Finite Group Databasebeta

← C3×#10595082 #13174679

Subgroups — C3×#10595082 #13174679

Order 1728.

1742 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3828C211yesmaximal, characteristic, complemented
2C2×C3×#3802C211yesmaximal, characteristic, complemented
3C32×#930C212yesmaximal, complemented
4C3×#63983C212yesmaximal, complemented
5C3×#63979C212yesmaximal, complemented
6C3×#63923C212yesmaximal, complemented
7C3×#63916C212yesmaximal, complemented
8C3×#63913C212yesmaximal, complemented
9C3×#63849C211yesmaximal, characteristic, complemented
10C3×#5607—32nomaximal
11#10595082C311yesmaximal, characteristic, direct product factor
12C22×C3×D32C2212yes—
13C22×C33×C4C2211yescharacteristic, complemented
14C2×C3×#638C2211yescharacteristic
15C2×C3×#638C2211yescharacteristic, complemented
16C3×#3828—24no—
17C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
18C2×C3×C4×C3⋊D3C2211yescharacteristic
19C2×C3×C4×C3⋊D3C2211yescharacteristic, complemented
20C2×C3×#634C2211yescharacteristic, complemented
21C2×C32×#67C2214yescomplemented
22C2×C32×D12C2212yes—
23C2×C3×#626C2214yescomplemented
24C2×C3×#625C2212yes—
25C3×#3802—24no—
26C32×(C2×D3)⋊C4C2214yescomplemented
27C32×C4⋊Dic3C2212yescomplemented
28C3×#3722C2212yes—
29C3×(C2×D3)⋊Dic3C2214yescomplemented
30C3×Dic32C2212yescomplemented
31C2×#3828C2×C311yescharacteristic, complemented
32C2×C3×D3×D4—32no—
33C2×C3×#235—32no—
34C2×C3×#235—61no—
35C2×#3802C2×C311yescharacteristic, complemented
36C32×#121—32no—
37C3×#940—34no—
38C3×#938—32no—
39C3×#937—34no—
40C3×#930—22no—
41C3×#930D312yescomplemented
42C3×#930C2×C312yescomplemented
43C3×#895—32no—
44C3×#892—32no—
45C3×#885—34no—
46C3×#882—34no—
47#63983C2×C312yescomplemented
48#63979C2×C312yescomplemented
49#63923C2×C312yescomplemented
50#63916C2×C312yescomplemented
51#63913C2×C312yescomplemented
52#63849C2×C311yescharacteristic, complemented
53C23×C33C2311yescharacteristic
54C22×C3×C3⋊D3C2311yescharacteristic
55C22×C3×C3⋊D3C2311yescharacteristic
56C22×C32×D3C2314yes—
57C2×C3×D32—24no—
58C2×C3×D32—44no—
59C2×C33×C4—22no—
60C2×C33×C4C2311yescharacteristic
61C2×C33×C4C2311yescharacteristic
62C3×#638—22no—
63C3×#638—22no—
64C2×C3×C3⋊Dic3C2311yescharacteristic
65C2×C3×C3⋊Dic3C2311yescharacteristic
66C3×C4⋊(C3⋊D3)—22no—
67C3×C4×C3⋊D3—22no—
68C3×C4×C3⋊D3D414yescomplemented
69C3×#634—22no—
70C32×#67—44no—
71C2×C32×Dic3C2314yes—
72C32×D12—24no—
73C3×#626—44no—
74C3×#625—24no—
75C3×#535—91no—
76#5607—32no—
77C23×C3×D3—34no—
78C22×D32C22×C312yes—
79C2×C32×D4—34no—
80C2×C32×D4—32no—
81C22×C32×C4—21no—
82C22×C32×C4—22no—
83C22×C32×C4—41no—
