Finite Group Databasebeta

← C3×D3×C4⋊S4 #13180689

Subgroups — C3×D3×C4⋊S4 #13180689

Order 1728.

1064 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 1064 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×S4C212yesmaximal, complemented
2C3×C4×D3×A4C211yesmaximal, characteristic, complemented
3C3×C4⋊(C3⋊S4)C211yesmaximal, characteristic, complemented
4C32×C4⋊S4C211yesmaximal, characteristic, complemented
5C3×#64207C212yesmaximal, complemented
6C2×C3×C4⋊S4—31nomaximal
7D3×C4⋊S4C311yesmaximal, characteristic, direct product factor
8C3×D3×#121—31nomaximal
9C2×C3×D3×A4C2211yescharacteristic
10C2×C3×C3⋊S4C2212yescomplemented
11C2×C32×S4C2212yescomplemented
12C3×D3×S4—24no—
13C32×C4×A4C2211yescharacteristic, complemented
14C3×D3×D12—41nomaximal
15C3×Dic3×A4C2211yescharacteristic, complemented
16C22×C3×S4—32no—
17C2×D3×S4C2×C312yescomplemented
18C2×C3×D3×D4—31no—
19C2×C3×D3×D4—32no—
20C22×C3×C4×D3D311yescharacteristic, complemented
21C2×C3×C4×A4—31no—
22C4×D3×A4—21no—
23C4×D3×A4C2×C311yescharacteristic, complemented
24C4⋊(C3⋊S4)C2×C311yescharacteristic, complemented
25C3×C4⋊S4—21no—
26C3×C4⋊S4—31no—
27C3×C4⋊S4—32no—
28C3×C4⋊S4—61no—
29C3×C4⋊S4D311yescharacteristic, direct product factor
30C3×C4⋊S4C2×C311yescharacteristic, complemented
31#64207C2×C312yescomplemented
32C32×#121—31no—
33C3×#939—32no—
34C3×#938—31no—
35C3×#930—31no—
36C3×#895—31no—
37C3×D3×C4⋊C4—31no—
38C3×#884—32no—
39C3×D3×C22⋊C4—32no—
40C2×C32×A4C2311yescharacteristic
41C2×C3×D32—42no—
42C3×D3×A4D412yescomplemented
43C3×C3⋊S4—22no—
44C32×S4—22no—
45C3×C4⋊(C3⋊D3)—41no—
46C32×D12—41no—
47C32×C4×D3—41no—
48C3×#626—42no—
49C2×C4⋊S4—31no—
50C2×C3×#121—91no—
51D3×#121—31no—
52C23×C3×D3—32no—
53C23×C3×D3C2×D311yescharacteristic
54C22×C3×A4—31no—
55C2×D3×A4—21no—
56C2×D3×A4C22×C311yescharacteristic
57C2×C3⋊S4C22×C312yescomplemented
58C2×C3×S4—22no—
59C2×C3×S4—32no—
60C2×C3×S4—64no—
61C2×C3×S4—62no—
62C2×C3×S4C2×D312yescomplemented
63C2×C3×S4C22×C312yescomplemented
64D3×S4—24no—
65C2×C32×D4—31no—
66C2×C32×D4—32no—
67C22×C32×C4C2×D311yescharacteristic, complemented
68C2×C3×#67—32no—
69C2×C3×#67—32no—
70C2×C3×#67—32no—
71C22×C3×Dic3C2×D311yescharacteristic, complemented
72C3×D3×D4—61no—
73C3×D3×D4—61no—
74C3×D3×D4—61no—
75C3×D3×D4—64no—
76C3×D3×D4—64no—
77C3×D3×D4—61no—
78C2×C3×D12—32no—
79C2×C3×D12—31no—
80C2×C3×D12—121no—
81C2×C3×C4×D3—31no—
82C2×C3×C4×D3—31no—
83C2×C3×C4×D3—31no—
84C2×C3×C4×D3—31no—
85C2×C3×C4×D3—32no—
86C3×C4×A4—21no—
87C3×C4×A4—21no—
88C3×C4×A4—21no—
89C3×C4×A4—31no—
90C3×C4×A4—41no—
