Finite Group Databasebeta

← C22×C3×C3⋊#1020 #72242702

Subgroups — C22×C3×C3⋊#1020 #72242702

Order 3456.

7258 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 7258 conjugacy classes of subgroups — too many to draw. Only its 162 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×C32×C22⋊A4C211yesmaximal, characteristic, complemented
2C2×C3×C3⋊#1020C216yesmaximal, direct product factor
3C22×C3⋊#1020C311yesmaximal, characteristic, direct product factor
4C22×C3×#1020—33nomaximal
5C22×C3×#953—31nomaximal
6C2×C32×C22⋊A4C2213yescomplemented
7C3×C3⋊#1020C2214yesdirect product factor
8C22×C3×C3⋊S4—43nomaximal
9C26×C32D311yescharacteristic, complemented
10C22×C3×C22⋊A4—21no—
11C22×C3×C22⋊A4—23no—
12C22×C3×C22⋊A4D313yescomplemented
13C22×C3×C22⋊A4C2×C311yescharacteristic, complemented
14C2×C3⋊#1020C2×C316yesdirect product factor
15C2×C3×#1020—318no—
16C23×C3×#67—33no—
17C2×C3×#953—318no—
18C2×C3×#953—36no—
19C22×C3×#217—33no—
20C32×C22⋊A4C2311yescharacteristic, complemented
21C22×C32×A4—43no—
22C22×C32×A4—81no—
23C2×C3×C3⋊S4—418no—
24C22×#1020—33no—
25C22×C3×#120—91no—
26C22×#953—31no—
27C25×C32—33no—
28C25×C32—39no—
29C25×C32—61no—
30C25×C32—63no—
31C25×C32C2×D313yescomplemented
32C24×C3×D3—31no—
33C2×C3×C22⋊A4—29no—
34C2×C3×C22⋊A4—23no—
35C2×C3×C22⋊A4C2×D319yescomplemented
36C2×C3×C22⋊A4C22×C313yescomplemented
37C3⋊#1020C22×C314yesdirect product factor
38C3×#1020—312no—
39C22×C3⋊S4—43no—
40C22×C3×S4—129no—
41C22×C3×#67—318no—
42C22×C3×#67—318no—
43C22×C3×#67—69no—
44C22×C3×#67—63no—
45C22×C3×#67—69no—
46C22×C3×#67—63no—
47C23×C3×Dic3—33no—
48C3×#953—336no—
49C3×#953—324no—
50C3×#953—34no—
51C2×C3×#217—318no—
52C2×C3×#217—318no—
53C22×C3×C3⋊D3—161no—
54C2×C32×A4—49no—
55C2×C32×A4—83no—
56C3×C3⋊S4—412no—
57C26×C3—21no—
58C26×C3C3×D311yescharacteristic, complemented
59C26×C3C3⋊D311yescharacteristic, complemented
60C22×C22⋊A4—23no—
61C22×C22⋊A4C3×D313yescomplemented
62C2×#1020—318no—
63C23×C3×D4—93no—
64C23×#67—33no—
65C2×C3×#120—918no—
66C2×C3×#120—96no—
67C22×C3×C22⋊C4—93no—
68C2×#953—318no—
69C2×#953—36no—
70C22×#217—33no—
71C24×C32—21no—
72C24×C32—31no—
73C24×C32—39no—
74C24×C32—39no—
75C24×C32—33no—
76C24×C32—39no—
77C24×C32—39no—
78C24×C32—39no—
79C24×C32—36no—
80C24×C32—63no—
81C24×C32—63no—
82C24×C32—63no—
83C24×C32—63no—
84C24×C32—618no—
85C24×C32—63no—
86C24×C32—69no—
87C24×C32—618no—
88C24×C32—69no—
89C24×C32—69no—
90C24×C32—62no—
91C24×C32S413yescomplemented
92C24×C32C22×D311yescharacteristic, complemented
93C23×C3×D3—36no—
94C23×C3×D3—69no—
95C23×C3×D3—63no—
96C3×C22⋊A4—21no—
97C3×C22⋊A4—23no—
98C3×C22⋊A4C22×D313yescomplemented
99C3×C22⋊A4C23×C311yescharacteristic, complemented
100C22×C3×A4—43no—
101C22×C3×A4—49no—
102C22×C3×A4—83no—
