Finite Group Databasebeta

← C3×#24387 #10642994

Subgroups — C3×#24387 #10642994

Order 768.

1626 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic, complemented
2C2×C3×#468C212yesmaximal, complemented
3C2×C3×#448C211yesmaximal, characteristic, complemented
4C2×C3×#407C211yesmaximal, characteristic, complemented
5C3×#2847C211yesmaximal, characteristic
6C3×#2036C212yesmaximal, complemented
7C3×#2000C212yesmaximal, complemented
8C3×#1894C212yesmaximal, complemented
9C3×#1874C211yesmaximal, characteristic, complemented
10C3×#1852C211yesmaximal, characteristic, complemented
11C3×#1787C211yesmaximal, characteristic, complemented
12#24387C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C22×C3×SD16C2212yescomplemented
16C22×C3×M16C2212yes—
17C2×C3×C22⋊Q8—21no—
18C2×C3×C22⋊Q8—21no—
19C2×C3×C22⋊Q8—28no—
20C2×C3×C22⋊Q8C2212yes—
21C2×C3×C22⋊Q8C2212yes—
22C2×C3×#121C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24C2×C3×#121C2211yescharacteristic
25C2×C3×#120—21no—
26C22×C3×C4⋊C4—21no—
27C22×C3×C4⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4—21no—
29C3×#468—28no—
30C3×#448—24no—
31C2×C3×#107C2212yescomplemented
32C2×C3×#103C2212yescomplemented
33C2×C3×#103C2212yescomplemented
34C2×C3×#103C2212yescomplemented
35C2×C3×#102C2212yescomplemented
36C3×#407—24no—
37C2×C3×C22⋊C8C2212yes—
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C3×#386—21no—
41C3×#386—21no—
42C3×#386—21no—
43C3×#380C2211yescharacteristic
44C3×#380C2211yescharacteristic
45C3×#380C2211yescharacteristic
46C3×#340C2212yescomplemented
47C3×#340C2212yescomplemented
48C22×C22⋊Q8C2×C311yescharacteristic, complemented
49C2×#468C2×C312yescomplemented
50C2×#448C2×C311yescharacteristic, complemented
51C2×#407C2×C311yescharacteristic, complemented
52#2847C2×C311yescharacteristic
53#2036C2×C312yescomplemented
54#2000C2×C312yescomplemented
55#1894C2×C312yescomplemented
56#1874C2×C311yescharacteristic, complemented
57#1852C2×C311yescharacteristic, complemented
58#1787C2×C311yescharacteristic, complemented
59C25×C3D411yescharacteristic
60C22×C3×Q8—24no—
61C22×C3×Q8—21no—
62C22×C3×Q8—22no—
63C22×C3×Q8—22no—
64C22×C3×Q8—42no—
65C22×C3×Q8C2312yes—
66C22×C3×D4—21no—
67C22×C3×D4—21no—
68C22×C3×D4—21no—
69C22×C3×D4C2311yescharacteristic
70C23×C3×C4—21no—
71C23×C3×C4—21no—
72C23×C3×C4—22no—
73C23×C3×C4—24no—
74C23×C3×C4—22no—
75C23×C3×C4—42no—
76C23×C3×C4D411yescharacteristic
77C23×C3×C4D411yescharacteristic
78C23×C3×C4D411yescharacteristic
79C23×C3×C4C2311yescharacteristic
80C23×C3×C4C2311yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C2×C3×SD16—24no—
83C2×C3×SD16—24no—
84C2×C3×SD16—42no—
85C2×C3×M16—24no—
86C2×C3×M16—24no—
87C2×C3×M16—42no—
88C22×C3×C8C2312yes—
89C22×C3×C8C2312yes—
90C3×C22⋊Q8—28no—
91C3×C22⋊Q8—28no—
92C3×C22⋊Q8—24no—
93C3×C22⋊Q8—24no—
94C3×C22⋊Q8—24no—
95C3×C22⋊Q8D418yescomplemented
96C3×#121—22no—
97C3×#121—24no—
98C3×#121—22no—
99C3×#121—42no—
100C3×#120—44no—
101C2×C3×C4⋊C4—28no—
102C2×C3×C4⋊C4—22no—
103C2×C3×C4⋊C4—22no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4—24no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2312yes—
110C2×C3×C22⋊C4—28no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—22no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C3×#107—24no—
120C3×#103—24no—
121C3×#103—24no—
122C3×#103—42no—
123C3×#102—24no—
124C3×C22⋊C8—22no—
125C3×C22⋊C8—24no—
126C3×C22⋊C8D414yescomplemented
127C3×#95—21no—
128C3×#95—21no—
129C3×#95—21no—
130C23×Q8C22×C311yescharacteristic
131C24×C4C22×C311yescharacteristic
132C22×SD16C22×C312yescomplemented
133C22×M16C22×C312yes—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—21no—
136C2×C22⋊Q8—28no—
137C2×C22⋊Q8C22×C312yes—
138C2×C22⋊Q8C22×C312yes—
139C2×#121C22×C311yescharacteristic
