Finite Group Databasebeta

← C3×#25768 #10644375

Subgroups — C3×#25768 #10644375

Order 768.

1670 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#548C211yesmaximal, characteristic, complemented
2C2×C3×#496C211yesmaximal, characteristic, complemented
3C2×C3×#460C211yesmaximal, characteristic, complemented
4C2×C3×#449C212yesmaximal, complemented
5C2×C3×#448C212yesmaximal, complemented
6C3×#2541C211yesmaximal, characteristic, complemented
7C3×#2000C212yesmaximal, complemented
8C3×#1999C212yesmaximal, complemented
9C3×#1983C211yesmaximal, characteristic, complemented
10C3×#1955C211yesmaximal, characteristic, complemented
11C3×#1763C211yesmaximal, characteristic, complemented
12#25768C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C23×C3×Q8C2211yescharacteristic
15C22×C3×SD16C2212yes—
16C22×C3×SD16C2212yes—
17C22×C3×D8C2212yes—
18C3×#548—24no—
19C3×#548—24no—
20C2×C3×#127—21no—
21C2×C3×#127C2211yescharacteristic
22C2×C3×#124—21no—
23C2×C3×#124C2211yescharacteristic
24C2×C3×C22⋊Q8—21no—
25C2×C3×C22⋊Q8C2211yescharacteristic
26C2×C3×#121—21no—
27C2×C3×#121C2211yescharacteristic
28C2×C3×#121C2212yes—
29C2×C3×#121C2212yes—
30C2×C3×C4×Q8C2211yescharacteristic
31C2×C3×C4×D4—21no—
32C2×C3×C4×D4C2211yescharacteristic
33C3×#496—24no—
34C3×#460—24no—
35C3×#449—28no—
36C3×#448—28no—
37C2×C3×C4⋊C8C2211yescharacteristic
38C2×C3×#103C2212yes—
39C2×C3×#103C2212yes—
40C2×C3×#102C2212yes—
41C2×C3×#102C2212yes—
42C2×C3×C22⋊C8C2212yes—
43C2×C3×C22⋊C8C2212yes—
44C2×C3×#97C2211yescharacteristic
45C3×#392—21no—
46C3×#392—21no—
47C3×#390—21no—
48C3×C4×C4⋊C4C2211yescharacteristic
49C3×#340C2212yes—
50C2×#548C2×C311yescharacteristic, complemented
51C2×#496C2×C311yescharacteristic, complemented
52C2×#460C2×C311yescharacteristic, complemented
53C2×#449C2×C312yescomplemented
54C2×#448C2×C312yescomplemented
55#2541C2×C311yescharacteristic, complemented
56#2000C2×C312yescomplemented
57#1999C2×C312yescomplemented
58#1983C2×C311yescharacteristic, complemented
59#1955C2×C311yescharacteristic, complemented
60#1763C2×C311yescharacteristic, complemented
61C2×C3×#41—22no—
62C2×C3×#41—22no—
63C2×C3×#41—24no—
64C2×C3×#41—42no—
65C22×C3×Q8—22no—
66C22×C3×Q8—22no—
67C22×C3×Q8—21no—
68C22×C3×Q8—24no—
69C22×C3×Q8—42no—
70C22×C3×Q8C2311yescharacteristic
71C22×C3×Q8C2311yescharacteristic
72C22×C3×D4—21no—
73C22×C3×D4—21no—
74C22×C3×D4—22no—
75C22×C3×D4—22no—
76C22×C3×D4—21no—
77C22×C3×D4—21no—
78C22×C3×D4D411yescharacteristic
79C22×C3×D4C2312yes—
80C22×C3×D4C2311yescharacteristic
81C23×C3×C4—21no—
82C23×C3×C4—21no—
83C23×C3×C4C2311yescharacteristic
84C23×C3×C4C2311yescharacteristic
85C2×C3×SD16—24no—
86C2×C3×SD16—24no—
87C2×C3×SD16—24no—
88C2×C3×SD16—24no—
89C2×C3×SD16—24no—
90C2×C3×SD16—42no—
91C2×C3×D8—24no—
92C2×C3×D8—24no—
93C2×C3×D8—42no—
94C22×C3×C8C2312yes—
95C22×C3×C8C2312yes—
96C3×#127—22no—
97C3×#127—22no—
98C3×#127—44no—
99C3×#124—28no—
100C3×#124—22no—
101C3×#124D414yescomplemented
102C3×C22⋊Q8—28no—
103C3×C22⋊Q8—22no—
104C3×C22⋊Q8—22no—
