Finite Group Databasebeta

← C3×#10591170 #13158349

Subgroups — C3×#10591170 #13158349

Order 1728.

950 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#235C211yesmaximal, characteristic
2C32×#924C211yesmaximal, characteristic, complemented
3C2×C3×#3718C211yesmaximal, characteristic, complemented
4C2×C3×#3715C211yesmaximal, characteristic, complemented
5C3×#63657C211yesmaximal, characteristic, complemented
6C3×#63565C211yesmaximal, characteristic, complemented
7C3×#63562C211yesmaximal, characteristic, complemented
8C3×#5239—31nomaximal
9C3×#5047—31nomaximal
10#10591170C311yesmaximal, characteristic, direct product factor
11C22×C33×C4C2211yescharacteristic
12C2×C32×#67—21no—
13C32×#235—22no—
14C32×#235—22no—
15C2×C32×D12C2211yescharacteristic
16C2×C32×C4×D3—21no—
17C2×C32×Dic6C2211yescharacteristic
18C2×C32×Dic6C2211yescharacteristic
19C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
20C2×C3×C3⋊(C3⋊C8)C2211yescharacteristic
21C32×#217—21no—
22C32×C4⋊Dic3C2211yescharacteristic
23C32×Dic3⋊C4—21no—
24C3×#3718—22no—
25C3×#3715—22no—
26C2×C32×#41—31no—
27C2×C3×#235—21no—
28C2×C3×#235D311yescharacteristic
29C2×C3×#235C2×C311yescharacteristic
30C32×C22⋊Q8—31no—
31C2×C3×#216—31no—
32C2×C3×#216—31no—
33C2×C3×#215—31no—
34C2×C3×#214—31no—
35C3×#924—21no—
36C3×#924D311yescharacteristic, complemented
37C3×#924C2×C311yescharacteristic, complemented
38C2×#3718C2×C311yescharacteristic, complemented
39C2×#3715C2×C311yescharacteristic, complemented
40#63657C2×C311yescharacteristic, complemented
41C3×#835—31no—
42C3×#832—31no—
43C3×#830—31no—
44C3×#830—31no—
45C3×#830—61no—
46C3×#810—31no—
47C3×#809—31no—
48#63565C2×C311yescharacteristic, complemented
49#63562C2×C311yescharacteristic, complemented
50C23×C33D411yescharacteristic
51C22×C32×D3—21no—
52C2×C33×C4—21no—
53C2×C33×C4—21no—
54C2×C33×C4D411yescharacteristic
55C2×C33×C4C2311yescharacteristic
56C32×#67—24no—
57C2×C32×Dic3—21no—
58C2×C32×Dic3—21no—
59C2×C32×Dic3—21no—
60C32×D12—21no—
61C32×D12D412yes—
62C32×C4×D3—24no—
63C32×Dic6—21no—
64C32×Dic6—21no—
65C32×Dic6—21no—
66C32×Dic6D412yes—
67C3×C3⋊(C3⋊C8)—21no—
68C3×C3⋊(C3⋊C8)—21no—
69C3×#452—91no—
70#5239—31no—
71#5047—31no—
72C32×#41—62no—
73C32×#41—62no—
74C2×C32×Q8—31no—
75C2×C32×Q8—31no—
76C2×C32×D4—31no—
77C2×C32×D4—61no—
78C22×C32×C4—21no—
79C22×C32×C4—21no—
80C22×C32×C4—21no—
81C22×C32×C4—41no—
82C22×C32×C4—61no—
83C22×C32×C4C2×D311yescharacteristic
84C22×C32×C4C2×D311yescharacteristic
85C22×C32×C4C22×C311yescharacteristic
86C2×C3×#67—22no—
87C2×C3×#67—21no—
88C2×C3×#67—21no—
89C3×#235—24no—
90C3×#235—24no—
91C3×#235—22no—
