Finite Group Databasebeta

← C3×#23936 #10642543

Subgroups — C3×#23936 #10642543

Order 768.

1520 conjugacy classes of subgroups.

The subgroup lattice has 682 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic, complemented
2C2×C3×#450C211yesmaximal, characteristic, complemented
3C2×C3×#447C211yesmaximal, characteristic
4C2×C3×#390C211yesmaximal, characteristic, complemented
5C3×#2025C212yesmaximal, complemented
6C3×#2012C212yesmaximal, complemented
7C3×#1880C212yesmaximal, complemented
8C3×#1879C212yesmaximal, complemented
9C3×#1874C211yesmaximal, characteristic, complemented
10C3×#1872C211yesmaximal, characteristic, complemented
11C3×#1817C211yesmaximal, characteristic, complemented
12#23936C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×D4C2211yescharacteristic
14C22×C3×SD16C2212yes—
15C22×C3×D8C2212yes—
16C3×#529—24no—
17C3×#529—24no—
18C2×C3×#126—21no—
19C2×C3×#125C2211yescharacteristic, complemented
20C2×C3×#124C2211yescharacteristic, complemented
21C2×C3×#123—21no—
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×#121C2211yescharacteristic
24C2×C3×C4×Q8C2211yescharacteristic, complemented
25C2×C3×C4×D4—21no—
26C2×C3×C4×D4C2211yescharacteristic, complemented
27C2×C3×#117—21no—
28C22×C3×C4⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4—21no—
30C22×C3×C22⋊C4—21no—
31C22×C3×C42C2211yescharacteristic
32C3×#450—24no—
33C3×#447—24no—
34C2×C3×#103C2212yescomplemented
35C2×C3×#102C2212yes—
36C2×C3×#102C2212yes—
37C2×C3×#102C2212yescomplemented
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C3×#390—21no—
41C3×#390—21no—
42C3×#390C2212yes—
43C3×#390C2212yes—
44C3×#340C2212yescomplemented
45C3×#340C2212yescomplemented
46C3×#336C2212yescomplemented
47C3×#336C2212yescomplemented
48C2×#529C2×C311yescharacteristic, complemented
49C2×#450C2×C311yescharacteristic, complemented
50C2×#447C2×C311yescharacteristic
51C2×#390C2×C311yescharacteristic, complemented
52#2025C2×C312yescomplemented
53#2012C2×C312yescomplemented
54#1880C2×C312yescomplemented
55#1879C2×C312yescomplemented
56#1874C2×C311yescharacteristic, complemented
57#1872C2×C311yescharacteristic, complemented
58#1817C2×C311yescharacteristic, complemented
59C25×C3—21no—
60C22×C3×Q8C2311yescharacteristic
61C22×C3×D4—21no—
62C22×C3×D4—24no—
63C22×C3×D4—21no—
64C22×C3×D4—22no—
65C22×C3×D4—22no—
66C22×C3×D4—42no—
67C22×C3×D4C2311yescharacteristic
68C22×C3×D4C2312yes—
69C23×C3×C4—21no—
70C23×C3×C4—21no—
71C23×C3×C4D411yescharacteristic
72C23×C3×C4D411yescharacteristic
73C23×C3×C4C2311yescharacteristic
74C2×C3×SD16—24no—
75C2×C3×SD16—24no—
76C2×C3×SD16—42no—
77C2×C3×D8—24no—
78C2×C3×D8—24no—
79C2×C3×D8—42no—
80C22×C3×C8C2312yes—
81C22×C3×C8C2312yes—
82C3×#126—28no—
83C3×#125—22no—
84C3×#125—22no—
85C3×#124—22no—
86C3×#124—22no—
87C3×#123—28no—
88C3×C22⋊Q8—22no—
89C3×C22⋊Q8D414yes—
90C3×#121—22no—
91C3×#121D414yes—
92C3×C4×Q8—22no—
93C3×C4×Q8—22no—
94C3×C4×D4—28no—
95C3×C4×D4—22no—
96C3×C4×D4—22no—
97C3×#117—28no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—42no—
104C2×C3×C4⋊C4C2312yes—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
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×C22⋊C4—22no—
113C2×C3×C22⋊C4—22no—
114C2×C3×C22⋊C4—22no—
115C2×C3×C22⋊C4—22no—
116C2×C3×C22⋊C4—44no—
117C2×C3×C22⋊C4—44no—
118C2×C3×C42—22no—
119C2×C3×C42—22no—
120C2×C3×C42—21no—
121C2×C3×C42D411yescharacteristic
122C2×C3×C42D411yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C3×#103—42no—
126C3×#102—24no—
127C3×#102—24no—
128C3×#102—42no—
129C3×C22⋊C8—22no—
130C3×C22⋊C8—22no—
131C23×D4C22×C311yescharacteristic