103C22×C3×A4—81no—
104C22×C3×A4—89no—
105C22×C3×A4—86no—
106C22×C3×A4—82no—
107C22×C3×A4—83no—
108C2×C3⋊S4—418no—
109C2×C3×S4—1254no—
110C2×C3×#67—336no—
111C2×C3×#67—312no—
112C2×C3×#67—618no—
113C2×C3×#67—636no—
114C2×C3×#67—618no—
115C2×C3×#67—618no—
116C2×C3×#67—618no—
117C2×C3×#67—618no—
118C2×C3×#67—618no—
119C22×C3×Dic3—318no—
120C22×C3×Dic3—69no—
121C22×C3×Dic3—63no—
122C3×#217—336no—
123C3×#217—312no—
124C22×#120—91noSylow
125C22×C33—161no—
126C2×C3×C3⋊D3—166no—
127C32×A4—43no—
128C32×A4—81no—
129C25×C3—23no—
130C25×C3—33no—
131C25×C3—33no—
132C25×C3—39no—
133C25×C3—39no—
134C25×C3—63no—
135C25×C3—69no—
136C25×C3—61no—
137C25×C3—61no—
138C25×C3—62no—
139C25×C3—63no—
140C25×C3—63no—
141C25×C3—66no—
142C25×C3—91no—
143C25×C3C2×C3×D313yescomplemented
144C25×C3C2×C3⋊D313yescomplemented
145C24×D3—31no—
146C2×C22⋊A4—29no—
147C2×C22⋊A4C2×C3×D319yescomplemented
148#1020—312no—
149C22×S4—129no—
150C22×C3×D4—918no—
151C22×C3×D4—918no—
152C22×C3×D4—189no—
153C22×C3×D4—183no—
154C22×C3×D4—189no—
155C22×C3×D4—183no—
156C23×C3×C4—93no—
157C22×#67—318no—
158C22×#67—318no—
159C22×#67—69no—
160C22×#67—63no—
161C22×#67—69no—
162C22×#67—63no—
163C23×Dic3—33no—
164C3×#120—936no—
165C3×#120—924no—
166C3×#120—94no—
167C2×C3×C22⋊C4—918no—
168C2×C3×C22⋊C4—918no—
169#953—336no—
170#953—324no—
171#953—34no—
172C2×#217—318no—
173C2×#217—318no—
174C23×C32—23no—
175C23×C32—33no—
176C23×C32—39no—
177C23×C32—33no—
178C23×C32—39no—
179C23×C32—39no—
180C23×C32—318no—
181C23×C32—39no—
182C23×C32—39no—
183C23×C32—39no—
184C23×C32—33no—
185C23×C32—39no—
186C23×C32—61no—
187C23×C32—63no—
188C23×C32—618no—
189C23×C32—618no—
190C23×C32—69no—
191C23×C32—618no—
192C23×C32—69no—
193C23×C32—69no—
194C23×C32—618no—
195C23×C32—618no—
196C23×C32—69no—
197C23×C32—69no—
198C23×C32—618no—
199C23×C32—63no—
200C23×C32—618no—
201C23×C32—66no—
202C23×C32—61no—
203C23×C32C2×S419yescomplemented
204C22×C3⋊D3—161no—
205C22×C3×D3—34no—
206C22×C3×D3—618no—
207C22×C3×D3—618no—
208C22×C3×D3—126no—
209C22×C3×D3—129no—
210C22×C3×D3—121no—
211C22×C3×D3—483no—
212C2×C3×A4—49no—
213C2×C3×A4—427no—
214C2×C3×A4—89no—
215C2×C3×A4—83no—
216C2×C3×A4—827no—
217C2×C3×A4—818no—
218C2×C3×A4—86no—
219C2×C3×A4—89no—
220C3⋊S4—412no—
221C3×S4—1236no—
222C3×#67—636no—
223C3×#67—612no—
224C3×#67—636no—
225C3×#67—612no—
226C2×C3×Dic3—312no—
227C2×C3×Dic3—618no—
228C2×C3×Dic3—618no—
229C26C3×C3⋊D311yescharacteristic, complemented
230C23×D4—93no—
231C2×#120—918no—
232C2×#120—96no—
233C22×C22⋊C4—93no—
234C2×C33—163no—
235C3×C3⋊D3—164no—
236C24×C3—22no—
237C24×C3—21no—
238C24×C3—21no—
239C24×C3—23no—
240C24×C3—21no—
241C24×C3—31no—
242C24×C3—31no—
243C24×C3—39no—
244C24×C3—39no—
245C24×C3—39no—
246C24×C3—33no—
247C24×C3—39no—