92C3×#235—22no—
93C3×#235—22no—
94C3×#235—22no—
95C2×C3×D12—21no—
96C2×C3×D12C2×D311yescharacteristic
97C2×C3×D12C22×C311yescharacteristic
98C2×C3×C4×D3—22no—
99C2×C3×C4×D3—21no—
100C2×C3×C4×D3—21no—
101C2×C3×Dic6—21no—
102C2×C3×Dic6—21no—
103C2×C3×Dic6C2×D311yescharacteristic
104C2×C3×Dic6C2×D311yescharacteristic
105C2×C3×Dic6C22×C311yescharacteristic
106C2×C3×Dic6C22×C311yescharacteristic
107C32×C4⋊C4—31no—
108C32×C4⋊C4—61no—
109C32×C22⋊C4—61no—
110C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
111C2×C3⋊(C3⋊C8)C22×C311yescharacteristic
112C3×#217—22no—
113C3×#217—21no—
114C3×#217—21no—
115C3×#216—62no—
116C3×#216—62no—
117C3×#215—62no—
118C3×#214—62no—
119C3×C4⋊Dic3—21no—
120C3×C4⋊Dic3C2×D311yescharacteristic
121C3×C4⋊Dic3C22×C311yescharacteristic
122C3×Dic3⋊C4—22no—
123C3×Dic3⋊C4—21no—
124C3×Dic3⋊C4—21no—
125C2×C3×C3⋊C8—31no—
126C2×C3×C3⋊C8—31no—
127C2×C3×C3⋊C8—31no—
128C2×C3×C3⋊C8—31no—
129C2×C3×C3⋊C8—61no—
130C2×C3×C3⋊C8—61no—
131#3718—22no—
132#3715—22no—
133C22×C33—21no—
134C22×C33—21no—
135C22×C33—21no—
136C22×C33C2×D411yescharacteristic
137C2×C32×D3—22no—
138C2×C32×D3—41no—
139C2×C32×D3—41no—
140C33×C4—21no—
141C33×C4C2×D411yescharacteristic
142C33×C4C2×D411yescharacteristic
143C32×Dic3—22no—
144C32×Dic3—41no—
145C32×Dic3—41no—
146C2×C3×#41—31no—
147C2×C3×#41—31no—
148C2×C3×#41—61no—
149C2×#235C3×D311yescharacteristic
150C2×C3×Q16—91no—
151C2×C3×SD16—91no—
152C3×C22⋊Q8—31no—
153C3×C22⋊Q8—31no—
154C3×C22⋊Q8—61no—
155C2×#216—31no—
156C2×#216—31no—
157C2×#215—31no—
158C2×#214—31no—
159#924C3×D311yescharacteristic, complemented
160C3×#103—91no—
161C3×#102—91no—
162C3×C22⋊C8—91no—
163#835—31no—
164#832—31no—
165#830—31no—
166#830—31no—
167#830—61no—
168#810—31no—
169#809—31no—
170C23×C32—21no—
171C23×C32—21no—
172C23×C32—21no—
173C23×C32—41no—
174C23×C32—61no—
175C23×C32#6711yescharacteristic
176C23×C32#6711yescharacteristic
177C23×C32C3×D411yescharacteristic
178C22×C3×D3—22no—
179C22×C3×D3—21no—
180C22×C3×D3—21no—
181C32×Q8—32no—
182C32×Q8—61no—
183C32×Q8—61no—
184C32×Q8—61no—
185C32×D4—32no—
186C32×D4—64no—
187C32×D4—61no—
188C2×C32×C4—21no—
189C2×C32×C4—21no—
190C2×C32×C4—22no—
191C2×C32×C4—22no—
192C2×C32×C4—21no—
193C2×C32×C4—21no—
194C2×C32×C4—21no—
195C2×C32×C4—21no—
196C2×C32×C4—21no—
197C2×C32×C4—21no—
198C2×C32×C4—21no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—21no—
202C2×C32×C4—41no—
203C2×C32×C4—41no—
204C2×C32×C4—41no—
205C2×C32×C4—41no—
206C2×C32×C4—41no—
207C2×C32×C4—41no—
208C2×C32×C4—42no—
209C2×C32×C4—42no—
210C2×C32×C4—64no—
211C2×C32×C4—61no—
212C2×C32×C4—61no—
213C2×C32×C4—61no—
