Finite Group Databasebeta

← C2×C3×#64309 #13181545

Subgroups — C2×C3×#64309 #13181545

Order 1728.

3722 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3830C211yesmaximal, characteristic, complemented
2C2×C32×#237C212yesmaximal, complemented
3C22×C3×#627C212yesmaximal, complemented
4C2×C3×#3805C212yesmaximal, complemented
5C2×C3×#3804C214yesmaximal, complemented
6C3×#64309C2116yesmaximal, direct product factor
7C2×C3×#3798C211yesmaximal, characteristic, complemented
8C2×C3×#3797C211yesmaximal, characteristic, complemented
9C2×C3×D3×Dic6C212yesmaximal, complemented
10C2×C3×#1010—32nomaximal
11C2×#64309C311yesmaximal, characteristic, direct product factor
12C2×C33×D4C2211yescharacteristic
13C2×C3×#638C2212yes—
14C22×C3×C3⋊Dic3C2212yes—
15C3×#3830C2218yescomplemented
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C2×C32×#67C2214yes—
19C22×C32×Dic3C2214yes—
20C32×#237C22116yescomplemented
21C2×C32×C4×D3C2212yes—
22C2×C32×Dic6C2212yes—
23C2×C3×#627C2214yes—
24C2×C3×#627C2212yes—
25C2×C3×#627C2211yescharacteristic
26C2×C3×#627C22116yescomplemented
27C2×C3×#626C2212yes—
28C2×C3×#625C2211yescharacteristic
29C2×C3×#624C2212yes—
30C3×#3805C22116yescomplemented
31C3×#3804C22132yescomplemented
32C2×C3×D3×Dic3C2214yes—
33C3×#3798C2218yescomplemented
34C3×#3797C2218yescomplemented
35C3×D3×Dic6C22116yescomplemented
36C2×C32×#41—32no—
37C2×#3830C2×C311yescharacteristic, complemented
38C3×#1010—332no—
39C2×C3×D3×Q8—32no—
40C2×C3×D3×Q8—32no—
41C2×C3×#237—22no—
42C2×C3×#237—32no—
43C2×C3×#237—34no—
44C2×C3×#237—34no—
45C2×C3×#237—61no—
46C2×C3×#237D312yescomplemented
47C2×C3×#237C2×C312yescomplemented
48C2×C3×#235—34no—
49C2×C3×#235—32no—
50C22×C3×Dic6—34no—
51C22×C3×Dic6—32no—
52C22×#627C2×C312yescomplemented
53C2×#3805C2×C312yescomplemented
54C2×#3804C2×C314yescomplemented
55#64309C2×C3116yesdirect product factor
56C2×#3798C2×C311yescharacteristic, complemented
57C2×#3797C2×C311yescharacteristic, complemented
58C2×D3×Dic6C2×C312yescomplemented
59C23×C33C2312yes—
60C22×C3×C3⋊D3C2311yescharacteristic
61C22×C32×D3C2312yes—
62C33×D4C2314yes—
63C2×C33×C4C2311yescharacteristic
64C3×#638C2318yes—
65C2×C3×C3⋊Dic3C2312yes—
66C2×C3×C3⋊Dic3C2318yes—
67C2×C3×C3⋊Dic3C2311yescharacteristic
68C3×C4×C3⋊D3C2314yes—
69C3×#634C2314yes—
70C32×#67C23116yes—
71C2×C32×Dic3C2314yes—
72C2×C32×Dic3C23116yes—
73C2×C32×Dic3C2312yes—
74C32×C4×D3C2318yes—
75C32×Dic6C2318yes—
76C3×#627C23116yes—
77C3×#627C2318yes—
78C3×#627C2314yes—
79C3×#626C2318yes—
80C3×#625C2314yes—
81C3×#624C2318yes—
82C3×D3×Dic3C23116yes—
83C2×C3×2−1+4—91no—
84C2×#1010—32no—
