Finite Group Databasebeta

← C3×#24386 #10642993

Subgroups — C3×#24386 #10642993

Order 768.

1548 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×C22⋊Q8C211yesmaximal, characteristic
2C2×C3×#470C212yesmaximal, complemented
3C2×C3×#451C211yesmaximal, characteristic, complemented
4C2×C3×#407C211yesmaximal, characteristic
5C3×#2848C211yesmaximal, characteristic
6C3×#2035C212yesmaximal, complemented
7C3×#2001C212yesmaximal, complemented
8C3×#1894C212yesmaximal, complemented
9C3×#1872C211yesmaximal, characteristic, complemented
10C3×#1853C211yesmaximal, characteristic, complemented
11C3×#1787C211yesmaximal, characteristic, complemented
12#24386C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C24×C3×C4C2211yescharacteristic
15C22×C3×Q16C2212yescomplemented
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⋊Q8C2211yescharacteristic
22C2×C3×C22⋊Q8C2211yescharacteristic
23C2×C3×C22⋊Q8C2212yes—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C22×C3×C4⋊C4—21no—
26C22×C3×C4⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4—21no—
28C3×#470—28no—
29C3×#451—24no—
30C2×C3×#106C2212yescomplemented
31C2×C3×#103C2212yescomplemented
32C2×C3×#103C2212yescomplemented
33C2×C3×#103C2212yescomplemented
34C2×C3×#103C2212yescomplemented
35C3×#407—24no—
36C2×C3×C22⋊C8C2212yes—
37C2×C3×C22⋊C8C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C3×#385—21no—
40C3×#385—21no—
41C3×#385—21no—
42C3×#380C2211yescharacteristic
43C3×#380C2211yescharacteristic
44C3×#380C2211yescharacteristic
45C3×#379—21no—
46C3×#340C2212yescomplemented
47C3×#340C2212yescomplemented
48C22×C22⋊Q8C2×C311yescharacteristic
49C2×#470C2×C312yescomplemented
50C2×#451C2×C311yescharacteristic, complemented
51C2×#407C2×C311yescharacteristic
52#2848C2×C311yescharacteristic
53#2035C2×C312yescomplemented
54#2001C2×C312yescomplemented
55#1894C2×C312yescomplemented
56#1872C2×C311yescharacteristic, complemented
57#1853C2×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×Q8C2311yescharacteristic
66C22×C3×Q8C2312yes—
67C23×C3×C4—21no—
68C23×C3×C4—21no—
69C23×C3×C4—22no—
70C23×C3×C4—24no—
71C23×C3×C4—22no—
72C23×C3×C4—42no—
73C23×C3×C4D411yescharacteristic
74C23×C3×C4D411yescharacteristic
75C23×C3×C4D411yescharacteristic
76C23×C3×C4C2311yescharacteristic
77C23×C3×C4C2311yescharacteristic
78C23×C3×C4C2311yescharacteristic
79C2×C3×Q16—24no—
80C2×C3×Q16—24no—
81C2×C3×Q16—42no—
82C2×C3×M16—24no—
83C2×C3×M16—24no—
84C2×C3×M16—42no—
85C22×C3×C8C2312yes—
86C22×C3×C8C2312yes—
87C3×C22⋊Q8—28no—
88C3×C22⋊Q8—28no—
89C3×C22⋊Q8—24no—
90C3×C22⋊Q8—24no—
91C3×C22⋊Q8—24no—
92C3×C22⋊Q8—22no—
93C3×C22⋊Q8—24no—
94C3×C22⋊Q8—22no—
95C3×C22⋊Q8—42no—
96C3×C22⋊Q8D418yes—
97C2×C3×C4⋊C4—28no—
98C2×C3×C4⋊C4—22no—
99C2×C3×C4⋊C4—22no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—24no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2312yes—
109C2×C3×C22⋊C4—28no—
110C2×C3×C22⋊C4—22no—
111C2×C3×C22⋊C4—22no—
112C2×C3×C22⋊C4—21no—
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—
118C3×#106—24no—
119C3×#103—24no—
120C3×#103—24no—
121C3×#103—24no—
122C3×#103—42no—
123C3×C22⋊C8—22no—
124C3×C22⋊C8—24no—
125C3×C22⋊C8D414yes—
126C3×#95—21no—
127C3×#95—21no—
128C3×#95—21no—
129C23×Q8C22×C311yescharacteristic
130C24×C4C22×C311yescharacteristic
131C22×Q16C22×C312yescomplemented
132C22×M16C22×C312yes—
133C2×C22⋊Q8—21no—
134C2×C22⋊Q8—21no—
135C2×C22⋊Q8—28no—
136C2×C22⋊Q8C22×C311yescharacteristic
137C2×C22⋊Q8C22×C311yescharacteristic
138C2×C22⋊Q8C22×C312yes—
139C2×C22⋊Q8C22×C312yes—
140C2×C22⋊Q8C22×C311yescharacteristic