214C2×C32×C4#6711yescharacteristic
215C2×C32×C4#6711yescharacteristic
216C2×C32×C4C3×D411yescharacteristic
217C2×C32×C4C22×D311yescharacteristic
218C2×C32×C4C22×D311yescharacteristic
219C2×C32×C4C23×C311yescharacteristic
220C3×#67—28no—
221C3×#67—24no—
222C3×#67—24no—
223C2×C3×Dic3—22no—
224C2×C3×Dic3—21no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—22no—
227C2×C3×Dic3—22no—
228C2×C3×Dic3—21no—
229C2×C3×Dic3—21no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C3×D12—22no—
233C3×D12—21no—
234C3×D12—21no—
235C3×D12—22no—
236C3×D12#6712yes—
237C3×D12C3×D412yes—
238C3×C4×D3—28no—
239C3×C4×D3—24no—
240C3×C4×D3—24no—
241C3×Dic6—22no—
242C3×Dic6—21no—
243C3×Dic6—21no—
244C3×Dic6—21no—
245C3×Dic6—21no—
246C3×Dic6—21no—
247C3×Dic6—21no—
248C3×Dic6—22no—
249C3×Dic6—41no—
250C3×Dic6—41no—
251C3×Dic6#6712yes—
252C3×Dic6C3×D412yes—
253C3⋊(C3⋊C8)—21no—
254C3⋊(C3⋊C8)—21no—
255C3×C3⋊C8—61no—
256C3×C3⋊C8—61no—
257C3×C3⋊C8—61no—
258C3×C3⋊C8—61no—
259C3×C3⋊C8—121no—
260C3×C3⋊C8—121no—
261#452—91noSylow
262C2×C33—41no—
263C2×C33#12011yescharacteristic
264C2×C33#13511yescharacteristic
265C2×C33#13711yescharacteristic
266C32×D3—42no—
267C3×#41—62no—
268C3×#41—62no—
269C3×#41—62no—
270C3×#41—62no—
271C3×#41—64no—
272C3×#41—64no—
273C2×C3×Q8—31no—
274C2×C3×Q8—31no—
275C2×C3×Q8—31no—
276C2×C3×Q8—31no—
277C2×C3×Q8—61no—
278C2×C3×Q8—61no—
279C2×C3×D4—31no—
280C2×C3×D4—31no—
281C2×C3×D4—61no—
282C2×C3×D4—62no—
283C2×C3×D4—61no—
284C2×C3×D4—61no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—41no—
289C22×C3×C4—62no—
290C22×C3×C4—61no—
291C22×C3×C4—61no—
292C22×C3×C4D3211yescharacteristic
293C22×C3×C4C2×C3×D311yescharacteristic
294C22×C3×C4C2×C3×D311yescharacteristic
295C2×#67—21no—
296#235—22no—
297#235—22no—
298C2×D12C2×C3×D311yescharacteristic
299C2×C4×D3—21no—
300C2×Dic6C2×C3×D311yescharacteristic
301C2×Dic6C2×C3×D311yescharacteristic
302C3×Q16—182no—
303C3×SD16—182no—
304C2×C3×C8—91no—
305C2×C3×C8—91no—
306C3×C4⋊C4—31no—
307C3×C4⋊C4—31no—
308C3×C4⋊C4—61no—
309C3×C4⋊C4—62no—
310C3×C4⋊C4—61no—
311C3×C4⋊C4—61no—
312C3×C22⋊C4—62no—
313C3×C22⋊C4—61no—
314C3×C22⋊C4—61no—
315#217—21no—
316#216—62no—
317#216—62no—
318#215—62no—
319#214—62no—
320C4⋊Dic3C2×C3×D311yescharacteristic
321Dic3⋊C4—21no—
322C2×C3⋊C8—31no—
323C2×C3⋊C8—31no—
324C2×C3⋊C8—31no—
325C2×C3⋊C8—31no—
326C2×C3⋊C8—61no—
327C2×C3⋊C8—61no—
328C22×C32—21no—
329C22×C32—21no—
330C22×C32—21no—
331C22×C32—22no—
332C22×C32—22no—
333C22×C32—22no—
334C22×C32—21no—
335C22×C32—21no—
336C22×C32—21no—
337C22×C32—21no—
338C22×C32—21no—
339C22×C32—21no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32—21no—
