Finite Group Databasebeta

← C2×C3×#64210 #13180729

Subgroups — C2×C3×#64210 #13180729

Order 1728.

1295 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1295 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C22×C3×D3×A4C211yesmaximal, characteristic, complemented
2C22×C3×C3⋊S4C211yesmaximal, characteristic, complemented
3C2×C32×SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4C3×#64210C214yesmaximal, direct product factor
5C2×C3×GL(2,ℤ/4)—31nomaximal
6C2×#64210C311yesmaximal, characteristic, direct product factor
7C2×C3×#882—31nomaximal
8C22×C32×A4C2211yescharacteristic
9C2×C3×D3×A4—22no—
10C2×C3×D3×A4C2212yescomplemented
11C2×C3×C3⋊S4—22no—
12C2×C3×C3⋊S4C2212yescomplemented
13C2×C3×#626—41nomaximal
14C32×SL(2,ℤ/4)C2212yescomplemented
15C24×C3×D3D311yescharacteristic, complemented
16C23×C3×A4—31no—
17C22×D3×A4—21no—
18C22×D3×A4C2×C311yescharacteristic, complemented
19C22×C3⋊S4C2×C311yescharacteristic, complemented
20C22×C3×S4—31no—
21C22×C3×S4—61no—
22C22×C3×#67—31no—
23C22×C3×D12—31no—
24C22×C3×D12—31no—
25C3×GL(2,ℤ/4)—34no—
26C2×C3×SL(2,ℤ/4)—21no—
27C2×C3×SL(2,ℤ/4)D311yescharacteristic, complemented
28C2×C3×SL(2,ℤ/4)C2×C311yescharacteristic, complemented
29#64210C2×C314yesdirect product factor
30C2×C32×C22⋊C4—31no—
31C2×C3×(C2×D3)⋊C4—31no—
32C2×C3×(C2×D3)⋊C4—31no—
33C3×#882—34no—
34C3×#882—34no—
35C22×C3×C3⋊D3—41no—
36C22×C32×D3—41no—
37C2×C32×A4D412yescomplemented
38C2×C32×A4C2311yescharacteristic
39C3×D3×A4—22no—
40C3×C3⋊S4—22no—
41C2×C32×Dic3—41no—
42C3×#626—44no—
43C2×GL(2,ℤ/4)—31no—
44C2×C3×#120—91no—
45C2×#882—31no—
46C24×C32C2×D311yescharacteristic
47C23×C3×D3—22no—
48C23×C3×D3—31no—
49C23×C3×D3—31no—
50C23×C3×D3—32no—
51C23×C3×D3—31no—
52C23×C3×D3—62no—
53C23×C3×D3C2×D312yescomplemented
54C22×C3×A4—21no—
55C22×C3×A4—21no—
56C22×C3×A4—21no—
57C22×C3×A4—32no—
58C22×C3×A4—41no—
59C22×C3×A4—62no—
60C22×C3×A4C2×D311yescharacteristic
61C22×C3×A4C22×C311yescharacteristic
62C2×D3×A4—24no—
63C2×D3×A4—22no—
64C2×D3×A4—22no—
65C2×D3×A4C22×C312yescomplemented
66C2×C3⋊S4—22no—
67C2×C3⋊S4C22×C312yescomplemented
68C2×C3×S4—32no—
69C2×C3×S4—62no—
70C2×C3×S4—64no—
71C2×C3×S4—62no—
72C22×C32×C4—31no—
73C22×C32×C4—31no—
74C2×C3×#67—32no—
75C2×C3×#67—32no—
76C2×C3×#67—62no—
77C2×C3×#67—62no—
78C2×C3×#67—121no—
79C22×C3×Dic3—31no—
80C2×C3×D12—34no—
81C2×C3×D12—34no—
82C2×C3×D12—64no—
83C2×C3×D12—61no—
84C2×C3×D12—62no—
85C2×C3×D12—61no—
86C2×#626—41no—
87C3×SL(2,ℤ/4)—22no—
88C3×SL(2,ℤ/4)C2×D312yescomplemented
89C3×SL(2,ℤ/4)C22×C312yescomplemented
90C32×C22⋊C4—32no—
91C32×C22⋊C4—32no—
