Finite Group Databasebeta

← C3×#32908 #10651515

Subgroups — C3×#32908 #10651515

Order 768.

1894 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C4×D4C211yesmaximal, characteristic, complemented
2C2×C3×#463C212yesmaximal, complemented
3C2×C3×#450C211yesmaximal, characteristic, complemented
4C2×C3×#447C211yesmaximal, characteristic
5C3×#2850C211yesmaximal, characteristic, complemented
6C3×#1879C212yesmaximal, complemented
7C3×#1877C212yesmaximal, complemented
8C3×#1874C211yesmaximal, characteristic, complemented
9C3×#1872C211yesmaximal, characteristic, complemented
10C3×#1804C212yesmaximal, complemented
11C3×#1797C211yesmaximal, characteristic, complemented
12#32908C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C24×C3×C4—21no—
15C22×C3×SD16C2212yes—
16C22×C3×D8C2212yes—
17C2×C3×#124C2211yescharacteristic, complemented
18C2×C3×C22⋊Q8C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4—28no—
21C2×C3×C4×D4—21no—
22C2×C3×C4×D4—21no—
23C2×C3×C4×D4C2212yes—
24C2×C3×C4×D4C2212yes—
25C22×C3×C4⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4—21no—
27C22×C3×C42C2211yescharacteristic
28C3×#463—28no—
29C3×#450—24no—
30C3×#447—24no—
31C2×C3×C4⋊C8C2212yescomplemented
32C2×C3×#103C2212yescomplemented
33C2×C3×#102C2212yes—
34C2×C3×#102C2212yes—
35C2×C3×#102C2212yescomplemented
36C2×C3×C22⋊C8C2211yescharacteristic
37C2×C3×C22⋊C8C2211yescharacteristic
38C3×#391C2211yescharacteristic, complemented
39C3×#390C2211yescharacteristic, complemented
40C3×#388—21no—
41C3×#388—21no—
42C3×#386—21no—
43C3×#386—21no—
44C3×#382C2211yescharacteristic, complemented
45C3×#340C2212yescomplemented
46C3×#340C2212yescomplemented
47C3×#336C2212yescomplemented
48C22×C4×D4C2×C311yescharacteristic, complemented
49C2×#463C2×C312yescomplemented
50C2×#450C2×C311yescharacteristic, complemented
51C2×#447C2×C311yescharacteristic
52#2850C2×C311yescharacteristic, complemented
53#1879C2×C312yescomplemented
54#1877C2×C312yescomplemented
55#1874C2×C311yescharacteristic, complemented
56#1872C2×C311yescharacteristic, complemented
57#1804C2×C312yescomplemented
58#1797C2×C311yescharacteristic, complemented
59C25×C3—21no—
60C22×C3×Q8C2311yescharacteristic
61C22×C3×D4—24no—
62C22×C3×D4—24no—
63C22×C3×D4—21no—
64C22×C3×D4—21no—
65C22×C3×D4—22no—
66C22×C3×D4D414yes—
67C22×C3×D4C2311yescharacteristic
68C22×C3×D4C2312yes—
69C23×C3×C4—28no—
70C23×C3×C4—21no—
71C23×C3×C4—22no—
72C23×C3×C4—22no—
73C23×C3×C4—44no—
74C23×C3×C4—44no—
75C23×C3×C4D411yescharacteristic
76C23×C3×C4D411yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C2×C3×SD16—24no—
79C2×C3×SD16—24no—
80C2×C3×SD16—24no—
81C2×C3×D8—24no—
82C2×C3×D8—24no—
83C2×C3×D8—24no—
84C22×C3×C8C2312yes—
85C22×C3×C8C2312yes—
86C3×#124—24no—
87C3×C22⋊Q8—22no—
88C3×C22⋊Q8—22no—
89C3×#121—22no—
90C3×#121—22no—
91C3×C4×D4—28no—
92C3×C4×D4—28no—
93C3×C4×D4—24no—
94C3×C4×D4—24no—
95C3×C4×D4—24no—
96C3×C4×D4D418yescomplemented
