Finite Group Databasebeta

← C3×#10595505 #13175101

Subgroups — C3×#10595505 #13175101

Order 1728.

1532 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64162C211yesmaximal, characteristic, complemented
2C32×#953C212yesmaximal, complemented
3C3×#63979C211yesmaximal, characteristic, complemented
4C3×#63975C211yesmaximal, characteristic, complemented
5C3×#63971C212yesmaximal, complemented
6C3×#63970C212yesmaximal, complemented
7C3×#63969C212yesmaximal, complemented
8C3×#63958C212yesmaximal, complemented
9C3×#63956C212yesmaximal, complemented
10C3×#5595—32nomaximal
11#10595505C311yesmaximal, characteristic, direct product factor
12C24×C33C2211yescharacteristic
13C2×C3×#638C2212yes—
14C2×C3×#638C2211yescharacteristic
15C2×C32×#67C2212yes—
16C2×C32×#67C2212yes—
17C2×C32×#67C2212yes—
18C2×C3×#626C2212yescomplemented
19C2×C3×#625C2211yescharacteristic, complemented
20C2×C3×#624C2211yescharacteristic, complemented
21C2×C3×D3×Dic3C2212yescomplemented
22C3×#3757C2212yes—
23C3×#3757C2211yescharacteristic
24C32×#217C2212yes—
25C32×#217C2212yes—
26C32×#217C2212yes—
27C3×#3724C2212yescomplemented
28C3×Dic3⋊Dic3C2212yescomplemented
29C3×Dic3⋊Dic3C2212yescomplemented
30C3×#3722C2211yescharacteristic, complemented
31C3×(C2×D3)⋊Dic3C2212yescomplemented
32C3×Dic32C2211yescharacteristic, complemented
33C32×#120—32no—
34#64162C2×C311yescharacteristic, complemented
35C3×#953—22no—
36C3×#953—32no—
37C3×#953—61no—
38C3×#953D312yescomplemented
39C3×#953C2×C312yescomplemented
40C3×#940—32no—
41C3×#939—32no—
42C3×#939—32no—
43C3×#938—32no—
44C3×#938—32no—
45C3×#935—32no—
46C3×#884—32no—
47C3×#884—32no—
48C3×#883—32no—
49C3×#883—32no—
50C3×#879—32no—
51C3×#879—32no—
52#63979C2×C311yescharacteristic, complemented
53#63975C2×C311yescharacteristic, complemented
54#63971C2×C312yescomplemented
55#63970C2×C312yescomplemented
56#63969C2×C312yescomplemented
57#63958C2×C312yescomplemented
58#63956C2×C312yescomplemented
59C23×C33—42no—
60C23×C33—41no—
61C23×C33C2312yes—
62C23×C33C2311yescharacteristic
63C22×C3×C3⋊D3C2311yescharacteristic
64C22×C32×D3C2312yes—
65C3×#638—42no—
66C3×#638—41no—
67C2×C3×C3⋊Dic3C2312yes—
68C2×C3×C3⋊Dic3C2311yescharacteristic
69C32×#67—42no—
70C32×#67—42no—
71C32×#67—42no—
72C2×C32×Dic3C2312yes—
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C3×#626—42no—
76C3×#625—41no—
77C3×#624—41no—
78C3×D3×Dic3—42no—
79C3×#560—91no—
80#5595—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—
89C2×#638C22×C312yes—
90C2×#638C22×C311yescharacteristic
91C2×C3×#67—22no—
92C2×C3×#67—22no—
93C2×C3×#67—22no—
94C2×C3×#67—32no—