141C22×C4⋊C4—21no—
142C22×C4⋊C4C22×C311yescharacteristic
143C22×C22⋊C4—21no—
144#470—28no—
145#451—24no—
146C2×#106C22×C312yescomplemented
147C2×#103C22×C312yescomplemented
148C2×#103C22×C312yescomplemented
149C2×#103C22×C312yescomplemented
150C2×#103C22×C312yescomplemented
151#407—24no—
152C2×C22⋊C8C22×C311yescharacteristic
153C2×C22⋊C8C22×C312yes—
154C2×C22⋊C8C22×C311yescharacteristic
155#385—21no—
156#385—21no—
157#385—21no—
158#380C22×C311yescharacteristic
159#380C22×C311yescharacteristic
160#380C22×C311yescharacteristic
161#379—21no—
162#340C22×C312yescomplemented
163#340C22×C312yescomplemented
164C24×C3—22no—
165C24×C3—22no—
166C24×C3—22no—
167C24×C3—22no—
168C24×C3—22no—
169C24×C3—41no—
170C24×C3—41no—
171C24×C3C2×D411yescharacteristic
172C24×C3C2×D411yescharacteristic
173C24×C3C2×D411yescharacteristic
174C2×C3×Q8—24no—
175C2×C3×Q8—22no—
176C2×C3×Q8—22no—
177C2×C3×Q8—22no—
178C2×C3×Q8—21no—
179C2×C3×Q8—22no—
180C2×C3×Q8—21no—
181C2×C3×Q8—22no—
182C2×C3×Q8—22no—
183C2×C3×Q8—22no—
184C2×C3×Q8—48no—
185C2×C3×Q8—48no—
186C2×C3×Q8—42no—
187C2×C3×Q8—42no—
188C2×C3×Q8C2×D414yes—
189C22×C3×C4—22no—
190C22×C3×C4—21no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—22no—
194C22×C3×C4—24no—
195C22×C3×C4—24no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—22no—
200C22×C3×C4—22no—
201C22×C3×C4—22no—
202C22×C3×C4—22no—
203C22×C3×C4—22no—
204C22×C3×C4—21no—
205C22×C3×C4—22no—
206C22×C3×C4—21no—
207C22×C3×C4—22no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—21no—
211C22×C3×C4—21no—
212C22×C3×C4—41no—
213C22×C3×C4—41no—
214C22×C3×C4—41no—
215C22×C3×C4—48no—
216C22×C3×C4—48no—
217C22×C3×C4—42no—
218C22×C3×C4—42no—
219C22×C3×C4—42no—
220C22×C3×C4—42no—
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2×D411yescharacteristic
223C22×C3×C4C2×D414yes—
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D412yes—
226C22×C3×C4#4112yes—
227C22×C3×C4C2411yescharacteristic
228C3×Q16—48no—
229C3×M16—48no—
230C2×C3×C8—22no—
231C2×C3×C8—22no—
232C2×C3×C8—22no—
233C2×C3×C8—22no—
234C2×C3×C8—22no—
235C2×C3×C8C2×D414yes—
236C3×C4⋊C4—24no—
237C3×C4⋊C4—28no—
238C3×C4⋊C4—28no—
239C3×C4⋊C4—22no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—22no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—22no—
244C3×C4⋊C4—42no—
245C3×C4⋊C4—42no—
246C3×C4⋊C4—42no—
247C3×C4⋊C4C2×D414yes—
248C3×C22⋊C4—28no—
249C3×C22⋊C4—28no—
250C3×C22⋊C4—42no—
251C3×C22⋊C4—42no—
252C3×C22⋊C4—42no—
253C3×C22⋊C4—42no—
254C3×C22⋊C4—42no—
255C3×C22⋊C4—42no—
256C25C3×D411yescharacteristic
257C22×Q8—24no—
258C22×Q8—21no—
259C22×Q8—22no—
260C22×Q8—22no—
261C22×Q8—42no—
262C22×Q8C23×C311yescharacteristic
263C22×Q8C23×C312yes—
264C23×C4—21no—
265C23×C4—21no—
266C23×C4—24no—
267C23×C4—22no—
268C23×C4—22no—
269C23×C4—42no—
270C23×C4C3×D411yescharacteristic
271C23×C4C3×D411yescharacteristic
272C23×C4C3×D411yescharacteristic
273C23×C4C23×C311yescharacteristic
274C23×C4C23×C311yescharacteristic
275C23×C4C23×C311yescharacteristic
276C2×Q16—24no—
277C2×Q16—24no—
278C2×Q16—42no—
279C2×M16—24no—
280C2×M16—24no—
281C2×M16—42no—
282C22×C8C23×C312yes—
283C22×C8C23×C312yes—
284C22⋊Q8—28no—
285C22⋊Q8—28no—
286C22⋊Q8—24no—
287C22⋊Q8—24no—
288C22⋊Q8—24no—
289C22⋊Q8—22no—
290C22⋊Q8—24no—
291C22⋊Q8—22no—
292C22⋊Q8—42no—
293C22⋊Q8C3×D418yes—
294C2×C4⋊C4—28no—
295C2×C4⋊C4—22no—
296C2×C4⋊C4—22no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—24no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4C23×C311yescharacteristic
303C2×C4⋊C4C23×C311yescharacteristic
304C2×C4⋊C4C23×C311yescharacteristic