85C32×#41—316no—
86C2×C32×Q8—32no—
87C2×C32×D4—21no—
88C2×C32×D4—22no—
89C2×C32×D4—34no—
90C2×C32×D4—41no—
91C2×C32×D4C2×D312yes—
92C2×C32×D4C22×C311yescharacteristic
93C22×C32×C4—34no—
94C22×C32×C4—32no—
95C2×#638C22×C312yes—
96C22×C3⋊Dic3C22×C312yes—
97#3830C22×C318yescomplemented
98C2×C4×C3⋊D3C22×C311yescharacteristic
99C2×#634C22×C311yescharacteristic
100C2×C3×#67—24no—
101C2×C3×#67—34no—
102C2×C3×#67—32no—
103C2×C3×#67—32no—
104C2×C3×#67—62no—
105C2×C3×#67C2×D314yes—
106C2×C3×#67C22×C314yes—
107C22×C3×Dic3—24no—
108C22×C3×Dic3—34no—
109C22×C3×Dic3—34no—
110C22×C3×Dic3—62no—
111C22×C3×Dic3C2×D314yes—
112C22×C3×Dic3C22×C314yes—
113C3×D3×Q8—316no—
114C3×D3×Q8—316no—
115C3×#237—216no—
116C3×#237—316no—
117C3×#237—332no—
118C3×#237—332no—
119C3×#237—68no—
120C3×#237C2×D3116yescomplemented
121C3×#237C22×C3116yescomplemented
122C3×#235—332no—
123C3×#235—316no—
124C2×C3×D12—32no—
125C2×C3×C4×D3—22no—
126C2×C3×C4×D3—34no—
127C2×C3×C4×D3—32no—
128C2×C3×C4×D3—34no—
129C2×C3×C4×D3—61no—
130C2×C3×C4×D3C2×D312yes—
131C2×C3×C4×D3C22×C312yes—
132C2×C3×Dic6—22no—
133C2×C3×Dic6—32no—
134C2×C3×Dic6—32no—
135C2×C3×Dic6—34no—
136C2×C3×Dic6—34no—
137C2×C3×Dic6—34no—
138C2×C3×Dic6—332no—
139C2×C3×Dic6—316no—
140C2×C3×Dic6—61no—
141C2×C3×Dic6C2×D312yes—
142C2×C3×Dic6C22×C312yes—
143C2×#627C22×C314yes—
144C2×#627C22×C312yes—
145C2×#627C22×C311yescharacteristic
146C2×#627C22×C3116yescomplemented
147C2×#626C22×C312yes—
148C2×#625C22×C311yescharacteristic
149C2×#624C22×C312yes—
150#3805C22×C3116yescomplemented
151#3804C22×C3132yescomplemented
152C2×D3×Dic3C22×C314yes—
153#3798C22×C318yescomplemented
154#3797C22×C318yescomplemented
155D3×Dic6C22×C3116yescomplemented
156C22×C33—24no—
157C22×C33C2414yes—
158C22×C33C2411yescharacteristic
159C2×C3×C3⋊D3—22no—
160C2×C3×C3⋊D3C2412yes—
161C2×C32×D3—24no—
162C2×C32×D3C2414yes—
163C33×C4C2412yes—
164C3×C3⋊Dic3C2414yes—
165C3×C3⋊Dic3C2412yes—
166C32×Dic3C2418yes—
167C32×Dic3C2414yes—
168C3×2−1+4—916no—
169C2×C3×#41—32no—
170C2×C3×#41—32no—
171C2×C3×#41—62no—
172C2×C3×#41—91no—
173C2×C3×#41—94no—
174C2×C3×#41—92no—
175C2×C3×#41—91no—
176C22×C3×Q8—92no—
177C22×C3×Q8—92no—
178C22×C3×Q8—91no—
179#1010—332no—
180C2×D3×Q8—32no—
181C2×D3×Q8—32no—
182C2×#237—32no—
183C2×#237—34no—
184C2×#237—34no—
185C2×#237—61no—
186C2×#237C3×D312yescomplemented
187C2×#235—34no—
188C2×#235—32no—
189C22×Dic6—34no—
190C22×Dic6—32no—
191C23×C32—22no—
192C23×C32—24no—
193C23×C32—32no—
194C23×C32—42no—
195C23×C32C22×D314yes—
196C23×C32C23×C312yes—
197C22×C3⋊D3C23×C311yescharacteristic
198C22×C3×D3—22no—
199C22×C3×D3—32no—
