Finite Group Databasebeta

← C3×#10591517 #13158544

Subgroups — C3×#10591517 #13158544

Order 1728.

916 conjugacy classes of subgroups.

The subgroup lattice has 694 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
2C2×C3×#3754C211yesmaximal, characteristic, complemented
3C32×#938C211yesmaximal, characteristic
4C2×C32×#214C211yesmaximal, characteristic, complemented
5C3×#63567C211yesmaximal, characteristic, complemented
6C3×#63565C211yesmaximal, characteristic, complemented
7C3×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
8C3×#5170—31nomaximal
9C3×#5040—31nomaximal
10#10591517C311yesmaximal, characteristic, direct product factor
11C2×C33×D4C2211yescharacteristic
12C2×C3×#634C2211yescharacteristic
13C2×C32×#67—21no—
14C2×C32×C4×D3C2211yescharacteristic
15C2×C32×Dic6C2211yescharacteristic
16C2×C3×#627—21no—
17C2×C3×D3×Dic3—21no—
18C3×D3×Dic6—22no—
19C3×D3×Dic6—22no—
20C3×#3754—22no—
21C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
22C32×#217—21no—
23C32×#214—22no—
24C32×C4⋊Dic3C2211yescharacteristic
25C2×C32×C3⋊C8C2211yescharacteristic
26C2×C3×D3×Q8—31no—
27C22×C3×Dic6—31no—
28C2×D3×Dic6C2×C311yescharacteristic, complemented
29C2×C32×SD16—31no—
30C32×#121—31no—
31C2×#3754C2×C311yescharacteristic, complemented
32C3×#938—21no—
33C3×#938D311yescharacteristic
34C3×#938C2×C311yescharacteristic
35C2×C3×#214—21no—
36C2×C3×#214—31no—
37C2×C3×#214—31no—
38C2×C3×#214—61no—
39C2×C3×#214D311yescharacteristic, complemented
40C2×C3×#214C2×C311yescharacteristic, complemented
41C3×#835—31no—
42C3×#830—31no—
43C3×(C2×D3)⋊C8—31no—
44C3×#816—31no—
45C3×#810—31no—
46C3×#810—31no—
47#63567C2×C311yescharacteristic, complemented
48#63565C2×C311yescharacteristic, complemented
49(C2×D3)⋊(C3⋊C8)C2×C311yescharacteristic, complemented
50C23×C33—21no—
51C22×C32×D3D411yescharacteristic
52C33×D4—21no—
53C33×D4—21no—
54C2×C33×C4C2311yescharacteristic
55C2×C3×C3⋊Dic3—21no—
56C3×#634—21no—
57C3×#634D412yescomplemented
58C32×#67—42no—
59C2×C32×Dic3—21no—
60C2×C32×Dic3—21no—
61C2×C32×Dic3D411yescharacteristic
62C32×C4×D3—21no—
63C32×C4×D3—21no—
64C32×Dic6—21no—
65C32×Dic6D412yescomplemented
66C3×#627—24no—
67C3×D3×Dic3—24no—
68C3×C3⋊(C3⋊C8)—21no—
69C32×C3⋊C8—21no—
70C3×#448—91no—
71#5170—31no—
72#5040—31no—
73C2×C32×Q8—31no—
74C2×C32×D4—21no—
75C2×C32×D4—21no—
76C2×C32×D4—21no—
77C2×C32×D4—41no—
78C2×C32×D4—61no—
79C2×C32×D4C2×D311yescharacteristic
80C2×C32×D4C2×D311yescharacteristic
81C2×C32×D4C22×C311yescharacteristic
82C22×C32×C4—31no—
83C2×#634C22×C311yescharacteristic
84C2×C3×#67—22no—
85C2×C3×#67—21no—
86C2×C3×#67—21no—
87C22×C3×Dic3—61no—
88C3×D3×Q8—62no—
89C3×D3×Q8—62no—
90C2×C3×C4×D3—21no—
