Finite Group Databasebeta

← C2×#11723643 #13178100

Subgroups — C2×#11723643 #13178100

Order 1728.

4916 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×C3⋊D3C211yesmaximal, characteristic, complemented
2C22×#6312C211yesmaximal, characteristic, complemented
3C22×C3×#638C211yesmaximal, characteristic, complemented
4C22×C32×#67C211yesmaximal, characteristic, complemented
5#11723643C218yesmaximal, direct product factor
6C2×#88804C211yesmaximal, characteristic, complemented
7C2×#88803C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
9C2×#64146—31nomaximal
10C2×#63983—34nomaximal
11C24×C33C2211yescharacteristic, complemented
12C23×C3⋊(C3⋊D3)C2211yescharacteristic
13C23×C3×C3⋊D3C2211yescharacteristic
14C23×C32×D3C2211yescharacteristic
15C22×D3×C3⋊D3—24no—
16C22×D3×C3⋊D3—24no—
17C22×D3×C3⋊D3—24no—
18C22×D3×C3⋊D3C2214yescomplemented
19C2×#6312—24no—
20C2×#6312C2214yescomplemented
21C22×C3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
22C2×C3×#638—24no—
23C2×C3×#638C2214yescomplemented
24C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
25C2×C32×#67—24no—
26C2×C32×#67C2214yescomplemented
27C22×C32×Dic3C2211yescharacteristic, complemented
28#88804C2214yescomplemented
29#88803C2214yescomplemented
30(C2×D3)⋊(C3⋊Dic3)C2214yescomplemented
31C24×C3⋊D3—31no—
32C23×D32—34no—
33C22×C32×D4—31no—
34C22×#638—31no—
35C22×#638—34no—
36C22×#638—64no—
37C22×#638D311yescharacteristic, complemented
38C22×C3×#67—34no—
39C22×C3×#67D314yescomplemented
40C2×#3757—31no—
41#64146—38no—
42C2×#3752—31no—
43C2×#3752—31no—
44#63983—332no—
45C2×#3722—34no—
46C2×(C2×D3)⋊Dic3—34no—
47C2×(C2×D3)⋊Dic3—34no—
48C23×C33—22no—
49C23×C33—22no—
50C23×C33—22no—
51C23×C33C2311yescharacteristic
52C23×C33C2312yescomplemented
53C22×C3⋊(C3⋊D3)—22no—
54C22×C3⋊(C3⋊D3)—22no—
55C22×C3⋊(C3⋊D3)D414yescomplemented
56C22×C3⋊(C3⋊D3)C2312yes—
57C22×C3×C3⋊D3—22no—
58C22×C3×C3⋊D3—22no—
59C22×C3×C3⋊D3D414yescomplemented
60C22×C3×C3⋊D3C2312yes—
61C22×C32×D3—22no—
62C22×C32×D3—22no—
63C22×C32×D3D414yescomplemented
64C22×C32×D3C2312yes—
65C2×D3×C3⋊D3—232no—
66C2×D3×C3⋊D3—28no—
67C2×D3×C3⋊D3—28no—
68C2×D3×C3⋊D3—28no—
69#6312—28no—
70C2×C3⋊(C3⋊Dic3)—22no—
71C2×C3⋊(C3⋊Dic3)C2312yescomplemented
72C3×#638—28no—
73C2×C3×C3⋊Dic3—22no—
74C2×C3×C3⋊Dic3C2312yescomplemented
75C32×#67—28no—
76C2×C32×Dic3—22no—
77C2×C32×Dic3C2312yescomplemented
78C2×#937—94no—
79C2×#937—91no—
80C24×C32—24no—
81C24×C32—31no—
82C24×C32C2×D314yescomplemented
83C24×C32C2×D311yescharacteristic, complemented
84C23×C3⋊D3—31no—
85C23×C3⋊D3—34no—
86C23×C3⋊D3—34no—
87C23×C3⋊D3—64no—
88C23×C3⋊D3—64no—