92C3×(C2×D3)⋊C4—34no—
93C3×(C2×D3)⋊C4—34no—
94C22×C33—41no—
95C2×C3×C3⋊D3—42no—
96C2×C3×C3⋊D3—82no—
97C2×C32×D3—42no—
98C2×C32×D3—82no—
99C32×A4C2×D411yescharacteristic, complemented
100C32×Dic3—42no—
101C25×C3—31no—
102C24×D3C3×D311yescharacteristic, complemented
103C23×A4—31no—
104C23×A4—61no—
105C22×S4—31no—
106C22×S4—61no—
107C22×C3×D4—91no—
108C22×C3×D4—91no—
109C22×C3×D4—91no—
110C22×#67—31no—
111C22×D12—31no—
112C22×D12—31no—
113GL(2,ℤ/4)—34no—
114C2×SL(2,ℤ/4)C3×D311yescharacteristic, complemented
115C3×#120—94no—
116C3×#120—94no—
117C2×C3×C22⋊C4—31no—
118C2×C3×C22⋊C4—31no—
119C2×C3×C22⋊C4—61no—
120C2×C3×C22⋊C4—91no—
121C2×C3×C22⋊C4—91no—
122C2×(C2×D3)⋊C4—31no—
123C2×(C2×D3)⋊C4—31no—
124#882—34no—
125#882—34no—
126C23×C32—31no—
127C23×C32—31no—
128C23×C32—32no—
129C23×C32—121no—
130C23×C32#6712yescomplemented
131C23×C32C22×D311yescharacteristic
132C22×C3⋊D3—41no—
133C22×C3×D3—22no—
134C22×C3×D3—32no—
135C22×C3×D3—34no—
136C22×C3×D3—31no—
137C22×C3×D3—32no—
138C22×C3×D3—32no—
139C22×C3×D3—32no—
140C22×C3×D3—41no—
141C22×C3×D3—62no—
142C22×C3×D3—62no—
143C22×C3×D3—61no—
144C22×C3×D3—62no—
145C22×C3×D3—64no—
146C22×C3×D3—64no—
147C22×C3×D3—62no—
148C22×C3×D3—62no—
149C22×C3×D3—61no—
150C22×C3×D3—62no—
151C22×C3×D3—61no—
152C22×C3×D3—81no—
153C22×C3×D3—121no—
154C22×C3×D3—241no—
155C22×C3×D3S411yescharacteristic, complemented
156C2×C3×A4—22no—
157C2×C3×A4—22no—
158C2×C3×A4—21no—
159C2×C3×A4—21no—
160C2×C3×A4—22no—
161C2×C3×A4—21no—
162C2×C3×A4—42no—
163C2×C3×A4—41no—
164C2×C3×A4—62no—
165C2×C3×A4D1212yescomplemented
166C2×C3×A4C3×D412yescomplemented
167C2×C3×A4C22×D311yescharacteristic
168C2×C3×A4C23×C311yescharacteristic
169D3×A4—24no—
170D3×A4—22no—
171C3⋊S4—22no—
172C3×S4—64no—
173C3×S4—62no—
174C2×C32×C4—32no—
175C2×C32×C4—32no—
176C2×C32×C4—62no—
177C2×C32×C4—61no—
178C2×C32×C4—61no—
179C3×#67—64no—
180C3×#67—62no—
181C3×#67—62no—
182C3×#67—124no—
183C2×C3×Dic3—32no—
184C2×C3×Dic3—41no—
185C2×C3×Dic3—41no—
186C2×C3×Dic3—62no—
187C2×C3×Dic3—81no—
188C3×D12—68no—
189C3×D12—64no—
190C3×D12—64no—
191#626—44no—
192C2×#120—91noSylow
193C2×C33—42no—
194C2×C33—41no—
195C3×C3⋊D3—82no—
196C32×D3—82no—
197C24×C3—21no—
198C24×C3—32no—
199C24×C3—62no—
200C24×C3—91no—
201C24×C3—91no—
202C24×C3—92no—
203C24×C3—91no—
204C24×C3—182no—
205C24×C3D3211yescharacteristic
206C24×C3C2×C3×D311yescharacteristic
207C23×D3—22no—
208C23×D3—31no—
209C23×D3—31no—
210C23×D3—32no—
211C23×D3—31no—
212C23×D3—62no—
213C23×D3C2×C3×D312yescomplemented
214C22×A4—21no—
215C22×A4—21no—
216C22×A4—32no—