91C2×C3×C4×D3—61no—
92C2×C3×C4×D3C2×D311yescharacteristic
93C2×C3×C4×D3C22×C311yescharacteristic
94C2×C3×Dic6—21no—
95C2×C3×Dic6—31no—
96C2×C3×Dic6—31no—
97C2×C3×Dic6—62no—
98C2×C3×Dic6—61no—
99C2×C3×Dic6—61no—
100C2×C3×Dic6—62no—
101C2×C3×Dic6—61no—
102C2×C3×Dic6C2×D311yescharacteristic
103C2×C3×Dic6C22×C311yescharacteristic
104C2×#627—21no—
105C2×D3×Dic3—21no—
106D3×Dic6—22no—
107D3×Dic6—22no—
108C32×SD16—62no—
109C2×C32×C8—31no—
110C32×C4⋊C4—31no—
111C32×C22⋊C4—61no—
112#3754—22no—
113C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
114C3×#217—22no—
115C3×#217—21no—
116C3×#217—21no—
117C3×#214—24no—
118C3×#214—22no—
119C3×#214—22no—
120C3×#214—62no—
121C3×#214—62no—
122C3×#214—64no—
123C3×C4⋊Dic3—21no—
124C3×C4⋊Dic3C2×D311yescharacteristic
125C3×C4⋊Dic3C22×C311yescharacteristic
126C2×C3×C3⋊C8—21no—
127C2×C3×C3⋊C8—31no—
128C2×C3×C3⋊C8—31no—
129C2×C3×C3⋊C8—61no—
130C2×C3×C3⋊C8C2×D311yescharacteristic
131C2×C3×C3⋊C8C22×C311yescharacteristic
132C22×C33—41no—
133C22×C33—41no—
134C22×C33—41no—
135C22×C33C2×D411yescharacteristic
136C2×C32×D3—21no—
137C2×C32×D3—21no—
138C2×C32×D3SD1612yescomplemented
139C33×C4C2×D411yescharacteristic
140C33×C4C2×D411yescharacteristic
141C3×C3⋊Dic3—22no—
142C32×Dic3—22no—
143C32×Dic3—21no—
144C32×Dic3—41no—
145C22×C3×Q8—91no—
146C2×D3×Q8—31no—
147C22×Dic6—31no—
148C2×C3×SD16—31no—
149C2×C3×SD16—31no—
150C2×C3×SD16—61no—
151C2×C3×SD16—91no—
152C3×#121—31no—
153C3×#121—31no—
154C3×#121—61no—
155#938C3×D311yescharacteristic
156C2×#214—31no—
157C2×#214—31no—
158C2×#214—61no—
159C2×#214C3×D311yescharacteristic, complemented
160C3×#103—91no—
161C3×#103—91no—
162C3×C22⋊C8—91no—
163#835—31no—
164#830—31no—
165(C2×D3)⋊C8—31no—
166#816—31no—
167#810—31no—
168#810—31no—
169C23×C32—21no—
170C23×C32—22no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—31no—
174C23×C32—41no—
175C23×C32—41no—
176C23×C32—42no—
177C22×C3×D3—21no—
178C22×C3×D3#6711yescharacteristic
179C22×C3×D3C3×D411yescharacteristic
180C32×Q8—32no—
181C32×Q8—61no—
182C32×D4—21no—
183C32×D4—21no—
184C32×D4—22no—
185C32×D4—22no—
186C32×D4—21no—
187C32×D4—21no—
188C32×D4—21no—
189C32×D4—21no—
190C32×D4—41no—
191C32×D4—41no—
192C32×D4—41no—
193C32×D4—41no—
194C32×D4—42no—
195C32×D4—42no—
196C32×D4—122no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—31no—
201C2×C32×C4—41no—
202C2×C32×C4—61no—
203C2×C32×C4—61no—
204C2×C32×C4—61no—
205C2×C32×C4—61no—
206C2×C32×C4C22×D311yescharacteristic
207C2×C32×C4C22×D311yescharacteristic
208C2×C32×C4C23×C311yescharacteristic
209C2×C3⋊Dic3—21no—
210#634—21no—
211#634C3×D412yescomplemented
212C3×#67—44no—
213C3×#67—42no—
214C3×#67—42no—
215C2×C3×Dic3—21no—