89C23×C3⋊D3—64no—
90C23×C3⋊D3—64no—
91C23×C3⋊D3C2×D311yescharacteristic
92C23×C3×D3—34no—
93C23×C3×D3C2×D314yes—
94C22×D32—316no—
95C22×D32—616no—
96C22×D32—616no—
97C22×D32—616no—
98C2×C32×D4—34no—
99C2×C32×D4—64no—
100C22×C32×C4—31no—
101C2×#638—24no—
102C2×#638—34no—
103C2×#638—316no—
104C2×#638—64no—
105C2×#638—616no—
106C2×#638—616no—
107C2×#638—632no—
108C2×#638C2×D314yescomplemented
109C22×C3⋊Dic3—31no—
110C22×C3⋊Dic3—34no—
111C22×C3⋊Dic3—64no—
112C22×C3⋊Dic3C2×D311yescharacteristic, complemented
113C2×C3×#67—216no—
114C2×C3×#67—316no—
115C2×C3×#67—616no—
116C2×C3×#67C2×D3116yescomplemented
117C22×C3×Dic3—34no—
118C22×C3×Dic3C2×D314yescomplemented
119#3757—34no—
120#3752—34no—
121#3752—34no—
122#3722—316no—
123(C2×D3)⋊Dic3—316no—
124(C2×D3)⋊Dic3—316no—
125C22×C33—22no—
126C22×C33—22no—
127C22×C33—22no—
128C22×C33—44no—
129C22×C33C2×D412yes—
130C22×C33C2×D412yes—
131C22×C33C2×D412yes—
132C22×C33C2411yescharacteristic
133C2×C3⋊(C3⋊D3)—28no—
134C2×C3⋊(C3⋊D3)—22no—
135C2×C3⋊(C3⋊D3)—22no—
136C2×C3⋊(C3⋊D3)C2×D414yescomplemented
137C2×C3×C3⋊D3—28no—
138C2×C3×C3⋊D3—22no—
139C2×C3×C3⋊D3—22no—
140C2×C3×C3⋊D3C2×D414yescomplemented
141C2×C32×D3—28no—
142C2×C32×D3—22no—
143C2×C32×D3—22no—
144C2×C32×D3C2×D414yescomplemented
145D3×C3⋊D3—232no—
146C3⋊(C3⋊Dic3)—22no—
147C3×C3⋊Dic3—22no—
148C32×Dic3—22no—
149C24×D3—94no—
150C24×D3—91no—
151C22×C3×D4—34no—
152C22×C3×D4—91no—
153C22×#67—34no—
154C22×#67—94no—
155C22×#67—91no—
156C22×#67—184no—
157C22×#67C3⋊D311yescharacteristic, complemented
158C2×#217—94no—
159C2×#217—91no—
160#937—932no—
161#937—98no—
162C2×(C2×D3)⋊C4—94no—
163C2×(C2×D3)⋊C4—94no—
164C2×(C2×D3)⋊C4—91no—
165C2×(C2×D3)⋊C4—91no—
166C23×C32—216no—
167C23×C32—28no—
168C23×C32—22no—
169C23×C32—22no—
170C23×C32—22no—
171C23×C32—24no—
172C23×C32—28no—
173C23×C32—28no—
174C23×C32—28no—
175C23×C32—34no—
176C23×C32—32no—
177C23×C32—48no—
178C23×C32—48no—
179C23×C32—62no—
180C23×C32—62no—
181C23×C32C22×D314yes—
182C23×C32C22×D311yescharacteristic
183C23×C32C22×D318yescomplemented
184C23×C32C22×D312yescomplemented
185C22×C3⋊D3—22no—
186C22×C3⋊D3—22no—
187C22×C3⋊D3—34no—
188C22×C3⋊D3—32no—
189C22×C3⋊D3—316no—
190C22×C3⋊D3—38no—
191C22×C3⋊D3—616no—
192C22×C3⋊D3—68no—
193C22×C3⋊D3—68no—
194C22×C3⋊D3—68no—
195C22×C3⋊D3—632no—
196C22×C3⋊D3—62no—
197C22×C3⋊D3—62no—
198C22×C3⋊D3—68no—
199C22×C3⋊D3—68no—
200C22×C3⋊D3—68no—
201C22×C3⋊D3—128no—
202C22×C3⋊D3—128no—
203C22×C3⋊D3#6714yescomplemented
204C22×C3⋊D3C22×D312yes—
205C22×C3×D3—28no—
206C22×C3×D3—28no—
207C22×C3×D3—316no—
208C22×C3×D3—38no—
209C22×C3×D3—68no—
210C22×C3×D3—68no—