95C2×C3×#67—32no—
96C2×C3×#67—32no—
97C2×C3×#67—32no—
98C2×C3×#67—32no—
99C2×C3×#67—62no—
100C2×C3×#67—61no—
101C2×C3×#67C2×D312yes—
102C2×C3×#67C2×D312yes—
103C2×C3×#67C2×D312yes—
104C2×C3×#67C22×C312yes—
105C2×C3×#67C22×C312yes—
106C2×C3×#67C22×C312yes—
107C22×C3×Dic3—32no—
108C2×C3×D12—32no—
109C2×C3×C4×D3—32no—
110C2×C3×C4×D3—32no—
111C2×#626C22×C312yescomplemented
112C2×#625C22×C311yescharacteristic, complemented
113C2×#624C22×C311yescharacteristic, complemented
114C2×D3×Dic3C22×C312yescomplemented
115C32×C22⋊C4—32no—
116C32×C22⋊C4—32no—
117C32×C22⋊C4—32no—
118#3757C22×C312yes—
119#3757C22×C311yescharacteristic
120C3×#217—22no—
121C3×#217—22no—
122C3×#217—22no—
123C3×#217—32no—
124C3×#217—32no—
125C3×#217—32no—
126C3×#217—32no—
127C3×#217—62no—
128C3×#217—61no—
129C3×#217C2×D312yes—
130C3×#217C2×D312yes—
131C3×#217C2×D312yes—
132C3×#217C22×C312yes—
133C3×#217C22×C312yes—
134C3×#217C22×C312yes—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×C4⋊Dic3—32no—
138C3×C4⋊Dic3—32no—
139C3×Dic3⋊C4—32no—
140C3×Dic3⋊C4—32no—
141C3×Dic3⋊C4—32no—
142C3×Dic3⋊C4—32no—
143C3×C4×Dic3—32no—
144#3724C22×C312yescomplemented
145Dic3⋊Dic3C22×C312yescomplemented
146Dic3⋊Dic3C22×C312yescomplemented
147#3722C22×C311yescharacteristic, complemented
148(C2×D3)⋊Dic3C22×C312yescomplemented
149Dic32C22×C311yescharacteristic, complemented
150C22×C33—22no—
151C22×C33—22no—
152C22×C33—22no—
153C22×C33—22no—
154C22×C33—21no—
155C22×C33—44no—
156C22×C33C2411yescharacteristic
157C2×C3×C3⋊D3—21no—
158C2×C3×C3⋊D3—22no—
159C2×C32×D3—22no—
160C2×C32×D3—22no—
161C2×C32×D3—22no—
162C3×C3⋊Dic3—22no—
163C3×C3⋊Dic3—21no—
164C32×Dic3—22no—
165C32×Dic3—22no—
166C32×Dic3—22no—
167C3×#127—91no—
168C3×#126—92no—
169C3×#123—91no—
170C3×#123—92no—
171C3×#121—92no—
172C3×#121—92no—
173C3×#121—92no—
174C3×#120—32no—
175C3×#120—32no—
176C3×#120—62no—
177C3×#120—91no—
178#953—32no—
179#953—61no—
180#953C3×D312yescomplemented
181#940—32no—
182#939—32no—
183#939—32no—
184#938—32no—
185#938—32no—
186#935—32no—
187#884—32no—
188#884—32no—
189#883—32no—
190#883—32no—
191#879—32no—
192#879—32no—
193C23×C32—22no—
194C23×C32—21no—
195C23×C32—22no—
196C23×C32—22no—
197C23×C32—22no—
198C23×C32—32no—
199C23×C32—42no—
200C23×C32—41no—
201C23×C32—42no—
202C23×C32—42no—
203C23×C32—42no—
204C23×C32—42no—
205C23×C32—41no—
206C23×C32—42no—
207C23×C32—44no—
208C23×C32—44no—
209C23×C32—44no—
210C23×C32—44no—
211C23×C32—48no—
212C23×C32—44no—
213C23×C32C22×D312yes—
214C23×C32C22×D312yes—
215C23×C32C22×D312yes—
216C23×C32C23×C312yes—
217C23×C32C23×C311yescharacteristic
218C22×C3⋊D3C23×C311yescharacteristic