248C24×C3—33no—
249C24×C3—39no—
250C24×C3—39no—
251C24×C3—39no—
252C24×C3—39no—
253C24×C3—39no—
254C24×C3—39no—
255C24×C3—36no—
256C24×C3—36no—
257C24×C3—69no—
258C24×C3—69no—
259C24×C3—69no—
260C24×C3—61no—
261C24×C3—69no—
262C24×C3—63no—
263C24×C3—69no—
264C24×C3—66no—
265C24×C3—63no—
266C24×C3—63no—
267C24×C3—66no—
268C24×C3—63no—
269C24×C3—63no—
270C24×C3—66no—
271C24×C3—63no—
272C24×C3—63no—
273C24×C3—63no—
274C24×C3—63no—
275C24×C3—618no—
276C24×C3—618no—
277C24×C3—63no—
278C24×C3—63no—
279C24×C3—69no—
280C24×C3—618no—
281C24×C3—69no—
282C24×C3—618no—
283C24×C3—69no—
284C24×C3—69no—
285C24×C3—69no—
286C24×C3—69no—
287C24×C3—66no—
288C24×C3—66no—
289C24×C3—66no—
290C24×C3—636no—
291C24×C3—618no—
292C24×C3—636no—
293C24×C3—618no—
294C24×C3—618no—
295C24×C3—62no—
296C24×C3—62no—
297C24×C3—64no—
298C24×C3—96no—
299C24×C3—189no—
300C24×C3—183no—
301C24×C3C3×S413yescomplemented
302C24×C3C3⋊S413yescomplemented
303C24×C3C22×C3×D311yescharacteristic, complemented
304C24×C3C22×C3⋊D311yescharacteristic, complemented
305C23×D3—36no—
306C23×D3—69no—
307C23×D3—63no—
308C22⋊A4—23no—
309C22⋊A4C22×C3×D313yescomplemented
310C22×A4—49no—
311C22×A4—83no—
312C22×A4—86no—
313C22×A4—89no—
314C2×S4—1254no—
315C2×C3×D4—936no—
316C2×C3×D4—912no—
317C2×C3×D4—1818no—
318C2×C3×D4—1836no—
319C2×C3×D4—1818no—
320C2×C3×D4—1818no—
321C2×C3×D4—1818no—
322C2×C3×D4—1818no—
323C2×C3×D4—1818no—
324C22×C3×C4—918no—
325C22×C3×C4—189no—
326C22×C3×C4—183no—
327C2×#67—336no—
328C2×#67—312no—
329C2×#67—618no—
330C2×#67—636no—
331C2×#67—618no—
332C2×#67—618no—
333C2×#67—618no—
334C2×#67—618no—
335C2×#67—618no—
336C22×Dic3—318no—
337C22×Dic3—69no—
338C22×Dic3—63no—
339C3×C22⋊C4—936no—
340C3×C22⋊C4—912no—
341#217—336no—
342#217—312no—
343C22×C32—21no—
344C22×C32—39no—
345C22×C32—31no—
346C22×C32—39no—
347C22×C32—36no—
348C22×C32—39no—
349C22×C32—39no—
350C22×C32—33no—
351C22×C32—39no—
352C22×C32—63no—
353C22×C32—63no—
354C22×C32—618no—
355C22×C32—69no—
356C22×C32—618no—
357C22×C32—69no—
358C22×C32—69no—
359C22×C32—63no—
360C22×C32—62no—
361C22×C32—63no—
362C22×C32—63no—
363C22×C32—161no—
364C22×C32—163no—
365C22×C32—323no—
366C22×C32—321no—
367C22×C32C22×S413yescomplemented
368C22×C32#102011yescharacteristic, complemented
369C2×C3⋊D3—166no—
370C2×C3×D3—612no—
371C2×C3×D3—1218no—
372C2×C3×D3—126no—
373C2×C3×D3—4818no—
374C3×A4—43no—
375C3×A4—49no—
376C3×A4—83no—
377C3×A4—81no—
378C3×A4—89no—
379C3×A4—86no—
380C3×A4—82no—
381C3×A4—83no—
382C3×Dic3—612no—
383C25—33no—
384C25—39no—
385C25—61no—
386C25—63no—
387C25—91no—
388C25C2×C3×C3⋊D313yescomplemented
389C22×D4—918no—
390C22×D4—918no—
391C22×D4—189no—
392C22×D4—183no—
393C22×D4—189no—
394C22×D4—183no—
395C23×C4—93no—
396#120—936no—