132C22×SD16C22×C312yes—
133C22×D8C22×C312yes—
134#529—24no—
135#529—24no—
136C2×#126—21no—
137C2×#125C22×C311yescharacteristic, complemented
138C2×#124C22×C311yescharacteristic, complemented
139C2×#123—21no—
140C2×C22⋊Q8C22×C311yescharacteristic
141C2×#121C22×C311yescharacteristic
142C2×C4×Q8C22×C311yescharacteristic, complemented
143C2×C4×D4—21no—
144C2×C4×D4C22×C311yescharacteristic, complemented
145C2×#117—21no—
146C22×C4⋊C4C22×C311yescharacteristic
147C22×C22⋊C4—21no—
148C22×C22⋊C4—21no—
149C22×C42C22×C311yescharacteristic
150#450—24no—
151#447—24no—
152C2×#103C22×C312yescomplemented
153C2×#102C22×C312yes—
154C2×#102C22×C312yes—
155C2×#102C22×C312yescomplemented
156C2×C22⋊C8C22×C311yescharacteristic
157C2×C22⋊C8C22×C311yescharacteristic
158#390—21no—
159#390—21no—
160#390C22×C312yes—
161#390C22×C312yes—
162#340C22×C312yescomplemented
163#340C22×C312yescomplemented
164#336C22×C312yescomplemented
165#336C22×C312yescomplemented
166C24×C3—24no—
167C24×C3—22no—
168C24×C3—21no—
169C24×C3—42no—
170C24×C3—42no—
171C24×C3—42no—
172C24×C3—42no—
173C24×C3—42no—
174C24×C3—42no—
175C24×C3C2×D411yescharacteristic
176C2×C3×Q8—21no—
177C2×C3×Q8—22no—
178C2×C3×Q8—22no—
179C2×C3×Q8C2×D412yes—
180C2×C3×D4—24no—
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—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—48no—
191C2×C3×D4—48no—
192C2×C3×D4—42no—
193C2×C3×D4—42no—
194C2×C3×D4—42no—
195C2×C3×D4—42no—
196C2×C3×D4C2×D412yes—
197C2×C3×D4#4114yes—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—24no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—22no—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—22no—
209C22×C3×C4—22no—
210C22×C3×C4—41no—
211C22×C3×C4—42no—
212C22×C3×C4—42no—
213C22×C3×C4—42no—
214C22×C3×C4—42no—
215C22×C3×C4—42no—
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D412yes—
221C22×C3×C4C2×D412yes—
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2411yescharacteristic
224C3×SD16—48no—
225C3×D8—48no—
226C2×C3×C8—22no—
227C2×C3×C8—22no—
228C2×C3×C8—22no—
229C2×C3×C8—22no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C3×C4⋊C4—24no—
233C3×C4⋊C4—24no—
234C3×C4⋊C4—24no—
235C3×C4⋊C4—24no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—42no—
241C3×C4⋊C4C2×D412yes—
242C3×C4⋊C4C2×D412yes—
243C3×C22⋊C4—24no—
244C3×C22⋊C4—24no—
245C3×C22⋊C4—24no—
246C3×C22⋊C4—24no—
247C3×C22⋊C4—24no—
248C3×C22⋊C4—44no—
249C3×C22⋊C4—44no—
250C3×C22⋊C4—44no—
251C3×C22⋊C4—44no—
252C3×C42—24no—
253C3×C42—22no—
254C3×C42—22no—
255C3×C42—21no—
256C3×C42—21no—
257C3×C42—21no—
258C3×C42—21no—
259C25—21no—
260C22×Q8C23×C311yescharacteristic
261C22×D4—21no—
262C22×D4—24no—
263C22×D4—21no—
264C22×D4—22no—
265C22×D4—22no—
266C22×D4—42no—
267C22×D4C23×C311yescharacteristic
268C22×D4C23×C312yes—
269C23×C4—21no—
270C23×C4—21no—
271C23×C4C3×D411yescharacteristic
272C23×C4C3×D411yescharacteristic
273C23×C4C23×C311yescharacteristic
274C2×SD16—24no—
275C2×SD16—24no—
276C2×SD16—42no—
277C2×D8—24no—
278C2×D8—24no—
279C2×D8—42no—
280C22×C8C23×C312yes—
281C22×C8C23×C312yes—
282#126—28no—
283#125—22no—
284#125—22no—
285#124—22no—
286#124—22no—
287#123—28no—
288C22⋊Q8—22no—
289C22⋊Q8C3×D414yes—
290#121—22no—
291#121C3×D414yes—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×D4—28no—
295C4×D4—22no—
296C4×D4—22no—
297#117—28no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—42no—
304C2×C4⋊C4C23×C312yes—
305C2×C4⋊C4C23×C311yescharacteristic
306C2×C4⋊C4C23×C311yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—22no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—44no—
317C2×C22⋊C4—44no—
318C2×C42—21no—
