Finite Group Databasebeta

← C3×#10595508 #13175099

Subgroups — C3×#10595508 #13175099

Order 1728.

1526 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3757C211yesmaximal, characteristic, complemented
2C32×#953C212yesmaximal, complemented
3C3×#63982C211yesmaximal, characteristic, complemented
4C3×#63980C211yesmaximal, characteristic, complemented
5C3×#67⋊Dic3C212yesmaximal, complemented
6C3×#63970C212yesmaximal, complemented
7C3×#63969C212yesmaximal, complemented
8C3×#63959C212yesmaximal, complemented
9C3×#63956C212yesmaximal, complemented
10C3×#5593—32nomaximal
11#10595508C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C22×C3×C3⋊Dic3C2211yescharacteristic
14C22×C3×C3⋊Dic3C2211yescharacteristic
15C2×C32×#67C2212yes—
16C2×C32×#67C2212yes—
17C2×C32×#67C2212yes—
18C2×C3×#627C2211yescharacteristic, complemented
19C2×C3×#625C2211yescharacteristic, complemented
20C2×C3×D3×Dic3C2212yescomplemented
21C3×#3757C2212yes—
22C3×#3757C2212yes—
23C32×#217C2212yes—
24C32×#217C2212yes—
25C32×#217C2212yes—
26C3×#3724C2211yescharacteristic, complemented
27C3×#3724C2211yescharacteristic, complemented
28C3×Dic3⋊Dic3C2212yescomplemented
29C3×Dic3⋊Dic3C2212yescomplemented
30C3×(C2×D3)⋊Dic3C2212yescomplemented
31C3×(C2×D3)⋊Dic3C2212yescomplemented
32C3×Dic32C2212yescomplemented
33C32×#120—32no—
34C2×#3757C2×C311yescharacteristic, complemented
35C3×#953—22no—
36C3×#953D312yescomplemented
37C3×#953C2×C312yescomplemented
38C2×C3×#217—32no—
39C2×C3×#217—61no—
40C3×#939—32no—
41C3×#939—32no—
42C3×#938—32no—
43C3×#936—32no—
44C3×#935—32no—
45C3×D4×Dic3—32no—
46C3×#885—32no—
47C3×#883—32no—
48C3×#67⋊C4—32no—
49C3×#879—32no—
50C3×#879—32no—
51C3×#878—32no—
52#63982C2×C311yescharacteristic, complemented
53#63980C2×C311yescharacteristic, complemented
54#67⋊Dic3C2×C312yescomplemented
55#63970C2×C312yescomplemented
56#63969C2×C312yescomplemented
57#63959C2×C312yescomplemented
58#63956C2×C312yescomplemented
59C23×C33—22no—
60C23×C33—41no—
61C23×C33—41no—
62C23×C33C2312yes—
63C23×C33C2311yescharacteristic
64C22×C32×D3C2312yes—
65C2×C3×C3⋊Dic3—41no—
66C2×C3×C3⋊Dic3—41no—
67C2×C3×C3⋊Dic3C2312yes—
68C2×C3×C3⋊Dic3C2311yescharacteristic
69C2×C3×C3⋊Dic3C2311yescharacteristic
70C32×#67—24no—
71C32×#67—42no—
72C32×#67—42no—
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C2×C32×Dic3C2312yes—
76C3×#627—41no—
77C3×#625—41no—
78C3×D3×Dic3—42no—
79C3×#538—91no—
80#5593—32no—
81C24×C32—21no—
82C24×C32—22no—
83C24×C32—41no—
84C24×C32C2×D312yes—
85C24×C32C22×C311yescharacteristic
86C2×C32×D4—32no—
87C2×C32×D4—32no—
88C2×C32×D4—32no—
89C22×C3⋊Dic3C22×C311yescharacteristic
90C22×C3⋊Dic3C22×C311yescharacteristic