211C22×C3×D3#67116yescomplemented
212C22×C3×D3C22×D318yes—
213C2×D32—632no—
214C2×D32—632no—
215C2×D32—6128no—
216C2×D32—632no—
217C32×D4—68no—
218C2×C32×C4—32no—
219C2×C32×C4—62no—
220#638—28no—
221#638—68no—
222#638—632no—
223#638—664no—
224C2×C3⋊Dic3—22no—
225C2×C3⋊Dic3—32no—
226C2×C3⋊Dic3—38no—
227C2×C3⋊Dic3—68no—
228C2×C3⋊Dic3—616no—
229C2×C3⋊Dic3—68no—
230C2×C3⋊Dic3—62no—
231C2×C3⋊Dic3C22×D312yescomplemented
232C3×#67—232no—
233C3×#67—632no—
234C2×C3×Dic3—28no—
235C2×C3×Dic3—38no—
236C2×C3×Dic3—68no—
237C2×C3×Dic3C22×D318yescomplemented
238C2×#120—271noSylow
239C2×C33—42no—
240C2×C33#12014yescomplemented
241C2×C33C22×D411yescharacteristic
242C2×C33C22×D411yescharacteristic
243C2×C33C22×D411yescharacteristic
244C3⋊(C3⋊D3)—24no—
245C3×C3⋊D3—24no—
246C32×D3—24no—
247C24×C3—24no—
248C24×C3—34no—
249C24×C3—91no—
250C24×C3D3214yescomplemented
251C24×C3C2×C3⋊D311yescharacteristic, complemented
252C23×D3—34no—
253C23×D3—916no—
254C23×D3—94no—
255C23×D3—91no—
256C23×D3—94no—
257C23×D3—184no—
258C23×D3—184no—
259C23×D3—184no—
260C23×D3—1816no—
261C23×D3—1816no—
262C23×D3—1816no—
263C23×D3—184no—
264C23×D3C2×C3⋊D311yescharacteristic
265C2×C3×D4—316no—
266C2×C3×D4—616no—
267C2×C3×D4—94no—
268C2×C3×D4—184no—
269C22×C3×C4—34no—
270C22×C3×C4—91no—
271C2×#67—24no—
272C2×#67—316no—
273C2×#67—616no—
274C2×#67—916no—
275C2×#67—94no—
276C2×#67—1816no—
277C2×#67—1816no—
278C2×#67—184no—
279C2×#67—1832no—
280C2×#67C2×C3⋊D314yescomplemented
281C22×Dic3—34no—
282C22×Dic3—94no—
283C22×Dic3—91no—
284C22×Dic3—184no—
285C22×Dic3C2×C3⋊D311yescharacteristic, complemented
286#217—916no—
287#217—94no—
288(C2×D3)⋊C4—916no—
289(C2×D3)⋊C4—916no—
290(C2×D3)⋊C4—94no—
291(C2×D3)⋊C4—94no—
292C22×C32—216no—
293C22×C32—28no—
294C22×C32—22no—
295C22×C32—22no—
296C22×C32—22no—
297C22×C32—24no—
298C22×C32—28no—
299C22×C32—28no—
300C22×C32—28no—
301C22×C32—28no—
302C22×C32—28no—
303C22×C32—34no—
304C22×C32—48no—
305C22×C32—48no—
306C22×C32—432no—
307C22×C32—416no—
308C22×C32—44no—
309C22×C32—68no—
310C22×C32—62no—
311C22×C32—62no—
312C22×C32D3×D418yes—
313C22×C32D3×D418yes—
314C22×C32D3×D412yes—
315C22×C32D3×D412yes—
316C22×C32C2×#6718yes—
317C22×C32C2×#6712yes—
318C22×C32C23×D314yes—
319C22×C32C23×D311yescharacteristic
320C2×C3⋊D3—28no—
321C2×C3⋊D3—22no—
322C2×C3⋊D3—22no—
323C2×C3⋊D3—34no—
324C2×C3⋊D3—316no—
325C2×C3⋊D3—616no—
326C2×C3⋊D3—632no—
327C2×C3⋊D3—68no—
328C2×C3⋊D3—62no—
329C2×C3⋊D3—62no—
330C2×C3⋊D3—632no—
331C2×C3⋊D3—68no—
332C2×C3⋊D3—68no—
333C2×C3⋊D3—128no—
334C2×C3⋊D3—128no—
335C2×C3⋊D3—1232no—
336C2×C3⋊D3C2×#6714yescomplemented
337C2×C3×D3—232no—
338C2×C3×D3—28no—