91C3×C4×A4C2×D311yescharacteristic, complemented
92C3×C4×A4C22×C311yescharacteristic, complemented
93D3×D12—41no—
94Dic3×A4—21no—
95Dic3×A4C22×C311yescharacteristic, complemented
96C32×C4⋊C4—31no—
97C32×C22⋊C4—32no—
98C3×#217—32no—
99C3×(C2×D3)⋊C4—32no—
100C3×(C2×D3)⋊C4—32no—
101C3×C4⋊Dic3—31no—
102C3×Dic3⋊C4—32no—
103C2×C3×C3⋊D3—42no—
104C2×C32×D3—41no—
105C2×C32×D3—42no—
106C32×A4C2×D411yescharacteristic, complemented
107C3×D32—84no—
108C33×C4—41no—
109C32×Dic3—41no—
110C22×S4—32no—
111C22×C3×D4—92no—
112C22×C3×D4—91no—
113C23×C3×C4—31no—
114C2×D3×D4—31no—
115C2×D3×D4—32no—
116C22×C4×D3C3×D311yescharacteristic, complemented
117C2×C4×A4—31no—
118C2×C4×A4—61no—
119C4⋊S4—32no—
120C4⋊S4—31no—
121C4⋊S4—61no—
122C4⋊S4C3×D311yescharacteristic, direct product factor
123C3×#121—31no—
124C3×#121—31no—
125C3×#121—61no—
126C3×#121—92no—
127C3×#121—91no—
128C3×#121—92no—
129C3×#121—91no—
130C3×#121—91no—
131C2×C3×C4⋊C4—91no—
132C2×C3×C22⋊C4—92no—
133#939—32no—
134#938—31no—
135#930—31no—
136#895—31no—
137D3×C4⋊C4—31no—
138#884—32no—
139D3×C22⋊C4—32no—
140C23×C32—32no—
141C23×C32C22×D311yescharacteristic
142C22×C3×D3—31no—
143C22×C3×D3—31no—
144C22×C3×D3—32no—
145C22×C3×D3—32no—
146C22×C3×D3—64no—
147C22×C3×D3—62no—
148C22×C3×D3—64no—
149C22×C3×D3—62no—
150C22×C3×D3—122no—
151C22×C3×D3D1212yescomplemented
152C2×C3×A4—21no—
153C2×C3×A4—21no—
154C2×C3×A4—21no—
155C2×C3×A4—32no—
156C2×C3×A4—41no—
157C2×C3×A4C22×D311yescharacteristic
158C2×C3×A4C23×C311yescharacteristic
159C2×D32—42no—
160D3×A4—22no—
161D3×A4C3×D412yescomplemented
162C3⋊S4—22no—
163C3×S4—22no—
164C3×S4—22no—
165C3×S4—42no—
166C3×S4—62no—
167C3×S4—122no—
168C32×D4—61no—
169C32×D4—62no—
170C32×D4—62no—
171C32×D4—61no—
172C2×C32×C4—31no—
173C2×C32×C4—31no—
174C2×C32×C4—32no—
175C2×C32×C4—121no—
176C4⋊(C3⋊D3)—41no—
177C3×#67—62no—
178C3×#67—64no—
179C3×#67—62no—
180C3×#67—62no—
181C3×#67—62no—
182C2×C3×Dic3—31no—
183C2×C3×Dic3—31no—
184C2×C3×Dic3—32no—
185C3×D12—41no—
186C3×D12—41no—
187C3×D12—61no—
188C3×D12—64no—
189C3×D12—61no—
190C3×D12—81no—
191C3×D12—121no—
192C3×D12—122no—
193C3×D12—241no—
194C3×C4×D3—31no—
195C3×C4×D3—31no—
196C3×C4×D3—31no—
197C3×C4×D3—41no—
198C3×C4×D3—61no—
199C3×C4×D3—64no—
200C3×C4×D3—81no—
201C3×C4×D3S411yescharacteristic, complemented
202#626—42no—
203C2×#121—91noSylow
204C2×C33—41no—
205C3×C3⋊D3—82no—
206C32×D3—42no—
207C32×D3—82no—
208C24×C3—31no—
209C24×C3—92no—
210C23×D3—32no—
211C23×D3C2×C3×D311yescharacteristic
212C22×A4—31no—
213C22×A4—61no—
214C2×S4—32no—
215C2×S4—62no—
216C2×S4—64no—
217C2×S4C2×C3×D312yescomplemented