343C22×C32—41no—
344C22×C32—41no—
345C22×C32—41no—
346C22×C32—41no—
347C22×C32—41no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32—42no—
351C22×C32—42no—
352C22×C32—42no—
353C22×C32—62no—
354C22×C32—121no—
355C22×C32—121no—
356C22×C32C2×#6711yescharacteristic
357C22×C32C2×#6711yescharacteristic
358C22×C32C2×C3×D411yescharacteristic
359C2×C3×D3—24no—
360C2×C3×D3—22no—
361C2×C3×D3—22no—
362C2×C3×D3—42no—
363C2×C3×D3—42no—
364C2×C3×D3—41no—
365C2×C3×D3—41no—
366C2×C3×D3—41no—
367C2×C3×D3—41no—
368C32×C4—21no—
369C32×C4—22no—
370C32×C4—21no—
371C32×C4—21no—
372C32×C4—21no—
373C32×C4—21no—
374C32×C4—21no—
375C32×C4—21no—
376C32×C4—21no—
377C32×C4—21no—
378C32×C4—41no—
379C32×C4—41no—
380C32×C4—41no—
381C32×C4—41no—
382C32×C4—42no—
383C32×C4—62no—
384C32×C4—121no—
385C32×C4—121no—
386C32×C4D3×D411yescharacteristic
387C32×C4D3×D411yescharacteristic
388C32×C4C2×#6711yescharacteristic
389C32×C4C2×#6711yescharacteristic
390C32×C4C2×C3×D411yescharacteristic
391C32×C4C2×C3×D411yescharacteristic
392C3×Dic3—24no—
393C3×Dic3—22no—
394C3×Dic3—22no—
395C3×Dic3—42no—
396C3×Dic3—42no—
397C3×Dic3—41no—
398C3×Dic3—41no—
399C3×Dic3—41no—
400C3×Dic3—41no—
401C2×#41—31no—
402C2×Q16—91no—
403C2×SD16—91no—
404C22⋊Q8—31no—
405#103—91no—
406#102—91no—
407C22⋊C8—91no—
408C33#45211yescharacteristic, complemented, Sylow
409C23×C3—21no—
410C23×C3—21no—
411C23×C3—21no—
412C23×C3—41no—
413C23×C3—62no—
414C23×C3—61no—
415C23×C3—61no—
416C23×C3#62511yescharacteristic
417C23×C3C3×#6711yescharacteristic
418C23×C3C3×#6711yescharacteristic
419C22×D3—21no—
420C3×Q8—32no—
421C3×Q8—32no—
422C3×Q8—62no—
423C3×Q8—62no—
424C3×Q8—61no—
425C3×Q8—61no—
426C3×Q8—61no—
427C3×Q8—61no—
428C3×Q8—61no—
429C3×Q8—61no—
430C3×Q8—121no—
431C3×Q8—121no—
432C3×D4—32no—
433C3×D4—32no—
434C3×D4—62no—
435C3×D4—62no—
436C3×D4—68no—
437C3×D4—64no—
438C3×D4—64no—
439C3×D4—61no—
440C3×D4—61no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—21no—
453C2×C3×C4—21no—
454C2×C3×C4—21no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—42no—
460C2×C3×C4—42no—
461C2×C3×C4—41no—
462C2×C3×C4—41no—
463C2×C3×C4—68no—
464C2×C3×C4—64no—
465C2×C3×C4—64no—
466C2×C3×C4—62no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—62no—
470C2×C3×C4—62no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4#62511yescharacteristic
476C2×C3×C4C3×#6711yescharacteristic
477C2×C3×C4C3×#6711yescharacteristic
478C2×C3×C4C2×D3211yescharacteristic
479C2×C3×C4C22×C3×D311yescharacteristic
480C2×C3×C4C22×C3×D311yescharacteristic
481#67—24no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485D12—21no—
486D12C3×#6712yes—