219C22×C3×D3—22no—
220C22×C3×D3—32no—
221C22×C3×D3—61no—
222C22×C3×D3C22×D312yes—
223C22×C3×D3C23×C312yes—
224C32×D4—122no—
225C32×D4—122no—
226C32×D4—122no—
227C2×C32×C4—32no—
228C2×C32×C4—32no—
229C2×C32×C4—32no—
230#638—42no—
231#638—41no—
232C2×C3⋊Dic3C23×C311yescharacteristic
233C2×C3⋊Dic3C23×C312yes—
234C3×#67—42no—
235C3×#67—42no—
236C3×#67—42no—
237C3×#67—42no—
238C3×#67—42no—
239C3×#67—42no—
240C3×#67—44no—
241C3×#67—44no—
242C3×#67—44no—
243C3×#67—122no—
244C3×#67—122no—
245C3×#67—122no—
246C3×#67—122no—
247C3×#67—122no—
248C3×#67—124no—
249C3×#67—122no—
250C2×C3×Dic3—22no—
251C2×C3×Dic3—22no—
252C2×C3×Dic3—22no—
253C2×C3×Dic3—32no—
254C2×C3×Dic3—32no—
255C2×C3×Dic3—32no—
256C2×C3×Dic3—61no—
257C2×C3×Dic3—62no—
258C2×C3×Dic3—122no—
259C2×C3×Dic3C22×D312yes—
260C2×C3×Dic3C22×D312yes—
261C2×C3×Dic3C22×D312yes—
262C2×C3×Dic3C23×C312yes—
263C2×C3×Dic3C23×C312yes—
264C2×C3×Dic3C23×C312yes—
265C3×D12—122no—
266C3×C4×D3—122no—
267C3×C4×D3—122no—
268#626—42no—
269#625—41no—
270#624—41no—
271D3×Dic3—42no—
272#560—91noSylow
273C2×C33—42no—
274C2×C33—41no—
275C2×C33H(5,𝔽2)12yes—
276C2×C33H(5,𝔽2)11yescharacteristic
277C3×C3⋊D3—41no—
278C32×D3—42no—
279C24×C3—22no—
280C24×C3—21no—
281C24×C3—41no—
282C24×C3D3211yescharacteristic
283C24×C3C2×C3×D312yes—
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—92no—
294C2×C3×D4—91no—
295C2×C3×D4—92no—
296C2×C3×D4—91no—
297C22×C3×C4—91no—
298C22×C3×C4—92no—
299C2×#67—32no—
300C2×#67—32no—
301C2×#67—32no—
302C2×#67—32no—
303C2×#67—32no—
304C2×#67—62no—
305C2×#67—61no—
306C2×#67C2×C3×D312yes—
307C2×#67C2×C3×D312yes—
308C2×#67C2×C3×D312yes—
309C22×Dic3—32no—
310C2×D12—32no—
311C2×C4×D3—32no—
312C2×C4×D3—32no—
313C3×C4⋊C4—92no—
314C3×C4⋊C4—92no—
315C3×C4⋊C4—92no—
316C3×C22⋊C4—32no—
317C3×C22⋊C4—32no—
318C3×C22⋊C4—32no—
319C3×C22⋊C4—32no—
320C3×C22⋊C4—32no—
321C3×C22⋊C4—32no—
322C3×C22⋊C4—62no—
323C3×C22⋊C4—62no—
324C3×C22⋊C4—62no—
325C3×C22⋊C4—91no—
326C3×C22⋊C4—92no—
327C3×C22⋊C4—92no—
328C3×C22⋊C4—91no—
329C3×C42—91no—
330#217—32no—
331#217—32no—
332#217—32no—
333#217—32no—
334#217—62no—
335#217—61no—
336#217C2×C3×D312yes—
337#217C2×C3×D312yes—
338#217C2×C3×D312yes—
339(C2×D3)⋊C4—32no—
340(C2×D3)⋊C4—32no—
341C4⋊Dic3—32no—
342C4⋊Dic3—32no—
343Dic3⋊C4—32no—
344Dic3⋊C4—32no—
345Dic3⋊C4—32no—
346Dic3⋊C4—32no—
347C4×Dic3—32no—
348C22×C32—22no—
349C22×C32—22no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—21no—
353C22×C32—24no—
354C22×C32—24no—
355C22×C32—24no—
356C22×C32—22no—
357C22×C32—24no—
358C22×C32—22no—
359C22×C32—22no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—22no—