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—24no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4C2311yescharacteristic
101C2×C3×C4⋊C4C2311yescharacteristic
102C2×C3×C4⋊C4C2312yes—
103C2×C3×C22⋊C4—28no—
104C2×C3×C22⋊C4—22no—
105C2×C3×C22⋊C4—22no—
106C2×C3×C22⋊C4—21no—
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
112C2×C3×C42—24no—
113C2×C3×C42D411yescharacteristic
114C2×C3×C42D411yescharacteristic
115C2×C3×C42C2311yescharacteristic
116C2×C3×C42C2311yescharacteristic
117C3×C4⋊C8—24no—
118C3×#103—24no—
119C3×#102—24no—
120C3×#102—24no—
121C3×#102—24no—
122C3×C22⋊C8—22no—
123C3×C22⋊C8—22no—
124C3×#95—21no—
125C3×#95—21no—
126C3×#95—21no—
127C3×#95—21no—
128C23×D4C22×C311yescharacteristic
129C24×C4—21no—
130C22×SD16C22×C312yes—
131C22×D8C22×C312yes—
132C2×#124C22×C311yescharacteristic, complemented
133C2×C22⋊Q8C22×C311yescharacteristic
134C2×#121C22×C311yescharacteristic
135C2×C4×D4—28no—
136C2×C4×D4—21no—
137C2×C4×D4—21no—
138C2×C4×D4C22×C312yes—
139C2×C4×D4C22×C312yes—
140C22×C4⋊C4C22×C311yescharacteristic
141C22×C22⋊C4—21no—
142C22×C42C22×C311yescharacteristic
143#463—28no—
144#450—24no—
145#447—24no—
146C2×C4⋊C8C22×C312yescomplemented
147C2×#103C22×C312yescomplemented
148C2×#102C22×C312yes—
149C2×#102C22×C312yes—
150C2×#102C22×C312yescomplemented
151C2×C22⋊C8C22×C311yescharacteristic
152C2×C22⋊C8C22×C311yescharacteristic
153#391C22×C311yescharacteristic, complemented
154#390C22×C311yescharacteristic, complemented
155#388—21no—
156#388—21no—
157#386—21no—
158#386—21no—
159#382C22×C311yescharacteristic, complemented
160#340C22×C312yescomplemented
161#340C22×C312yescomplemented
162#336C22×C312yescomplemented
163C24×C3—24no—
164C24×C3—24no—
165C24×C3—24no—
166C24×C3—22no—
167C24×C3—21no—
168C24×C3—42no—
169C24×C3—42no—
170C24×C3—42no—
171C24×C3—42no—
172C24×C3C2×D411yescharacteristic
173C2×C3×Q8—22no—
174C2×C3×Q8—21no—
175C2×C3×Q8—21no—
176C2×C3×Q8—22no—
177C2×C3×D4—24no—
178C2×C3×D4—24no—
179C2×C3×D4—216no—
180C2×C3×D4—216no—
181C2×C3×D4—24no—
182C2×C3×D4—22no—
183C2×C3×D4—22no—
184C2×C3×D4—21no—
185C2×C3×D4—22no—
186C2×C3×D4—22no—
187C2×C3×D4—21no—
188C2×C3×D4—22no—
189C2×C3×D4—42no—
190C2×C3×D4—42no—
191C2×C3×D4—42no—
192C2×C3×D4C2×D414yes—
193C2×C3×D4C2×D414yes—
194C2×C3×D4#4114yes—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—24no—
201C22×C3×C4—28no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—28no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—41no—
210C22×C3×C4—432no—
211C22×C3×C4—44no—
212C22×C3×C4—44no—
213C22×C3×C4—44no—
214C22×C3×C4—42no—
215C22×C3×C4—42no—
216C22×C3×C4—44no—
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D412yes—
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4#4112yes—
224C22×C3×C4C2411yescharacteristic
225C3×SD16—48no—
226C3×D8—48no—
227C2×C3×C8—22no—
228C2×C3×C8—22no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C3×C4⋊C4—24no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—21no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—42no—