217C22×A4—41no—
218C22×A4—62no—
219C22×A4—64no—
220C22×A4—62no—
221C22×A4C2×C3×D311yescharacteristic
222C2×S4—32no—
223C2×S4—62no—
224C2×S4—64no—
225C2×S4—62no—
226C2×C3×D4—94no—
227C2×C3×D4—94no—
228C2×C3×D4—92no—
229C2×C3×D4—92no—
230C2×C3×D4—181no—
231C2×C3×D4—182no—
232C2×C3×D4—184no—
233C2×C3×D4—181no—
234C2×C3×D4—182no—
235C2×C3×D4—182no—
236C22×C3×C4—31no—
237C22×C3×C4—31no—
238C22×C3×C4—31no—
239C22×C3×C4—31no—
240C22×C3×C4—61no—
241C22×C3×C4—61no—
242C22×C3×C4—91no—
243C2×#67—32no—
244C2×#67—32no—
245C2×#67—62no—
246C2×#67—62no—
247C2×#67—121no—
248C22×Dic3—31no—
249C2×D12—34no—
250C2×D12—34no—
251C2×D12—64no—
252C2×D12—61no—
253C2×D12—62no—
254C2×D12—61no—
255SL(2,ℤ/4)C2×C3×D312yescomplemented
256C3×C22⋊C4—32no—
257C3×C22⋊C4—32no—
258C3×C22⋊C4—32no—
259C3×C22⋊C4—32no—
260C3×C22⋊C4—62no—
261C3×C22⋊C4—62no—
262C3×C22⋊C4—94no—
263C3×C22⋊C4—94no—
264(C2×D3)⋊C4—34no—
265(C2×D3)⋊C4—34no—
266C22×C32—32no—
267C22×C32—31no—
268C22×C32—32no—
269C22×C32—32no—
270C22×C32—31no—
271C22×C32—31no—
272C22×C32—41no—
273C22×C32—41no—
274C22×C32—61no—
275C22×C32—81no—
276C22×C32—81no—
277C22×C32—81no—
278C22×C32—122no—
279C22×C32—161no—
280C22×C32—242no—
281C22×C32C2×#6711yescharacteristic, complemented
282C22×C32C2×S411yescharacteristic
283C2×C3⋊D3—42no—
284C2×C3⋊D3—82no—
285C2×C3×D3—22no—
286C2×C3×D3—34no—
287C2×C3×D3—32no—
288C2×C3×D3—42no—
289C2×C3×D3—62no—
290C2×C3×D3—62no—
291C2×C3×D3—64no—
292C2×C3×D3—64no—
293C2×C3×D3—62no—
294C2×C3×D3—62no—
295C2×C3×D3—62no—
296C2×C3×D3—62no—
297C2×C3×D3—62no—
298C2×C3×D3—82no—
299C2×C3×D3—84no—
300C2×C3×D3—82no—
301C2×C3×D3—122no—
302C2×C3×D3—122no—
303C2×C3×D3—122no—
304C2×C3×D3—242no—
305C2×C3×D3—242no—
306C2×C3×D3—244no—
307C2×C3×D3C2×S412yescomplemented
308C3×A4—21no—
309C3×A4—21no—
310C3×A4—21no—
311C3×A4—41no—
312C3×A4C2×D1211yescharacteristic, complemented
313C3×A4C2×C3×D411yescharacteristic, complemented
314C32×C4—62no—
315C32×C4—62no—
316C3×Dic3—42no—
317C3×Dic3—42no—
318C3×Dic3—62no—
319C3×Dic3—82no—
320C25—31no—
321C22×D4—91no—
322C22×D4—91no—
323C22×D4—91no—
324#120—94no—
325#120—94no—
326C2×C22⋊C4—31no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—91no—
329C33—41noSylow
330C23×C3—22no—
331C23×C3—21no—
332C23×C3—31no—
333C23×C3—31no—
334C23×C3—31no—
335C23×C3—31no—
336C23×C3—32no—
337C23×C3—32no—
338C23×C3—31no—
339C23×C3—61no—
340C23×C3—61no—
341C23×C3—62no—
342C23×C3—62no—
343C23×C3—92no—
344C23×C3—92no—
345C23×C3—92no—
346C23×C3—94no—
347C23×C3—92no—
348C23×C3—91no—
349C23×C3—121no—
350C23×C3—182no—
351C23×C3—182no—
352C23×C3—182no—