200C22×C3×D3—61no—
201C22×C3×D3C22×D312yes—
202C22×C3×D3C23×C312yes—
203C32×Q8—38no—
204C32×D4—24no—
205C32×D4—28no—
206C32×D4—316no—
207C32×D4—44no—
208C32×D4C22×D318yes—
209C32×D4C23×C314yes—
210C2×C32×C4—21no—
211C2×C32×C4—22no—
212C2×C32×C4—32no—
213C2×C32×C4—34no—
214C2×C32×C4—316no—
215C2×C32×C4—38no—
216C2×C32×C4—41no—
217C2×C32×C4C22×D312yes—
218C2×C32×C4C23×C311yescharacteristic
219#638C23×C318yes—
220C2×C3⋊Dic3C23×C312yes—
221C2×C3⋊Dic3C23×C318yes—
222C2×C3⋊Dic3C23×C311yescharacteristic
223C4×C3⋊D3C23×C314yes—
224#634C23×C314yes—
225C3×#67—216no—
226C3×#67—316no—
227C3×#67—38no—
228C3×#67—38no—
229C3×#67—68no—
230C3×#67C22×D3116yes—
231C3×#67C23×C3116yes—
232C2×C3×Dic3—24no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—216no—
235C2×C3×Dic3—34no—
236C2×C3×Dic3—32no—
237C2×C3×Dic3—316no—
238C2×C3×Dic3—316no—
239C2×C3×Dic3—62no—
240C2×C3×Dic3—61no—
241C2×C3×Dic3—68no—
242C2×C3×Dic3C22×D312yes—
243C2×C3×Dic3C22×D314yes—
244C2×C3×Dic3C22×D3116yes—
245C2×C3×Dic3C23×C314yes—
246C2×C3×Dic3C23×C3116yes—
247C2×C3×Dic3C23×C312yes—
248C3×D12—38no—
249C3×C4×D3—28no—
250C3×C4×D3—316no—
251C3×C4×D3—38no—
252C3×C4×D3—316no—
253C3×C4×D3—64no—
254C3×C4×D3C22×D318yes—
255C3×C4×D3C23×C318yes—
256C3×Dic6—28no—
257C3×Dic6—38no—
258C3×Dic6—38no—
259C3×Dic6—316no—
260C3×Dic6—316no—
261C3×Dic6—316no—
262C3×Dic6—64no—
263C3×Dic6C22×D318yes—
264C3×Dic6C23×C318yes—
265#627C23×C3116yes—
266#627C23×C318yes—
267#627C23×C314yes—
268#626C23×C318yes—
269#625C23×C314yes—
270#624C23×C318yes—
271D3×Dic3C23×C3116yes—
272C2×2−1+4—91noSylow
273C2×C33—24no—
274C2×C332−1+412yescomplemented
275C2×C33C2511yescharacteristic
276C3×C3⋊D3—22no—
277C32×D3—24no—
278C3×#41—316no—
279C3×#41—316no—
280C3×#41—616no—
281C3×#41—98no—
282C3×#41—932no—
283C3×#41—916no—
284C3×#41—98no—
285C2×C3×Q8—32no—
286C2×C3×Q8—32no—
287C2×C3×Q8—62no—
288C2×C3×Q8—91no—
289C2×C3×Q8—94no—
290C2×C3×Q8—92no—
291C2×C3×Q8—916no—
292C2×C3×Q8—916no—
293C2×C3×Q8—98no—
294C2×C3×Q8—91no—
295C2×C3×D4—21no—
296C2×C3×D4—22no—
297C2×C3×D4—34no—
298C2×C3×D4—34no—
299C2×C3×D4—41no—
300C2×C3×D4—64no—
301C2×C3×D4—92no—
302C2×C3×D4—91no—
303C2×C3×D4—92no—
304C2×C3×D4D3211yescharacteristic
305C2×C3×D4C2×C3×D312yes—
306C22×C3×C4—34no—
307C22×C3×C4—34no—
308C22×C3×C4—32no—
309C22×C3×C4—32no—
310C22×C3×C4—62no—
311C22×C3×C4—64no—
312C22×C3×C4—92no—
313C22×C3×C4—94no—
314C22×C3×C4—92no—
315C22×C3×C4—91no—
316C2×#67—34no—
317C2×#67—32no—
318C2×#67—32no—
319C2×#67—62no—
320C2×#67C2×C3×D314yes—
321C22×Dic3—34no—
322C22×Dic3—34no—
323C22×Dic3—62no—
324C22×Dic3C2×C3×D314yes—
325D3×Q8—316no—