140C2×#121C22×C311yescharacteristic
141C2×#121C22×C311yescharacteristic
142C2×#120—21no—
143C22×C4⋊C4—21no—
144C22×C4⋊C4C22×C311yescharacteristic
145C22×C22⋊C4—21no—
146#468—28no—
147#448—24no—
148C2×#107C22×C312yescomplemented
149C2×#103C22×C312yescomplemented
150C2×#103C22×C312yescomplemented
151C2×#103C22×C312yescomplemented
152C2×#102C22×C312yescomplemented
153#407—24no—
154C2×C22⋊C8C22×C311yescharacteristic
155C2×C22⋊C8C22×C312yes—
156C2×C22⋊C8C22×C311yescharacteristic
157#386—21no—
158#386—21no—
159#386—21no—
160#380C22×C311yescharacteristic
161#380C22×C311yescharacteristic
162#380C22×C311yescharacteristic
163#340C22×C312yescomplemented
164#340C22×C312yescomplemented
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—22no—
170C24×C3—21no—
171C24×C3—41no—
172C24×C3—41no—
173C24×C3C2×D411yescharacteristic
174C24×C3C2×D411yescharacteristic
175C24×C3C2×D411yescharacteristic
176C2×C3×Q8—24no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8—22no—
180C2×C3×Q8—22no—
181C2×C3×Q8—22no—
182C2×C3×Q8—48no—
183C2×C3×Q8—48no—
184C2×C3×Q8—42no—
185C2×C3×Q8—42no—
186C2×C3×Q8C2×D414yes—
187C2×C3×D4—22no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—22no—
191C2×C3×D4—42no—
192C2×C3×D4—42no—
193C2×C3×D4—42no—
194C2×C3×D4—42no—
195C2×C3×D4—42no—
196C2×C3×D4—42no—
197C2×C3×D4—42no—
198C2×C3×D4—42no—
199C2×C3×D4—42no—
200C22×C3×C4—22no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—24no—
206C22×C3×C4—24no—
207C22×C3×C4—22no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—22no—
211C22×C3×C4—22no—
212C22×C3×C4—22no—
213C22×C3×C4—22no—
214C22×C3×C4—22no—
215C22×C3×C4—21no—
216C22×C3×C4—22no—
217C22×C3×C4—21no—
218C22×C3×C4—22no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—41no—
223C22×C3×C4—41no—
224C22×C3×C4—41no—
225C22×C3×C4—48no—
226C22×C3×C4—48no—
227C22×C3×C4—42no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4—42no—
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D414yes—
234C22×C3×C4C2×D411yescharacteristic
235C22×C3×C4C2×D412yes—
236C22×C3×C4#4112yes—
237C22×C3×C4C2411yescharacteristic
238C3×SD16—48no—
239C3×M16—48no—
240C2×C3×C8—22no—
241C2×C3×C8—22no—
242C2×C3×C8—22no—
243C2×C3×C8—22no—
244C2×C3×C8—22no—
245C2×C3×C8C2×D414yes—
246C3×C4⋊C4—24no—
247C3×C4⋊C4—28no—
248C3×C4⋊C4—28no—
249C3×C4⋊C4—22no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—22no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—22no—
254C3×C4⋊C4C2×D414yes—
255C3×C22⋊C4—28no—
256C3×C22⋊C4—28no—
257C3×C22⋊C4—42no—
258C3×C22⋊C4—42no—
259C3×C22⋊C4—42no—
260C3×C22⋊C4—42no—
261C3×C22⋊C4—42no—
262C3×C22⋊C4—42no—
263C25C3×D411yescharacteristic
264C22×Q8—24no—
265C22×Q8—21no—
266C22×Q8—22no—
267C22×Q8—22no—
268C22×Q8—42no—
269C22×Q8C23×C312yes—
270C22×D4—21no—
271C22×D4—21no—
272C22×D4—21no—
273C22×D4C23×C311yescharacteristic
274C23×C4—21no—
275C23×C4—21no—
276C23×C4—24no—
277C23×C4—22no—
278C23×C4—22no—
279C23×C4—42no—
280C23×C4C3×D411yescharacteristic
281C23×C4C3×D411yescharacteristic
282C23×C4C3×D411yescharacteristic
283C23×C4C23×C311yescharacteristic
284C23×C4C23×C311yescharacteristic
285C23×C4C23×C311yescharacteristic
286C2×SD16—24no—
287C2×SD16—24no—
288C2×SD16—42no—
289C2×M16—24no—
290C2×M16—24no—
291C2×M16—42no—
292C22×C8C23×C312yes—
293C22×C8C23×C312yes—
294C22⋊Q8—28no—
295C22⋊Q8—28no—
296C22⋊Q8—24no—
297C22⋊Q8—24no—
298C22⋊Q8—24no—
299C22⋊Q8C3×D418yescomplemented
300#121—22no—
301#121—24no—
302#121—22no—
303#121—42no—
304#120—44no—
305C2×C4⋊C4—28no—
306C2×C4⋊C4—22no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—24no—
310C2×C4⋊C4C23×C311yescharacteristic
311C2×C4⋊C4C23×C311yescharacteristic
312C2×C4⋊C4C23×C311yescharacteristic
313C2×C4⋊C4C23×C312yes—
314C2×C22⋊C4—28no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—22no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323#107—24no—
