Finite Group Databasebeta

← C2×C3×#64209 #13180728

Subgroups — C2×C3×#64209 #13180728

Order 1728.

1331 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 1331 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×C32×S4C211yesmaximal, characteristic, complemented
3C2×C3×C3⋊SL(2,ℤ/4)C211yesmaximal, characteristic, complemented
4C3×#64209C214yesmaximal, direct product factor
5C2×C3×GL(2,ℤ/4)—31nomaximal
6C2×#64209C311yesmaximal, characteristic, direct product factor
7C2×C3×#937—31nomaximal
8C22×C32×A4C2211yescharacteristic
9C2×C3×D3×A4—22no—
10C2×C3×D3×A4C2212yescomplemented
11C2×C32×S4—22no—
12C2×C32×S4C2212yescomplemented
13C2×C3×#625—41nomaximal
14C3×C3⋊SL(2,ℤ/4)C2212yescomplemented
15C24×C3×D3D311yescharacteristic, complemented
16C23×C3×A4—31no—
17C22×D3×A4—21no—
18C22×D3×A4C2×C311yescharacteristic, complemented
19C22×C3×S4—21no—
20C22×C3×S4D311yescharacteristic, complemented
21C22×C3×S4C2×C311yescharacteristic, complemented
22C22×C32×D4—31no—
23C22×C3×#67—31no—
24C22×C3×#67—31no—
25C2×C3⋊SL(2,ℤ/4)C2×C311yescharacteristic, complemented
26C3×GL(2,ℤ/4)—34no—
27C2×C3×SL(2,ℤ/4)—31no—
28C2×C3×SL(2,ℤ/4)—61no—
29#64209C2×C314yesdirect product factor
30C2×C3×#217—31no—
31C3×#937—34no—
32C3×#937—34no—
33C2×C3×(C2×D3)⋊C4—31no—
34C2×C3×(C2×D3)⋊C4—31no—
35C22×C32×D3—41no—
36C22×C32×D3—41no—
37C2×C32×A4D412yescomplemented
38C2×C32×A4C2311yescharacteristic
39C3×D3×A4—22no—
40C32×S4—22no—
41C2×C3×C3⋊Dic3—41no—
42C3×#625—44no—
43C2×GL(2,ℤ/4)—31no—
44C2×C3×#120—91no—
45C2×#937—31no—
46C24×C32—31no—
47C24×C32C2×D311yescharacteristic
48C23×C3×D3—22no—
49C23×C3×D3—31no—
50C23×C3×D3—31no—
51C23×C3×D3—32no—
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—24no—
67C2×C3×S4—22no—
68C2×C3×S4—22no—
69C2×C3×S4—22no—
70C2×C3×S4C2×D312yescomplemented
71C2×C3×S4C22×C312yescomplemented
72C2×C32×D4—32no—
73C2×C32×D4—32no—
74C2×C32×D4—62no—
75C2×C32×D4—62no—
76C22×C32×C4—31no—
77C2×C3×#67—34no—
78C2×C3×#67—34no—
79C2×C3×#67—64no—
80C2×C3×#67—62no—
81C2×C3×#67—61no—
82C2×C3×#67—61no—
83C2×C3×#67—121no—
84C22×C3×Dic3—31no—
85C22×C3×Dic3—31no—
86C2×#625—41no—
87C3⋊SL(2,ℤ/4)C22×C312yescomplemented
88C3×SL(2,ℤ/4)—32no—
89C3×SL(2,ℤ/4)—62no—
90C3×#217—32no—
91C3×#217—32no—
92C3×(C2×D3)⋊C4—34no—
93C3×(C2×D3)⋊C4—34no—
94C22×C33—41no—
95C2×C32×D3—42no—
96C2×C32×D3—42no—
97C2×C32×D3—82no—
98C2×C32×D3—82no—
99C32×A4C2×D411yescharacteristic, complemented
100C3×C3⋊Dic3—42no—
101C25×C3—31no—