364C22×C32—22no—
365C22×C32—22no—
366C22×C32—22no—
367C22×C32—21no—
368C22×C32—22no—
369C22×C32—41no—
370C22×C32—42no—
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—44no—
380C22×C32—42no—
381C22×C32—44no—
382C22×C32—44no—
383C22×C32—44no—
384C22×C32—416no—
385C22×C32—48no—
386C22×C32—416no—
387C22×C32—44no—
388C22×C32—48no—
389C22×C32—62no—
390C22×C32—62no—
391C22×C32—62no—
392C22×C32C23×D312yes—
393C22×C32C24×C311yescharacteristic
394C2×C3⋊D3—21no—
395C2×C3⋊D3—22no—
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—
405C2×C3×D3—62no—
406C2×C3×D3—62no—
407C2×C3×D3—62no—
408C2×C3×D3—121no—
409C2×C3×D3—122no—
410C32×C4—62no—
411C32×C4—62no—
412C32×C4—62no—
413C3⋊Dic3—22no—
414C3⋊Dic3—21no—
415C3×Dic3—22no—
416C3×Dic3—22no—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—22no—
421C3×Dic3—42no—
422C3×Dic3—42no—
423C3×Dic3—42no—
424C3×Dic3—62no—
425C3×Dic3—62no—
426C3×Dic3—62no—
427C3×Dic3—122no—
428C3×Dic3—121no—
429#127—91no—
430#126—92no—
431#123—91no—
432#123—92no—
433#121—92no—
434#121—92no—
435#121—92no—
436#120—32no—
437#120—91no—
438C33#56011yescharacteristic, complemented, Sylow
439C23×C3—22no—
440C23×C3—22no—
441C23×C3—22no—
442C23×C3—22no—
443C23×C3—21no—
444C23×C3—32no—
445C23×C3—32no—
446C23×C3—41no—
447C23×C3—42no—
448C23×C3—42no—
449C23×C3—42no—
450C23×C3—42no—
451C23×C3—42no—
452C23×C3—44no—
453C23×C3—44no—
454C23×C3—44no—
455C23×C3—44no—
456C23×C3—44no—
457C23×C3—48no—
458C23×C3—42no—
459C23×C3—41no—
460C23×C3—62no—
461C23×C3—91no—
462C23×C3C2×D3212yes—
463C23×C3C2×D3211yescharacteristic
464C23×C3C22×C3×D312yes—
465C23×C3C22×C3×D312yes—
466C23×C3C22×C3×D312yes—
467C22×D3—32no—
468C22×D3—61no—
469C22×D3C22×C3×D312yes—
470C3×D4—122no—
471C3×D4—122no—
472C3×D4—122no—
473C3×D4—122no—
474C3×D4—122no—
475C3×D4—122no—
476C3×D4—124no—
477C3×D4—124no—
478C3×D4—124no—
479C3×D4—362no—
480C3×D4—362no—
481C3×D4—361no—
482C3×D4—361no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—32no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—62no—
492C2×C3×C4—91no—
493C2×C3×C4—92no—
494C2×C3×C4—361no—
495C2×C3×C4—362no—
496#67—42no—
497#67—42no—
498#67—42no—
499#67—122no—
500#67—122no—
501#67—122no—
502#67—122no—
503#67—122no—
504#67—124no—
505#67—122no—
506C2×Dic3—32no—
507C2×Dic3—32no—
508C2×Dic3—32no—
509C2×Dic3—61no—
510C2×Dic3—62no—
511C2×Dic3—122no—
512C2×Dic3C22×C3×D312yes—
513C2×Dic3C22×C3×D312yes—
514C2×Dic3C22×C3×D312yes—
515D12—122no—
516C4×D3—122no—
517C4×D3—122no—
518C2×C32—21no—
519C2×C32—22no—
520C2×C32—22no—
521C2×C32—22no—
522C2×C32—22no—
523C2×C32—42no—