326D3×Q8—316no—
327#237—316no—
328#237—332no—
329#237—332no—
330#237—68no—
331#237C2×C3×D3116yescomplemented
332#235—332no—
333#235—316no—
334C2×D12—32no—
335C2×C4×D3—34no—
336C2×C4×D3—32no—
337C2×C4×D3—34no—
338C2×C4×D3—61no—
339C2×C4×D3C2×C3×D312yes—
340C2×Dic6—32no—
341C2×Dic6—32no—
342C2×Dic6—34no—
343C2×Dic6—34no—
344C2×Dic6—34no—
345C2×Dic6—332no—
346C2×Dic6—316no—
347C2×Dic6—61no—
348C2×Dic6C2×C3×D312yes—
349C22×C32—28no—
350C22×C32—24no—
351C22×C32—24no—
352C22×C32—21no—
353C22×C32—22no—
354C22×C32—28no—
355C22×C32—34no—
356C22×C32—41no—
357C22×C32—44no—
358C22×C32—44no—
359C22×C32—48no—
360C22×C32—64no—
361C22×C32—84no—
362C22×C32C23×D318yes—
363C22×C32C23×D312yes—
364C22×C32C24×C314yes—
365C22×C32C24×C311yescharacteristic
366C2×C3⋊D3—22no—
367C2×C3⋊D3C24×C312yes—
368C2×C3×D3—24no—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—34no—
372C2×C3×D3—44no—
373C2×C3×D3—62no—
374C2×C3×D3—64no—
375C2×C3×D3—122no—
376C2×C3×D3C23×D314yes—
377C2×C3×D3C24×C314yes—
378C32×C4—22no—
379C32×C4—24no—
380C32×C4—34no—
381C32×C4—38no—
382C32×C4—42no—
383C32×C4C23×D314yes—
384C32×C4C24×C312yes—
385C3⋊Dic3C24×C314yes—
386C3⋊Dic3C24×C312yes—
387C3×Dic3—28no—
388C3×Dic3—24no—
389C3×Dic3—38no—
390C3×Dic3—34no—
391C3×Dic3—64no—
392C3×Dic3—62no—
393C3×Dic3C23×D314yes—
394C3×Dic3C23×D318yes—
395C3×Dic3C24×C318yes—
396C3×Dic3C24×C314yes—
3972−1+4—916no—
398C2×#41—32no—
399C2×#41—91no—
400C2×#41—94no—
401C2×#41—92no—
402C2×#41—91no—
403C22×Q8—92no—
404C22×Q8—92no—
405C22×Q8—91no—
406C33C2×2−1+411yescharacteristic, complemented, Sylow
407C23×C3—24no—
408C23×C3—22no—
409C23×C3—32no—
410C23×C3—32no—
411C23×C3—42no—
412C23×C3—62no—
413C23×C3—91no—
414C23×C3C2×D3212yes—
415C23×C3C22×C3×D314yes—
416C22×D3—32no—
417C22×D3—61no—
418C22×D3C22×C3×D312yes—
419C3×Q8—38no—
420C3×Q8—38no—
421C3×Q8—68no—
422C3×Q8—94no—
423C3×Q8—916no—
424C3×Q8—98no—
425C3×Q8—94no—
426C3×D4—28no—
427C3×D4—24no—
428C3×D4—316no—
429C3×D4—316no—
430C3×D4—44no—
431C3×D4—616no—
432C3×D4—98no—
433C3×D4—94no—
434C3×D4—98no—
435C3×D4C2×D3214yes—
436C3×D4C22×C3×D318yes—
437C2×C3×C4—22no—
438C2×C3×C4—21no—
439C2×C3×C4—316no—
440C2×C3×C4—32no—
441C2×C3×C4—34no—
442C2×C3×C4—32no—
443C2×C3×C4—34no—
444C2×C3×C4—316no—
445C2×C3×C4—38no—
446C2×C3×C4—38no—
447C2×C3×C4—41no—
448C2×C3×C4—68no—
449C2×C3×C4—62no—
450C2×C3×C4—64no—
451C2×C3×C4—616no—
452C2×C3×C4—98no—
453C2×C3×C4—916no—
454C2×C3×C4—98no—
455C2×C3×C4—92no—
456C2×C3×C4—91no—
457C2×C3×C4—94no—
458C2×C3×C4C2×D3211yescharacteristic
459C2×C3×C4C22×C3×D312yes—
460#67—316no—
461#67—38no—
462#67—38no—
463#67—68no—
