718—21no—
144#3715—21no—
145C22×C33—21no—
146C22×C33C2×D411yescharacteristic
147C2×C32×D3—22no—
148C2×C32×D3—21no—
149C2×C32×D3—42no—
150C2×C32×D3—82no—
151C33×C4—21no—
152C33×C4C2×D411yescharacteristic
153C33×C4C2×D411yescharacteristic
154C3×C3⋊Dic3—41no—
155C32×Dic3—21no—
156C32×Dic3—41no—
157C3×H(5,𝔽2)—31no—
158C3×H(5,𝔽2)—31no—
159C3×H(5,𝔽2)—61no—
160#1009C3×D311yescharacteristic
161C3×#137—31no—
162C3×#137—31no—
163C3×#137—61no—
164C3×#137—91no—
165C3×#124—91no—
166#951—31no—
167#951C3×D311yescharacteristic, complemented
168#947—31no—
169#942—31no—
170#936—31no—
171C3×#104—91no—
172C3×#104—91no—
173C3×#100—91no—
174#837—31no—
175#837—31no—
176#837—31no—
177#837—61no—
178#833—31no—
179#825—31no—
180#823—31no—
181C23×C32—32no—
182C23×C32—62no—
183C22×C3×D3—24no—
184C22×C3×D3—22no—
185C22×C3×D3—22no—
186C22×C3×D3—22no—
187C22×C3×D3#6712yes—
188C22×C3×D3C3×D412yes—
189C32×Q8—21no—
190C32×Q8—21no—
191C32×Q8—21no—
192C32×Q8—31no—
193C32×Q8—41no—
194C32×Q8—61no—
195C32×Q8—61no—
196C32×Q8#6711yescharacteristic
197C32×Q8#6711yescharacteristic
198C32×Q8C3×D411yescharacteristic
199C32×D4—21no—
200C32×D4—22no—
201C32×D4—21no—
202C32×D4—21no—
203C32×D4—21no—
204C32×D4—21no—
205C32×D4—21no—
206C32×D4—31no—
207C32×D4—41no—
208C32×D4—41no—
209C32×D4—41no—
210C32×D4—42no—
211C32×D4—62no—
212C32×D4—62no—
213C32×D4—61no—
214C32×D4—61no—
215C32×D4—61no—
216C32×D4#6711yescharacteristic
217C32×D4#6711yescharacteristic
218C32×D4C3×D411yescharacteristic
219C2×C32×C4—21no—
220C2×C32×C4—22no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—41no—
227C2×C32×C4—41no—
228C2×C32×C4—41no—
229C2×C32×C4—42no—
230C2×C32×C4—62no—
231C2×C32×C4—61no—
232C2×C32×C4—61no—
233C2×C32×C4C22×D311yescharacteristic
234C2×C32×C4C22×D311yescharacteristic
235C2×C32×C4C23×C311yescharacteristic
236C2×C3⋊Dic3—21no—
237C3×#67—24no—
238C3×#67—22no—
239C3×#67—22no—
240C3×#67—22no—
241C3×#67—21no—
242C3×#67—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—41no—
246C2×C3×Dic3—61no—
247C2×C3×Dic3—61no—
248C2×C3×Dic3—121no—
249C3×D12—22no—
250C3×D12—24no—
251C3×D12—22no—
252C3×D12—22no—
253C3×D12—22no—
254C3×D12—21no—
255C3×D12—21no—
256C3×D12—21no—
257C3×D12—21no—
258C3×D12—21no—
259C3×D12#6711yescharacteristic
260C3×D12C3×D411yescharacteristic
261C3×C4×D3—24no—
262C3×C4×D3—22no—
263C3×C4×D3—22no—
264C3×C4×D3—22no—
265C3×C4×D3—21no—
266C3×C4×D3—21no—
267C3×Dic6—22no—
268C3×Dic6—21no—
269C3×Dic6—21no—
270C3×Dic6—21no—
271C3×Dic6—21no—
272C3×Dic6—21no—
273C3×Dic6—41no—
274C3×Dic6#6711yescharacteristic
275C3×Dic6C3×D411yescharacteristic
276C32×C8—61no—
277C3⋊(C3⋊C8)—21no—
278C3×C3⋊C8—22no—
279C3×C3⋊C8—21no—
280C3×C3⋊C8—21no—
281C3×C3⋊C8—61no—
282C3×C3⋊C8—61no—
283C3×C3⋊C8—121no—
284#455—91noSylow
285C2×C33—21no—
286C2×C33—41no—
287C2×C33#12011yescharacteristic
288C32×D3—42no—
289C32×D3—41no—
290C3×#41—21no—
291C3×#41—21no—
292C3×#41—21no—
293C3×#41—31no—
294C3×#41—31no—
295C3×#41—41no—
296C3×#41—61no—
297C3×#41—61no—
298C3×#41—61no—
299C3×#41—62no—
300C3×#41—62no—
301C3×#41—61no—
302C3×#41—61no—
303C3×#41D3211yescharacteristic