216C2×C3×Dic3—21no—
217C2×C3×Dic3—22no—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—41no—
222C2×C3×Dic3—64no—
223C2×C3×Dic3—61no—
224C2×C3×Dic3—61no—
225C2×C3×Dic3—121no—
226C2×C3×Dic3#6711yescharacteristic
227C2×C3×Dic3C3×D411yescharacteristic
228C3×C4×D3—21no—
229C3×C4×D3—21no—
230C3×C4×D3—21no—
231C3×C4×D3—21no—
232C3×C4×D3—41no—
233C3×C4×D3—41no—
234C3×C4×D3—64no—
235C3×Dic6—21no—
236C3×Dic6—21no—
237C3×Dic6—22no—
238C3×Dic6—32no—
239C3×Dic6—32no—
240C3×Dic6—41no—
241C3×Dic6—62no—
242C3×Dic6—64no—
243C3×Dic6—64no—
244C3×Dic6—61no—
245C3×Dic6—61no—
246C3×Dic6—121no—
247C3×Dic6#6712yescomplemented
248C3×Dic6C3×D412yescomplemented
249#627—24no—
250D3×Dic3—24no—
251C32×C8—61no—
252C3⋊(C3⋊C8)—21no—
253C3×C3⋊C8—22no—
254C3×C3⋊C8—21no—
255C3×C3⋊C8—21no—
256C3×C3⋊C8—62no—
257C3×C3⋊C8—61no—
258C3×C3⋊C8—61no—
259#448—91noSylow
260C2×C33—81no—
261C2×C33#12011yescharacteristic
262C2×C33C2×SD1611yescharacteristic
263C2×C33#13711yescharacteristic
264C32×D3—22no—
265C2×C3×Q8—31no—
266C2×C3×Q8—31no—
267C2×C3×Q8—61no—
268C2×C3×Q8—91no—
269C2×C3×Q8—181no—
270C2×C3×Q8—182no—
271C2×C3×Q8—182no—
272C2×C3×D4—21no—
273C2×C3×D4—21no—
274C2×C3×D4—21no—
275C2×C3×D4—41no—
276C2×C3×D4—61no—
277C2×C3×D4—61no—
278C2×C3×D4—62no—
279C2×C3×D4D3211yescharacteristic
280C2×C3×D4C2×C3×D311yescharacteristic
281C2×C3×D4C2×C3×D311yescharacteristic
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—61no—
285C22×C3×C4—181no—
286C2×#67—21no—
287C22×Dic3—61no—
288D3×Q8—62no—
289D3×Q8—62no—
290C2×C4×D3—61no—
291C2×C4×D3C2×C3×D311yescharacteristic
292C2×Dic6—31no—
293C2×Dic6—31no—
294C2×Dic6—61no—
295C2×Dic6—62no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—62no—
299C2×Dic6C2×C3×D311yescharacteristic
300C3×SD16—62no—
301C3×SD16—62no—
302C3×SD16—64no—
303C3×SD16—182no—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8—61no—
307C2×C3×C8—91no—
308C3×C4⋊C4—31no—
309C3×C4⋊C4—31no—
310C3×C4⋊C4—61no—
311C3×C22⋊C4—61no—
312C3×C22⋊C4—61no—
313C3×C22⋊C4—62no—
314#217—21no—
315#214—22no—
316#214—62no—
317#214—62no—
318#214—64no—
319C4⋊Dic3C2×C3×D311yescharacteristic
320C2×C3⋊C8—31no—
321C2×C3⋊C8—31no—
322C2×C3⋊C8—61no—
323C2×C3⋊C8C2×C3×D311yescharacteristic
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—21no—
327C22×C32—32no—
328C22×C32—41no—
329C22×C32—42no—
330C22×C32—42no—
331C22×C32—42no—
332C22×C32—44no—
333C22×C32—41no—
334C22×C32—41no—
335C22×C32—41no—
336C22×C32—41no—
337C22×C32—41no—
338C22×C32—42no—
339C22×C32—42no—
340C22×C32—41no—
341C22×C32—41no—
342C22×C32—41no—
343C22×C32—41no—
344C22×C32—61no—
345C22×C32—61no—
346C22×C32—81no—
347C22×C32—81no—
348C22×C32—81no—
349C22×C32—81no—
350C22×C32—82no—