91C2×C3×#67—22no—
92C2×C3×#67—22no—
93C2×C3×#67—22no—
94C2×C3×#67—32no—
95C2×C3×#67C2×D312yes—
96C2×C3×#67C2×D312yes—
97C2×C3×#67C2×D312yes—
98C2×C3×#67C22×C312yes—
99C2×C3×#67C22×C312yes—
100C2×C3×#67C22×C312yes—
101C22×C3×Dic3—32no—
102C22×C3×Dic3—32no—
103C22×C3×Dic3—32no—
104C22×C3×Dic3—61no—
105C22×C3×Dic3—61no—
106C2×C3×C4×D3—32no—
107C2×C3×Dic6—32no—
108C2×#627C22×C311yescharacteristic, complemented
109C2×#625C22×C311yescharacteristic, complemented
110C2×D3×Dic3C22×C312yescomplemented
111C32×C22⋊C4—32no—
112C32×C22⋊C4—32no—
113C32×C22⋊C4—32no—
114#3757C22×C312yes—
115#3757C22×C312yes—
116C3×#217—22no—
117C3×#217—22no—
118C3×#217—22no—
119C3×#217—32no—
120C3×#217—32no—
121C3×#217—32no—
122C3×#217—32no—
123C3×#217—32no—
124C3×#217—32no—
125C3×#217—62no—
126C3×#217—62no—
127C3×#217C2×D312yes—
128C3×#217C2×D312yes—
129C3×#217C2×D312yes—
130C3×#217C22×C312yes—
131C3×#217C22×C312yes—
132C3×#217C22×C312yes—
133C3×(C2×D3)⋊C4—32no—
134C3×(C2×D3)⋊C4—32no—
135C3×C4⋊Dic3—32no—
136C3×C4⋊Dic3—32no—
137C3×Dic3⋊C4—32no—
138C3×Dic3⋊C4—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×C4×Dic3—32no—
142C3×C4×Dic3—32no—
143#3724C22×C311yescharacteristic, complemented
144#3724C22×C311yescharacteristic, complemented
145Dic3⋊Dic3C22×C312yescomplemented
146Dic3⋊Dic3C22×C312yescomplemented
147(C2×D3)⋊Dic3C22×C312yescomplemented
148(C2×D3)⋊Dic3C22×C312yescomplemented
149Dic32C22×C312yescomplemented
150C22×C33—21no—
151C22×C33—21no—
152C22×C33—22no—
153C22×C33—22no—
154C22×C33—22no—
155C22×C33—44no—
156C22×C33#4112yes—
157C22×C33C2411yescharacteristic
158C2×C32×D3—22no—
159C2×C32×D3—22no—
160C2×C32×D3—22no—
161C3×C3⋊Dic3—22no—
162C3×C3⋊Dic3—21no—
163C3×C3⋊Dic3—21no—
164C32×Dic3—22no—
165C32×Dic3—22no—
166C32×Dic3—22no—
167C3×#126—92no—
168C3×#124—92no—
169C3×#123—92no—
170C3×C22⋊Q8—91no—
171C3×#121—92no—
172C3×#121—91no—
173C3×#120—32no—
174C3×#120—32no—
175C3×#120—62no—
176C3×C4×D4—92no—
177C2×C3×C22⋊C4—91no—
178#953C3×D312yescomplemented
179C2×#217—32no—
180C2×#217—61no—
181#939—32no—
182#939—32no—
183#938—32no—
184#936—32no—
185#935—32no—
186D4×Dic3—32no—
187#885—32no—
188#883—32no—
189#67⋊C4—32no—
190#879—32no—
191#879—32no—
192#878—32no—
193C23×C32—22no—
194C23×C32—24no—
195C23×C32—24no—
196C23×C32—21no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—22no—
200C23×C32—22no—
201C23×C32—32no—
202C23×C32—41no—
203C23×C32—42no—
204C23×C32—44no—
205C23×C32—44no—
206C23×C32—42no—
207C23×C32—42no—
208C23×C32—41no—
209C23×C32—41no—
210C23×C32—42no—
211C23×C32—42no—
212C23×C32—44no—
213C23×C32—44no—
214C23×C32—44no—
215C23×C32—44no—
216C23×C32C22×D312yes—
217C23×C32C22×D312yes—
218C23×C32C22×D312yes—