304C3×#41C2×C3×D311yescharacteristic
305C3×#41C2×C3×D311yescharacteristic
306C2×C3×Q8—31no—
307C2×C3×Q8—31no—
308C2×C3×Q8—61no—
309C2×C3×D4—31no—
310C2×C3×D4—31no—
311C2×C3×D4—61no—
312C2×C3×D4—61no—
313C2×C3×D4—61no—
314C2×C3×D4—62no—
315C2×C3×D4—62no—
316C2×C3×D4—62no—
317C2×C3×D4—64no—
318C2×C3×D4—62no—
319C2×C3×D4—61no—
320C2×C3×D4—61no—
321#239—21no—
322D3×D4—22no—
323D3×D4—21no—
324#235—21no—
325#235C2×C3×D311yescharacteristic
326C2×D12—21no—
327C2×D12C2×C3×D311yescharacteristic
328C2×Dic6C2×C3×D311yescharacteristic, complemented
329C3×Q16—62no—
330C3×Q16—61no—
331C3×Q16—61no—
332C3×Q16—181no—
333C3×SD16—62no—
334C3×SD16—61no—
335C3×SD16—61no—
336C3×SD16—181no—
337C3×M16—31no—
338C3×M16—31no—
339C3×M16—61no—
340C3×M16—91no—
341C3×C22⋊C4—182no—
342C3×C42—91no—
343#217—62no—
344#216—21no—
345#216—61no—
346#216—61no—
347#215—61no—
348#214—21no—
349#214—61no—
350(C2×D3)⋊C4—62no—
351C4×Dic3—31no—
352C4×Dic3—31no—
353C4×Dic3—61no—
354#208—31no—
355#208—31no—
356#208—61no—
357#208C2×C3×D311yescharacteristic, complemented
358C22×C32—21no—
359C22×C32—22no—
360C22×C32—21no—
361C22×C32—21no—
362C22×C32—21no—
363C22×C32—21no—
364C22×C32—21no—
365C22×C32—41no—
366C22×C32—41no—
367C22×C32—41no—
368C22×C32—42no—
369C22×C32—61no—
370C22×C32—62no—
371C22×C32—122no—
372C22×C32—242no—
373C22×C32D3×D411yescharacteristic
374C22×C32C2×#6711yescharacteristic
375C22×C32C2×C3×D411yescharacteristic
376C2×C3×D3—24no—
377C2×C3×D3—22no—
378C2×C3×D3—22no—
379C2×C3×D3—21no—
380C2×C3×D3—22no—
381C2×C3×D3—21no—
382C2×C3×D3—42no—
383C2×C3×D3—42no—
384C2×C3×D3—82no—
385C2×C3×D3—84no—
386C2×C3×D3—82no—
387C2×C3×D3—82no—
388C32×C4—21no—
389C32×C4—22no—
390C32×C4—21no—
391C32×C4—21no—
392C32×C4—21no—
393C32×C4—21no—
394C32×C4—21no—
395C32×C4—21no—
396C32×C4—21no—
397C32×C4—21no—
398C32×C4—41no—
399C32×C4—41no—
400C32×C4—41no—
401C32×C4—41no—
402C32×C4—42no—
403C32×C4—61no—
404C32×C4—121no—
405C32×C4D3×D411yescharacteristic
406C32×C4C2×#6711yescharacteristic
407C32×C4C2×#6711yescharacteristic
408C32×C4C2×#6711yescharacteristic
409C32×C4C2×C3×D411yescharacteristic
410C32×C4C2×C3×D411yescharacteristic
411C3⋊Dic3—41no—
412C3×Dic3—22no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—42no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C3×Dic3—121no—
419C3×Dic3—121no—
420C3×Dic3—122no—
421H(5,𝔽2)—31no—
422#137—31no—
423#137—91no—
424#124—91no—
425#104—91no—
426#104—91no—
427#100—91no—
428C33#45511yescharacteristic, complemented, Sylow
429C23×C3—32no—
430C23×C3—32no—
431C23×C3—62no—
432C23×C3—64no—
433C23×C3—62no—
434C23×C3—62no—
435C22×D3—22no—
436C22×D3C3×#6712yes—
437C3×Q8—21no—
438C3×Q8—21no—
439C3×Q8—21no—
440C3×Q8—31no—
441C3×Q8—31no—
442C3×Q8—41no—
443C3×Q8—61no—
444C3×Q8—62no—
445C3×Q8—61no—
446C3×Q8—61no—
447C3×Q8—61no—
448C3×Q8—61no—
449C3×Q8—121no—
450C3×Q8#62511yescharacteristic
451C3×Q8C3×#6711yescharacteristic
452C3×Q8C3×#6711yescharacteristic
453C3×D4—22no—
454C3×D4—21no—
455C3×D4—21no—
456C3×D4—21no—
457C3×D4—21no—
458C3×D4—21no—
459C3×D4—21no—
460C3×D4—31no—