102C24×D3C3×D311yescharacteristic, complemented
103C23×A4—31no—
104C23×A4—61no—
105C22×S4C3×D311yescharacteristic, complemented
106C22×C3×D4—31no—
107C22×C3×D4—31no—
108C22×C3×D4—61no—
109C22×C3×D4—91no—
110C22×C3×D4—91no—
111C22×#67—31no—
112C22×#67—31no—
113GL(2,ℤ/4)—34no—
114C2×SL(2,ℤ/4)—31no—
115C2×SL(2,ℤ/4)—61no—
116C3×#120—94no—
117C3×#120—94no—
118C2×C3×C22⋊C4—91no—
119C2×C3×C22⋊C4—91no—
120C2×C3×C22⋊C4—91no—
121C2×#217—31no—
122#937—34no—
123#937—34no—
124C2×(C2×D3)⋊C4—31no—
125C2×(C2×D3)⋊C4—31no—
126C23×C32—31no—
127C23×C32—31no—
128C23×C32—32no—
129C23×C32—32no—
130C23×C32—62no—
131C23×C32—62no—
132C23×C32—61no—
133C23×C32—61no—
134C23×C32—121no—
135C23×C32#6712yescomplemented
136C23×C32C22×D311yescharacteristic
137C22×C3×D3—22no—
138C22×C3×D3—32no—
139C22×C3×D3—34no—
140C22×C3×D3—31no—
141C22×C3×D3—32no—
142C22×C3×D3—32no—
143C22×C3×D3—41no—
144C22×C3×D3—41no—
145C22×C3×D3—41no—
146C22×C3×D3—62no—
147C22×C3×D3—62no—
148C22×C3×D3—61no—
149C22×C3×D3—62no—
150C22×C3×D3—64no—
151C22×C3×D3—64no—
152C22×C3×D3—62no—
153C22×C3×D3—81no—
154C22×C3×D3—81no—
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×A4#6712yescomplemented
166C2×C3×A4C3×D412yescomplemented
167C2×C3×A4C22×D311yescharacteristic
168C2×C3×A4C23×C311yescharacteristic
169D3×A4—24no—
170D3×A4—22no—
171C3×S4—24no—
172C3×S4—22no—
173C3×S4—22no—
174C32×D4—64no—
175C32×D4—62no—
176C32×D4—62no—
177C2×C32×C4—32no—
178C2×C32×C4—62no—
179C2×C3⋊Dic3—41no—
180C3×#67—68no—
181C3×#67—64no—
182C3×#67—64no—
183C3×#67—124no—
184C2×C3×Dic3—32no—
185C2×C3×Dic3—32no—
186C2×C3×Dic3—62no—
187C2×C3×Dic3—61no—
188C2×C3×Dic3—61no—
189C2×C3×Dic3—121no—
190C2×C3×Dic3—241no—
191#625—44no—
192C2×#120—91noSylow
193C2×C33—42no—
194C2×C33—41no—
195C32×D3—82no—
196C32×D3—82no—
197C24×C3—21no—
198C24×C3—31no—
199C24×C3—31no—
200C24×C3—32no—
201C24×C3—61no—
202C24×C3—62no—
203C24×C3—91no—
204C24×C3—91no—
205C24×C3—92no—
206C24×C3—182no—
207C24×C3D3211yescharacteristic
208C24×C3C2×C3×D311yescharacteristic
209C23×D3—22no—
210C23×D3—31no—
211C23×D3—31no—
212C23×D3—32no—
213C23×D3—62no—
214C23×D3C2×C3×D312yescomplemented
215C22×A4—21no—
216C22×A4—21no—
217C22×A4—32no—
218C22×A4—41no—
219C22×A4—62no—
220C22×A4—64no—
221C22×A4—62no—
222C22×A4C2×C3×D311yescharacteristic
223C2×S4—22no—
224C2×S4C2×C3×D312yescomplemented
225C2×C3×D4—32no—
226C2×C3×D4—32no—
227C2×C3×D4—32no—
228C2×C3×D4—32no—
229C2×C3×D4—62no—
230C2×C3×D4—62no—
231C2×C3×D4—64no—