84C22×C32×C4C2×D312yescomplemented
85C22×C32×C4C22×C311yescharacteristic, complemented
86C2×#638C22×C311yescharacteristic
87C2×#638C22×C311yescharacteristic, complemented
88#3828—24no—
89C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
90C2×C4×C3⋊D3C22×C311yescharacteristic
91C2×C4×C3⋊D3C22×C311yescharacteristic, complemented
92C2×#634C22×C311yescharacteristic, complemented
93C2×C3×#67—24no—
94C2×C3×#67—32no—
95C2×C3×#67—32no—
96C2×C3×#67—34no—
97C2×C3×#67—34no—
98C2×C3×#67—61no—
99C2×C3×#67—61no—
100C2×C3×#67C2×D314yescomplemented
101C2×C3×#67C22×C314yescomplemented
102C3×D3×D4—68no—
103C3×#235—68no—
104C3×#235—68no—
105C2×C3×D12—22no—
106C2×C3×D12—32no—
107C2×C3×D12—34no—
108C2×C3×D12—61no—
109C2×C3×D12C2×D312yes—
110C2×C3×D12C22×C312yes—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—61no—
114C2×C3×C4×D3—61no—
115C2×C3×Dic6—32no—
116C2×C3×Dic6—61no—
117C2×#626C22×C314yescomplemented
118C2×#625C22×C312yes—
119#3802—24no—
120C32×C4⋊C4—32no—
121C32×C22⋊C4—34no—
122C3×#217—34no—
123C3×(C2×D3)⋊C4—24no—
124C3×(C2×D3)⋊C4—34no—
125C3×(C2×D3)⋊C4—34no—
126C3×(C2×D3)⋊C4C2×D314yescomplemented
127C3×(C2×D3)⋊C4C22×C314yescomplemented
128C3×C4⋊Dic3—22no—
129C3×C4⋊Dic3C2×D312yescomplemented
130C3×C4⋊Dic3C22×C312yescomplemented
131C3×C4×Dic3—34no—
132#3722C22×C312yes—
133(C2×D3)⋊Dic3C22×C314yescomplemented
134Dic32C22×C312yescomplemented
135C22×C33—21no—
136C22×C33—22no—
137C22×C33C2411yescharacteristic
138C2×C3×C3⋊D3—22no—
139C2×C3×C3⋊D3—21no—
140C2×C3×C3⋊D3—22no—
141C2×C3×C3⋊D3C2×D412yes—
142C2×C32×D3—24no—
143C2×C32×D3—24no—
144C2×C32×D3—24no—
145C3×D32—48no—
146C33×C4—21no—
147C33×C4C2×D412yes—
148C3×C3⋊Dic3—21no—
149C3×C3⋊Dic3C2×D412yes—
150C32×Dic3—24no—
151C2×C3×#41—91no—
152C22×C3×D4—91no—
153C2×D3×D4—32no—
154C2×#235—32no—
155C2×#235—61no—
156C3×#127—92no—
157C3×#124—92no—
158C3×#121—32no—
159C3×#121—32no—
160C3×#121—62no—
161C3×#121—92no—
162C3×#120—92no—
163C3×#120—92no—
164C3×#117—91no—
165#940—34no—
166#938—32no—
167#937—34no—
168#930C3×D312yescomplemented
169#895—32no—
170#892—32no—
171#885—34no—
172#882—34no—
173C23×C32—21no—
174C23×C32—22no—
175C23×C32—34no—
176C23×C32—41no—
177C23×C32C22×D312yes—
178C23×C32C23×C311yescharacteristic
179C22×C3⋊D3C23×C311yescharacteristic
180C22×C3⋊D3C23×C311yescharacteristic
181C22×C3×D3—24no—
182C22×C3×D3—32no—
183C22×C3×D3—32no—
184C22×C3×D3—61no—
185C22×C3×D3—61no—
186C22×C3×D3—68no—
187C22×C3×D3—124no—
188C22×C3×D3—124no—
189C22×C3×D3C22×D314yes—
190C22×C3×D3C23×C314yes—
191C2×D32—24no—
192C2×D32—44no—
193C32×D4—64no—
194C32×D4—124no—
195C2×C32×C4—22no—
196C2×C32×C4—24no—