461C3×D4—31no—
462C3×D4—41no—
463C3×D4—41no—
464C3×D4—42no—
465C3×D4—41no—
466C3×D4—61no—
467C3×D4—64no—
468C3×D4—62no—
469C3×D4—62no—
470C3×D4—62no—
471C3×D4—62no—
472C3×D4—64no—
473C3×D4—62no—
474C3×D4—62no—
475C3×D4—62no—
476C3×D4—61no—
477C3×D4—61no—
478C3×D4—61no—
479C3×D4—61no—
480C3×D4—61no—
481C3×D4—61no—
482C3×D4#62511yescharacteristic
483C3×D4C3×#6711yescharacteristic
484C3×D4C3×#6711yescharacteristic
485C2×C3×C4—22no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—42no—
495C2×C3×C4—41no—
496C2×C3×C4—64no—
497C2×C3×C4—62no—
498C2×C3×C4—62no—
499C2×C3×C4—62no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—121no—
505C2×C3×C4—181no—
506C2×C3×C4C2×D3211yescharacteristic
507C2×C3×C4C22×C3×D311yescharacteristic
508C2×C3×C4C22×C3×D311yescharacteristic
509#67—22no—
510#67—21no—
511C2×Dic3—21no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—121no—
515D12—22no—
516D12—21no—
517D12—21no—
518D12C3×#6711yescharacteristic
519C4×D3—22no—
520C4×D3—21no—
521Dic6—21no—
522Dic6—21no—
523Dic6C3×#6711yescharacteristic
524C3×C8—62no—
525C3×C8—61no—
526C3×C8—61no—
527C3×C8—181no—
528C3⋊C8—21no—
529C3⋊C8—61no—
530C3⋊C8—61no—
531C3⋊C8—121no—
532C2×C32—21no—
533C2×C32—21no—
534C2×C32—21no—
535C2×C32—21no—
536C2×C32—21no—
537C2×C32—21no—
538C2×C32—41no—
539C2×C32—41no—
540C2×C32—41no—
541C2×C32—41no—
542C2×C32—41no—
543C2×C32—42no—
544C2×C32—41no—
545C2×C32—41no—
546C2×C32—81no—
547C2×C32—81no—
548C2×C32—81no—
549C2×C32—82no—
550C2×C32—122no—
551C2×C32—121no—
552C2×C32#93711yescharacteristic
553C2×C32#95311yescharacteristic
554C2×C32C3×#12011yescharacteristic
555C3×D3—44no—
556C3×D3—42no—
557C3×D3—42no—
558C3×D3—41no—
559C3×D3—42no—
560C3×D3—41no—
561#41—31no—
562#41—61no—
563#41—61no—
564#41C3×D3211yescharacteristic
565C2×Q8—31no—
566C2×D4—31no—
567C2×D4—61no—
568C2×D4—62no—
569C2×D4—61no—
570Q16—61no—
571Q16—181no—
572SD16—61no—
573SD16—181no—
574M16—31no—
575M16—91no—
576C22⋊C4—182no—
577C42—91no—
578C22×C3—22no—
579C22×C3—21no—
580C22×C3—21no—
581C22×C3—21no—
582C22×C3—21no—
583C22×C3—21no—
584C22×C3—21no—
585C22×C3—41no—
586C22×C3—41no—
587C22×C3—42no—
588C22×C3—41no—
589C22×C3—62no—
590C22×C3—64no—
591C22×C3—61no—
592C22×C3—62no—
593C22×C3—61no—
594C22×C3—62no—
595C22×C3—122no—
596C22×C3—122no—
597C22×C3—242no—
598C22×C3—244no—
599C22×C3—242no—
600C22×C3—242no—
601C22×C3D3×#6711yescharacteristic
602C22×C3C3×D3×D411yescharacteristic
603C22×C3C2×C3×#6711yescharacteristic
604C2×D3—22no—
605C2×D3—21no—
606C2×D3—42no—
607C2×D3—82no—
608C3×C4—22no—
609C3×C4—21no—
610C3×C4—21no—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—21no—
614C3×C4—21no—
615C3×C4—21no—
616C3×C4—21no—
617C3×C4—21no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—62no—
624C3×C4—61no—
625C3×C4—61no—
626C3×C4—122no—
627C3×C4—121no—
628C3×C4—121no—
629C3×C4—361no—
630C3×C4C2×#62511yescharacteristic
631C3×C4D3×#6711yescharacteristic
632C3×C4C3×D3×D411yescharacteristic
633C3×C4C2×C3×#6711yescharacteristic
634C3×C4C2×C3×#6711yescharacteristic
635C3×C4C2×C3×#6711yescharacteristic
636Dic3—21no—