232C2×C3×D4—62no—
233C2×C3×D4—62no—
234C2×C3×D4—64no—
235C2×C3×D4—62no—
236C2×C3×D4—62no—
237C2×C3×D4—94no—
238C2×C3×D4—94no—
239C2×C3×D4—181no—
240C2×C3×D4—182no—
241C2×C3×D4—184no—
242C2×C3×D4—181no—
243C22×C3×C4—31no—
244C22×C3×C4—31no—
245C22×C3×C4—61no—
246C22×C3×C4—91no—
247C22×C3×C4—91no—
248C2×#67—34no—
249C2×#67—34no—
250C2×#67—64no—
251C2×#67—62no—
252C2×#67—61no—
253C2×#67—61no—
254C2×#67—121no—
255C22×Dic3—31no—
256C22×Dic3—31no—
257SL(2,ℤ/4)—32no—
258SL(2,ℤ/4)—62no—
259C3×C22⋊C4—94no—
260C3×C22⋊C4—94no—
261C3×C22⋊C4—92no—
262C3×C22⋊C4—92no—
263#217—32no—
264#217—32no—
265(C2×D3)⋊C4—34no—
266(C2×D3)⋊C4—34no—
267C22×C32—32no—
268C22×C32—31no—
269C22×C32—32no—
270C22×C32—32no—
271C22×C32—31no—
272C22×C32—31no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—62no—
276C22×C32—61no—
277C22×C32—62no—
278C22×C32—62no—
279C22×C32—81no—
280C22×C32—81no—
281C22×C32—81no—
282C22×C32—122no—
283C22×C32—122no—
284C22×C32—122no—
285C22×C32—161no—
286C22×C32—242no—
287C22×C32C2×#6711yescharacteristic, complemented
288C22×C32C2×S411yescharacteristic
289C2×C3×D3—22no—
290C2×C3×D3—34no—
291C2×C3×D3—32no—
292C2×C3×D3—42no—
293C2×C3×D3—42no—
294C2×C3×D3—42no—
295C2×C3×D3—62no—
296C2×C3×D3—62no—
297C2×C3×D3—64no—
298C2×C3×D3—64no—
299C2×C3×D3—62no—
300C2×C3×D3—62no—
301C2×C3×D3—82no—
302C2×C3×D3—84no—
303C2×C3×D3—82no—
304C2×C3×D3—82no—
305C2×C3×D3—82no—
306C2×C3×D3—84no—
307C2×C3×D3—82no—
308C2×C3×D3C2×S412yescomplemented
309C3×A4—21no—
310C3×A4—21no—
311C3×A4—21no—
312C3×A4—41no—
313C3×A4C2×#6711yescharacteristic, complemented
314C3×A4C2×C3×D411yescharacteristic, complemented
315C32×C4—62no—
316C3⋊Dic3—42no—
317C3×Dic3—62no—
318C3×Dic3—62no—
319C3×Dic3—122no—
320C3×Dic3—242no—
321C25—31no—
322C22×D4—31no—
323C22×D4—91no—
324C22×D4—91no—
325#120—94no—
326#120—94no—
327C2×C22⋊C4—91no—
328C2×C22⋊C4—91no—
329C2×C22⋊C4—91no—
330C33—41noSylow
331C23×C3—22no—
332C23×C3—21no—
333C23×C3—31no—
334C23×C3—31no—
335C23×C3—31no—
336C23×C3—31no—
337C23×C3—32no—
338C23×C3—32no—
339C23×C3—31no—
340C23×C3—32no—
341C23×C3—32no—
342C23×C3—61no—
343C23×C3—61no—
344C23×C3—62no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—61no—
348C23×C3—62no—
349C23×C3—62no—
350C23×C3—61no—
351C23×C3—62no—
352C23×C3—64no—
353C23×C3—61no—
354C23×C3—61no—
355C23×C3—62no—
356C23×C3—92no—
357C23×C3—92no—
358C23×C3—92no—
359C23×C3—94no—
360C23×C3—91no—
361C23×C3—121no—
362C23×C3—121no—
363C23×C3—121no—
364C23×C3—122no—