353C23×C3—181no—
354C23×C3—184no—
355C23×C3—182no—
356C23×C3—181no—
357C23×C3—182no—
358C23×C3—182no—
359C23×C3—184no—
360C23×C3—181no—
361C23×C3—241no—
362C23×C3#62612yescomplemented
363C23×C3C3×#6712yescomplemented
364C23×C3C2×D3211yescharacteristic
365C23×C3C22×C3×D311yescharacteristic
366C22×D3—22no—
367C22×D3—32no—
368C22×D3—34no—
369C22×D3—31no—
370C22×D3—32no—
371C22×D3—32no—
372C22×D3—32no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—61no—
376C22×D3—62no—
377C22×D3—64no—
378C22×D3—64no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—61no—
382C22×D3—62no—
383C22×D3—61no—
384C22×D3—121no—
385C22×D3—241no—
386C22×D3C3×S411yescharacteristic, complemented
387C2×A4—22no—
388C2×A4—22no—
389C2×A4—21no—
390C2×A4—21no—
391C2×A4—42no—
392C2×A4—41no—
393C2×A4—64no—
394C2×A4—62no—
395C2×A4C3×D1212yescomplemented
396C2×A4C22×C3×D311yescharacteristic
397S4—64no—
398S4—62no—
399C3×D4—184no—
400C3×D4—188no—
401C3×D4—184no—
402C3×D4—184no—
403C3×D4—182no—
404C3×D4—182no—
405C2×C3×C4—32no—
406C2×C3×C4—32no—
407C2×C3×C4—32no—
408C2×C3×C4—32no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4—61no—
413C2×C3×C4—62no—
414C2×C3×C4—61no—
415C2×C3×C4—61no—
416C2×C3×C4—61no—
417C2×C3×C4—92no—
418C2×C3×C4—121no—
419C2×C3×C4—121no—
420C2×C3×C4—122no—
421C2×C3×C4—182no—
422#67—64no—
423#67—62no—
424#67—62no—
425#67—124no—
426C2×Dic3—32no—
427C2×Dic3—41no—
428C2×Dic3—62no—
429D12—68no—
430D12—64no—
431D12—64no—
432C2×C32—31no—
433C2×C32—31no—
434C2×C32—32no—
435C2×C32—42no—
436C2×C32—41no—
437C2×C32—41no—
438C2×C32—42no—
439C2×C32—81no—
440C2×C32—82no—
441C2×C32—82no—
442C2×C32—81no—
443C2×C32—81no—
444C2×C32—82no—
445C2×C32—162no—
446C2×C32—161no—
447C2×C32—242no—
448C2×C32GL(2,ℤ/4)12yescomplemented
449C2×C32C22×S411yescharacteristic
450C3⋊D3—82no—
451C3×D3—22no—
452C3×D3—62no—
453C3×D3—82no—
454C3×D3—84no—
455C3×D3—122no—
456C3×D3—242no—
457C3×D3—244no—
458C24—32no—
459C24—62no—
460C24—91no—
461C24—91no—
462C24—92no—
463C24—91no—
464C24—182no—
465C24C3×D3211yescharacteristic
466C2×D4—94no—
467C2×D4—94no—
468C2×D4—92no—
469C2×D4—92no—
470C2×D4—181no—
471C2×D4—182no—
472C2×D4—184no—
473C2×D4—181no—
474C2×D4—182no—
475C2×D4—182no—
476C22×C4—31no—
477C22×C4—31no—
478C22×C4—91no—
479C22⋊C4—32no—
480C22⋊C4—32no—
481C22⋊C4—94no—
482C22⋊C4—94no—
483C22×C3—21no—
484C22×C3—21no—
485C22×C3—32no—
486C22×C3—31no—
487C22×C3—32no—
488C22×C3—31no—
489C22×C3—32no—
490C22×C3—32no—
491C22×C3—31no—
492C22×C3—31no—
493C22×C3—31no—
494C22×C3—31no—
495C22×C3—32no—
496C22×C3—32no—
497C22×C3—32no—
498C22×C3—41no—