197C2×C32×C4—24no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—22no—
201C2×C32×C4—22no—
202C2×C32×C4—34no—
203C2×C32×C4—41no—
204C2×C32×C4—41no—
205C2×C32×C4—44no—
206C2×C32×C4—44no—
207C2×C32×C4C22×D312yes—
208C2×C32×C4C22×D312yes—
209C2×C32×C4C23×C311yescharacteristic
210C2×C32×C4C23×C311yescharacteristic
211#638—22no—
212#638—22no—
213C2×C3⋊Dic3C23×C311yescharacteristic
214C2×C3⋊Dic3C23×C311yescharacteristic
215C4⋊(C3⋊D3)—22no—
216C4×C3⋊D3—22no—
217C4×C3⋊D3C3×D414yescomplemented
218#634—22no—
219C3×#67—44no—
220C3×#67—44no—
221C3×#67—48no—
222C3×#67—68no—
223C3×#67—64no—
224C3×#67—64no—
225C3×#67—64no—
226C3×#67—64no—
227C3×#67—124no—
228C2×C3×Dic3—24no—
229C2×C3×Dic3—32no—
230C2×C3×Dic3—32no—
231C2×C3×Dic3—61no—
232C2×C3×Dic3—61no—
233C2×C3×Dic3C22×D314yes—
234C2×C3×Dic3C23×C314yes—
235C3×D12—24no—
236C3×D12—24no—
237C3×D12—44no—
238C3×D12—64no—
239C3×D12—64no—
240C3×D12—124no—
241C3×C4×D3—38no—
242C3×C4×D3—64no—
243C3×C4×D3—64no—
244C3×C4×D3—64no—
245C3×Dic6—64no—
246C3×Dic6—64no—
247#626—44no—
248#625—24no—
249#535—91noSylow
250C2×C33—41no—
251C2×C33C22×D411yescharacteristic
252C2×C33H(5,𝔽2)12yes—
253C3×C3⋊D3—22no—
254C3×C3⋊D3—41no—
255C32×D3—44no—
256C24×C3—92no—
257C23×D3—34no—
258C3×#41—184no—
259C2×C3×Q8—91no—
260C2×C3×D4—34no—
261C2×C3×D4—34no—
262C2×C3×D4—32no—
263C2×C3×D4—32no—
264C2×C3×D4—62no—
265C2×C3×D4—64no—
266C2×C3×D4—94no—
267C2×C3×D4—92no—
268C2×C3×D4—91no—
269C2×C3×D4—91no—
270C2×C3×D4—91no—
271C2×C3×D4—184no—
272C22×C3×C4—21no—
273C22×C3×C4—22no—
274C22×C3×C4—41no—
275C22×C3×C4—91no—
276C22×C3×C4—91no—
277C22×C3×C4D3211yescharacteristic, complemented
278C22×C3×C4C2×C3×D312yescomplemented
279C2×#67—32no—
280C2×#67—32no—
281C2×#67—34no—
282C2×#67—34no—
283C2×#67—61no—
284C2×#67—61no—
285C2×#67C2×C3×D314yescomplemented
286D3×D4—68no—
287#235—68no—
288#235—68no—
289C2×D12—32no—
290C2×D12—34no—
291C2×D12—61no—
292C2×D12C2×C3×D312yes—
293C2×C4×D3—32no—
294C2×C4×D3—32no—
295C2×C4×D3—61no—
296C2×C4×D3—61no—
297C2×Dic6—32no—
298C2×Dic6—61no—
299C3×C4⋊C4—32no—
300C3×C4⋊C4—32no—
301C3×C4⋊C4—62no—
302C3×C22⋊C4—34no—
303C3×C22⋊C4—34no—
304C3×C22⋊C4—64no—
305C3×C22⋊C4—92no—
306C3×C22⋊C4—94no—
307C3×C42—92no—
308#217—34no—
309(C2×D3)⋊C4—34no—
310(C2×D3)⋊C4—34no—
311(C2×D3)⋊C4C2×C3×D314yescomplemented
312C4⋊Dic3C2×C3×D312yescomplemented
313C4×Dic3—34no—
314C22×C32—22no—
315C22×C32—21no—
316C22×C32—24no—
317C22×C32—22no—
318C22×C32—22no—
319C22×C32—22no—
320C22×C32—22no—
321C22×C32—21no—
322C22×C32—22no—
323C22×C32—41no—
324C22×C32—42no—
325C22×C32—42no—
326C22×C32—42no—
327C22×C32—42no—
328C22×C32—44no—