487C4×D3—24no—
488Dic6—21no—
489Dic6—21no—
490Dic6—21no—
491Dic6C3×#6712yes—
492C3×C8—181no—
493C3×C8—181no—
494C3⋊C8—61no—
495C3⋊C8—61no—
496C3⋊C8—61no—
497C3⋊C8—61no—
498C3⋊C8—121no—
499C3⋊C8—121no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—21no—
503C2×C32—21no—
504C2×C32—21no—
505C2×C32—21no—
506C2×C32—21no—
507C2×C32—21no—
508C2×C32—21no—
509C2×C32—41no—
510C2×C32—41no—
511C2×C32—41no—
512C2×C32—42no—
513C2×C32—42no—
514C2×C32—42no—
515C2×C32—44no—
516C2×C32—41no—
517C2×C32—41no—
518C2×C32—41no—
519C2×C32—122no—
520C2×C32#93711yescharacteristic
521C2×C32#94211yescharacteristic
522C2×C32#95011yescharacteristic
523C2×C32#95011yescharacteristic
524C2×C32#95111yescharacteristic
525C2×C32#95311yescharacteristic
526C2×C32C3×#12011yescharacteristic
527C2×C32C3×#13511yescharacteristic
528C2×C32C3×#13711yescharacteristic
529C3×D3—44no—
530C3×D3—42no—
531C3×D3—42no—
532#41—62no—
533#41—62no—
534C2×Q8—31no—
535C2×Q8—31no—
536C2×D4—31no—
537C2×D4—61no—
538C22×C4—61no—
539C22×C4C3×D3211yescharacteristic
540Q16—182no—
541SD16—182no—
542C2×C8—91no—
543C2×C8—91no—
544C4⋊C4—31no—
545C4⋊C4—61no—
546C22⋊C4—61no—
547C22×C3—22no—
548C22×C3—22no—
549C22×C3—22no—
550C22×C3—21no—
551C22×C3—21no—
552C22×C3—21no—
553C22×C3—21no—
554C22×C3—21no—
555C22×C3—21no—
556C22×C3—21no—
557C22×C3—21no—
558C22×C3—21no—
559C22×C3—21no—
560C22×C3—21no—
561C22×C3—21no—
562C22×C3—41no—
563C22×C3—41no—
564C22×C3—41no—
565C22×C3—41no—
566C22×C3—41no—
567C22×C3—41no—
568C22×C3—42no—
569C22×C3—42no—
570C22×C3—42no—
571C22×C3—41no—
572C22×C3—64no—
573C22×C3—62no—
574C22×C3—62no—
575C22×C3—122no—
576C22×C3—122no—
577C22×C3—121no—
578C22×C3—121no—
579C22×C3—121no—
580C22×C3—121no—
581C22×C3C2×#62511yescharacteristic
582C22×C3C2×C3×#6711yescharacteristic
583C22×C3C2×C3×#6711yescharacteristic
584C2×D3—22no—
585C2×D3—41no—
586C2×D3—41no—
587C3×C4—22no—
588C3×C4—21no—
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—21no—
594C3×C4—21no—
595C3×C4—21no—
596C3×C4—21no—
597C3×C4—41no—
598C3×C4—41no—
599C3×C4—42no—
600C3×C4—41no—
601C3×C4—41no—
602C3×C4—64no—
603C3×C4—62no—
604C3×C4—62no—
605C3×C4—122no—
606C3×C4—122no—
607C3×C4—121no—
608C3×C4—121no—
609C3×C4—121no—
610C3×C4—121no—
611C3×C4D3×#6711yescharacteristic
612C3×C4D3×#6711yescharacteristic
613C3×C4C3×D3×D411yescharacteristic
614C3×C4C3×D3×D411yescharacteristic
615C3×C4C2×C3×#6711yescharacteristic
616C3×C4C2×C3×#6711yescharacteristic
617Dic3—22no—
618Dic3—41no—
619Dic3—41no—
620C32—21no—
621C32—21no—
622C32—21no—
623C32—41no—
624C32#504711yescharacteristic, complemented
625C32#523911yescharacteristic, complemented