319C2×C42—22no—
320C2×C42—22no—
321C2×C42C3×D411yescharacteristic
322C2×C42C3×D411yescharacteristic
323C2×C42C23×C311yescharacteristic
324C2×C42C23×C311yescharacteristic
325#103—42no—
326#102—24no—
327#102—24no—
328#102—42no—
329C22⋊C8—22no—
330C22⋊C8—22no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—22no—
336C23×C3—24no—
337C23×C3—48no—
338C23×C3—48no—
339C23×C3—48no—
340C23×C3—42no—
341C23×C3—41no—
342C23×C3—42no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—41no—
349C23×C3—41no—
350C23×C3—41no—
351C23×C3—42no—
352C23×C3—84no—
353C23×C3—84no—
354C23×C3—84no—
355C23×C3—84no—
356C23×C3#12012yes—
357C23×C3#13512yes—
358C23×C3AGL(1,ℤ/8)12yes—
359C23×C3C22×D411yescharacteristic
360C3×Q8—24no—
361C3×Q8—42no—
362C3×D4—24no—
363C3×D4—24no—
364C3×D4—24no—
365C3×D4—48no—
366C3×D4—48no—
367C3×D4—42no—
368C3×D4—42no—
369C3×D4—42no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—24no—
375C2×C3×C4—24no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—44no—
389C2×C3×C4—48no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—44no—
397C2×C3×C4—42no—
398C2×C3×C4—42no—
399C2×C3×C4—42no—
400C2×C3×C4—84no—
401C2×C3×C4#12012yes—
402C2×C3×C4AGL(1,ℤ/8)12yes—
403C2×C3×C4C22×D411yescharacteristic
404C2×C3×C4C22×D411yescharacteristic
405C2×C3×C4C2×#4112yes—
406C2×C3×C4H(5,𝔽2)12yes—
407C3×C8—42no—
408C3×C8—42no—
409C24—24no—
410C24—21no—
411C24—22no—
412C24—42no—
413C24—42no—
414C24—42no—
415C24—42no—
416C24—42no—
417C24—42no—
418C24C2×C3×D411yescharacteristic
419C2×Q8—21no—
420C2×Q8—22no—
421C2×Q8—22no—
422C2×Q8C2×C3×D412yes—
423C2×D4—24no—
424C2×D4—24no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—48no—
434C2×D4—48no—
435C2×D4—42no—
436C2×D4—42no—
437C2×D4—42no—
438C2×D4—42no—
439C2×D4C2×C3×D412yes—
440C2×D4C3×#4114yes—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—24no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—41no—
454C22×C4—42no—
455C22×C4—42no—
456C22×C4—42no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4C2×C3×D411yescharacteristic
460C22×C4C2×C3×D411yescharacteristic
461C22×C4C2×C3×D411yescharacteristic
462C22×C4C2×C3×D411yescharacteristic
463C22×C4C2×C3×D412yes—
464C22×C4C2×C3×D412yes—
465C22×C4C2×C3×D411yescharacteristic
466C22×C4C24×C311yescharacteristic
467SD16—48no—
468D8—48no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C4⋊C4—24no—
476C4⋊C4—24no—
477C4⋊C4—24no—
478C4⋊C4—24no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—42no—
484C4⋊C4C2×C3×D412yes—
485C4⋊C4C2×C3×D412yes—
486C22⋊C4—24no—
487C22⋊C4—24no—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—24no—
491C22⋊C4—44no—
492C22⋊C4—44no—
493C22⋊C4—44no—
494C22⋊C4—44no—
495C42—24no—
496C42—22no—
497C42—22no—
498C42—21no—
499C42—21no—
500C42—21no—
501C42—21no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—44no—
509C22×C3—44no—
510C22×C3—44no—
511C22×C3—42no—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—816no—
515C22×C3—81no—
516C22×C3—81no—
517C22×C3—81no—
518C22×C3—82no—
519C22×C3—81no—
520C22×C3—82no—
521C22×C3—82no—
522C22×C3—82no—
523C22×C3#44914yes—
524C22×C3C2×#12011yescharacteristic
525C22×C3#52511yescharacteristic
526C22×C3#53511yescharacteristic
527C22×C3C2×#13511yescharacteristic
528C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
529C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
530C22×C3#57511yescharacteristic
531C3×C4—22no—
532C3×C4—22no—
533C3×C4—42no—
534C3×C4—41no—
535C3×C4—41no—
536C3×C4—42no—
537C3×C4—41no—
538C3×C4—42no—
539C3×C4—82no—
540C3×C4#54612yes—
541C3×C4#54612yes—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—22no—