339C2×C3×D3—28no—
340C2×C3×D3—316no—
341C2×C3×D3—632no—
342C2×C3×D3—68no—
343C2×C3×D3—68no—
344C2×C3×D3C2×#67116yescomplemented
345D32—6128no—
346C32×C4—62no—
347C3⋊Dic3—22no—
348C3⋊Dic3—616no—
349C3⋊Dic3—68no—
350C3⋊Dic3—62no—
351C3×Dic3—28no—
352C3×Dic3—68no—
353C25—271no—
354C22×D4—31no—
355C22×D4—91no—
356C22×D4—271no—
357#120—278no—
358C2×C22⋊C4—271no—
359C2×C22⋊C4—271no—
360C2×C22⋊C4—271no—
361C33C2×#12011yescharacteristic, complemented, Sylow
362C23×C3—216no—
363C23×C3—28no—
364C23×C3—28no—
365C23×C3—28no—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—24no—
370C23×C3—28no—
371C23×C3—38no—
372C23×C3—316no—
373C23×C3—48no—
374C23×C3—48no—
375C23×C3—68no—
376C23×C3—68no—
377C23×C3—92no—
378C23×C3—94no—
379C23×C3—182no—
380C23×C3—182no—
381C23×C3C2×D3214yes—
382C23×C3C2×D3218yescomplemented
383C23×C3C22×C3⋊D311yescharacteristic
384C23×C3C22×C3⋊D312yescomplemented
385C22×D3—22no—
386C22×D3—22no—
387C22×D3—38no—
388C22×D3—316no—
389C22×D3—68no—
390C22×D3—68no—
391C22×D3—98no—
392C22×D3—92no—
393C22×D3—916no—
394C22×D3—94no—
395C22×D3—188no—
396C22×D3—1816no—
397C22×D3—188no—
398C22×D3—188no—
399C22×D3—1832no—
400C22×D3—1832no—
401C22×D3—1832no—
402C22×D3—1832no—
403C22×D3—18128no—
404C22×D3—188no—
405C22×D3—188no—
406C22×D3—182no—
407C22×D3—182no—
408C22×D3—188no—
409C22×D3—368no—
410C22×D3—368no—
411C22×D3#63814yescomplemented
412C22×D3C22×C3⋊D312yes—
413C3×D4—632no—
414C3×D4—188no—
415C2×C3×C4—38no—
416C2×C3×C4—68no—
417C2×C3×C4—92no—
418C2×C3×C4—182no—
419#67—28no—
420#67—632no—
421#67—1832no—
422#67—188no—
423#67—1864no—
424C2×Dic3—22no—
425C2×Dic3—38no—
426C2×Dic3—68no—
427C2×Dic3—98no—
428C2×Dic3—92no—
429C2×Dic3—188no—
430C2×Dic3—1816no—
431C2×Dic3—188no—
432C2×Dic3—182no—
433C2×Dic3C22×C3⋊D312yescomplemented
434C2×C32—24no—
435C2×C32—24no—
436C2×C32—24no—
437C2×C32—216no—
438C2×C32—416no—
439C2×C32—48no—
440C2×C32—42no—
441C2×C32—64no—
442C2×C32#937116yescomplemented
443C2×C32#93714yescomplemented
444C2×C32C2×D3×D414yes—
445C2×C32C2×D3×D414yes—
446C2×C32C2×D3×D411yescharacteristic
447C2×C32C2×D3×D411yescharacteristic
448C2×C32C22×#6714yes—
449C2×C32C22×#6711yescharacteristic
450C3⋊D3—24no—
451C3⋊D3—64no—
452C3⋊D3—616no—
453C3⋊D3—1216no—
454C3×D3—216no—
455C3×D3—616no—
456C24—31no—
457C24—91no—
458C24—274no—
459C24—271no—
460C24—544no—
461C24—544no—
462C24—544no—
463C24D3×C3⋊D311yescharacteristic, complemented
464C2×D4—34no—
465C2×D4—64no—
466C2×D4—94no—
467C2×D4—184no—
468C2×D4—274no—
469C2×D4—544no—
470C22×C4—31no—
471C22×C4—91no—
472C22×C4—271no—
473C22⋊C4—274no—
474C22⋊C4—274no—
475C22⋊C4—274no—