105C3×#121—28no—
106C3×#121—22no—
107C3×#121—22no—
108C3×#121—24no—
109C3×#121—24no—
110C3×#121—42no—
111C3×#121—42no—
112C3×C4×Q8—22no—
113C3×C4×Q8D414yescomplemented
114C3×C4×D4—28no—
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C2×C3×C4⋊C4—21no—
118C2×C3×C4⋊C4—21no—
119C2×C3×C4⋊C4D411yescharacteristic
120C2×C3×C4⋊C4C2312yes—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C22⋊C4—21no—
123C2×C3×C22⋊C4—21no—
124C2×C3×C22⋊C4—21no—
125C2×C3×C22⋊C4—21no—
126C2×C3×C22⋊C4—22no—
127C2×C3×C22⋊C4—22no—
128C2×C3×C22⋊C4D411yescharacteristic
129C2×C3×C22⋊C4D411yescharacteristic
130C2×C3×C42—21no—
131C2×C3×C42—21no—
132C2×C3×C42C2311yescharacteristic
133C3×C4⋊C8—22no—
134C3×#103—24no—
135C3×#103D418yescomplemented
136C3×#102—24no—
137C3×#102—24no—
138C3×C22⋊C8—24no—
139C3×C22⋊C8—24no—
140C3×#97—22no—
141C3×#95—21no—
142C22×#41C22×C311yescharacteristic
143C23×Q8C22×C311yescharacteristic
144C22×SD16C22×C312yes—
145C22×SD16C22×C312yes—
146C22×D8C22×C312yes—
147#548—24no—
148#548—24no—
149C2×#127—21no—
150C2×#127C22×C311yescharacteristic
151C2×#124—21no—
152C2×#124C22×C311yescharacteristic
153C2×C22⋊Q8—21no—
154C2×C22⋊Q8C22×C311yescharacteristic
155C2×#121—21no—
156C2×#121C22×C311yescharacteristic
157C2×#121C22×C312yes—
158C2×#121C22×C312yes—
159C2×C4×Q8C22×C311yescharacteristic
160C2×C4×D4—21no—
161C2×C4×D4C22×C311yescharacteristic
162#496—24no—
163#460—24no—
164#449—28no—
165#448—28no—
166C2×C4⋊C8C22×C311yescharacteristic
167C2×#103C22×C312yes—
168C2×#103C22×C312yes—
169C2×#102C22×C312yes—
170C2×#102C22×C312yes—
171C2×C22⋊C8C22×C312yes—
172C2×C22⋊C8C22×C312yes—
173C2×#97C22×C311yescharacteristic
174#392—21no—
175#392—21no—
176#390—21no—
177C4×C4⋊C4C22×C311yescharacteristic
178#340C22×C312yes—
179C24×C3—21no—
180C24×C3—22no—
181C24×C3C2×D411yescharacteristic
182C24×C3C2×D411yescharacteristic
183C3×#41—48no—
184C3×#41—44no—
185C3×#41—44no—
186C2×C3×Q8—24no—
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—22no—
190C2×C3×Q8—22no—
191C2×C3×Q8—22no—
192C2×C3×Q8—44no—
193C2×C3×Q8—48no—
194C2×C3×Q8—44no—
195C2×C3×Q8—44no—
196C2×C3×Q8C2×D412yes—
197C2×C3×Q8C2×D414yes—
198C2×C3×Q8C2×D412yes—
199C2×C3×D4—24no—
200C2×C3×D4—24no—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—22no—
204C2×C3×D4—21no—
205C2×C3×D4—22no—
206C2×C3×D4—22no—
207C2×C3×D4—22no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—41no—
213C2×C3×D4—44no—
214C2×C3×D4—44no—
215C2×C3×D4—44no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4—44no—
221C2×C3×D4—44no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4—82no—
225C2×C3×D4—82no—
226C2×C3×D4—82no—
227C2×C3×D4C2×D412yes—
228C22×C3×C4—21no—
229C22×C3×C4—24no—
230C22×C3×C4—24no—
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—21no—
234C22×C3×C4—22no—
235C22×C3×C4—22no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—21no—
240C22×C3×C4—22no—
241C22×C3×C4—22no—
242C22×C3×C4—44no—
243C22×C3×C4—44no—
244C22×C3×C4C2×D411yescharacteristic
245C22×C3×C4C2×D411yescharacteristic
246C22×C3×C4C2×D411yescharacteristic