305C2×C4⋊C4C23×C312yes—
306C2×C22⋊C4—28no—
307C2×C22⋊C4—22no—
308C2×C22⋊C4—22no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315#106—24no—
316#103—24no—
317#103—24no—
318#103—24no—
319#103—42no—
320C22⋊C8—22no—
321C22⋊C8—24no—
322C22⋊C8C3×D414yes—
323#95—21no—
324#95—21no—
325#95—21no—
326C23×C3—21no—
327C23×C3—21no—
328C23×C3—21no—
329C23×C3—21no—
330C23×C3—28no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—21no—
334C23×C3—21no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—21no—
340C23×C3—21no—
341C23×C3—21no—
342C23×C3—21no—
343C23×C3—44no—
344C23×C3—44no—
345C23×C3—44no—
346C23×C3—44no—
347C23×C3—44no—
348C23×C3—44no—
349C23×C3#12012yes—
350C23×C3#12112yes—
351C23×C3#13712yes—
352C23×C3#13712yes—
353C23×C3#13712yes—
354C23×C3C22×D411yescharacteristic
355C3×Q8—24no—
356C3×Q8—24no—
357C3×Q8—48no—
358C3×Q8—42no—
359C3×Q8—42no—
360C3×Q8—42no—
361C3×Q8—42no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—24no—
367C2×C3×C4—24no—
368C2×C3×C4—24no—
369C2×C3×C4—24no—
370C2×C3×C4—24no—
371C2×C3×C4—24no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—44no—
376C2×C3×C4—44no—
377C2×C3×C4—44no—
378C2×C3×C4—48no—
379C2×C3×C4—48no—
380C2×C3×C4—42no—
381C2×C3×C4—42no—
382C2×C3×C4—42no—
383C2×C3×C4—42no—
384C2×C3×C4—42no—
385C2×C3×C4—42no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
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—41no—
397C2×C3×C4—41no—
398C2×C3×C4#12012yes—
399C2×C3×C4#12112yes—
400C2×C3×C4C22×D411yescharacteristic
401C2×C3×C4C22×D412yes—
402C2×C3×C4C2×#4111yescharacteristic
403C2×C3×C4H(5,𝔽2)12yes—
404C3×C8—24no—
405C3×C8—42no—
406C24—22no—
407C24—22no—
408C24—22no—
409C24—22no—
410C24—22no—
411C24—41no—
412C24—41no—
413C24C2×C3×D411yescharacteristic
414C24C2×C3×D411yescharacteristic
415C24C2×C3×D411yescharacteristic
416C2×Q8—24no—
417C2×Q8—22no—
418C2×Q8—22no—
419C2×Q8—22no—
420C2×Q8—21no—
421C2×Q8—22no—
422C2×Q8—21no—
423C2×Q8—22no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×Q8—48no—
427C2×Q8—48no—
428C2×Q8—42no—
429C2×Q8—42no—
430C2×Q8C2×C3×D414yes—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—22no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—21no—
449C22×C4—22no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—21no—
454C22×C4—41no—
455C22×C4—41no—
456C22×C4—41no—
457C22×C4—48no—
458C22×C4—48no—
459C22×C4—42no—
460C22×C4—42no—
461C22×C4—42no—
462C22×C4—42no—
463C22×C4C2×C3×D411yescharacteristic
464C22×C4C2×C3×D411yescharacteristic
465C22×C4C2×C3×D414yes—
466C22×C4C2×C3×D411yescharacteristic
467C22×C4C2×C3×D412yes—
468C22×C4C3×#4112yes—
469C22×C4C24×C311yescharacteristic
470Q16—48no—
471M16—48no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8C2×C3×D414yes—
478C4⋊C4—24no—
479C4⋊C4—28no—
480C4⋊C4—28no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—22no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4C2×C3×D414yes—
490C22⋊C4—28no—
491C22⋊C4—28no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—22no—
503C22×C3—22no—
504C22×C3—22no—
505C22×C3—22no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—416no—
511C22×C3—41no—
512C22×C3—41no—
513C22×C3—41no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—41no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3#47014yescomplemented
520C22×C3C2×#12011yescharacteristic
521C22×C3C2×#12111yescharacteristic
522C22×C3#53411yescharacteristic
523C22×C3C2×#13711yescharacteristic
524C22×C3C2×#13711yescharacteristic
525C22×C3C2×#13711yescharacteristic
526C22×C3#57511yescharacteristic