397#120—924no—
398#120—94no—
399C2×C22⋊C4—918no—
400C2×C22⋊C4—918no—
401C33—161noSylow
402C23×C3—26no—
403C23×C3—23no—
404C23×C3—23no—
405C23×C3—29no—
406C23×C3—33no—
407C23×C3—39no—
408C23×C3—33no—
409C23×C3—39no—
410C23×C3—33no—
411C23×C3—33no—
412C23×C3—39no—
413C23×C3—39no—
414C23×C3—39no—
415C23×C3—39no—
416C23×C3—318no—
417C23×C3—39no—
418C23×C3—39no—
419C23×C3—39no—
420C23×C3—318no—
421C23×C3—39no—
422C23×C3—39no—
423C23×C3—39no—
424C23×C3—33no—
425C23×C3—39no—
426C23×C3—33no—
427C23×C3—39no—
428C23×C3—63no—
429C23×C3—63no—
430C23×C3—69no—
431C23×C3—69no—
432C23×C3—63no—
433C23×C3—69no—
434C23×C3—69no—
435C23×C3—69no—
436C23×C3—69no—
437C23×C3—69no—
438C23×C3—618no—
439C23×C3—61no—
440C23×C3—61no—
441C23×C3—62no—
442C23×C3—62no—
443C23×C3—63no—
444C23×C3—63no—
445C23×C3—66no—
446C23×C3—618no—
447C23×C3—618no—
448C23×C3—618no—
449C23×C3—618no—
450C23×C3—69no—
451C23×C3—618no—
452C23×C3—69no—
453C23×C3—69no—
454C23×C3—618no—
455C23×C3—69no—
456C23×C3—69no—
457C23×C3—69no—
458C23×C3—618no—
459C23×C3—618no—
460C23×C3—618no—
461C23×C3—618no—
462C23×C3—69no—
463C23×C3—69no—
464C23×C3—69no—
465C23×C3—618no—
466C23×C3—69no—
467C23×C3—618no—
468C23×C3—66no—
469C23×C3—63no—
470C23×C3—63no—
471C23×C3—618no—
472C23×C3—636no—
473C23×C3—618no—
474C23×C3—636no—
475C23×C3—636no—
476C23×C3—618no—
477C23×C3—618no—
478C23×C3—618no—
479C23×C3—636no—
480C23×C3—636no—
481C23×C3—636no—
482C23×C3—618no—
483C23×C3—618no—
484C23×C3—66no—
485C23×C3—66no—
486C23×C3—636no—
487C23×C3—612no—
488C23×C3—61no—
489C23×C3—61no—
490C23×C3—94no—
491C23×C3—1818no—
492C23×C3—1818no—
493C23×C3—366no—
494C23×C3—369no—
495C23×C3—361no—
496C23×C3C2×C3×S419yescomplemented
497C23×C3C2×C3⋊S419yescomplemented
498C22×D3—34no—
499C22×D3—618no—
500C22×D3—618no—
501C22×D3—126no—
502C22×D3—129no—
503C22×D3—121no—
504C22×D3—483no—
505C2×A4—427no—
506C2×A4—89no—
507C2×A4—818no—
508C2×A4—827no—
509S4—1236no—
510C3×D4—1836no—
511C3×D4—1812no—
512C3×D4—1836no—
513C3×D4—1812no—
514C2×C3×C4—912no—
515C2×C3×C4—1818no—
516C2×C3×C4—1818no—
517#67—636no—
518#67—612no—
519#67—636no—
520#67—612no—
521C2×Dic3—312no—
522C2×Dic3—618no—
523C2×Dic3—618no—
524C2×C32—33no—
525C2×C32—39no—
526C2×C32—61no—
527C2×C32—63no—
528C2×C32—163no—
529C2×C32—169no—
530C2×C32—329no—
531C2×C32—323no—
532C2×C32C2×#102013yescomplemented
533C3⋊D3—164no—
534C3×D3—124no—
535C3×D3—4812no—
536C24—21no—
537C24—31no—
538C24—39no—
539C24—39no—
540C24—33no—
541C24—39no—
542C24—39no—
543C24—39no—
544C24—36no—
545C24—63no—
546C24—63no—
547C24—63no—
548C24—63no—
549C24—618no—
550C24—63no—
551C24—69no—
552C24—618no—
553C24—69no—
554C24—69no—
555C24—62no—
556C24—96no—
557C24—189no—
558C24—183no—
559C24C3×C3⋊S413yescomplemented