240C3×C4⋊C4C2×D414yes—
241C3×C22⋊C4—28no—
242C3×C22⋊C4—28no—
243C3×C22⋊C4—42no—
244C3×C22⋊C4—42no—
245C3×C22⋊C4—42no—
246C3×C22⋊C4—42no—
247C3×C22⋊C4—42no—
248C3×C22⋊C4—42no—
249C3×C42—22no—
250C3×C42—22no—
251C3×C42—22no—
252C3×C42C2×D414yes—
253C25—21no—
254C22×Q8C23×C311yescharacteristic
255C22×D4—24no—
256C22×D4—24no—
257C22×D4—21no—
258C22×D4—21no—
259C22×D4—22no—
260C22×D4C3×D414yes—
261C22×D4C23×C311yescharacteristic
262C22×D4C23×C312yes—
263C23×C4—28no—
264C23×C4—21no—
265C23×C4—22no—
266C23×C4—22no—
267C23×C4—44no—
268C23×C4—44no—
269C23×C4C3×D411yescharacteristic
270C23×C4C3×D411yescharacteristic
271C23×C4C23×C311yescharacteristic
272C2×SD16—24no—
273C2×SD16—24no—
274C2×SD16—24no—
275C2×D8—24no—
276C2×D8—24no—
277C2×D8—24no—
278C22×C8C23×C312yes—
279C22×C8C23×C312yes—
280#124—24no—
281C22⋊Q8—22no—
282C22⋊Q8—22no—
283#121—22no—
284#121—22no—
285C4×D4—28no—
286C4×D4—28no—
287C4×D4—24no—
288C4×D4—24no—
289C4×D4—24no—
290C4×D4C3×D418yescomplemented
291C2×C4⋊C4—21no—
292C2×C4⋊C4—24no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4C23×C311yescharacteristic
295C2×C4⋊C4C23×C311yescharacteristic
296C2×C4⋊C4C23×C312yes—
297C2×C22⋊C4—28no—
298C2×C22⋊C4—22no—
299C2×C22⋊C4—22no—
300C2×C22⋊C4—21no—
301C2×C22⋊C4—21no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—21no—
305C2×C22⋊C4—21no—
306C2×C42—24no—
307C2×C42C3×D411yescharacteristic
308C2×C42C3×D411yescharacteristic
309C2×C42C23×C311yescharacteristic
310C2×C42C23×C311yescharacteristic
311C4⋊C8—24no—
312#103—24no—
313#102—24no—
314#102—24no—
315#102—24no—
316C22⋊C8—22no—
317C22⋊C8—22no—
318#95—21no—
319#95—21no—
320#95—21no—
321#95—21no—
322C23×C3—21no—
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—216no—
327C23×C3—24no—
328C23×C3—24no—
329C23×C3—24no—
330C23×C3—48no—
331C23×C3—48no—
332C23×C3—48no—
333C23×C3—48no—
334C23×C3—48no—
335C23×C3—42no—
336C23×C3—42no—
337C23×C3—42no—
338C23×C3—42no—
339C23×C3—48no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—41no—
347C23×C3#12112yes—
348C23×C3#13512yes—
349C23×C3AGL(1,ℤ/8)12yes—
350C23×C3C22×D411yescharacteristic
351C3×Q8—42no—
352C3×Q8—42no—
353C3×D4—216no—
354C3×D4—24no—
355C3×D4—24no—
356C3×D4—24no—
357C3×D4—42no—
358C3×D4—42no—
359C3×D4—84no—
360C3×D4#12118yes—
361C2×C3×C4—28no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—21no—
367C2×C3×C4—21no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—21no—
373C2×C3×C4—24no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—44no—
377C2×C3×C4—416no—
378C2×C3×C4—416no—
379C2×C3×C4—48no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4#12012yes—
392C2×C3×C4#12012yes—
393C2×C3×C4#12112yes—
394C2×C3×C4AGL(1,ℤ/8)12yes—
395C2×C3×C4C22×D411yescharacteristic
396C2×C3×C4C22×D412yes—
397C2×C3×C4C2×#4112yes—
398C2×C3×C4C2×#4111yescharacteristic
399C3×C8—42no—
400C3×C8—42no—
401C24—24no—
402C24—24no—
403C24—24no—
404C24—22no—
405C24—21no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—42no—