247C22×C3×C4C2×D411yescharacteristic
248C22×C3×C4C2411yescharacteristic
249C3×SD16—48no—
250C3×SD16—48no—
251C3×D8—48no—
252C2×C3×C8—22no—
253C2×C3×C8—22no—
254C2×C3×C8—22no—
255C2×C3×C8—22no—
256C2×C3×C8—22no—
257C2×C3×C8C2×D414yes—
258C3×C4⋊C4—24no—
259C3×C4⋊C4—24no—
260C3×C4⋊C4—22no—
261C3×C4⋊C4—21no—
262C3×C4⋊C4—22no—
263C3×C4⋊C4C2×D412yes—
264C3×C4⋊C4C2×D414yes—
265C3×C22⋊C4—24no—
266C3×C22⋊C4—24no—
267C3×C22⋊C4—24no—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—22no—
270C3×C22⋊C4—22no—
271C3×C22⋊C4—44no—
272C3×C22⋊C4—44no—
273C3×C42—24no—
274C3×C42—42no—
275C3×C42C2×D412yes—
276C3×C42C2×D412yes—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—24no—
280C2×#41—42no—
281C22×Q8—22no—
282C22×Q8—22no—
283C22×Q8—21no—
284C22×Q8—24no—
285C22×Q8—42no—
286C22×Q8C23×C311yescharacteristic
287C22×Q8C23×C311yescharacteristic
288C22×D4—21no—
289C22×D4—21no—
290C22×D4—22no—
291C22×D4—22no—
292C22×D4—21no—
293C22×D4—21no—
294C22×D4C3×D411yescharacteristic
295C22×D4C23×C312yes—
296C22×D4C23×C311yescharacteristic
297C23×C4—21no—
298C23×C4—21no—
299C23×C4C23×C311yescharacteristic
300C23×C4C23×C311yescharacteristic
301C2×SD16—24no—
302C2×SD16—24no—
303C2×SD16—24no—
304C2×SD16—24no—
305C2×SD16—24no—
306C2×SD16—42no—
307C2×D8—24no—
308C2×D8—24no—
309C2×D8—42no—
310C22×C8C23×C312yes—
311C22×C8C23×C312yes—
312#127—22no—
313#127—22no—
314#127—44no—
315#124—28no—
316#124—22no—
317#124C3×D414yescomplemented
318C22⋊Q8—28no—
319C22⋊Q8—22no—
320C22⋊Q8—22no—
321#121—28no—
322#121—22no—
323#121—22no—
324#121—24no—
325#121—24no—
326#121—42no—
327#121—42no—
328C4×Q8—22no—
329C4×Q8C3×D414yescomplemented
330C4×D4—28no—
331C4×D4—22no—
332C4×D4—22no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4C3×D411yescharacteristic
336C2×C4⋊C4C23×C311yescharacteristic
337C2×C4⋊C4C23×C312yes—
338C2×C22⋊C4—21no—
339C2×C22⋊C4—21no—
340C2×C22⋊C4—21no—
341C2×C22⋊C4—21no—
342C2×C22⋊C4—22no—
343C2×C22⋊C4—22no—
344C2×C22⋊C4C3×D411yescharacteristic
345C2×C22⋊C4C3×D411yescharacteristic
346C2×C42—21no—
347C2×C42—21no—
348C2×C42C23×C311yescharacteristic
349C4⋊C8—22no—
350#103—24no—
351#103C3×D418yescomplemented
352#102—24no—
353#102—24no—
354C22⋊C8—24no—
355C22⋊C8—24no—
356#97—22no—
357#95—21no—
358C23×C3—21no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—22no—
362C23×C3—21no—
363C23×C3—22no—
364C23×C3—22no—
365C23×C3—21no—
366C23×C3—21no—
367C23×C3—22no—
368C23×C3—42no—
369C23×C3—41no—
370C23×C3—41no—
371C23×C3—42no—
372C23×C3—42no—
373C23×C3—42no—
374C23×C3—42no—
375C23×C3—42no—
376C23×C3—42no—
377C23×C3—42no—
378C23×C3—42no—
379C23×C3AGL(1,ℤ/8)12yes—
380C23×C3C22×D411yescharacteristic
381C3×Q8—22no—
382C3×Q8—24no—
383C3×Q8—24no—
384C3×Q8—48no—
385C3×Q8—41no—
386C3×Q8—41no—
387C3×Q8#12714yescomplemented
388C3×D4—24no—
389C3×D4—44no—
390C3×D4—48no—
391C3×D4—48no—
392C3×D4—41no—
393C3×D4—42no—
394C3×D4—41no—
395C3×D4—42no—
396C3×D4—42no—
397C3×D4—42no—
398C3×D4—84no—
399C3×D4—84no—
400C3×D4—88no—
401C3×D4—88no—
402C2×C3×C4—22no—