219C23×C32C23×C312yes—
220C23×C32C23×C311yescharacteristic
221C22×C3×D3—22no—
222C22×C3×D3C22×D312yes—
223C22×C3×D3C23×C312yes—
224C32×D4—64no—
225C32×D4—122no—
226C32×D4—122no—
227C2×C32×C4—32no—
228C2×C32×C4—32no—
229C2×C32×C4—32no—
230C2×C3⋊Dic3—41no—
231C2×C3⋊Dic3—41no—
232C2×C3⋊Dic3C23×C312yes—
233C2×C3⋊Dic3C23×C311yescharacteristic
234C2×C3⋊Dic3C23×C311yescharacteristic
235C3×#67—24no—
236C3×#67—24no—
237C3×#67—44no—
238C3×#67—42no—
239C3×#67—42no—
240C3×#67—42no—
241C3×#67—42no—
242C3×#67—44no—
243C3×#67—44no—
244C3×#67—122no—
245C2×C3×Dic3—22no—
246C2×C3×Dic3—22no—
247C2×C3×Dic3—22no—
248C2×C3×Dic3—32no—
249C2×C3×Dic3—32no—
250C2×C3×Dic3—32no—
251C2×C3×Dic3—32no—
252C2×C3×Dic3—62no—
253C2×C3×Dic3—61no—
254C2×C3×Dic3—61no—
255C2×C3×Dic3—122no—
256C2×C3×Dic3—122no—
257C2×C3×Dic3—122no—
258C2×C3×Dic3—122no—
259C2×C3×Dic3—122no—
260C2×C3×Dic3C22×D312yes—
261C2×C3×Dic3C22×D312yes—
262C2×C3×Dic3C22×D312yes—
263C2×C3×Dic3C23×C312yes—
264C2×C3×Dic3C23×C312yes—
265C2×C3×Dic3C23×C312yes—
266C3×C4×D3—122no—
267C3×Dic6—122no—
268#627—41no—
269#625—41no—
270D3×Dic3—42no—
271#538—91noSylow
272C2×C33—22no—
273C2×C33—42no—
274C2×C33C2×#4111yescharacteristic
275C2×C33H(5,𝔽2)11yescharacteristic
276C2×C33H(5,𝔽2)11yescharacteristic
277C32×D3—42no—
278C24×C3—21no—
279C24×C3—22no—
280C24×C3—41no—
281C24×C3D3211yescharacteristic
282C24×C3C2×C3×D312yes—
283C2×C3×Q8—91no—
284C2×C3×D4—32no—
285C2×C3×D4—32no—
286C2×C3×D4—32no—
287C2×C3×D4—32no—
288C2×C3×D4—32no—
289C2×C3×D4—32no—
290C2×C3×D4—62no—
291C2×C3×D4—62no—
292C2×C3×D4—62no—
293C2×C3×D4—91no—
294C22×C3×C4—92no—
295C22×C3×C4—91no—
296C22×C3×C4—91no—
297C2×#67—32no—
298C2×#67C2×C3×D312yes—
299C2×#67C2×C3×D312yes—
300C2×#67C2×C3×D312yes—
301C22×Dic3—32no—
302C22×Dic3—32no—
303C22×Dic3—32no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C2×C4×D3—32no—
307C2×Dic6—32no—
308C3×C4⋊C4—91no—
309C3×C4⋊C4—91no—
310C3×C4⋊C4—92no—
311C3×C4⋊C4—92no—
312C3×C22⋊C4—32no—
313C3×C22⋊C4—32no—
314C3×C22⋊C4—32no—
315C3×C22⋊C4—32no—
316C3×C22⋊C4—32no—
317C3×C22⋊C4—32no—
318C3×C22⋊C4—62no—
319C3×C22⋊C4—62no—
320C3×C22⋊C4—62no—
321C3×C22⋊C4—92no—
322C3×C22⋊C4—92no—
323C3×C22⋊C4—92no—
324C3×C22⋊C4—92no—
325C3×C42—92no—
326#217—32no—
327#217—32no—
328#217—32no—
329#217—32no—
330#217—32no—
331#217—32no—
332#217—62no—
333#217—62no—
334#217C2×C3×D312yes—
335#217C2×C3×D312yes—
336#217C2×C3×D312yes—
337(C2×D3)⋊C4—32no—
338(C2×D3)⋊C4—32no—
339C4⋊Dic3—32no—
340C4⋊Dic3—32no—
341Dic3⋊C4—32no—
342Dic3⋊C4—32no—
343Dic3⋊C4—32no—
344Dic3⋊C4—32no—
345C4×Dic3—32no—
346C4×Dic3—32no—
347C22×C32—21no—
348C22×C32—21no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—22no—