351C22×C32—82no—
352C22×C32D3×D411yescharacteristic
353C22×C32C2×#6711yescharacteristic
354C22×C32C2×C3×D411yescharacteristic
355C2×C3×D3—21no—
356C2×C3×D3—21no—
357C2×C3×D3—21no—
358C2×C3×D3—21no—
359C2×C3×D3—22no—
360C2×C3×D3—41no—
361C2×C3×D3—41no—
362C2×C3×D3#21412yescomplemented
363C2×C3×D3C3×SD1612yescomplemented
364C32×C4—21no—
365C32×C4—21no—
366C32×C4—21no—
367C32×C4—21no—
368C32×C4—21no—
369C32×C4—21no—
370C32×C4—41no—
371C32×C4—41no—
372C32×C4—61no—
373C32×C4—62no—
374C32×C4—121no—
375C32×C4D3×D411yescharacteristic
376C32×C4D3×D411yescharacteristic
377C32×C4D3×D411yescharacteristic
378C32×C4C2×#6711yescharacteristic
379C32×C4C2×C3×D411yescharacteristic
380C32×C4C2×C3×D411yescharacteristic
381C3⋊Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3—21no—
384C3×Dic3—22no—
385C3×Dic3—21no—
386C3×Dic3—42no—
387C3×Dic3—41no—
388C3×Dic3—42no—
389C3×Dic3—41no—
390C3×Dic3—41no—
391C3×Dic3—62no—
392C3×Dic3—62no—
393C3×Dic3—122no—
394C22×Q8—91no—
395C2×SD16—31no—
396C2×SD16—91no—
397#121—31no—
398#103—91no—
399#103—91no—
400C22⋊C8—91no—
401C33#44811yescharacteristic, complemented, Sylow
402C23×C3—22no—
403C23×C3—21no—
404C23×C3—21no—
405C23×C3—21no—
406C23×C3—31no—
407C23×C3—31no—
408C23×C3—41no—
409C23×C3—41no—
410C23×C3—42no—
411C23×C3—61no—
412C22×D3C3×#6711yescharacteristic
413C3×Q8—32no—
414C3×Q8—32no—
415C3×Q8—62no—
416C3×Q8—61no—
417C3×Q8—61no—
418C3×Q8—92no—
419C3×Q8—121no—
420C3×Q8—184no—
421C3×Q8—181no—
422C3×D4—22no—
423C3×D4—22no—
424C3×D4—21no—
425C3×D4—21no—
426C3×D4—21no—
427C3×D4—21no—
428C3×D4—21no—
429C3×D4—21no—
430C3×D4—41no—
431C3×D4—41no—
432C3×D4—41no—
433C3×D4—41no—
434C3×D4—42no—
435C3×D4—42no—
436C3×D4—122no—
437C3×D4—122no—
438C3×D4—124no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—41no—
445C2×C3×C4—61no—
446C2×C3×C4—61no—
447C2×C3×C4—61no—
448C2×C3×C4—61no—
449C2×C3×C4—61no—
450C2×C3×C4—61no—
451C2×C3×C4—61no—
452C2×C3×C4—62no—
453C2×C3×C4—61no—
454C2×C3×C4—61no—
455C2×C3×C4—121no—
456C2×C3×C4—121no—
457C2×C3×C4—121no—
458C2×C3×C4—184no—
459C2×C3×C4—181no—
460C2×C3×C4C2×D3211yescharacteristic
461C2×C3×C4C22×C3×D311yescharacteristic
462C2×C3×C4C22×C3×D311yescharacteristic
463#67—42no—
464C2×Dic3—21no—
465C2×Dic3—21no—
466C2×Dic3—64no—
467C2×Dic3—61no—
468C2×Dic3—61no—
469C2×Dic3—121no—
470C2×Dic3C3×#6711yescharacteristic
471C4×D3—21no—
472C4×D3—21no—
473C4×D3—64no—
474Dic6—21no—
475Dic6—32no—
476Dic6—32no—
477Dic6—62no—
478Dic6—64no—
479Dic6—64no—
480Dic6—61no—
481Dic6—61no—
482Dic6—121no—
483Dic6C3×#6712yescomplemented
484C3×C8—62no—
485C3×C8—61no—
486C3×C8—61no—
487C3×C8—181no—
488C3⋊C8—21no—
489C3⋊C8—62no—
490C3⋊C8—61no—
491C3⋊C8—61no—
492C2×C32—21no—