218C2×C3×D4—31no—
219C2×C3×D4—31no—
220C2×C3×D4—32no—
221C2×C3×D4—32no—
222C2×C3×D4—62no—
223C2×C3×D4—61no—
224C2×C3×D4—91no—
225C2×C3×D4—92no—
226C2×C3×D4—92no—
227C2×C3×D4—92no—
228C2×C3×D4—92no—
229C2×C3×D4—181no—
230C2×C3×D4—181no—
231C2×C3×D4—181no—
232C2×C3×D4—181no—
233C2×C3×D4—184no—
234C2×C3×D4—184no—
235C22×C3×C4—21no—
236C22×C3×C4—31no—
237C22×C3×C4—91no—
238C22×C3×C4—91no—
239C22×C3×C4—91no—
240C22×C3×C4—91no—
241C22×C3×C4—92no—
242C22×C3×C4D3211yescharacteristic, complemented
243C22×C3×C4C2×C3×D311yescharacteristic, complemented
244C2×#67—32no—
245C2×#67—32no—
246C2×#67—32no—
247C22×Dic3C2×C3×D311yescharacteristic, complemented
248D3×D4—61no—
249D3×D4—61no—
250D3×D4—61no—
251D3×D4—64no—
252D3×D4—64no—
253D3×D4—61no—
254C2×D12—32no—
255C2×D12—31no—
256C2×D12—121no—
257C2×C4×D3—31no—
258C2×C4×D3—31no—
259C2×C4×D3—31no—
260C2×C4×D3—31no—
261C2×C4×D3—32no—
262C4×A4—21no—
263C4×A4—21no—
264C4×A4—31no—
265C4×A4—41no—
266C4×A4—61no—
267C4×A4C2×C3×D311yescharacteristic, complemented
268C3×C4⋊C4—31no—
269C3×C4⋊C4—31no—
270C3×C4⋊C4—61no—
271C3×C4⋊C4—92no—
272C3×C4⋊C4—91no—
273C3×C22⋊C4—32no—
274C3×C22⋊C4—32no—
275C3×C22⋊C4—62no—
276C3×C22⋊C4—92no—
277C3×C22⋊C4—92no—
278C3×C22⋊C4—92no—
279#217—32no—
280(C2×D3)⋊C4—32no—
281(C2×D3)⋊C4—32no—
282C4⋊Dic3—31no—
283Dic3⋊C4—32no—
284C22×C32—31no—
285C22×C32—31no—
286C22×C32—62no—
287C22×C32—62no—
288C22×C32—62no—
289C22×C32—121no—
290C22×C32C2×D1211yescharacteristic, complemented
291C2×C3⋊D3—42no—
292C2×C3×D3—31no—
293C2×C3×D3—32no—
294C2×C3×D3—32no—
295C2×C3×D3—32no—
296C2×C3×D3—42no—
297C2×C3×D3—42no—
298C2×C3×D3—41no—
299C2×C3×D3—61no—
300C2×C3×D3—62no—
301C2×C3×D3—62no—
302C2×C3×D3—62no—
303C2×C3×D3—82no—
304C2×C3×D3—81no—
305C2×C3×D3—122no—
306C2×C3×D3—124no—
307C2×C3×D3—124no—
308C2×C3×D3—242no—
309C2×C3×D3—244no—
310C2×C3×D3C2×S411yescharacteristic
311C3×A4—21no—
312C3×A4—21no—
313C3×A4—21no—
314C3×A4—41no—
315C3×A4D3×D411yescharacteristic, complemented
316C3×A4C2×C3×D411yescharacteristic, complemented
317D32—84no—
318C32×C4—31no—
319C32×C4—41no—
320C32×C4—41no—
321C32×C4—62no—
322C32×C4—81no—
323C32×C4—81no—
324C32×C4—81no—
325C32×C4—121no—
326C32×C4—161no—
327C32×C4C2×S411yescharacteristic, complemented
328C3×Dic3—31no—
329C3×Dic3—41no—
330C3×Dic3—62no—
331C3×Dic3—81no—
332C3×Dic3C2×S411yescharacteristic, complemented
333C22×D4—92no—
334C22×D4—91no—
335C23×C4—31no—
336#121—31no—
337#121—92no—
338#121—91no—
339#121—92no—
340#121—91no—
341#121—91no—
342C2×C4⋊C4—91no—
343C2×C22⋊C4—92no—
344C33—41noSylow
345C23×C3—21no—
346C23×C3—32no—
347C23×C3—32no—