476C22×C3—216no—
477C22×C3—28no—
478C22×C3—28no—
479C22×C3—28no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—24no—
484C22×C3—28no—
485C22×C3—28no—
486C22×C3—28no—
487C22×C3—316no—
488C22×C3—48no—
489C22×C3—48no—
490C22×C3—432no—
491C22×C3—44no—
492C22×C3—416no—
493C22×C3—68no—
494C22×C3—68no—
495C22×C3—632no—
496C22×C3—94no—
497C22×C3—182no—
498C22×C3—182no—
499C22×C3—188no—
500C22×C3D3×#6718yes—
501C22×C3D3×#6718yes—
502C22×C3#381118yes—
503C22×C3D4×C3⋊D312yes—
504C22×C3D4×C3⋊D312yes—
505C22×C3C2×#63812yes—
506C22×C3C22×D3214yes—
507C22×C3C23×C3⋊D311yescharacteristic
508C2×D3—22no—
509C2×D3—22no—
510C2×D3—28no—
511C2×D3—316no—
512C2×D3—68no—
513C2×D3—68no—
514C2×D3—632no—
515C2×D3—916no—
516C2×D3—94no—
517C2×D3—1816no—
518C2×D3—1832no—
519C2×D3—18128no—
520C2×D3—188no—
521C2×D3—188no—
522C2×D3—182no—
523C2×D3—182no—
524C2×D3—188no—
525C2×D3—1832no—
526C2×D3—368no—
527C2×D3—368no—
528C2×D3—3632no—
529C2×D3C2×#63814yescomplemented
530C3×C4—68no—
531C3×C4—182no—
532Dic3—22no—
533Dic3—68no—
534Dic3—1816no—
535Dic3—188no—
536Dic3—182no—
537C32—24no—
538C32C2×#93714yescomplemented
539C32C2×#93711yescharacteristic, complemented
540C23—22no—
541C23—22no—
542C23—22no—
543C23—32no—
544C23—34no—
545C23—62no—
546C23—62no—
547C23—92no—
548C23—94no—
549C23—182no—
550C23—182no—
551C23—272no—
552C23—274no—
553C23—548no—
554C23—548no—
555C23—548no—
556C23—5432no—
557C23—542no—
558C23—542no—
559C23C2×D3×C3⋊D311yescharacteristic
560C23C2×D3×C3⋊D312yescomplemented
561D4—68no—
562D4—188no—
563D4—548no—
564C2×C4—32no—
565C2×C4—62no—
566C2×C4—92no—
567C2×C4—182no—
568C2×C4—272no—
569C2×C4—542no—
570C2×C3—24no—
571C2×C3—24no—
572C2×C3—24no—
573C2×C3—216no—
574C2×C3—416no—
575C2×C3—42no—
576C2×C3—48no—
577C2×C3—616no—
578C2×C3—184no—
579C2×C3#63983116yescomplemented
580C2×C3#6414614yescomplemented
581C2×C3C2×D3×#6714yes—
582C2×C3C2×D3×#6714yes—
583C2×C3C2×#381114yes—
584C2×C3C2×D4×C3⋊D311yescharacteristic
585C2×C3C2×D4×C3⋊D311yescharacteristic
586C2×C3C22×#63811yescharacteristic
587D3—24no—
588D3—616no—
589D3—184no—
590D3—1816no—
591D3—3616no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—34no—
596C22—44no—
597C22—62no—
598C22—62no—
599C22—68no—
600C22—94no—
601C22—182no—
602C22—182no—
603C22—188no—
604C22—274no—
605C22—5432no—
606C22—542no—
607C22—542no—
608C22—548no—
609C22D3×#63812yes—
610C22C3⋊D3×#6712yes—
611C22#8903912yes—
612C22C22×D3×C3⋊D311yescharacteristic
613C4—62no—
614C4—182no—
615C4—542no—
616C3—24no—
617C3C2×#6398314yescomplemented
618C3C2×#6414611yescharacteristic, complemented
619C2—42no—
620C2—64no—
621C2—184no—
622C2—544no—