493C2×C32—21no—
494C2×C32—21no—
495C2×C32—21no—
496C2×C32—21no—
497C2×C32—21no—
498C2×C32—21no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—41no—
502C2×C32—41no—
503C2×C32—41no—
504C2×C32—62no—
505C2×C32—82no—
506C2×C32—82no—
507C2×C32—82no—
508C2×C32—84no—
509C2×C32—81no—
510C2×C32—81no—
511C2×C32—81no—
512C2×C32D3×SD1611yescharacteristic
513C2×C32#91511yescharacteristic
514C2×C32C2×#21411yescharacteristic
515C2×C32#93711yescharacteristic
516C2×C32#93711yescharacteristic
517C2×C32#95111yescharacteristic
518C2×C32C3×#12011yescharacteristic
519C2×C32C2×C3×SD1611yescharacteristic
520C2×C32C3×#13711yescharacteristic
521C3×D3—22no—
522C3×D3—22no—
523C3×D3—42no—
524C2×Q8—31no—
525C2×Q8—91no—
526C2×Q8—181no—
527C2×Q8—182no—
528C2×Q8—182no—
529C2×D4—61no—
530C2×D4C3×D3211yescharacteristic
531C22×C4—31no—
532C22×C4—181no—
533SD16—62no—
534SD16—182no—
535C2×C8—31no—
536C2×C8—91no—
537C4⋊C4—31no—
538C22⋊C4—61no—
539C22×C3—21no—
540C22×C3—21no—
541C22×C3—21no—
542C22×C3—32no—
543C22×C3—32no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—42no—
547C22×C3—42no—
548C22×C3—42no—
549C22×C3—44no—
550C22×C3—41no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—41no—
554C22×C3—41no—
555C22×C3—41no—
556C22×C3—41no—
557C22×C3—41no—
558C22×C3—41no—
559C22×C3—41no—
560C22×C3—62no—
561C22×C3—61no—
562C22×C3—61no—
563C22×C3—61no—
564C22×C3—61no—
565C22×C3—81no—
566C22×C3—81no—
567C22×C3—81no—
568C22×C3—81no—
569C22×C3—82no—
570C22×C3—82no—
571C22×C3—121no—
572C22×C3—121no—
573C22×C3D3×#6711yescharacteristic
574C22×C3C3×D3×D411yescharacteristic
575C22×C3C2×C3×#6711yescharacteristic
576C2×D3—21no—
577C2×D3—21no—
578C2×D3C3×#21412yescomplemented
579C3×C4—21no—
580C3×C4—21no—
581C3×C4—21no—
582C3×C4—21no—
583C3×C4—21no—
584C3×C4—21no—
585C3×C4—41no—
586C3×C4—41no—
587C3×C4—61no—
588C3×C4—62no—
589C3×C4—61no—
590C3×C4—62no—
591C3×C4—121no—
592C3×C4—122no—
593C3×C4—122no—
594C3×C4—121no—
595C3×C4—121no—
596C3×C4—182no—
597C3×C4D3×#6711yescharacteristic
598C3×C4#381111yescharacteristic
599C3×C4C3×D3×D411yescharacteristic
600C3×C4C3×D3×D411yescharacteristic
601C3×C4C3×D3×D411yescharacteristic
602C3×C4C2×C3×#6711yescharacteristic
603Dic3—22no—
604Dic3—21no—
605Dic3—41no—
606Dic3—62no—
607Dic3—62no—
608Dic3—122no—
609C32—21no—
610C32—21no—
611C32—21no—
612C32—41no—
613C32#504011yescharacteristic, complemented
614C32#517011yescharacteristic, complemented
615C32C3×#44811yescharacteristic, complemented
616C23—21no—
617C23—31no—
618Q8—32no—
619Q8—61no—
620Q8—92no—
621Q8—184no—
622Q8—181no—
623D4—21no—
624D4—21no—
625D4—122no—
626C2×C4—31no—
627C2×C4—61no—
628C2×C4—61no—
629C2×C4—61no—
630C2×C4—61no—