524C2×C32—41no—
525C2×C32—44no—
526C2×C32—44no—
527C2×C32—44no—
528C2×C32—44no—
529C2×C32—42no—
530C2×C32—48no—
531C2×C32—44no—
532C2×C32—42no—
533C2×C32—41no—
534C2×C32—42no—
535C2×C32—42no—
536C2×C32—42no—
537C2×C32—122no—
538C2×C32#100412yes—
539C2×C32#100412yes—
540C2×C32#100412yes—
541C2×C32C3×H(5,𝔽2)12yes—
542C2×C32C3×H(5,𝔽2)11yescharacteristic
543C3⋊D3—41no—
544C3×D3—42no—
545C3×D3—42no—
546C3×D3—82no—
547C3×D3—122no—
548C3×D3—241no—
549C24C3×D3211yescharacteristic
550C2×D4—32no—
551C2×D4—32no—
552C2×D4—32no—
553C2×D4—92no—
554C2×D4—91no—
555C2×D4—92no—
556C2×D4—91no—
557C22×C4—91no—
558C22×C4—92no—
559C4⋊C4—92no—
560C4⋊C4—92no—
561C4⋊C4—92no—
562C22⋊C4—32no—
563C22⋊C4—32no—
564C22⋊C4—32no—
565C22⋊C4—91no—
566C22⋊C4—92no—
567C22⋊C4—92no—
568C22⋊C4—91no—
569C42—91no—
570C22×C3—22no—
571C22×C3—24no—
572C22×C3—24no—
573C22×C3—24no—
574C22×C3—24no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—21no—
579C22×C3—22no—
580C22×C3—22no—
581C22×C3—22no—
582C22×C3—22no—
583C22×C3—22no—
584C22×C3—22no—
585C22×C3—22no—
586C22×C3—22no—
587C22×C3—22no—
588C22×C3—22no—
589C22×C3—21no—
590C22×C3—22no—
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—42no—
600C22×C3—44no—
601C22×C3—44no—
602C22×C3—44no—
603C22×C3—42no—
604C22×C3—44no—
605C22×C3—48no—
606C22×C3—416no—
607C22×C3—416no—
608C22×C3—48no—
609C22×C3—44no—
610C22×C3—41no—
611C22×C3—62no—
612C22×C3—62no—
613C22×C3—62no—
614C22×C3—62no—
615C22×C3—62no—
616C22×C3—62no—
617C22×C3—122no—
618C22×C3—122no—
619C22×C3—122no—
620C22×C3—181no—
621C22×C3—182no—
622C22×C3C22×D3211yescharacteristic
623C22×C3C23×C3×D312yes—
624C2×D3—22no—
625C2×D3—22no—
626C2×D3—22no—
627C2×D3—62no—
628C2×D3—62no—
629C2×D3—62no—
630C2×D3—121no—
631C2×D3—122no—
632C3×C4—62no—
633C3×C4—62no—
634C3×C4—62no—
635C3×C4—62no—
636C3×C4—62no—
637C3×C4—62no—
638C3×C4—122no—
639C3×C4—122no—
640C3×C4—122no—
641C3×C4—182no—
642C3×C4—181no—
643Dic3—22no—
644Dic3—22no—
645Dic3—22no—
646Dic3—62no—
647Dic3—62no—
648Dic3—62no—
649Dic3—122no—
650Dic3—121no—
651C32—22no—
652C32—21no—
653C32—41no—
654C32#559512yescomplemented
655C32C3×#56011yescharacteristic, complemented
656C23—32no—
657C23—41no—
658C23—42no—
659C23—91no—
660C23C2×C3×D3212yes—
661C23C2×C3×D3211yescharacteristic
662D4—122no—
663D4—122no—
664D4—122no—
665D4—362no—
666D4—362no—
667D4—361no—
668D4—361no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—32no—
672C2×C4—91no—
673C2×C4—92no—
674C2×C4—361no—
675C2×C4—362no—
676C2×C3—21no—
677C2×C3—22no—
678C2×C3—22no—
679C2×C3—22no—
680C2×C3—22no—
681C2×C3—44no—
682C2×C3—42no—
683C2×C3—44no—
684C2×C3—44no—