365C23×C3—182no—
366C23×C3—182no—
367C23×C3—182no—
368C23×C3—181no—
369C23×C3—184no—
370C23×C3—182no—
371C23×C3—184no—
372C23×C3—241no—
373C23×C3#62512yescomplemented
374C23×C3C3×#6712yescomplemented
375C23×C3C2×D3211yescharacteristic
376C23×C3C22×C3×D311yescharacteristic
377C22×D3—22no—
378C22×D3—32no—
379C22×D3—34no—
380C22×D3—31no—
381C22×D3—32no—
382C22×D3—32no—
383C22×D3—41no—
384C22×D3—62no—
385C22×D3—62no—
386C22×D3—61no—
387C22×D3—62no—
388C22×D3—64no—
389C22×D3—64no—
390C22×D3—62no—
391C22×D3C3×S411yescharacteristic, complemented
392C2×A4—22no—
393C2×A4—22no—
394C2×A4—21no—
395C2×A4—21no—
396C2×A4—42no—
397C2×A4—41no—
398C2×A4—64no—
399C2×A4—62no—
400C2×A4C3×#6712yescomplemented
401C2×A4C22×C3×D311yescharacteristic
402S4—22no—
403C3×D4—64no—
404C3×D4—64no—
405C3×D4—62no—
406C3×D4—64no—
407C3×D4—62no—
408C3×D4—64no—
409C3×D4—68no—
410C3×D4—62no—
411C3×D4—62no—
412C3×D4—184no—
413C3×D4—188no—
414C3×D4—184no—
415C2×C3×C4—32no—
416C2×C3×C4—32no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—64no—
421C2×C3×C4—92no—
422C2×C3×C4—92no—
423C2×C3×C4—182no—
424C2×C3×C4—181no—
425C2×C3×C4—181no—
426#67—68no—
427#67—64no—
428#67—64no—
429#67—124no—
430C2×Dic3—32no—
431C2×Dic3—32no—
432C2×Dic3—62no—
433C2×Dic3—61no—
434C2×Dic3—61no—
435C2×Dic3—121no—
436C2×Dic3—241no—
437C2×C32—31no—
438C2×C32—31no—
439C2×C32—32no—
440C2×C32—42no—
441C2×C32—41no—
442C2×C32—41no—
443C2×C32—42no—
444C2×C32—82no—
445C2×C32—81no—
446C2×C32—82no—
447C2×C32—81no—
448C2×C32—81no—
449C2×C32—82no—
450C2×C32—122no—
451C2×C32—162no—
452C2×C32—161no—
453C2×C32—242no—
454C2×C32GL(2,ℤ/4)12yescomplemented
455C2×C32C22×S411yescharacteristic
456C3×D3—22no—
457C3×D3—62no—
458C3×D3—82no—
459C3×D3—84no—
460C3×D3—82no—
461C3×D3—82no—
462C3×D3—84no—
463C24—31no—
464C24—32no—
465C24—62no—
466C24—91no—
467C24—91no—
468C24—92no—
469C24—182no—
470C24C3×D3211yescharacteristic
471C2×D4—32no—
472C2×D4—32no—
473C2×D4—62no—
474C2×D4—62no—
475C2×D4—94no—
476C2×D4—94no—
477C2×D4—181no—
478C2×D4—182no—
479C2×D4—184no—
480C2×D4—181no—
481C22×C4—31no—
482C22×C4—91no—
483C22×C4—91no—
484C22⋊C4—94no—
485C22⋊C4—94no—
486C22⋊C4—92no—
487C22⋊C4—92no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—32no—
491C22×C3—31no—
492C22×C3—32no—
493C22×C3—31no—
494C22×C3—32no—
495C22×C3—32no—
496C22×C3—31no—
497C22×C3—31no—
498C22×C3—31no—
499C22×C3—31no—
500C22×C3—32no—
501C22×C3—32no—
502C22×C3—32no—
503C22×C3—41no—
504C22×C3—62no—