464#67C22×C3×D3116yes—
465C2×Dic3—34no—
466C2×Dic3—32no—
467C2×Dic3—316no—
468C2×Dic3—316no—
469C2×Dic3—62no—
470C2×Dic3—61no—
471C2×Dic3—68no—
472C2×Dic3C22×C3×D312yes—
473C2×Dic3C22×C3×D314yes—
474C2×Dic3C22×C3×D3116yes—
475D12—38no—
476C4×D3—316no—
477C4×D3—38no—
478C4×D3—316no—
479C4×D3—64no—
480C4×D3C22×C3×D318yes—
481Dic6—38no—
482Dic6—38no—
483Dic6—316no—
484Dic6—316no—
485Dic6—316no—
486Dic6—64no—
487Dic6C22×C3×D318yes—
488C2×C32—28no—
489C2×C32—24no—
490C2×C32—22no—
491C2×C32—24no—
492C2×C32—21no—
493C2×C32—22no—
494C2×C32—42no—
495C2×C32—41no—
496C2×C32—44no—
497C2×C32—48no—
498C2×C32—64no—
499C2×C32—84no—
500C2×C32#101014yescomplemented
501C2×C32C3×2−1+412yescomplemented
502C2×C32C24×D312yes—
503C2×C32C25×C311yescharacteristic
504C3⋊D3—22no—
505C3×D3—24no—
506C3×D3—24no—
507C3×D3—44no—
508C3×D3—64no—
509C3×D3—122no—
510#41—316no—
511#41—98no—
512#41—932no—
513#41—916no—
514#41—98no—
515C2×Q8—32no—
516C2×Q8—91no—
517C2×Q8—94no—
518C2×Q8—92no—
519C2×Q8—916no—
520C2×Q8—916no—
521C2×Q8—98no—
522C2×Q8—91no—
523C2×D4—34no—
524C2×D4—92no—
525C2×D4—91no—
526C2×D4—92no—
527C2×D4C3×D3211yescharacteristic
528C22×C4—34no—
529C22×C4—32no—
530C22×C4—92no—
531C22×C4—94no—
532C22×C4—92no—
533C22×C4—91no—
534C22×C3—24no—
535C22×C3—28no—
536C22×C3—21no—
537C22×C3—22no—
538C22×C3—24no—
539C22×C3—28no—
540C22×C3—34no—
541C22×C3—34no—
542C22×C3—44no—
543C22×C3—48no—
544C22×C3—41no—
545C22×C3—44no—
546C22×C3—64no—
547C22×C3—64no—
548C22×C3—64no—
549C22×C3—84no—
550C22×C3—92no—
551C22×C3—124no—
552C22×C3—182no—
553C22×C3C22×D3214yes—
554C22×C3C22×D3211yescharacteristic
555C22×C3C23×C3×D318yes—
556C22×C3C23×C3×D312yes—
557C2×D3—24no—
558C2×D3—34no—
559C2×D3—62no—
560C2×D3—64no—
561C2×D3—122no—
562C2×D3C23×C3×D314yes—
563C3×C4—22no—
564C3×C4—24no—
565C3×C4—34no—
566C3×C4—38no—
567C3×C4—34no—
568C3×C4—38no—
569C3×C4—42no—
570C3×C4—64no—
571C3×C4—68no—
572C3×C4—94no—
573C3×C4—92no—
574C3×C4C22×D3212yes—
575C3×C4C23×C3×D314yes—
576Dic3—38no—
577Dic3—34no—
578Dic3—64no—
579Dic3—62no—
580Dic3C23×C3×D314yes—
581Dic3C23×C3×D318yes—
582C32—21no—
583C32—22no—
584C32—41no—
585C32C2×#101012yescomplemented
586C32C2×C3×2−1+411yescharacteristic, complemented
587C23—32no—
588C23—91no—
589C23C2×C3×D3212yes—
590Q8—38no—
591Q8—94no—
592Q8—916no—
593Q8—98no—
594Q8—94no—
595D4—316no—
596D4—98no—
597D4—94no—
598D4—98no—
599D4C2×C3×D3214yes—
600C2×C4—32no—
601C2×C4—34no—
602C2×C4—316no—
603C2×C4—38no—
604C2×C4—98no—
605C2×C4—916no—
606C2×C4—92no—
607C2×C4—91no—
608C2×C4—98no—
609C2×C4—94no—
610C2×C4C2×C3×D3211yescharacteristic
611C2×C3—24no—