499C22×C3—61no—
500C22×C3—62no—
501C22×C3—61no—
502C22×C3—62no—
503C22×C3—62no—
504C22×C3—61no—
505C22×C3—61no—
506C22×C3—61no—
507C22×C3—62no—
508C22×C3—81no—
509C22×C3—81no—
510C22×C3—94no—
511C22×C3—92no—
512C22×C3—122no—
513C22×C3—121no—
514C22×C3—161no—
515C22×C3—182no—
516C22×C3—182no—
517C22×C3—184no—
518C22×C3—182no—
519C22×C3—184no—
520C22×C3—182no—
521C22×C3—182no—
522C22×C3—182no—
523C22×C3—182no—
524C22×C3—242no—
525C22×C3—242no—
526C22×C3—244no—
527C22×C3—362no—
528C22×C3—362no—
529C22×C3C2×#62611yescharacteristic, complemented
530C22×C3C2×C3×#6711yescharacteristic, complemented
531C22×C3D3×S411yescharacteristic
532C22×C3C2×C3×S411yescharacteristic
533C2×D3—22no—
534C2×D3—34no—
535C2×D3—32no—
536C2×D3—62no—
537C2×D3—62no—
538C2×D3—64no—
539C2×D3—64no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—62no—
543C2×D3—62no—
544C2×D3—62no—
545C2×D3—122no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—242no—
549C2×D3—242no—
550C2×D3—244no—
551C2×D3C2×C3×S412yescomplemented
552A4—21no—
553A4—21no—
554A4—41no—
555A4C2×C3×D1211yescharacteristic, complemented
556C3×C4—62no—
557C3×C4—62no—
558C3×C4—62no—
559C3×C4—62no—
560C3×C4—122no—
561C3×C4—122no—
562C3×C4—182no—
563Dic3—42no—
564Dic3—62no—
565C32—41no—
566C32—41no—
567C32—81no—
568C32—81no—
569C32—81no—
570C32—161no—
571C32C2×GL(2,ℤ/4)11yescharacteristic, complemented
572C23—31no—
573C23—31no—
574C23—32no—
575C23—31no—
576C23—62no—
577C23—92no—
578C23—92no—
579C23—92no—
580C23—94no—
581C23—92no—
582C23—91no—
583C23—182no—
584C23—182no—
585C23—182no—
586C23—181no—
587C23—184no—
588C23—182no—
589C23—182no—
590C23—182no—
591C23—181no—
592C23—184no—
593C23—181no—
594C23C3×#62612yescomplemented
595C23C2×C3×D3211yescharacteristic
596D4—184no—
597D4—188no—
598D4—184no—
599D4—184no—
600D4—182no—
601D4—182no—
602C2×C4—32no—
603C2×C4—32no—
604C2×C4—62no—
605C2×C4—61no—
606C2×C4—61no—
607C2×C4—92no—
608C2×C4—182no—
609C2×C3—22no—
610C2×C3—21no—
611C2×C3—31no—
612C2×C3—31no—
613C2×C3—32no—
614C2×C3—31no—
615C2×C3—31no—
616C2×C3—32no—
617C2×C3—42no—
618C2×C3—41no—
619C2×C3—61no—
620C2×C3—61no—
621C2×C3—62no—
622C2×C3—62no—
623C2×C3—82no—
624C2×C3—82no—
625C2×C3—81no—
626C2×C3—81no—
627C2×C3—162no—
628C2×C3—161no—
629C2×C3—182no—
630C2×C3—242no—
631C2×C3—244no—
632C2×C3—362no—
633C2×C3#6421012yesdirect product factor
634C2×C3C3×GL(2,ℤ/4)12yescomplemented
635C2×C3C2×D3×S411yescharacteristic
636C2×C3C22×C3×S411yescharacteristic
637D3—22no—
638D3—62no—
639D3—122no—
640D3—242no—
641D3—244no—
642C22—32no—
643C22—31no—
644C22—32no—