505C22×C3—61no—
506C22×C3—62no—
507C22×C3—61no—
508C22×C3—62no—
509C22×C3—61no—
510C22×C3—61no—
511C22×C3—61no—
512C22×C3—62no—
513C22×C3—62no—
514C22×C3—62no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—64no—
518C22×C3—62no—
519C22×C3—62no—
520C22×C3—81no—
521C22×C3—81no—
522C22×C3—94no—
523C22×C3—92no—
524C22×C3—122no—
525C22×C3—122no—
526C22×C3—121no—
527C22×C3—122no—
528C22×C3—124no—
529C22×C3—122no—
530C22×C3—122no—
531C22×C3—124no—
532C22×C3—122no—
533C22×C3—122no—
534C22×C3—161no—
535C22×C3—182no—
536C22×C3—182no—
537C22×C3—184no—
538C22×C3—182no—
539C22×C3—184no—
540C22×C3—182no—
541C22×C3—242no—
542C22×C3—242no—
543C22×C3—244no—
544C22×C3C2×#62511yescharacteristic, complemented
545C22×C3C2×C3×#6711yescharacteristic, complemented
546C22×C3D3×S411yescharacteristic
547C22×C3C2×C3×S411yescharacteristic
548C2×D3—22no—
549C2×D3—34no—
550C2×D3—32no—
551C2×D3—42no—
552C2×D3—62no—
553C2×D3—62no—
554C2×D3—64no—
555C2×D3—64no—
556C2×D3—62no—
557C2×D3—62no—
558C2×D3—82no—
559C2×D3C2×C3×S412yescomplemented
560A4—21no—
561A4—21no—
562A4—41no—
563A4C2×C3×#6711yescharacteristic, complemented
564C3×C4—62no—
565C3×C4—62no—
566C3×C4—64no—
567C3×C4—182no—
568C3×C4—182no—
569Dic3—62no—
570Dic3—62no—
571Dic3—122no—
572Dic3—242no—
573C32—41no—
574C32—41no—
575C32—81no—
576C32—81no—
577C32—81no—
578C32—161no—
579C32C2×GL(2,ℤ/4)11yescharacteristic, complemented
580C23—31no—
581C23—31no—
582C23—32no—
583C23—31no—
584C23—32no—
585C23—62no—
586C23—62no—
587C23—61no—
588C23—61no—
589C23—62no—
590C23—92no—
591C23—92no—
592C23—92no—
593C23—94no—
594C23—91no—
595C23—182no—
596C23—182no—
597C23—182no—
598C23—181no—
599C23—184no—
600C23—182no—
601C23—184no—
602C23C3×#62512yescomplemented
603C23C2×C3×D3211yescharacteristic
604D4—64no—
605D4—62no—
606D4—62no—
607D4—184no—
608D4—188no—
609D4—184no—
610C2×C4—32no—
611C2×C4—62no—
612C2×C4—92no—
613C2×C4—92no—
614C2×C4—182no—
615C2×C4—181no—
616C2×C4—181no—
617C2×C3—22no—
618C2×C3—21no—
619C2×C3—31no—
620C2×C3—31no—
621C2×C3—32no—
622C2×C3—31no—
623C2×C3—31no—
624C2×C3—32no—
625C2×C3—42no—
626C2×C3—41no—
627C2×C3—61no—
628C2×C3—61no—
629C2×C3—62no—
630C2×C3—62no—
631C2×C3—82no—
632C2×C3—82no—
633C2×C3—81no—
634C2×C3—81no—
635C2×C3—124no—
636C2×C3—122no—
637C2×C3—122no—
638C2×C3—162no—
639C2×C3—161no—
640C2×C3—182no—
641C2×C3—242no—
642C2×C3—244no—
643C2×C3#6420912yesdirect product factor
644C2×C3C3×GL(2,ℤ/4)12yescomplemented