560C24C22×C3×C3⋊D311yescharacteristic, complemented
561C2×D4—936no—
562C2×D4—912no—
563C2×D4—1818no—
564C2×D4—1836no—
565C2×D4—1818no—
566C2×D4—1818no—
567C2×D4—1818no—
568C2×D4—1818no—
569C2×D4—1818no—
570C22×C4—918no—
571C22×C4—189no—
572C22×C4—183no—
573C22⋊C4—936no—
574C22⋊C4—912no—
575C22×C3—22no—
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—23no—
579C22×C3—21no—
580C22×C3—39no—
581C22×C3—39no—
582C22×C3—31no—
583C22×C3—39no—
584C22×C3—31no—
585C22×C3—39no—
586C22×C3—36no—
587C22×C3—36no—
588C22×C3—39no—
589C22×C3—39no—
590C22×C3—39no—
591C22×C3—39no—
592C22×C3—33no—
593C22×C3—39no—
594C22×C3—33no—
595C22×C3—39no—
596C22×C3—69no—
597C22×C3—69no—
598C22×C3—69no—
599C22×C3—61no—
600C22×C3—69no—
601C22×C3—66no—
602C22×C3—63no—
603C22×C3—69no—
604C22×C3—66no—
605C22×C3—66no—
606C22×C3—63no—
607C22×C3—63no—
608C22×C3—63no—
609C22×C3—618no—
610C22×C3—69no—
611C22×C3—618no—
612C22×C3—63no—
613C22×C3—618no—
614C22×C3—69no—
615C22×C3—618no—
616C22×C3—69no—
617C22×C3—69no—
618C22×C3—69no—
619C22×C3—69no—
620C22×C3—66no—
621C22×C3—63no—
622C22×C3—63no—
623C22×C3—66no—
624C22×C3—66no—
625C22×C3—636no—
626C22×C3—618no—
627C22×C3—636no—
628C22×C3—618no—
629C22×C3—618no—
630C22×C3—64no—
631C22×C3—62no—
632C22×C3—62no—
633C22×C3—63no—
634C22×C3—63no—
635C22×C3—63no—
636C22×C3—63no—
637C22×C3—163no—
638C22×C3—1812no—
639C22×C3—323no—
640C22×C3—3618no—
641C22×C3—366no—
642C22×C3C22×C3×S413yescomplemented
643C22×C3C22×C3⋊S413yescomplemented
644C22×C3C3×#102011yescharacteristic, complemented
645C22×C3C3⋊#102011yescharacteristic, direct product factor
646C2×D3—612no—
647C2×D3—1218no—
648C2×D3—126no—
649C2×D3—4818no—
650A4—49no—
651A4—83no—
652A4—86no—
653A4—89no—
654C3×C4—1812no—
655Dic3—612no—
656C32—161no—
657C32—163no—
658C32—323no—
659C32—321no—
660C32C22×#102011yescharacteristic, complemented
661C23—23no—
662C23—33no—
663C23—39no—
664C23—33no—
665C23—39no—
666C23—39no—
667C23—318no—
668C23—39no—
669C23—39no—
670C23—39no—
671C23—33no—
672C23—39no—
673C23—61no—
674C23—63no—
675C23—618no—
676C23—618no—
677C23—69no—
678C23—618no—
679C23—69no—
680C23—69no—
681C23—618no—
682C23—618no—
683C23—69no—
684C23—69no—
685C23—618no—
686C23—63no—
687C23—618no—
688C23—66no—
689C23—61no—
690C23—94no—
691C23—1818no—
692C23—1818no—
693C23—366no—
694C23—369no—
695C23—361no—
696C23C2×C3×C3⋊S419yescomplemented
697D4—1836no—
698D4—1812no—
699D4—1836no—
700D4—1812no—
701C2×C4—912no—
702C2×C4—1818no—
703C2×C4—1818no—
704C2×C3—23no—
705C2×C3—33no—
706C2×C3—39no—
707C2×C3—33no—
708C2×C3—39no—
709C2×C3—63no—
710C2×C3—69no—
711C2×C3—62no—
712C2×C3—66no—
713C2×C3—61no—
714C2×C3—63no—
715C2×C3—61no—
716C2×C3—63no—
717C2×C3—169no—
718C2×C3—329no—
719C2×C3—364no—
720C2×C3C2×C3×#102013yescomplemented