324#103—24no—
325#103—24no—
326#103—42no—
327#102—24no—
328C22⋊C8—22no—
329C22⋊C8—24no—
330C22⋊C8C3×D414yescomplemented
331#95—21no—
332#95—21no—
333#95—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—28no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—21no—
351C23×C3—44no—
352C23×C3—44no—
353C23×C3—44no—
354C23×C3—44no—
355C23×C3—44no—
356C23×C3—44no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3#12012yes—
365C23×C3#12112yes—
366C23×C3AGL(1,ℤ/8)12yes—
367C23×C3#13712yes—
368C23×C3#13712yes—
369C23×C3C22×D411yescharacteristic
370C3×Q8—24no—
371C3×Q8—24no—
372C3×Q8—48no—
373C3×Q8—42no—
374C3×Q8—42no—
375C3×D4—42no—
376C3×D4—42no—
377C3×D4—84no—
378C3×D4—84no—
379C3×D4—84no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—24no—
385C2×C3×C4—24no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—24no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—44no—
394C2×C3×C4—44no—
395C2×C3×C4—44no—
396C2×C3×C4—48no—
397C2×C3×C4—48no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—42no—
401C2×C3×C4—42no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4#12012yes—
414C2×C3×C4#12112yes—
415C2×C3×C4C22×D411yescharacteristic
416C2×C3×C4C22×D412yes—
417C2×C3×C4C2×#4111yescharacteristic
418C2×C3×C4H(5,𝔽2)12yes—
419C3×C8—24no—
420C3×C8—42no—
421C24—22no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—21no—
427C24—41no—
428C24—41no—
429C24C2×C3×D411yescharacteristic
430C24C2×C3×D411yescharacteristic
431C24C2×C3×D411yescharacteristic
432C2×Q8—24no—
433C2×Q8—22no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—48no—
439C2×Q8—48no—
440C2×Q8—42no—
441C2×Q8—42no—
442C2×Q8C2×C3×D414yes—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—22no—
447C2×D4—42no—
448C2×D4—42no—
449C2×D4—42no—
450C2×D4—42no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—42no—
456C22×C4—22no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—21no—
472C22×C4—22no—
473C22×C4—21no—
474C22×C4—22no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479C22×C4—41no—
480C22×C4—41no—
481C22×C4—48no—
482C22×C4—48no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4C2×C3×D411yescharacteristic
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D414yes—
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D412yes—
492C22×C4C3×#4112yes—
493C22×C4C24×C311yescharacteristic
494SD16—48no—
495M16—48no—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8C2×C3×D414yes—
502C4⋊C4—24no—
503C4⋊C4—28no—
504C4⋊C4—28no—
505C4⋊C4—22no—
506C4⋊C4—21no—
507C4⋊C4—22no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4C2×C3×D414yes—
511C22⋊C4—28no—
512C22⋊C4—28no—
513C22⋊C4—42no—
514C22⋊C4—42no—
515C22⋊C4—42no—
516C22⋊C4—42no—
517C22⋊C4—42no—
518C22⋊C4—42no—
519C22×C3—22no—
520C22×C3—22no—
521C22×C3—22no—
522C22×C3—22no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—22no—
526C22×C3—22no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—416no—
532C22×C3—41no—
533C22×C3—41no—
534C22×C3—41no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—41no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—81no—
541C22×C3—81no—
542C22×C3—81no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—81no—
547C22×C3#46814yescomplemented
548C22×C3C2×#12011yescharacteristic
549C22×C3C2×#12111yescharacteristic
550C22×C3#53411yescharacteristic
551C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
552C22×C3C2×#13711yescharacteristic
553C22×C3C2×#13711yescharacteristic
554C22×C3#57511yescharacteristic
555C3×C4—22no—
556C3×C4—22no—
557C3×C4—41no—
558C3×C4—44no—
559C3×C4—44no—
560C3×C4—81no—
561C3×C4—81no—
562C3×C4—81no—
563C3×C4D4212yes—
564C3×C4#54612yes—
565C23—21no—
566C23—21no—
567C23—21no—
568C23—21no—