685C2×C3—44no—
686C2×C3—48no—
687C2×C3—44no—
688C2×C3—42no—
689C2×C3—42no—
690C2×C3—42no—
691C2×C3—42no—
692C2×C3—41no—
693C2×C3—41no—
694C2×C3—42no—
695C2×C3—122no—
696C2×C3—122no—
697C2×C3—242no—
698C2×C3—361no—
699C2×C3#6433011yescharacteristic
700C2×C3#6433012yes—
701C2×C3C3×#100412yes—
702C2×C3C3×#100412yes—
703C2×C3C3×#100412yes—
704D3—42no—
705D3—122no—
706D3—241no—
707C22—22no—
708C22—22no—
709C22—22no—
710C22—21no—
711C22—22no—
712C22—44no—
713C22—62no—
714C22—62no—
715C22—62no—
716C22—181no—
717C22—182no—
718C22C22×C3×D3211yescharacteristic
719C4—62no—
720C4—62no—
721C4—62no—
722C4—182no—
723C4—181no—
724C3—21no—
725C3—22no—
726C3—41no—
727C3#1059550511yescharacteristic, direct product factor
728C3C3×#559512yescomplemented
729C2—42no—
730C2—41no—
731C2—122no—
732C2—361no—
733C2C3×#6433011yescharacteristic
734C2C3×#6433012yes—
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC24×C33C22
socleC22×C33C24
hypercenterC24×C3D32
hypocenterC32C3×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C24×C3

Complements

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

NH ≅ G/Ntype
1. C3×#64162C2semidirect
2. C32×#953C2semidirect
3. C3×#63979C2semidirect
4. C3×#63975C2semidirect
5. C3×#63971C2semidirect
6. C3×#63970C2semidirect
7. C3×#63969C2semidirect
8. C3×#63958C2semidirect
9. C3×#63956C2semidirect
11. #10595505C3direct (N × H)
18. C2×C3×#626C22semidirect
19. C2×C3×#625C22semidirect
20. C2×C3×#624C22semidirect
21. C2×C3×D3×Dic3C22semidirect
27. C3×#3724C22semidirect
28. C3×Dic3⋊Dic3C22semidirect
29. C3×Dic3⋊Dic3C22semidirect
30. C3×#3722C22semidirect
31. C3×(C2×D3)⋊Dic3C22semidirect
32. C3×Dic32C22semidirect
34. #64162C2×C3semidirect
38. C3×#953D3semidirect
39. C3×#953C2×C3semidirect
52. #63979C2×C3semidirect
53. #63975C2×C3semidirect
54. #63971C2×C3semidirect
55. #63970C2×C3semidirect
56. #63969C2×C3semidirect
57. #63958C2×C3semidirect
58. #63956C2×C3semidirect
111. C2×#626C22×C3semidirect
112. C2×#625C22×C3semidirect
113. C2×#624C22×C3semidirect
114. C2×D3×Dic3C22×C3semidirect
144. #3724C22×C3semidirect
145. Dic3⋊Dic3C22×C3semidirect
146. Dic3⋊Dic3C22×C3semidirect
147. #3722C22×C3semidirect
148. (C2×D3)⋊Dic3C22×C3semidirect
149. Dic32C22×C3semidirect
180. #953C3×D3semidirect
438. C33#560semidirect
654. C32#5595semidirect
655. C32C3×#560semidirect
727. C3#10595505direct (N × H)
728. C3C3×#5595semidirect

Maximal subgroups

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

subgroupindex
C3×#641622
C32×#9532
C3×#639792
C3×#639752
C3×#639712
C3×#639702
C3×#639692
C3×#639582
C3×#639562
C3×#55953
#105955053