329C22×C32—64no—
330C22×C32—64no—
331C22×C32—64no—
332C22×C32C23×D312yes—
333C22×C32C24×C311yescharacteristic
334C2×C3⋊D3—21no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3C2×C3×D412yes—
338C2×C3×D3—24no—
339C2×C3×D3—24no—
340C2×C3×D3—24no—
341C2×C3×D3—24no—
342C2×C3×D3—24no—
343C2×C3×D3—24no—
344C2×C3×D3—34no—
345C2×C3×D3—44no—
346C2×C3×D3—44no—
347C2×C3×D3—44no—
348C2×C3×D3—62no—
349C2×C3×D3—62no—
350C2×C3×D3—62no—
351C2×C3×D3—62no—
352C2×C3×D3—62no—
353C2×C3×D3—62no—
354C2×C3×D3—62no—
355C2×C3×D3—122no—
356C2×C3×D3—122no—
357C2×C3×D3—1216no—
358D32—48no—
359C32×C4—21no—
360C32×C4—22no—
361C32×C4—22no—
362C32×C4—22no—
363C32×C4—24no—
364C32×C4—42no—
365C32×C4—42no—
366C32×C4—42no—
367C32×C4—64no—
368C32×C4D3×D414yes—
369C32×C4C2×C3×D412yes—
370C3⋊Dic3—21no—
371C3⋊Dic3C2×C3×D412yes—
372C3×Dic3—24no—
373C3×Dic3—24no—
374C3×Dic3—34no—
375C3×Dic3—44no—
376C3×Dic3—62no—
377C3×Dic3—62no—
378C3×Dic3—62no—
379C2×#41—91no—
380C22×D4—91no—
381#127—92no—
382#124—92no—
383#121—32no—
384#121—92no—
385#120—92no—
386#120—92no—
387#117—91no—
388C33#53511yescharacteristic, complemented, Sylow
389C23×C3—22no—
390C23×C3—21no—
391C23×C3—34no—
392C23×C3—34no—
393C23×C3—41no—
394C23×C3—64no—
395C23×C3—91no—
396C23×C3—91no—
397C23×C3—184no—
398C23×C3—364no—
399C23×C3C2×D3211yescharacteristic
400C23×C3C22×C3×D312yes—
401C22×D3—32no—
402C22×D3—32no—
403C22×D3—61no—
404C22×D3—61no—
405C22×D3—68no—
406C22×D3—124no—
407C22×D3—124no—
408C22×D3C22×C3×D314yes—
409C3×Q8—182no—
410C3×D4—64no—
411C3×D4—64no—
412C3×D4—124no—
413C3×D4—124no—
414C3×D4—124no—
415C3×D4—128no—
416C3×D4—182no—
417C3×D4—182no—
418C3×D4—184no—
419C3×D4—182no—
420C3×D4—364no—
421C2×C3×C4—24no—
422C2×C3×C4—22no—
423C2×C3×C4—24no—
424C2×C3×C4—22no—
425C2×C3×C4—21no—
426C2×C3×C4—21no—
427C2×C3×C4—22no—
428C2×C3×C4—34no—
429C2×C3×C4—34no—
430C2×C3×C4—44no—
431C2×C3×C4—44no—
432C2×C3×C4—41no—
433C2×C3×C4—41no—
434C2×C3×C4—64no—
435C2×C3×C4—91no—
436C2×C3×C4—94no—
437C2×C3×C4—91no—
438C2×C3×C4—182no—
439C2×C3×C4C2×D3211yescharacteristic
440C2×C3×C4C2×D3211yescharacteristic
441C2×C3×C4C22×C3×D312yes—
442C2×C3×C4C22×C3×D312yes—
443#67—44no—
444#67—68no—
445#67—64no—
446#67—64no—
447#67—64no—
448#67—64no—
449#67—124no—
450C2×Dic3—32no—
451C2×Dic3—32no—
452C2×Dic3—61no—
453C2×Dic3—61no—
454C2×Dic3C22×C3×D314yes—
455D12—24no—
456D12—64no—
457D12—64no—
458D12—124no—
459C4×D3—38no—
460C4×D3—64no—
461C4×D3—64no—
462C4×D3—64no—
463Dic6—64no—
464Dic6—64no—
465C2×C32—22no—
466C2×C32—21no—
467C2×C32—22no—
468C2×C32—22no—
469C2×C32—22no—
470C2×C32—41no—
471C2×C32—42no—
472C2×C32—42no—