403C2×C3×C4—24no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4—22no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
411C2×C3×C4—24no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—48no—
415C2×C3×C4—48no—
416C2×C3×C4—42no—
417C2×C3×C4—42no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—42no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—42no—
426C2×C3×C4—42no—
427C2×C3×C4#12012yes—
428C2×C3×C4#12012yes—
429C2×C3×C4C22×D411yescharacteristic
430C2×C3×C4C22×D412yes—
431C2×C3×C4C22×D411yescharacteristic
432C2×C3×C4H(5,𝔽2)12yes—
433C3×C8—24no—
434C3×C8—42no—
435C24—21no—
436C24—22no—
437C24C2×C3×D411yescharacteristic
438C24C2×C3×D411yescharacteristic
439#41—48no—
440#41—44no—
441#41—44no—
442C2×Q8—24no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—22no—
448C2×Q8—44no—
449C2×Q8—48no—
450C2×Q8—44no—
451C2×Q8—44no—
452C2×Q8C2×C3×D412yes—
453C2×Q8C2×C3×D414yes—
454C2×Q8C2×C3×D412yes—
455C2×D4—24no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—22no—
459C2×D4—22no—
460C2×D4—21no—
461C2×D4—22no—
462C2×D4—22no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—41no—
469C2×D4—44no—
470C2×D4—44no—
471C2×D4—44no—
472C2×D4—42no—
473C2×D4—42no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—44no—
477C2×D4—44no—
478C2×D4—42no—
479C2×D4—42no—
480C2×D4—82no—
481C2×D4—82no—
482C2×D4—82no—
483C2×D4C2×C3×D412yes—
484C22×C4—21no—
485C22×C4—24no—
486C22×C4—24no—
487C22×C4—22no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—44no—
499C22×C4—44no—
500C22×C4C2×C3×D411yescharacteristic
501C22×C4C2×C3×D411yescharacteristic
502C22×C4C2×C3×D411yescharacteristic
503C22×C4C2×C3×D411yescharacteristic
504C22×C4C24×C311yescharacteristic
505SD16—48no—
506SD16—48no—
507D8—48no—
508C2×C8—22no—
509C2×C8—22no—
510C2×C8—22no—
511C2×C8—22no—
512C2×C8—22no—
513C2×C8C2×C3×D414yes—
514C4⋊C4—24no—
515C4⋊C4—24no—
516C4⋊C4—22no—
517C4⋊C4—21no—
518C4⋊C4—22no—
519C4⋊C4C2×C3×D412yes—
520C4⋊C4C2×C3×D414yes—
521C22⋊C4—24no—
522C22⋊C4—24no—
523C22⋊C4—24no—
524C22⋊C4—24no—
525C22⋊C4—22no—
526C22⋊C4—22no—
527C22⋊C4—44no—
528C22⋊C4—44no—
529C42—24no—
530C42—42no—
531C42C2×C3×D412yes—
532C42C2×C3×D412yes—
533C22×C3—22no—
534C22×C3—24no—
535C22×C3—41no—
536C22×C3—41no—
537C22×C3—42no—
538C22×C3—42no—
539C22×C3—41no—
540C22×C3—41no—
541C22×C3—42no—
542C22×C3—42no—
543C22×C3—41no—
544C22×C3—42no—
545C22×C3—42no—
546C22×C3—82no—
547C22×C3—82no—
548C22×C3—82no—
549C22×C3—82no—
550C22×C3—82no—
551C22×C3—82no—
552C22×C3—82no—
553C22×C3—82no—
554C22×C3—82no—
555C22×C3C2×#12011yescharacteristic
556C22×C3D4212yes—
557C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
558C22×C3#57511yescharacteristic
559C22×C3#57712yes—
560C3×C4—24no—
561C3×C4—22no—
562C3×C4—22no—
563C3×C4—41no—
564C3×C4—41no—
565C3×C4—42no—
566C3×C4—42no—
567C3×C4—44no—
568C3×C4C2×#12711yescharacteristic
569C3×C4#53511yescharacteristic
570C3×C4D4212yes—
571C23—21no—
572C23—22no—
573C23—21no—
574C23—22no—
575C23—21no—
576C23—21no—
577C23—22no—
578C23—21no—
579C23—22no—