547C23—24no—
548C23—48no—
549C23—48no—
550C23—48no—
551C23—41no—
552C23—42no—
553C23—42no—
554C23—42no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—42no—
559C23—42no—
560C23—41no—
561C23—42no—
562C23—41no—
563C23—84no—
564C23—84no—
565C23—84no—
566C23—84no—
567C23C3×#12012yes—
568C23C3×#13512yes—
569C23C3×AGL(1,ℤ/8)12yes—
570C23C22×C3×D411yescharacteristic
571Q8—24no—
572Q8—42no—
573D4—24no—
574D4—24no—
575D4—24no—
576D4—48no—
577D4—48no—
578D4—42no—
579D4—42no—
580D4—42no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—44no—
600C2×C4—48no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—44no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—42no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—84no—
612C2×C4C3×#12012yes—
613C2×C4C3×AGL(1,ℤ/8)12yes—
614C2×C4C22×C3×D411yescharacteristic
615C2×C4C22×C3×D411yescharacteristic
616C2×C4C2×C3×#4112yes—
617C2×C4C3×H(5,𝔽2)12yes—
618C8—42no—
619C8—42no—
620C2×C3—24no—
621C2×C3—82no—
622C2×C3—84no—
623C2×C3#240411yescharacteristic
624C2×C3C2×#44911yescharacteristic
625C2×C3#300611yescharacteristic
626C2×C3#310511yescharacteristic
627C2×C3#311411yescharacteristic
628C2×C3#321111yescharacteristic
629C2×C3#321711yescharacteristic
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—44no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—44no—
641C22—44no—
642C22—816no—
643C22—82no—
644C22—81no—
645C22—82no—
646C22—81no—
647C22—82no—
648C22—82no—
649C22—81no—
650C22—81no—
651C22C3×#44914yes—
652C22C2×C3×#12011yescharacteristic
653C22C3×#52511yescharacteristic
654C22C3×#53511yescharacteristic
655C22C2×C3×#13511yescharacteristic
656C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
657C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
658C22C3×#57511yescharacteristic
659C4—22no—
660C4—22no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—42no—
665C4—41no—
666C4—42no—
667C4—82no—
668C4C3×#54612yes—
669C4C3×#54612yes—
670C3#2393611yescharacteristic, direct product factor, Sylow
671C2—24no—
672C2—84no—
673C2—82no—
674C2C3×#240411yescharacteristic
675C2C2×C3×#44911yescharacteristic
676C2C3×#300611yescharacteristic
677C2C3×#310511yescharacteristic
678C2C3×#311411yescharacteristic
679C2C3×#321111yescharacteristic
680C2C3×#321711yescharacteristic
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. C2×C3×#529C2semidirect
2. C2×C3×#450C2semidirect
4. C2×C3×#390C2semidirect
5. C3×#2025C2semidirect
6. C3×#2012C2semidirect
7. C3×#1880C2semidirect
8. C3×#1879C2semidirect
9. C3×#1874C2semidirect
10. C3×#1872C2semidirect
11. C3×#1817C2semidirect
12. #23936C3direct (N × H)
19. C2×C3×#125C22semidirect
20. C2×C3×#124C22semidirect
24. C2×C3×C4×Q8C22semidirect
26. C2×C3×C4×D4C22semidirect
34. C2×C3×#103C22semidirect
37. C2×C3×#102C22semidirect
44. C3×#340C22semidirect
45. C3×#340C22semidirect
46. C3×#336C22semidirect
47. C3×#336C22semidirect
48. C2×#529C2×C3semidirect
49. C2×#450C2×C3semidirect
51. C2×#390C2×C3semidirect
52. #2025C2×C3semidirect
53. #2012C2×C3semidirect
54. #1880C2×C3semidirect
55. #1879C2×C3semidirect
56. #1874C2×C3semidirect
57. #1872C2×C3semidirect
58. #1817C2×C3semidirect
137. C2×#125C22×C3semidirect
138. C2×#124C22×C3semidirect
142. C2×C4×Q8C22×C3semidirect
144. C2×C4×D4C22×C3semidirect
152. C2×#103C22×C3semidirect
155. C2×#102C22×C3semidirect
162. #340C22×C3semidirect
163. #340C22×C3semidirect
164. #336C22×C3semidirect
165. #336C22×C3semidirect
670. C3#23936direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C2×C3×#4502
C2×C3×#4472
C2×C3×#3902
C3×#20252
C3×#20122
C3×#18802
C3×#18792
C3×#18742
C3×#18722
C3×#18172
#239363