721C2×C3C2×C3⋊#102013yesdirect product factor
722D3—124no—
723D3—4812no—
724C22—21no—
725C22—39no—
726C22—31no—
727C22—39no—
728C22—36no—
729C22—39no—
730C22—39no—
731C22—33no—
732C22—39no—
733C22—63no—
734C22—63no—
735C22—618no—
736C22—69no—
737C22—618no—
738C22—69no—
739C22—69no—
740C22—63no—
741C22—62no—
742C22—63no—
743C22—63no—
744C22—1812no—
745C22—3618no—
746C22—366no—
747C22C22×C3×C3⋊S413yescomplemented
748C22C3×C3⋊#102011yescharacteristic, direct product factor
749C4—1812no—
750C3—21no—
751C3—163no—
752C3—323no—
753C3C22×C3×#102011yescharacteristic, complemented
754C3C22×C3⋊#102011yescharacteristic, direct product factor
755C2—33no—
756C2—39no—
757C2—61no—
758C2—63no—
759C2—364no—
760C2C2×C3×C3⋊#102013yesdirect product factor
subgroupG/H
center, hypercenterC22×C3C3⋊#1020
commutator, cosocle, hypocenterC3×C22⋊A4C23×C3
FrattiniC1G
Fitting, socleC26×C32D3
LCSG ▷ C3×C22⋊A4
UCSC1 ◁ C22×C3

Complements

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

NH ≅ G/Ntype
1. C22×C32×C22⋊A4C2semidirect
2. C2×C3×C3⋊#1020C2direct (N × H)
3. C22×C3⋊#1020C3direct (N × H)
6. C2×C32×C22⋊A4C22semidirect
7. C3×C3⋊#1020C22direct (N × H)
9. C26×C32D3semidirect
12. C22×C3×C22⋊A4D3semidirect
13. C22×C3×C22⋊A4C2×C3semidirect
14. C2×C3⋊#1020C2×C3direct (N × H)
20. C32×C22⋊A4C23semidirect
31. C25×C32C2×D3semidirect
35. C2×C3×C22⋊A4C2×D3semidirect
36. C2×C3×C22⋊A4C22×C3semidirect
37. C3⋊#1020C22×C3direct (N × H)
58. C26×C3C3×D3semidirect
59. C26×C3C3⋊D3semidirect
61. C22×C22⋊A4C3×D3semidirect
91. C24×C32S4semidirect
92. C24×C32C22×D3semidirect
98. C3×C22⋊A4C22×D3semidirect
99. C3×C22⋊A4C23×C3semidirect
143. C25×C3C2×C3×D3semidirect
144. C25×C3C2×C3⋊D3semidirect
147. C2×C22⋊A4C2×C3×D3semidirect
203. C23×C32C2×S4semidirect
229. C26C3×C3⋊D3semidirect
301. C24×C3C3×S4semidirect
302. C24×C3C3⋊S4semidirect
303. C24×C3C22×C3×D3semidirect
304. C24×C3C22×C3⋊D3semidirect
309. C22⋊A4C22×C3×D3semidirect
367. C22×C32C22×S4semidirect
368. C22×C32#1020semidirect
388. C25C2×C3×C3⋊D3semidirect
496. C23×C3C2×C3×S4semidirect
497. C23×C3C2×C3⋊S4semidirect
532. C2×C32C2×#1020semidirect
559. C24C3×C3⋊S4semidirect
560. C24C22×C3×C3⋊D3semidirect
642. C22×C3C22×C3×S4semidirect
643. C22×C3C22×C3⋊S4semidirect
644. C22×C3C3×#1020semidirect
645. C22×C3C3⋊#1020direct (N × H)
660. C32C22×#1020semidirect
696. C23C2×C3×C3⋊S4semidirect
720. C2×C3C2×C3×#1020semidirect
721. C2×C3C2×C3⋊#1020direct (N × H)
747. C22C22×C3×C3⋊S4semidirect
748. C22C3×C3⋊#1020direct (N × H)
753. C3C22×C3×#1020semidirect
754. C3C22×C3⋊#1020direct (N × H)
760. C2C2×C3×C3⋊#1020direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C32×C22⋊A42
C2×C3×C3⋊#10202
C22×C3⋊#10203
C22×C3×#10203
C22×C3×#9533
C22×C3×C3⋊S44