580C23—22no—
581C23—41no—
582C23—41no—
583C23—42no—
584C23—42no—
585C23—42no—
586C23—42no—
587C23—42no—
588C23—42no—
589C23—42no—
590C23—42no—
591C23—42no—
592C23C3×AGL(1,ℤ/8)12yes—
593C23C22×C3×D411yescharacteristic
594Q8—22no—
595Q8—24no—
596Q8—24no—
597Q8—48no—
598Q8—41no—
599Q8—41no—
600Q8C3×#12714yescomplemented
601D4—24no—
602D4—44no—
603D4—48no—
604D4—48no—
605D4—41no—
606D4—42no—
607D4—41no—
608D4—42no—
609D4—42no—
610D4—42no—
611D4—84no—
612D4—84no—
613D4—88no—
614D4—88no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—48no—
628C2×C4—48no—
629C2×C4—42no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4C3×#12012yes—
641C2×C4C3×#12012yes—
642C2×C4C22×C3×D411yescharacteristic
643C2×C4C22×C3×D412yes—
644C2×C4C22×C3×D411yescharacteristic
645C2×C4C3×H(5,𝔽2)12yes—
646C8—24no—
647C8—42no—
648C2×C3—42no—
649C2×C3—81no—
650C2×C3—82no—
651C2×C3—162no—
652C2×C3#243311yescharacteristic
653C2×C3#300611yescharacteristic
654C2×C3#301011yescharacteristic
655C2×C3#326512yes—
656C2×C3#327112yes—
657C22—22no—
658C22—24no—
659C22—41no—
660C22—41no—
661C22—42no—
662C22—42no—
663C22—41no—
664C22—41no—
665C22—42no—
666C22—42no—
667C22—41no—
668C22—42no—
669C22—42no—
670C22—82no—
671C22—82no—
672C22—82no—
673C22—82no—
674C22—82no—
675C22—82no—
676C22—82no—
677C22—82no—
678C22—82no—
679C22C2×C3×#12011yescharacteristic
680C22C3×D4212yes—
681C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
682C22C3×#57511yescharacteristic
683C22C3×#57712yes—
684C4—24no—
685C4—22no—
686C4—22no—
687C4—41no—
688C4—41no—
689C4—42no—
690C4—42no—
691C4—44no—
692C4C2×C3×#12711yescharacteristic
693C4C3×#53511yescharacteristic
694C4C3×D4212yes—
695C3#2576811yescharacteristic, direct product factor, Sylow
696C2—42no—
697C2—81no—
698C2—82no—
699C2—162no—
700C2C3×#243311yescharacteristic
701C2C3×#300611yescharacteristic
702C2C3×#301011yescharacteristic
703C2C3×#326512yes—
704C2C3×#327112yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C2×C3×C4×D4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#548C2semidirect
2. C2×C3×#496C2semidirect
3. C2×C3×#460C2semidirect
4. C2×C3×#449C2semidirect
5. C2×C3×#448C2semidirect
6. C3×#2541C2semidirect
7. C3×#2000C2semidirect
8. C3×#1999C2semidirect
9. C3×#1983C2semidirect
10. C3×#1955C2semidirect
11. C3×#1763C2semidirect
12. #25768C3direct (N × H)
50. C2×#548C2×C3semidirect
51. C2×#496C2×C3semidirect
52. C2×#460C2×C3semidirect
53. C2×#449C2×C3semidirect
54. C2×#448C2×C3semidirect
55. #2541C2×C3semidirect
56. #2000C2×C3semidirect
57. #1999C2×C3semidirect
58. #1983C2×C3semidirect
59. #1955C2×C3semidirect
60. #1763C2×C3semidirect
101. C3×#124D4semidirect
113. C3×C4×Q8D4semidirect
135. C3×#103D4semidirect
317. #124C3×D4semidirect
329. C4×Q8C3×D4semidirect
351. #103C3×D4semidirect
387. C3×Q8#127semidirect
600. Q8C3×#127semidirect
695. C3#25768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5482
C2×C3×#4962
C2×C3×#4602
C2×C3×#4492
C2×C3×#4482
C3×#25412
C3×#20002
C3×#19992
C3×#19832
C3×#19552
C3×#17632
#257683