410C24C2×C3×D411yescharacteristic
411C2×Q8—22no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—22no—
415C2×D4—24no—
416C2×D4—24no—
417C2×D4—216no—
418C2×D4—216no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—22no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—42no—
430C2×D4C2×C3×D414yes—
431C2×D4C2×C3×D414yes—
432C2×D4C3×#4114yes—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—22no—
438C22×C4—24no—
439C22×C4—28no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—28no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—41no—
448C22×C4—432no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—44no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—44no—
455C22×C4C2×C3×D411yescharacteristic
456C22×C4C2×C3×D411yescharacteristic
457C22×C4C2×C3×D411yescharacteristic
458C22×C4C2×C3×D411yescharacteristic
459C22×C4C2×C3×D412yes—
460C22×C4C2×C3×D411yescharacteristic
461C22×C4C3×#4112yes—
462C22×C4C24×C311yescharacteristic
463SD16—48no—
464D8—48no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—22no—
471C4⋊C4—24no—
472C4⋊C4—22no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—42no—
478C4⋊C4C2×C3×D414yes—
479C22⋊C4—28no—
480C22⋊C4—28no—
481C22⋊C4—42no—
482C22⋊C4—42no—
483C22⋊C4—42no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42C2×C3×D414yes—
491C22×C3—22no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—28no—
498C22×C3—432no—
499C22×C3—44no—
500C22×C3—44no—
501C22×C3—44no—
502C22×C3—44no—
503C22×C3—44no—
504C22×C3—44no—
505C22×C3—81no—
506C22×C3—81no—
507C22×C3—81no—
508C22×C3—81no—
509C22×C3—81no—
510C22×C3—81no—
511C22×C3—81no—
512C22×C3#46314yescomplemented
513C22×C3C2×#12011yescharacteristic
514C22×C3C2×#12111yescharacteristic
515C22×C3#52511yescharacteristic
516C22×C3C2×#13511yescharacteristic
517C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
518C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
519C22×C3#57511yescharacteristic
520C3×C4—22no—
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—41no—
525C3×C4—44no—
526C3×C4—81no—
527C3×C4—81no—
528C3×C4—81no—
529C3×C4C2×#12112yes—
530C3×C4#52512yes—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—216no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—48no—
540C23—48no—
541C23—48no—
542C23—48no—
543C23—48no—
544C23—42no—
545C23—42no—
546C23—42no—
547C23—42no—
548C23—48no—
549C23—41no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23C3×#12112yes—
557C23C3×#13512yes—
558C23C3×AGL(1,ℤ/8)12yes—
559C23C22×C3×D411yescharacteristic
560Q8—42no—
561Q8—42no—
562D4—216no—
563D4—24no—
564D4—24no—
565D4—24no—
566D4—42no—
567D4—42no—
568D4—84no—
569D4C3×#12118yes—
570C2×C4—28no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—24no—
585C2×C4—44no—
586C2×C4—416no—
587C2×C4—416no—
588C2×C4—48no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4C3×#12012yes—
601C2×C4C3×#12012yes—
602C2×C4C3×#12112yes—
603C2×C4C3×AGL(1,ℤ/8)12yes—