569C23—28no—
570C23—21no—
571C23—21no—
572C23—21no—
573C23—21no—
574C23—21no—
575C23—21no—
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—44no—
583C23—44no—
584C23—44no—
585C23—44no—
586C23—44no—
587C23—44no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23C3×#12012yes—
596C23C3×#12112yes—
597C23C3×AGL(1,ℤ/8)12yes—
598C23C3×#13712yes—
599C23C3×#13712yes—
600C23C22×C3×D411yescharacteristic
601Q8—24no—
602Q8—24no—
603Q8—48no—
604Q8—42no—
605Q8—42no—
606D4—42no—
607D4—42no—
608D4—84no—
609D4—84no—
610D4—84no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—24no—
616C2×C4—24no—
617C2×C4—24no—
618C2×C4—24no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—44no—
625C2×C4—44no—
626C2×C4—44no—
627C2×C4—48no—
628C2×C4—48no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4C3×#12012yes—
645C2×C4C3×#12112yes—
646C2×C4C22×C3×D411yescharacteristic
647C2×C4C22×C3×D412yes—
648C2×C4C2×C3×#4111yescharacteristic
649C2×C4C3×H(5,𝔽2)12yes—
650C8—24no—
651C8—42no—
652C2×C3—24no—
653C2×C3—42no—
654C2×C3—42no—
655C2×C3—161no—
656C2×C3#241011yescharacteristic
657C2×C3#300411yescharacteristic
658C2×C3#300611yescharacteristic
659C2×C3C2×#46811yescharacteristic
660C2×C3#305611yescharacteristic
661C2×C3#319311yescharacteristic
662C2×C3#319611yescharacteristic
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22—22no—
675C22—416no—
676C22—41no—
677C22—41no—
678C22—41no—
679C22—41no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22C3×#46814yescomplemented
692C22C2×C3×#12011yescharacteristic
693C22C2×C3×#12111yescharacteristic
694C22C3×#53411yescharacteristic
695C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
696C22C2×C3×#13711yescharacteristic
697C22C2×C3×#13711yescharacteristic
698C22C3×#57511yescharacteristic
699C4—22no—
700C4—22no—
701C4—41no—
702C4—44no—
703C4—44no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4C3×D4212yes—
708C4C3×#54612yes—
709C3#2438711yescharacteristic, direct product factor, Sylow
710C2—24no—
711C2—42no—
712C2—42no—
713C2—161no—
714C2C3×#241011yescharacteristic
715C2C3×#300411yescharacteristic
716C2C3×#300611yescharacteristic
717C2C2×C3×#46811yescharacteristic
718C2C3×#305611yescharacteristic
719C2C3×#319311yescharacteristic
720C2C3×#319611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#2847C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C24×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C22⋊Q8C2semidirect
2. C2×C3×#468C2semidirect
3. C2×C3×#448C2semidirect
4. C2×C3×#407C2semidirect
6. C3×#2036C2semidirect
7. C3×#2000C2semidirect
8. C3×#1894C2semidirect
9. C3×#1874C2semidirect
10. C3×#1852C2semidirect
11. C3×#1787C2semidirect
12. #24387C3direct (N × H)
15. C22×C3×SD16C22semidirect
31. C2×C3×#107C22semidirect
32. C2×C3×#103C22semidirect
33. C2×C3×#103C22semidirect
34. C2×C3×#103C22semidirect
35. C2×C3×#102C22semidirect
46. C3×#340C22semidirect
47. C3×#340C22semidirect
48. C22×C22⋊Q8C2×C3semidirect
49. C2×#468C2×C3semidirect
50. C2×#448C2×C3semidirect
51. C2×#407C2×C3semidirect
53. #2036C2×C3semidirect
54. #2000C2×C3semidirect
55. #1894C2×C3semidirect
56. #1874C2×C3semidirect
57. #1852C2×C3semidirect
58. #1787C2×C3semidirect
95. C3×C22⋊Q8D4semidirect
126. C3×C22⋊C8D4semidirect
132. C22×SD16C22×C3semidirect
148. C2×#107C22×C3semidirect
149. C2×#103C22×C3semidirect
150. C2×#103C22×C3semidirect
151. C2×#103C22×C3semidirect
152. C2×#102C22×C3semidirect
163. #340C22×C3semidirect
164. #340C22×C3semidirect
299. C22⋊Q8C3×D4semidirect
330. C22⋊C8C3×D4semidirect
547. C22×C3#468semidirect
691. C22C3×#468semidirect
709. C3#24387direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C22⋊Q82
C2×C3×#4682
C2×C3×#4482
C2×C3×#4072
C3×#28472
C3×#20362
C3×#20002
C3×#18942
C3×#18742
C3×#18522
C3×#17872
#243873