612C2×C3—28no—
613C2×C3—21no—
614C2×C3—22no—
615C2×C3—22no—
616C2×C3—24no—
617C2×C3—44no—
618C2×C3—48no—
619C2×C3—41no—
620C2×C3—42no—
621C2×C3—64no—
622C2×C3—64no—
623C2×C3—84no—
624C2×C3—124no—
625C2×C3—182no—
626C2×C3#6430912yesdirect product factor
627C2×C3C3×#101014yescomplemented
628C2×C3C23×D3211yescharacteristic
629C2×C3C24×C3×D312yes—
630D3—24no—
631D3—64no—
632D3—122no—
633C22—24no—
634C22—34no—
635C22—64no—
636C22—92no—
637C22—182no—
638C22C22×C3×D3214yes—
639C22C22×C3×D3211yescharacteristic
640C4—34no—
641C4—38no—
642C4—94no—
643C4—92no—
644C4C22×C3×D3212yes—
645C3—21no—
646C3—22no—
647C3—41no—
648C3C2×#6430911yescharacteristic, direct product factor
649C3C2×C3×#101012yescomplemented
650C2—24no—
651C2—64no—
652C2—182no—
653C2C3×#6430912yesdirect product factor
654C2C23×C3×D3211yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC2×C32C25×C3
FrattiniC2C23×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C2×C3×2−1+4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3830C2semidirect
2. C2×C32×#237C2semidirect
3. C22×C3×#627C2semidirect
4. C2×C3×#3805C2semidirect
5. C2×C3×#3804C2semidirect
6. C3×#64309C2direct (N × H)
7. C2×C3×#3798C2semidirect
8. C2×C3×#3797C2semidirect
9. C2×C3×D3×Dic6C2semidirect
11. C2×#64309C3direct (N × H)
15. C3×#3830C22semidirect
20. C32×#237C22semidirect
26. C2×C3×#627C22semidirect
30. C3×#3805C22semidirect
31. C3×#3804C22semidirect
33. C3×#3798C22semidirect
34. C3×#3797C22semidirect
35. C3×D3×Dic6C22semidirect
37. C2×#3830C2×C3semidirect
46. C2×C3×#237D3semidirect
47. C2×C3×#237C2×C3semidirect
52. C22×#627C2×C3semidirect
53. C2×#3805C2×C3semidirect
54. C2×#3804C2×C3semidirect
55. #64309C2×C3direct (N × H)
56. C2×#3798C2×C3semidirect
57. C2×#3797C2×C3semidirect
58. C2×D3×Dic6C2×C3semidirect
97. #3830C22×C3semidirect
120. C3×#237C2×D3semidirect
121. C3×#237C22×C3semidirect
146. C2×#627C22×C3semidirect
150. #3805C22×C3semidirect
151. #3804C22×C3semidirect
153. #3798C22×C3semidirect
154. #3797C22×C3semidirect
155. D3×Dic6C22×C3semidirect
186. C2×#237C3×D3semidirect
274. C2×C332−1+4semidirect
331. #237C2×C3×D3semidirect
406. C33C2×2−1+4semidirect
500. C2×C32#1010semidirect
501. C2×C32C3×2−1+4semidirect
585. C32C2×#1010semidirect
586. C32C2×C3×2−1+4semidirect
626. C2×C3#64309direct (N × H)
627. C2×C3C3×#1010semidirect
648. C3C2×#64309direct (N × H)
649. C3C2×C3×#1010semidirect
653. C2C3×#64309direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#38302
C2×C32×#2372
C22×C3×#6272
C2×C3×#38052
C2×C3×#38042
C3×#643092
C2×C3×#37982
C2×C3×#37972
C2×C3×D3×Dic62
C2×C3×#10103
C2×#643093