348C23×C3—32no—
349C23×C3—62no—
350C23×C3—91no—
351C23×C3—91no—
352C23×C3—92no—
353C23×C3—92no—
354C23×C3—182no—
355C23×C3—184no—
356C23×C3—182no—
357C23×C3—184no—
358C23×C3C2×D3211yescharacteristic
359C23×C3C22×C3×D311yescharacteristic
360C22×D3—31no—
361C22×D3—31no—
362C22×D3—32no—
363C22×D3—32no—
364C22×D3—62no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—62no—
368C22×D3—122no—
369C22×D3C3×D1212yescomplemented
370C2×A4—21no—
371C2×A4—21no—
372C2×A4—32no—
373C2×A4—41no—
374C2×A4—62no—
375C2×A4C22×C3×D311yescharacteristic
376S4—22no—
377S4—62no—
378S4—122no—
379C3×D4—61no—
380C3×D4—61no—
381C3×D4—62no—
382C3×D4—62no—
383C3×D4—62no—
384C3×D4—62no—
385C3×D4—61no—
386C3×D4—61no—
387C3×D4—121no—
388C3×D4—121no—
389C3×D4—122no—
390C3×D4—122no—
391C3×D4—182no—
392C3×D4—181no—
393C3×D4—184no—
394C3×D4—182no—
395C3×D4—182no—
396C3×D4—184no—
397C3×D4—182no—
398C3×D4—181no—
399C2×C3×C4—31no—
400C2×C3×C4—31no—
401C2×C3×C4—31no—
402C2×C3×C4—31no—
403C2×C3×C4—31no—
404C2×C3×C4—32no—
405C2×C3×C4—32no—
406C2×C3×C4—61no—
407C2×C3×C4—61no—
408C2×C3×C4—62no—
409C2×C3×C4—91no—
410C2×C3×C4—91no—
411C2×C3×C4—91no—
412C2×C3×C4—91no—
413C2×C3×C4—91no—
414C2×C3×C4—92no—
415C2×C3×C4—121no—
416C2×C3×C4—181no—
417C2×C3×C4—184no—
418C2×C3×C4—241no—
419#67—62no—
420#67—64no—
421#67—62no—
422#67—62no—
423#67—62no—
424C2×Dic3—31no—
425C2×Dic3—31no—
426C2×Dic3—32no—
427D12—41no—
428D12—61no—
429D12—64no—
430D12—61no—
431D12—121no—
432D12—122no—
433D12—241no—
434C4×D3—31no—
435C4×D3—31no—
436C4×D3—31no—
437C4×D3—61no—
438C4×D3—64no—
439C4×D3C3×S411yescharacteristic, complemented
440C2×C32—31no—
441C2×C32—31no—
442C2×C32—41no—
443C2×C32—41no—
444C2×C32—81no—
445C2×C32—81no—
446C2×C32—81no—
447C2×C32—122no—
448C2×C32—122no—
449C2×C32—161no—
450C2×C32C22×S411yescharacteristic
451C3⋊D3—82no—
452C3×D3—32no—
453C3×D3—42no—
454C3×D3—82no—
455C3×D3—82no—
456C3×D3—82no—
457C3×D3—122no—
458C3×D3—162no—
459C3×D3—242no—
460C3×D3—482no—
461C3×D3C4⋊S412yesdirect product factor
462C24—31no—
463C24—92no—
464C2×D4—31no—
465C2×D4—32no—
466C2×D4—91no—
467C2×D4—92no—
468C2×D4—92no—
469C2×D4—92no—
470C2×D4—92no—
471C2×D4—181no—
472C2×D4—181no—
473C2×D4—181no—
474C2×D4—181no—
475C2×D4—184no—
476C2×D4—184no—
477C22×C4—31no—
478C22×C4—91no—
479C22×C4—91no—
480C22×C4—91no—
481C22×C4—91no—
482C22×C4—92no—
483C22×C4C3×D3211yescharacteristic, complemented
484C4⋊C4—31no—
485C4⋊C4—92no—
486C4⋊C4—91no—
487C22⋊C4—32no—
488C22⋊C4—92no—
489C22⋊C4—92no—
490C22⋊C4—92no—
491C22×C3—21no—
492C22×C3—31no—
493C22×C3—31no—
494C22×C3—31no—
495C22×C3—31no—