637Dic3—41no—
638Dic3—121no—
639Dic3—121no—
640Dic3—122no—
641C32—21no—
642C32—21no—
643C32—21no—
644C32—41no—
645C32#520211yescharacteristic, complemented
646C32#524211yescharacteristic, complemented
647C32C3×#45511yescharacteristic, complemented
648C23—32no—
649C23—62no—
650Q8—31no—
651Q8—61no—
652Q8—61no—
653Q8C3×#62511yescharacteristic
654D4—21no—
655D4—31no—
656D4—62no—
657D4—62no—
658D4—61no—
659D4—61no—
660D4—61no—
661D4C3×#62511yescharacteristic
662C2×C4—21no—
663C2×C4—62no—
664C2×C4—61no—
665C2×C4—61no—
666C2×C4—181no—
667C2×C4C2×C3×D3211yescharacteristic
668C8—61no—
669C8—181no—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—21no—
674C2×C3—21no—
675C2×C3—21no—
676C2×C3—41no—
677C2×C3—41no—
678C2×C3—41no—
679C2×C3—42no—
680C2×C3—41no—
681C2×C3—41no—
682C2×C3—41no—
683C2×C3—41no—
684C2×C3—81no—
685C2×C3—81no—
686C2×C3—81no—
687C2×C3—82no—
688C2×C3—124no—
689C2×C3—122no—
690C2×C3—122no—
691C2×C3—121no—
692C2×C3—122no—
693C2×C3—121no—
694C2×C3#6397611yescharacteristic
695C2×C3C3×#93711yescharacteristic
696C2×C3C3×#95311yescharacteristic
697D3—42no—
698D3—41no—
699C22—21no—
700C22—61no—
701C22—62no—
702C22—122no—
703C22—242no—
704C22C3×D3×#6711yescharacteristic
705C4—21no—
706C4—61no—
707C4—121no—
708C4—361no—
709C4C2×C3×#62511yescharacteristic
710C4C3×D3×#6711yescharacteristic
711C3—21no—
712C3—21no—
713C3—21no—
714C3—41no—
715C3#1059166411yescharacteristic, direct product factor
716C3C3×#520211yescharacteristic, complemented
717C3C3×#524211yescharacteristic, complemented
718C2—21no—
719C2—41no—
720C2—122no—
721C2—121no—
722C2C3×#6397611yescharacteristic
subgroupG/H
centerC2×C3#63976
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC33×#41C22
socleC2×C33#120
prime radicalC32×#1009C2
hypercenterC3×#41D32
hypocenterC32C3×#455
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×#41

Complements

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

NH ≅ G/Ntype
2. C32×#951C2semidirect
3. C3×#63863C2semidirect
4. C3×#63827C2semidirect
5. C3×#63664C2semidirect
6. C3×#63568C2semidirect
7. C3×#63558C2semidirect
10. #10591664C3direct (N × H)
19. C2×C32×Dic6C22semidirect
20. C3×C4×C3⋊Dic3C22semidirect
21. C3×#3748C22semidirect
24. C32×#208C22semidirect
35. C3×#951D3semidirect
36. C3×#951C2×C3semidirect
40. #63863C2×C3semidirect
41. #63827C2×C3semidirect
42. #63664C2×C3semidirect
50. #63568C2×C3semidirect
51. #63558C2×C3semidirect
114. C2×C3×Dic6C2×D3semidirect
115. C2×C3×Dic6C22×C3semidirect
119. C4×C3⋊Dic3C22×C3semidirect
120. #3748C22×C3semidirect
140. C3×#208C2×D3semidirect
141. C3×#208C22×C3semidirect
167. #951C3×D3semidirect
328. C2×Dic6C2×C3×D3semidirect
357. #208C2×C3×D3semidirect
428. C33#455semidirect
645. C32#5202semidirect
646. C32#5242semidirect
647. C32C3×#455semidirect
715. C3#10591664direct (N × H)
716. C3C3×#5202semidirect
717. C3C3×#5242semidirect

Maximal subgroups

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

subgroupindex
C32×#10092
C32×#9512
C3×#638632
C3×#638272
C3×#636642
C3×#635682
C3×#635582
C3×#52423
C3×#52023
#105916643