356C22×C32—24no—
357C22×C32—24no—
358C22×C32—24no—
359C22×C32—22no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—21no—
366C22×C32—22no—
367C22×C32—22no—
368C22×C32—24no—
369C22×C32—42no—
370C22×C32—41no—
371C22×C32—42no—
372C22×C32—42no—
373C22×C32—42no—
374C22×C32—42no—
375C22×C32—42no—
376C22×C32—42no—
377C22×C32—42no—
378C22×C32—42no—
379C22×C32—42no—
380C22×C32—42no—
381C22×C32—44no—
382C22×C32—44no—
383C22×C32—44no—
384C22×C32—44no—
385C22×C32—48no—
386C22×C32—48no—
387C22×C32—416no—
388C22×C32—416no—
389C22×C32—62no—
390C22×C32—62no—
391C22×C32—62no—
392C22×C32#23714yes—
393C22×C32C3×#4112yes—
394C22×C32C23×D312yes—
395C22×C32C24×C311yescharacteristic
396C2×C3×D3—22no—
397C2×C3×D3—22no—
398C2×C3×D3—22no—
399C2×C3×D3—22no—
400C2×C3×D3—22no—
401C2×C3×D3—22no—
402C2×C3×D3—42no—
403C2×C3×D3—42no—
404C2×C3×D3—42no—
405C32×C4—62no—
406C32×C4—62no—
407C32×C4—62no—
408C3⋊Dic3—22no—
409C3⋊Dic3—21no—
410C3⋊Dic3—21no—
411C3×Dic3—22no—
412C3×Dic3—22no—
413C3×Dic3—22no—
414C3×Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—42no—
418C3×Dic3—42no—
419C3×Dic3—42no—
420C3×Dic3—62no—
421C3×Dic3—62no—
422C3×Dic3—62no—
423C3×Dic3—62no—
424C3×Dic3—122no—
425C3×Dic3—121no—
426C3×Dic3—121no—
427#126—92no—
428#124—92no—
429#123—92no—
430C22⋊Q8—91no—
431#121—92no—
432#121—91no—
433#120—32no—
434C4×D4—92no—
435C2×C22⋊C4—91no—
436C33#53811yescharacteristic, complemented, Sylow
437C23×C3—24no—
438C23×C3—22no—
439C23×C3—24no—
440C23×C3—21no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—32no—
446C23×C3—32no—
447C23×C3—44no—
448C23×C3—44no—
449C23×C3—41no—
450C23×C3—41no—
451C23×C3—42no—
452C23×C3—42no—
453C23×C3—42no—
454C23×C3—42no—
455C23×C3—44no—
456C23×C3—44no—
457C23×C3—44no—
458C23×C3—44no—
459C23×C3—42no—
460C23×C3—41no—
461C23×C3—62no—
462C23×C3C2×D3212yes—
463C23×C3C2×D3211yescharacteristic
464C23×C3C22×C3×D312yes—
465C23×C3C22×C3×D312yes—
466C23×C3C22×C3×D312yes—
467C22×D3C22×C3×D312yes—
468C3×Q8—361no—
469C3×D4—64no—
470C3×D4—64no—
471C3×D4—124no—
472C3×D4—122no—
473C3×D4—122no—
474C3×D4—122no—
475C3×D4—122no—
476C3×D4—124no—
477C3×D4—124no—
478C3×D4—361no—
479C2×C3×C4—32no—
480C2×C3×C4—32no—
481C2×C3×C4—32no—
482C2×C3×C4—32no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488C2×C3×C4—92no—
489C2×C3×C4—91no—
490C2×C3×C4—91no—
491C2×C3×C4—362no—
492C2×C3×C4—361no—
493C2×C3×C4—361no—
494#67—24no—
495#67—42no—
496#67—42no—
497#67—122no—
498C2×Dic3—32no—
499C2×Dic3—32no—
500C2×Dic3—32no—
501C2×Dic3—32no—
502C2×Dic3—62no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—122no—
506C2×Dic3—122no—
507C2×Dic3—122no—
508C2×Dic3—122no—
509C2×Dic3—122no—