527C3×C4—22no—
528C3×C4—22no—
529C3×C4—41no—
530C3×C4—44no—
531C3×C4—44no—
532C3×C4—81no—
533C3×C4—81no—
534C3×C4—81no—
535C3×C4—81no—
536C3×C4D4212yes—
537C3×C4#54612yes—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—28no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—44no—
556C23—44no—
557C23—44no—
558C23—44no—
559C23—44no—
560C23—44no—
561C23C3×#12012yes—
562C23C3×#12112yes—
563C23C3×#13712yes—
564C23C3×#13712yes—
565C23C3×#13712yes—
566C23C22×C3×D411yescharacteristic
567Q8—24no—
568Q8—24no—
569Q8—48no—
570Q8—42no—
571Q8—42no—
572Q8—42no—
573Q8—42no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—24no—
583C2×C4—24no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—44no—
588C2×C4—44no—
589C2×C4—44no—
590C2×C4—48no—
591C2×C4—48no—
592C2×C4—42no—
593C2×C4—42no—
594C2×C4—42no—
595C2×C4—42no—
596C2×C4—42no—
597C2×C4—42no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4C3×#12012yes—
611C2×C4C3×#12112yes—
612C2×C4C22×C3×D411yescharacteristic
613C2×C4C22×C3×D412yes—
614C2×C4C2×C3×#4111yescharacteristic
615C2×C4C3×H(5,𝔽2)12yes—
616C8—24no—
617C8—42no—
618C2×C3—24no—
619C2×C3—42no—
620C2×C3—42no—
621C2×C3#241011yescharacteristic
622C2×C3#300411yescharacteristic
623C2×C3#300711yescharacteristic
624C2×C3C2×#47011yescharacteristic
625C2×C3#305611yescharacteristic
626C2×C3#319511yescharacteristic
627C2×C3#319611yescharacteristic
628C22—22no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—416no—
641C22—41no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—41no—
647C22—41no—
648C22—41no—
649C22C3×#47014yescomplemented
650C22C2×C3×#12011yescharacteristic
651C22C2×C3×#12111yescharacteristic
652C22C3×#53411yescharacteristic
653C22C2×C3×#13711yescharacteristic
654C22C2×C3×#13711yescharacteristic
655C22C2×C3×#13711yescharacteristic
656C22C3×#57511yescharacteristic
657C4—22no—
658C4—22no—
659C4—41no—
660C4—44no—
661C4—44no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4—81no—
666C4C3×D4212yes—
667C4C3×#54612yes—
668C3#2438611yescharacteristic, direct product factor, Sylow
669C2—24no—
670C2—42no—
671C2—42no—
672C2C3×#241011yescharacteristic
673C2C3×#300411yescharacteristic
674C2C3×#300711yescharacteristic
675C2C2×C3×#47011yescharacteristic
676C2C3×#305611yescharacteristic
677C2C3×#319511yescharacteristic
678C2C3×#319611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC25×C3D4
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
2. C2×C3×#470C2semidirect
3. C2×C3×#451C2semidirect
6. C3×#2035C2semidirect
7. C3×#2001C2semidirect
8. C3×#1894C2semidirect
9. C3×#1872C2semidirect
10. C3×#1853C2semidirect
11. C3×#1787C2semidirect
12. #24386C3direct (N × H)
15. C22×C3×Q16C22semidirect
30. C2×C3×#106C22semidirect
31. C2×C3×#103C22semidirect
32. C2×C3×#103C22semidirect
33. C2×C3×#103C22semidirect
34. C2×C3×#103C22semidirect
46. C3×#340C22semidirect
47. C3×#340C22semidirect
49. C2×#470C2×C3semidirect
50. C2×#451C2×C3semidirect
53. #2035C2×C3semidirect
54. #2001C2×C3semidirect
55. #1894C2×C3semidirect
56. #1872C2×C3semidirect
57. #1853C2×C3semidirect
58. #1787C2×C3semidirect
131. C22×Q16C22×C3semidirect
146. C2×#106C22×C3semidirect
147. C2×#103C22×C3semidirect
148. C2×#103C22×C3semidirect
149. C2×#103C22×C3semidirect
150. C2×#103C22×C3semidirect
162. #340C22×C3semidirect
163. #340C22×C3semidirect
519. C22×C3#470semidirect
649. C22C3×#470semidirect
668. C3#24386direct (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×#4702
C2×C3×#4512
C2×C3×#4072
C3×#28482
C3×#20352
C3×#20012
C3×#18942
C3×#18722
C3×#18532
C3×#17872
#243863