473C2×C32—44no—
474C2×C32—44no—
475C2×C32—42no—
476C2×C32—41no—
477C2×C32—124no—
478C2×C32C2×D3×D412yes—
479C2×C32#100412yes—
480C2×C32#100912yes—
481C2×C32C22×C3×D411yescharacteristic
482C2×C32C3×H(5,𝔽2)12yes—
483C3⋊D3—22no—
484C3⋊D3—41no—
485C3×D3—44no—
486C3×D3—44no—
487C3×D3—64no—
488C3×D3—84no—
489C3×D3—122no—
490C3×D3—122no—
491C3×D3—122no—
492C24—92no—
493#41—184no—
494C2×Q8—91no—
495C2×D4—34no—
496C2×D4—32no—
497C2×D4—94no—
498C2×D4—92no—
499C2×D4—91no—
500C2×D4—91no—
501C2×D4—91no—
502C2×D4—184no—
503C22×C4—91no—
504C22×C4—91no—
505C22×C4C3×D3211yescharacteristic, complemented
506C4⋊C4—32no—
507C22⋊C4—34no—
508C22⋊C4—92no—
509C22⋊C4—94no—
510C42—92no—
511C22×C3—22no—
512C22×C3—24no—
513C22×C3—22no—
514C22×C3—21no—
515C22×C3—22no—
516C22×C3—22no—
517C22×C3—22no—
518C22×C3—21no—
519C22×C3—22no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—42no—
523C22×C3—42no—
524C22×C3—44no—
525C22×C3—41no—
526C22×C3—64no—
527C22×C3—64no—
528C22×C3—64no—
529C22×C3—64no—
530C22×C3—64no—
531C22×C3—64no—
532C22×C3—92no—
533C22×C3—124no—
534C22×C3—124no—
535C22×C3—124no—
536C22×C3—182no—
537C22×C3—182no—
538C22×C3—181no—
539C22×C3—368no—
540C22×C3C22×D3211yescharacteristic
541C22×C3C23×C3×D312yes—
542C2×D3—24no—
543C2×D3—24no—
544C2×D3—24no—
545C2×D3—34no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—62no—
549C2×D3—62no—
550C2×D3—62no—
551C2×D3—62no—
552C2×D3—62no—
553C2×D3—122no—
554C2×D3—122no—
555C2×D3—1216no—
556C3×C4—22no—
557C3×C4—21no—
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—24no—
561C3×C4—42no—
562C3×C4—42no—
563C3×C4—42no—
564C3×C4—64no—
565C3×C4—64no—
566C3×C4—92no—
567C3×C4—124no—
568C3×C4—181no—
569C3×C4#381112yes—
570C3×C4C3×D3×D414yes—
571Dic3—24no—
572Dic3—34no—
573Dic3—62no—
574Dic3—62no—
575Dic3—62no—
576C32—21no—
577C32—22no—
578C32—41no—
579C32#560712yescomplemented
580C32C3×#53511yescharacteristic, complemented
581C23—34no—
582C23—91no—
583C23—91no—
584C23—184no—
585C23—364no—
586C23C2×C3×D3211yescharacteristic
587Q8—182no—
588D4—64no—
589D4—124no—
590D4—182no—
591D4—182no—
592D4—184no—
593D4—182no—
594D4—364no—
595C2×C4—22no—
596C2×C4—34no—
597C2×C4—91no—
598C2×C4—94no—
599C2×C4—91no—
600C2×C4—182no—
601C2×C4C2×C3×D3211yescharacteristic
602C2×C4C2×C3×D3211yescharacteristic
603C2×C3—21no—
604C2×C3—22no—
605C2×C3—22no—
606C2×C3—22no—
607C2×C3—22no—
608C2×C3—42no—
609C2×C3—44no—
610C2×C3—44no—
611C2×C3—41no—
612C2×C3—42no—
613C2×C3—41no—
614C2×C3—42no—
615C2×C3—124no—
616C2×C3—124no—
617C2×C3—182no—
618C2×C3—244no—
619C2×C3—361no—
620C2×C3#6430712yes—
621C2×C3C2×#381111yescharacteristic