626C32C3×#45211yescharacteristic, complemented
627C23—61no—
628C23C3×#62511yescharacteristic
629Q8—32no—
630Q8—61no—
631Q8—61no—
632Q8—61no—
633D4—32no—
634D4—64no—
635D4—61no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—64no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4C3×#62511yescharacteristic
643C2×C4C2×C3×D3211yescharacteristic
644C8—181no—
645C8—181no—
646C2×C3—21no—
647C2×C3—21no—
648C2×C3—21no—
649C2×C3—21no—
650C2×C3—21no—
651C2×C3—21no—
652C2×C3—21no—
653C2×C3—21no—
654C2×C3—21no—
655C2×C3—42no—
656C2×C3—42no—
657C2×C3—42no—
658C2×C3—44no—
659C2×C3—41no—
660C2×C3—41no—
661C2×C3—41no—
662C2×C3—41no—
663C2×C3—41no—
664C2×C3—41no—
665C2×C3—124no—
666C2×C3—122no—
667C2×C3—122no—
668C2×C3#6382211yescharacteristic
669C2×C3#6382711yescharacteristic
670C2×C3#6397611yescharacteristic
671C2×C3C3×#93711yescharacteristic
672C2×C3C3×#94211yescharacteristic
673C2×C3C3×#95011yescharacteristic
674C2×C3C3×#95011yescharacteristic
675C2×C3C3×#95111yescharacteristic
676C2×C3C3×#95311yescharacteristic
677D3—42no—
678C22—21no—
679C22—21no—
680C22—21no—
681C22—62no—
682C22—121no—
683C22—121no—
684C22C2×C3×#62511yescharacteristic
685C4—21no—
686C4—62no—
687C4—121no—
688C4—121no—
689C4C3×D3×#6711yescharacteristic
690C4C3×D3×#6711yescharacteristic
691C3—21no—
692C3—21no—
693C3—21no—
694C3—41no—
695C3#1059117011yescharacteristic, direct product factor
696C3C3×#504711yescharacteristic, complemented
697C3C3×#523911yescharacteristic, complemented
698C2—41no—
699C2—122no—
700C2C3×#6382211yescharacteristic
701C2C3×#6382711yescharacteristic
702C2C3×#6397611yescharacteristic
subgroupG/H
centerC22×C3C2×#625
commutator, cosocleC2×C32×C4C23×C3
FrattiniC2×C4C2×C3×D32
FittingC22×C33×C4C22
socleC22×C33C2×D4
prime radicalC2×C32×#235C2
hypercenterC22×C3×C4D32
hypocenterC32C3×#452
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
2. C32×#924C2semidirect
3. C2×C3×#3718C2semidirect
4. C2×C3×#3715C2semidirect
5. C3×#63657C2semidirect
6. C3×#63565C2semidirect
7. C3×#63562C2semidirect
10. #10591170C3direct (N × H)
36. C3×#924D3semidirect
37. C3×#924C2×C3semidirect
38. C2×#3718C2×C3semidirect
39. C2×#3715C2×C3semidirect
40. #63657C2×C3semidirect
48. #63565C2×C3semidirect
49. #63562C2×C3semidirect
159. #924C3×D3semidirect
408. C33#452semidirect
624. C32#5047semidirect
625. C32#5239semidirect
626. C32C3×#452semidirect
695. C3#10591170direct (N × H)
696. C3C3×#5047semidirect
697. C3C3×#5239semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2352
C32×#9242
C2×C3×#37182
C2×C3×#37152
C3×#636572
C3×#635652
C3×#635622
C3×#52393
C3×#50473
#105911703