496C22×C3—31no—
497C22×C3—61no—
498C22×C3—61no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—62no—
502C22×C3—62no—
503C22×C3—62no—
504C22×C3—62no—
505C22×C3—92no—
506C22×C3—92no—
507C22×C3—92no—
508C22×C3—91no—
509C22×C3—121no—
510C22×C3—122no—
511C22×C3—122no—
512C22×C3—122no—
513C22×C3—181no—
514C22×C3—182no—
515C22×C3—182no—
516C22×C3—182no—
517C22×C3—241no—
518C22×C3—364no—
519C22×C3—364no—
520C22×C3D3×D1211yescharacteristic, complemented
521C22×C3C2×C3×D1211yescharacteristic, complemented
522C2×D3—31no—
523C2×D3—32no—
524C2×D3—32no—
525C2×D3—32no—
526C2×D3—42no—
527C2×D3—61no—
528C2×D3—62no—
529C2×D3—62no—
530C2×D3—62no—
531C2×D3—122no—
532C2×D3—124no—
533C2×D3—124no—
534C2×D3—242no—
535C2×D3—244no—
536C2×D3C2×C3×S411yescharacteristic
537A4—21no—
538A4—21no—
539A4—41no—
540A4C3×D3×D411yescharacteristic, complemented
541C3×C4—21no—
542C3×C4—31no—
543C3×C4—31no—
544C3×C4—31no—
545C3×C4—41no—
546C3×C4—61no—
547C3×C4—62no—
548C3×C4—62no—
549C3×C4—81no—
550C3×C4—81no—
551C3×C4—91no—
552C3×C4—121no—
553C3×C4—122no—
554C3×C4—161no—
555C3×C4—182no—
556C3×C4—241no—
557C3×C4D3×S411yescharacteristic, complemented
558C3×C4C2×C3×S411yescharacteristic, complemented
559Dic3—31no—
560Dic3—62no—
561Dic3C2×C3×S411yescharacteristic, complemented
562C32—41no—
563C32—41no—
564C32—81no—
565C32—81no—
566C32—81no—
567C32—161no—
568C32C2×C4⋊S411yescharacteristic, complemented
569C23—32no—
570C23—32no—
571C23—91no—
572C23—91no—
573C23—92no—
574C23—92no—
575C23—182no—
576C23—184no—
577C23—182no—
578C23—184no—
579C23C2×C3×D3211yescharacteristic
580D4—61no—
581D4—62no—
582D4—62no—
583D4—61no—
584D4—182no—
585D4—181no—
586D4—184no—
587D4—182no—
588D4—182no—
589D4—184no—
590D4—182no—
591D4—181no—
592C2×C4—31no—
593C2×C4—31no—
594C2×C4—31no—
595C2×C4—32no—
596C2×C4—91no—
597C2×C4—91no—
598C2×C4—91no—
599C2×C4—91no—
600C2×C4—91no—
601C2×C4—92no—
602C2×C4—181no—
603C2×C4—184no—
604C2×C3—21no—
605C2×C3—31no—
606C2×C3—31no—
607C2×C3—32no—
608C2×C3—31no—
609C2×C3—31no—
610C2×C3—41no—
611C2×C3—61no—
612C2×C3—61no—
613C2×C3—81no—
614C2×C3—81no—
615C2×C3—92no—
616C2×C3—122no—
617C2×C3—122no—
618C2×C3—122no—
619C2×C3—161no—
620C2×C3—242no—
621C2×C3—242no—
622C2×C3—362no—
623C2×C3C2×D3×S411yescharacteristic
624C2×C3C22×C3×S411yescharacteristic
625D3—32no—
626D3—82no—
627D3—122no—
628D3—242no—
629D3—482no—
630D3C3×C4⋊S412yesdirect product factor
631C22—31no—
632C22—31no—
633C22—31no—
634C22—62no—
635C22—62no—
636C22—62no—
637C22—92no—
638C22—92no—
639C22—92no—
640C22—91no—
641C22—181no—
642C22—182no—
643C22—182no—