623C2#1172364314yesdirect product factor
624C2C2×D3×#63811yescharacteristic
625C2C2×C3⋊D3×#6711yescharacteristic
626C2C2×#8903911yescharacteristic
subgroupG/H
centerC23C2×D3×C3⋊D3
commutator, cosocleC22×C33C24
FrattiniC22C22×D3×C3⋊D3
FittingC24×C33C22
socleC23×C33C23
hypercenterC24D3×C3⋊D3
hypocenterC33C2×#120
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C23 ◁ C24

Complements

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

NH ≅ G/Ntype
1. C23×D3×C3⋊D3C2semidirect
2. C22×#6312C2semidirect
3. C22×C3×#638C2semidirect
4. C22×C32×#67C2semidirect
5. #11723643C2direct (N × H)
6. C2×#88804C2semidirect
7. C2×#88803C2semidirect
8. C2×(C2×D3)⋊(C3⋊Dic3)C2semidirect
11. C24×C33C22semidirect
18. C22×D3×C3⋊D3C22semidirect
20. C2×#6312C22semidirect
21. C22×C3⋊(C3⋊Dic3)C22semidirect
23. C2×C3×#638C22semidirect
24. C22×C3×C3⋊Dic3C22semidirect
26. C2×C32×#67C22semidirect
27. C22×C32×Dic3C22semidirect
28. #88804C22semidirect
29. #88803C22semidirect
30. (C2×D3)⋊(C3⋊Dic3)C22semidirect
37. C22×#638D3semidirect
39. C22×C3×#67D3semidirect
52. C23×C33C23semidirect
55. C22×C3⋊(C3⋊D3)D4semidirect
59. C22×C3×C3⋊D3D4semidirect
63. C22×C32×D3D4semidirect
71. C2×C3⋊(C3⋊Dic3)C23semidirect
74. C2×C3×C3⋊Dic3C23semidirect
77. C2×C32×Dic3C23semidirect
82. C24×C32C2×D3semidirect
83. C24×C32C2×D3semidirect
108. C2×#638C2×D3semidirect
112. C22×C3⋊Dic3C2×D3semidirect
116. C2×C3×#67C2×D3semidirect
118. C22×C3×Dic3C2×D3semidirect
136. C2×C3⋊(C3⋊D3)C2×D4semidirect
140. C2×C3×C3⋊D3C2×D4semidirect
144. C2×C32×D3C2×D4semidirect
157. C22×#67C3⋊D3semidirect
183. C23×C32C22×D3semidirect
184. C23×C32C22×D3semidirect
203. C22×C3⋊D3#67semidirect
211. C22×C3×D3#67semidirect
231. C2×C3⋊Dic3C22×D3semidirect
237. C2×C3×Dic3C22×D3semidirect
240. C2×C33#120semidirect
250. C24×C3D32semidirect
251. C24×C3C2×C3⋊D3semidirect
280. C2×#67C2×C3⋊D3semidirect
285. C22×Dic3C2×C3⋊D3semidirect
336. C2×C3⋊D3C2×#67semidirect
344. C2×C3×D3C2×#67semidirect
361. C33C2×#120semidirect
382. C23×C3C2×D32semidirect
384. C23×C3C22×C3⋊D3semidirect
411. C22×D3#638semidirect
433. C2×Dic3C22×C3⋊D3semidirect
442. C2×C32#937semidirect
443. C2×C32#937semidirect
463. C24D3×C3⋊D3semidirect
529. C2×D3C2×#638semidirect
538. C32C2×#937semidirect
539. C32C2×#937semidirect
560. C23C2×D3×C3⋊D3semidirect
579. C2×C3#63983semidirect
580. C2×C3#64146semidirect
617. C3C2×#63983semidirect
618. C3C2×#64146semidirect
623. C2#11723643direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3×C3⋊D32
C22×#63122
C22×C3×#6382
C22×C32×#672
#117236432
C2×#888042
C2×#888032
C2×(C2×D3)⋊(C3⋊Dic3)2
C2×#641463
C2×#639833