645C2×C3C2×D3×S411yescharacteristic
646C2×C3C22×C3×S411yescharacteristic
647D3—22no—
648D3—62no—
649D3—82no—
650C22—32no—
651C22—31no—
652C22—32no—
653C22—32no—
654C22—31no—
655C22—31no—
656C22—32no—
657C22—61no—
658C22—62no—
659C22—62no—
660C22—62no—
661C22—62no—
662C22—94no—
663C22—92no—
664C22—122no—
665C22—122no—
666C22—182no—
667C22—182no—
668C22—184no—
669C22—182no—
670C22—184no—
671C22—182no—
672C22C2×C3×#62511yescharacteristic, complemented
673C22C3×D3×S411yescharacteristic
674C4—62no—
675C4—182no—
676C4—182no—
677C3—21no—
678C3—41no—
679C3—81no—
680C3—81no—
681C3—161no—
682C3C2×#6420911yescharacteristic, direct product factor
683C3C2×C3×GL(2,ℤ/4)11yescharacteristic, complemented
684C2—31no—
685C2—31no—
686C2—32no—
687C2—62no—
688C2—122no—
689C2—182no—
690C2C3×#6420912yesdirect product factor
691C2C2×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×C32×S4C2semidirect
3. C2×C3×C3⋊SL(2,ℤ/4)C2semidirect
4. C3×#64209C2direct (N × H)
6. C2×#64209C3direct (N × H)
10. C2×C3×D3×A4C22semidirect
12. C2×C32×S4C22semidirect
14. C3×C3⋊SL(2,ℤ/4)C22semidirect
15. C24×C3×D3D3semidirect
18. C22×D3×A4C2×C3semidirect
20. C22×C3×S4D3semidirect
21. C22×C3×S4C2×C3semidirect
25. C2×C3⋊SL(2,ℤ/4)C2×C3semidirect
29. #64209C2×C3direct (N × H)
37. C2×C32×A4D4semidirect
53. C23×C3×D3C2×D3semidirect
65. C2×D3×A4C22×C3semidirect
70. C2×C3×S4C2×D3semidirect
71. C2×C3×S4C22×C3semidirect
87. C3⋊SL(2,ℤ/4)C22×C3semidirect
99. C32×A4C2×D4semidirect
102. C24×D3C3×D3semidirect
105. C22×S4C3×D3semidirect
135. C23×C32#67semidirect
155. C22×C3×D3S4semidirect
165. C2×C3×A4#67semidirect
166. C2×C3×A4C3×D4semidirect
214. C23×D3C2×C3×D3semidirect
224. C2×S4C2×C3×D3semidirect
287. C22×C32C2×#67semidirect
308. C2×C3×D3C2×S4semidirect
313. C3×A4C2×#67semidirect
314. C3×A4C2×C3×D4semidirect
373. C23×C3#625semidirect
374. C23×C3C3×#67semidirect
391. C22×D3C3×S4semidirect
400. C2×A4C3×#67semidirect
454. C2×C32GL(2,ℤ/4)semidirect
544. C22×C3C2×#625semidirect
545. C22×C3C2×C3×#67semidirect
559. C2×D3C2×C3×S4semidirect
563. A4C2×C3×#67semidirect
579. C32C2×GL(2,ℤ/4)semidirect
602. C23C3×#625semidirect
643. C2×C3#64209direct (N × H)
644. C2×C3C3×GL(2,ℤ/4)semidirect
672. C22C2×C3×#625semidirect
682. C3C2×#64209direct (N × H)
683. C3C2×C3×GL(2,ℤ/4)semidirect
690. C2C3×#64209direct (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×C32×S42
C2×C3×C3⋊SL(2,ℤ/4)2
C3×#642092
C2×C3×GL(2,ℤ/4)3
C2×#642093
C2×C3×#9373
C2×C3×#6254