644C22—182no—
645C22—364no—
646C22—364no—
647C22C3×D3×D1211yescharacteristic, complemented
648C4—31no—
649C4—31no—
650C4—62no—
651C4—91no—
652C4—182no—
653C4C3×D3×S411yescharacteristic, complemented
654C3—21no—
655C3—41no—
656C3—81no—
657C3—81no—
658C3—161no—
659C3D3×C4⋊S411yescharacteristic, direct product factor
660C3C2×C3×C4⋊S411yescharacteristic, complemented
661C2—31no—
662C2—31no—
663C2—32no—
664C2—92no—
665C2—122no—
666C2—362no—
667C2C2×C3×D3×S411yescharacteristic
subgroupG/H
centerC2×C3C2×D3×S4
commutator, cosocleC2×C3×A4C23×C3
FrattiniC2C2×C3×D3×S4
FittingC22×C32×C4C2×D3
socleC23×C32C22×D3
hypercenterC3×C4D3×S4
hypocenterC3×A4C2×C3×D4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C2×C3 ◁ C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×D3×S4C2semidirect
2. C3×C4×D3×A4C2semidirect
3. C3×C4⋊(C3⋊S4)C2semidirect
4. C32×C4⋊S4C2semidirect
5. C3×#64207C2semidirect
7. D3×C4⋊S4C3direct (N × H)
10. C2×C3×C3⋊S4C22semidirect
11. C2×C32×S4C22semidirect
13. C32×C4×A4C22semidirect
15. C3×Dic3×A4C22semidirect
17. C2×D3×S4C2×C3semidirect
20. C22×C3×C4×D3D3semidirect
23. C4×D3×A4C2×C3semidirect
24. C4⋊(C3⋊S4)C2×C3semidirect
29. C3×C4⋊S4D3direct (N × H)
30. C3×C4⋊S4C2×C3semidirect
31. #64207C2×C3semidirect
42. C3×D3×A4D4semidirect
57. C2×C3⋊S4C22×C3semidirect
62. C2×C3×S4C2×D3semidirect
63. C2×C3×S4C22×C3semidirect
67. C22×C32×C4C2×D3semidirect
71. C22×C3×Dic3C2×D3semidirect
91. C3×C4×A4C2×D3semidirect
92. C3×C4×A4C22×C3semidirect
95. Dic3×A4C22×C3semidirect
106. C32×A4C2×D4semidirect
116. C22×C4×D3C3×D3semidirect
122. C4⋊S4C3×D3direct (N × H)
151. C22×C3×D3D12semidirect
161. D3×A4C3×D4semidirect
201. C3×C4×D3S4semidirect
217. C2×S4C2×C3×D3semidirect
242. C22×C3×C4D32semidirect
243. C22×C3×C4C2×C3×D3semidirect
247. C22×Dic3C2×C3×D3semidirect
267. C4×A4C2×C3×D3semidirect
290. C22×C32C2×D12semidirect
315. C3×A4D3×D4semidirect
316. C3×A4C2×C3×D4semidirect
327. C32×C4C2×S4semidirect
332. C3×Dic3C2×S4semidirect
369. C22×D3C3×D12semidirect
439. C4×D3C3×S4semidirect
461. C3×D3C4⋊S4direct (N × H)
483. C22×C4C3×D32semidirect
520. C22×C3D3×D12semidirect
521. C22×C3C2×C3×D12semidirect
540. A4C3×D3×D4semidirect
557. C3×C4D3×S4semidirect
558. C3×C4C2×C3×S4semidirect
561. Dic3C2×C3×S4semidirect
568. C32C2×C4⋊S4semidirect
630. D3C3×C4⋊S4direct (N × H)
647. C22C3×D3×D12semidirect
653. C4C3×D3×S4semidirect
659. C3D3×C4⋊S4direct (N × H)
660. C3C2×C3×C4⋊S4semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×S42
C3×C4×D3×A42
C3×C4⋊(C3⋊S4)2
C32×C4⋊S42
C3×#642072
C2×C3×C4⋊S43
D3×C4⋊S43
C3×D3×#1213
C3×D3×D124