645C22—32no—
646C22—31no—
647C22—31no—
648C22—32no—
649C22—61no—
650C22—62no—
651C22—94no—
652C22—92no—
653C22—182no—
654C22—182no—
655C22—184no—
656C22—182no—
657C22—184no—
658C22—182no—
659C22—182no—
660C22—182no—
661C22—182no—
662C22—362no—
663C22—362no—
664C22C2×C3×#62611yescharacteristic, complemented
665C22C3×D3×S411yescharacteristic
666C4—62no—
667C4—62no—
668C4—182no—
669C3—21no—
670C3—41no—
671C3—81no—
672C3—81no—
673C3—161no—
674C3C2×#6421011yescharacteristic, direct product factor
675C3C2×C3×GL(2,ℤ/4)11yescharacteristic, complemented
676C2—31no—
677C2—31no—
678C2—32no—
679C2—62no—
680C2—182no—
681C2—362no—
682C2C3×#6421012yesdirect product factor
683C2C2×C3×D3×S411yescharacteristic
subgroupG/H
center, hypercenterC22×C3D3×S4
commutator, cosocleC2×C3×A4C23×C3
FrattiniC2C2×C3×D3×S4
Fitting, socleC24×C32C2×D3
hypocenterC3×A4C2×C3×D4
LCSG ▷ C2×C3×A4 ▷ C3×A4
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×A4C2semidirect
2. C22×C3×C3⋊S4C2semidirect
3. C2×C32×SL(2,ℤ/4)C2semidirect
4. C3×#64210C2direct (N × H)
6. C2×#64210C3direct (N × H)
10. C2×C3×D3×A4C22semidirect
12. C2×C3×C3⋊S4C22semidirect
14. C32×SL(2,ℤ/4)C22semidirect
15. C24×C3×D3D3semidirect
18. C22×D3×A4C2×C3semidirect
19. C22×C3⋊S4C2×C3semidirect
27. C2×C3×SL(2,ℤ/4)D3semidirect
28. C2×C3×SL(2,ℤ/4)C2×C3semidirect
29. #64210C2×C3direct (N × H)
37. C2×C32×A4D4semidirect
53. C23×C3×D3C2×D3semidirect
65. C2×D3×A4C22×C3semidirect
67. C2×C3⋊S4C22×C3semidirect
88. C3×SL(2,ℤ/4)C2×D3semidirect
89. C3×SL(2,ℤ/4)C22×C3semidirect
99. C32×A4C2×D4semidirect
102. C24×D3C3×D3semidirect
114. C2×SL(2,ℤ/4)C3×D3semidirect
130. C23×C32#67semidirect
155. C22×C3×D3S4semidirect
165. C2×C3×A4D12semidirect
166. C2×C3×A4C3×D4semidirect
213. C23×D3C2×C3×D3semidirect
255. SL(2,ℤ/4)C2×C3×D3semidirect
281. C22×C32C2×#67semidirect
307. C2×C3×D3C2×S4semidirect
312. C3×A4C2×D12semidirect
313. C3×A4C2×C3×D4semidirect
362. C23×C3#626semidirect
363. C23×C3C3×#67semidirect
386. C22×D3C3×S4semidirect
395. C2×A4C3×D12semidirect
448. C2×C32GL(2,ℤ/4)semidirect
529. C22×C3C2×#626semidirect
530. C22×C3C2×C3×#67semidirect
551. C2×D3C2×C3×S4semidirect
555. A4C2×C3×D12semidirect
571. C32C2×GL(2,ℤ/4)semidirect
594. C23C3×#626semidirect
633. C2×C3#64210direct (N × H)
634. C2×C3C3×GL(2,ℤ/4)semidirect
664. C22C2×C3×#626semidirect
674. C3C2×#64210direct (N × H)
675. C3C2×C3×GL(2,ℤ/4)semidirect
682. C2C3×#64210direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×A42
C22×C3×C3⋊S42
C2×C32×SL(2,ℤ/4)2
C3×#642102
C2×C3×GL(2,ℤ/4)3
C2×#642103
C2×C3×#8823
C2×C3×#6264