510C2×Dic3C22×C3×D312yes—
511C2×Dic3C22×C3×D312yes—
512C2×Dic3C22×C3×D312yes—
513C4×D3—122no—
514Dic6—122no—
515C2×C32—22no—
516C2×C32—24no—
517C2×C32—24no—
518C2×C32—21no—
519C2×C32—21no—
520C2×C32—21no—
521C2×C32—22no—
522C2×C32—22no—
523C2×C32—22no—
524C2×C32—41no—
525C2×C32—41no—
526C2×C32—41no—
527C2×C32—44no—
528C2×C32—44no—
529C2×C32—44no—
530C2×C32—44no—
531C2×C32—44no—
532C2×C32—48no—
533C2×C32—42no—
534C2×C32—42no—
535C2×C32—42no—
536C2×C32—122no—
537C2×C32C2×#23712yes—
538C2×C32#100412yes—
539C2×C32#100412yes—
540C2×C32C2×C3×#4111yescharacteristic
541C2×C32C3×H(5,𝔽2)11yescharacteristic
542C2×C32C3×H(5,𝔽2)11yescharacteristic
543C3×D3—42no—
544C3×D3—42no—
545C3×D3—82no—
546C24C3×D3211yescharacteristic
547C2×Q8—91no—
548C2×D4—32no—
549C2×D4—32no—
550C2×D4—32no—
551C2×D4—91no—
552C22×C4—92no—
553C22×C4—91no—
554C22×C4—91no—
555C4⋊C4—92no—
556C4⋊C4—92no—
557C4⋊C4—91no—
558C4⋊C4—91no—
559C22⋊C4—32no—
560C22⋊C4—32no—
561C22⋊C4—32no—
562C22⋊C4—92no—
563C22⋊C4—92no—
564C22⋊C4—92no—
565C22⋊C4—92no—
566C42—92no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—21no—
570C22×C3—21no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—24no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—21no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—24no—
589C22×C3—42no—
590C22×C3—42no—
591C22×C3—42no—
592C22×C3—42no—
593C22×C3—42no—
594C22×C3—42no—
595C22×C3—42no—
596C22×C3—42no—
597C22×C3—42no—
598C22×C3—42no—
599C22×C3—44no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—48no—
603C22×C3—48no—
604C22×C3—44no—
605C22×C3—416no—
606C22×C3—416no—
607C22×C3—41no—
608C22×C3—42no—
609C22×C3—62no—
610C22×C3—62no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—62no—
615C22×C3—122no—
616C22×C3—122no—
617C22×C3—122no—
618C22×C3#380512yes—
619C22×C3C3×#23714yes—
620C22×C3C22×D3211yescharacteristic
621C22×C3C23×C3×D312yes—
622C2×D3—22no—
623C2×D3—22no—
624C2×D3—22no—
625C3×C4—62no—
626C3×C4—62no—
627C3×C4—62no—
628C3×C4—62no—
629C3×C4—62no—
630C3×C4—62no—
631C3×C4—122no—
632C3×C4—122no—
633C3×C4—122no—
634C3×C4—182no—
635C3×C4—181no—
636C3×C4—181no—
637Dic3—22no—
638Dic3—22no—
639Dic3—22no—
640Dic3—62no—
641Dic3—62no—
642Dic3—62no—
643Dic3—62no—
644Dic3—122no—
645Dic3—121no—
646Dic3—121no—
647C32—22no—
648C32—21no—
649C32—41no—
650C32#559312yescomplemented
651C32C3×#53811yescharacteristic, complemented
652C23—22no—
653C23—32no—
654C23—41no—
655C23—41no—
656C23C2×C3×D3212yes—
657C23C2×C3×D3211yescharacteristic
658Q8—361no—
659D4—64no—
660D4—122no—
661D4—122no—
662D4—361no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—92no—
667C2×C4—91no—
668C2×C4—91no—
669C2×C4—362no—
670C2×C4—361no—