604C2×C4C22×C3×D411yescharacteristic
605C2×C4C22×C3×D412yes—
606C2×C4C2×C3×#4112yes—
607C2×C4C2×C3×#4111yescharacteristic
608C8—42no—
609C8—42no—
610C2×C3—24no—
611C2×C3—48no—
612C2×C3—161no—
613C2×C3#284711yescharacteristic
614C2×C3#300211yescharacteristic
615C2×C3#300311yescharacteristic
616C2×C3C2×#46311yescharacteristic
617C2×C3#303611yescharacteristic
618C2×C3#310511yescharacteristic
619C2×C3#311411yescharacteristic
620C22—22no—
621C22—22no—
622C22—22no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—28no—
627C22—432no—
628C22—44no—
629C22—44no—
630C22—44no—
631C22—44no—
632C22—44no—
633C22—44no—
634C22—81no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22C3×#46314yescomplemented
642C22C2×C3×#12011yescharacteristic
643C22C2×C3×#12111yescharacteristic
644C22C3×#52511yescharacteristic
645C22C2×C3×#13511yescharacteristic
646C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
647C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
648C22C3×#57511yescharacteristic
649C4—22no—
650C4—22no—
651C4—22no—
652C4—22no—
653C4—41no—
654C4—44no—
655C4—81no—
656C4—81no—
657C4—81no—
658C4C2×C3×#12112yes—
659C4C3×#52512yes—
660C3#3290811yescharacteristic, direct product factor, Sylow
661C2—24no—
662C2—48no—
663C2—161no—
664C2C3×#284711yescharacteristic
665C2C3×#300211yescharacteristic
666C2C3×#300311yescharacteristic
667C2C2×C3×#46311yescharacteristic
668C2C3×#303611yescharacteristic
669C2C3×#310511yescharacteristic
670C2C3×#311411yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#447C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×C3×C4×D4C2semidirect
2. C2×C3×#463C2semidirect
3. C2×C3×#450C2semidirect
5. C3×#2850C2semidirect
6. C3×#1879C2semidirect
7. C3×#1877C2semidirect
8. C3×#1874C2semidirect
9. C3×#1872C2semidirect
10. C3×#1804C2semidirect
11. C3×#1797C2semidirect
12. #32908C3direct (N × H)
17. C2×C3×#124C22semidirect
31. C2×C3×C4⋊C8C22semidirect
32. C2×C3×#103C22semidirect
35. C2×C3×#102C22semidirect
38. C3×#391C22semidirect
39. C3×#390C22semidirect
44. C3×#382C22semidirect
45. C3×#340C22semidirect
46. C3×#340C22semidirect
47. C3×#336C22semidirect
48. C22×C4×D4C2×C3semidirect
49. C2×#463C2×C3semidirect
50. C2×#450C2×C3semidirect
52. #2850C2×C3semidirect
53. #1879C2×C3semidirect
54. #1877C2×C3semidirect
55. #1874C2×C3semidirect
56. #1872C2×C3semidirect
57. #1804C2×C3semidirect
58. #1797C2×C3semidirect
96. C3×C4×D4D4semidirect
132. C2×#124C22×C3semidirect
146. C2×C4⋊C8C22×C3semidirect
147. C2×#103C22×C3semidirect
150. C2×#102C22×C3semidirect
153. #391C22×C3semidirect
154. #390C22×C3semidirect
159. #382C22×C3semidirect
160. #340C22×C3semidirect
161. #340C22×C3semidirect
162. #336C22×C3semidirect
290. C4×D4C3×D4semidirect
512. C22×C3#463semidirect
641. C22C3×#463semidirect
660. C3#32908direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×C4×D42
C2×C3×#4632
C2×C3×#4502
C2×C3×#4472
C3×#28502
C3×#18792
C3×#18772
C3×#18742
C3×#18722
C3×#18042
C3×#17972
#329083