622C2×C3C2×C3×D3×D412yes—
623C2×C3C3×#100412yes—
624C2×C3C3×#100912yes—
625D3—44no—
626D3—64no—
627D3—122no—
628D3—122no—
629D3—122no—
630C22—21no—
631C22—22no—
632C22—64no—
633C22—64no—
634C22—64no—
635C22—92no—
636C22—182no—
637C22—181no—
638C22—182no—
639C22—368no—
640C22C22×C3×D3211yescharacteristic
641C4—21no—
642C4—64no—
643C4—92no—
644C4—181no—
645C4C3×#381112yes—
646C3—21no—
647C3—22no—
648C3—41no—
649C3#1059508211yescharacteristic, direct product factor
650C3C3×#560712yescomplemented
651C2—41no—
652C2—124no—
653C2—182no—
654C2—361no—
655C2C3×#6430712yes—
656C2C2×C3×#381111yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC22×C33×C4C22
socleC22×C33C24
hypercenterC22×C3×C4D32
hypocenterC32C3×#535
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3828C2semidirect
2. C2×C3×#3802C2semidirect
3. C32×#930C2semidirect
4. C3×#63983C2semidirect
5. C3×#63979C2semidirect
6. C3×#63923C2semidirect
7. C3×#63916C2semidirect
8. C3×#63913C2semidirect
9. C3×#63849C2semidirect
11. #10595082C3direct (N × H)
13. C22×C33×C4C22semidirect
15. C2×C3×#638C22semidirect
19. C2×C3×C4×C3⋊D3C22semidirect
20. C2×C3×#634C22semidirect
21. C2×C32×#67C22semidirect
23. C2×C3×#626C22semidirect
26. C32×(C2×D3)⋊C4C22semidirect
27. C32×C4⋊Dic3C22semidirect
29. C3×(C2×D3)⋊Dic3C22semidirect
30. C3×Dic32C22semidirect
31. C2×#3828C2×C3semidirect
35. C2×#3802C2×C3semidirect
41. C3×#930D3semidirect
42. C3×#930C2×C3semidirect
47. #63983C2×C3semidirect
48. #63979C2×C3semidirect
49. #63923C2×C3semidirect
50. #63916C2×C3semidirect
51. #63913C2×C3semidirect
52. #63849C2×C3semidirect
68. C3×C4×C3⋊D3D4semidirect
84. C22×C32×C4C2×D3semidirect
85. C22×C32×C4C22×C3semidirect
87. C2×#638C22×C3semidirect
91. C2×C4×C3⋊D3C22×C3semidirect
92. C2×#634C22×C3semidirect
100. C2×C3×#67C2×D3semidirect
101. C2×C3×#67C22×C3semidirect
117. C2×#626C22×C3semidirect
126. C3×(C2×D3)⋊C4C2×D3semidirect
127. C3×(C2×D3)⋊C4C22×C3semidirect
129. C3×C4⋊Dic3C2×D3semidirect
130. C3×C4⋊Dic3C22×C3semidirect
133. (C2×D3)⋊Dic3C22×C3semidirect
134. Dic32C22×C3semidirect
168. #930C3×D3semidirect
217. C4×C3⋊D3C3×D4semidirect
277. C22×C3×C4D32semidirect
278. C22×C3×C4C2×C3×D3semidirect
285. C2×#67C2×C3×D3semidirect
311. (C2×D3)⋊C4C2×C3×D3semidirect
312. C4⋊Dic3C2×C3×D3semidirect
388. C33#535semidirect
505. C22×C4C3×D32semidirect
579. C32#5607semidirect
580. C32C3×#535semidirect
649. C3#10595082direct (N × H)
650. C3C3×#5607semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38282
C2×C3×#38022
C32×#9302
C3×#639832
C3×#639792
C3×#639232
C3×#639162
C3×#639132
C3×#638492
C3×#56073
#105950823