671C2×C4—361no—
672C2×C3—24no—
673C2×C3—24no—
674C2×C3—22no—
675C2×C3—22no—
676C2×C3—21no—
677C2×C3—21no—
678C2×C3—21no—
679C2×C3—22no—
680C2×C3—22no—
681C2×C3—44no—
682C2×C3—44no—
683C2×C3—44no—
684C2×C3—44no—
685C2×C3—44no—
686C2×C3—48no—
687C2×C3—42no—
688C2×C3—42no—
689C2×C3—42no—
690C2×C3—41no—
691C2×C3—41no—
692C2×C3—41no—
693C2×C3—122no—
694C2×C3—122no—
695C2×C3—242no—
696C2×C3C2×#380511yescharacteristic
697C2×C3#6433011yescharacteristic
698C2×C3#6433011yescharacteristic
699C2×C3C2×C3×#23712yes—
700C2×C3C3×#100412yes—
701C2×C3C3×#100412yes—
702D3—42no—
703C22—21no—
704C22—21no—
705C22—22no—
706C22—22no—
707C22—22no—
708C22—44no—
709C22—62no—
710C22—62no—
711C22—62no—
712C22C3×#380512yes—
713C22C22×C3×D3211yescharacteristic
714C4—62no—
715C4—62no—
716C4—62no—
717C4—182no—
718C4—181no—
719C4—181no—
720C3—21no—
721C3—22no—
722C3—41no—
723C3#1059550811yescharacteristic, direct product factor
724C3C3×#559312yescomplemented
725C2—22no—
726C2—42no—
727C2—122no—
728C2C2×C3×#380511yescharacteristic
729C2C3×#6433011yescharacteristic
730C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
hypercenterC24×C3D32
hypocenterC32C3×#538
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3757C2semidirect
2. C32×#953C2semidirect
3. C3×#63982C2semidirect
4. C3×#63980C2semidirect
5. C3×#67⋊Dic3C2semidirect
6. C3×#63970C2semidirect
7. C3×#63969C2semidirect
8. C3×#63959C2semidirect
9. C3×#63956C2semidirect
11. #10595508C3direct (N × H)
18. C2×C3×#627C22semidirect
19. C2×C3×#625C22semidirect
20. C2×C3×D3×Dic3C22semidirect
26. C3×#3724C22semidirect
27. C3×#3724C22semidirect
28. C3×Dic3⋊Dic3C22semidirect
29. C3×Dic3⋊Dic3C22semidirect
30. C3×(C2×D3)⋊Dic3C22semidirect
31. C3×(C2×D3)⋊Dic3C22semidirect
32. C3×Dic32C22semidirect
34. C2×#3757C2×C3semidirect
36. C3×#953D3semidirect
37. C3×#953C2×C3semidirect
52. #63982C2×C3semidirect
53. #63980C2×C3semidirect
54. #67⋊Dic3C2×C3semidirect
55. #63970C2×C3semidirect
56. #63969C2×C3semidirect
57. #63959C2×C3semidirect
58. #63956C2×C3semidirect
108. C2×#627C22×C3semidirect
109. C2×#625C22×C3semidirect
110. C2×D3×Dic3C22×C3semidirect
143. #3724C22×C3semidirect
144. #3724C22×C3semidirect
145. Dic3⋊Dic3C22×C3semidirect
146. Dic3⋊Dic3C22×C3semidirect
147. (C2×D3)⋊Dic3C22×C3semidirect
148. (C2×D3)⋊Dic3C22×C3semidirect
149. Dic32C22×C3semidirect
178. #953C3×D3semidirect
436. C33#538semidirect
650. C32#5593semidirect
651. C32C3×#538semidirect
723. C3#10595508direct (N × H)
724. C3C3×#5593semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37572
C32×#9532
C3×#639822
C3×#639802
C3×#67⋊Dic32
C3×#639702
C3×#639692
C3×#639592
C3×#639562
C3×#55933
#105955083