631C2×C4—184no—
632C2×C4—181no—
633C2×C4C2×C3×D3211yescharacteristic
634C8—61no—
635C8—181no—
636C2×C3—21no—
637C2×C3—21no—
638C2×C3—21no—
639C2×C3—21no—
640C2×C3—21no—
641C2×C3—21no—
642C2×C3—21no—
643C2×C3—21no—
644C2×C3—21no—
645C2×C3—41no—
646C2×C3—41no—
647C2×C3—41no—
648C2×C3—62no—
649C2×C3—62no—
650C2×C3—82no—
651C2×C3—82no—
652C2×C3—82no—
653C2×C3—84no—
654C2×C3—81no—
655C2×C3—81no—
656C2×C3—81no—
657C2×C3—122no—
658C2×C3D3×#21411yescharacteristic
659C2×C3#6392911yescharacteristic
660C2×C3#6398311yescharacteristic
661C2×C3C3×D3×SD1611yescharacteristic
662C2×C3C3×#91511yescharacteristic
663C2×C3C2×C3×#21411yescharacteristic
664C2×C3C3×#93711yescharacteristic
665C2×C3C3×#93711yescharacteristic
666C2×C3C3×#95111yescharacteristic
667D3—22no—
668C22—32no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—61no—
673C22—61no—
674C22C3×D3×#6711yescharacteristic
675C4—61no—
676C4—62no—
677C4—121no—
678C4—182no—
679C4C3×D3×#6711yescharacteristic
680C4C3×#381111yescharacteristic
681C3—21no—
682C3—21no—
683C3—21no—
684C3—41no—
685C3#1059151711yescharacteristic, direct product factor
686C3C3×#504011yescharacteristic, complemented
687C3C3×#517011yescharacteristic, complemented
688C2—62no—
689C2—81no—
690C2C3×D3×#21411yescharacteristic
691C2C3×#6392911yescharacteristic
692C2C3×#6398311yescharacteristic
subgroupG/H
centerC22×C3D3×#67
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC2×C33×D4C22
socleC22×C33C2×D4
prime radicalC32×#938C2
hypercenterC2×C3×D4D32
hypocenterC32C3×#448
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×C4 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×Dic6C2semidirect
2. C2×C3×#3754C2semidirect
4. C2×C32×#214C2semidirect
5. C3×#63567C2semidirect
6. C3×#63565C2semidirect
7. C3×(C2×D3)⋊(C3⋊C8)C2semidirect
10. #10591517C3direct (N × H)
28. C2×D3×Dic6C2×C3semidirect
31. C2×#3754C2×C3semidirect
39. C2×C3×#214D3semidirect
40. C2×C3×#214C2×C3semidirect
47. #63567C2×C3semidirect
48. #63565C2×C3semidirect
49. (C2×D3)⋊(C3⋊C8)C2×C3semidirect
57. C3×#634D4semidirect
65. C32×Dic6D4semidirect
138. C2×C32×D3SD16semidirect
159. C2×#214C3×D3semidirect
211. #634C3×D4semidirect
247. C3×Dic6#67semidirect
248. C3×Dic6C3×D4semidirect
362. C2×C3×D3#214semidirect
363. C2×C3×D3C3×SD16semidirect
401. C33#448semidirect
483. Dic6C3×#67semidirect
578. C2×D3C3×#214semidirect
613. C32#5040semidirect
614. C32#5170semidirect
615. C32C3×#448semidirect
685. C3#10591517direct (N × H)
686. C3C3×#5040semidirect
687. C3C3×#5170semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×Dic62
C2×C3×#37542
C32×#9382
C2×C32×#2142
C3×#635672
C3×#635652
C3×(C2×D3)⋊(C3⋊C8)2
C3×#51703
C3×#50403
#105915173