Finite Group Databasebeta

← #13178712

Subgroups — #13178712

Order 1728.

1018 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64155C211yesmaximal, characteristic
2C3×Q8×C3⋊Dic3C211yesmaximal, characteristic, complemented
3C3×#64153C211yesmaximal, characteristic, complemented
4#11723680C211yesmaximal, characteristic, complemented
5#11723679C212yesmaximal, complemented
6#11723676C212yesmaximal
7#11723675C212yesmaximal
8#11723674C211yesmaximal, characteristic
9#11723673C211yesmaximal, characteristic
10#11723669C212yesmaximal, complemented
11#11723668C211yesmaximal, characteristic, complemented
12#10595354—31nomaximal
13#10595349—31nomaximal
14#10595348—31nomaximal
15C2×C33×Q8C2211yescharacteristic
16C2×C3×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#634C2211yescharacteristic
18C3×#3752C2212yes—
19C3×C4⋊(C3⋊Dic3)C2212yes—
20C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
22C3×#3750C2212yes—
23C3×#3750C2212yes—
24C3×#3750C2212yes—
25C3×C4×C3⋊Dic3C2211yescharacteristic
26C3×C4×C3⋊Dic3C2211yescharacteristic
27C3×C4×C3⋊Dic3C2212yes—
28#88815C2212yes—
29#88815C2211yescharacteristic
30#88815C2212yes—
31#88815C2212yes—
32#88815C2211yescharacteristic
33#88815C2212yes—
34#88814C2211yescharacteristic
35#88814C2211yescharacteristic
36#88814C2212yes—
37#88813C2212yes—
38#64155D311yescharacteristic
39Q8×C3⋊Dic3D311yescharacteristic, complemented
40#64153D311yescharacteristic, complemented
41C3×#946—31no—
42C3×#946—31no—
43C3×#946—61no—
44C3×Q8×Dic3—31no—
45C3×Q8×Dic3—31no—
46C3×Q8×Dic3—61no—
47C3×#944—31no—
48C3×#944—31no—
49C3×#944—61no—
50#63874—31no—
51#63872—31no—
52#63871—31no—
53#63870—32no—
54#63869—31no—
55#63869—31no—
56#63868—32no—
57#63867—32no—
58#63867—32no—
59#63862—32no—
60#63861—32no—
61#63859—32no—
62#63858—32no—
63#63857—31no—
64#63856—31no—
65#63855—31no—
66#63855—31no—
67#63848—32no—
68#63847—32no—
69#63846—32no—
70#63845—32no—
71#63844—31no—
72#63843—31no—
73Dic3×Dic6—31no—
74C22×C3×C3⋊D3C2311yescharacteristic
75C33×Q8—22no—
76C2×C33×C4C2312yes—
77C2×C33×C4C2311yescharacteristic
78C2×C3×C3⋊Dic3C2311yescharacteristic
79C2×C3×C3⋊Dic3C2311yescharacteristic
80C2×C3×C3⋊Dic3C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2312yes—
83C2×C3×C3⋊Dic3C2312yes—
84C2×C3×C3⋊Dic3C2311yescharacteristic
85C2×C3×C3⋊Dic3C2312yes—
86C3×C4×C3⋊D3—22no—
87C3×#634—22no—
88#5731—91no—
89#5625—91no—
90#5583—91no—
91C2×C32×Q8—21no—
92C2×C32×Q8—21no—
93C2×C32×Q8—21no—
94C2×C32×Q8—41no—
95C2×C32×Q8C2×D311yescharacteristic
96C2×C32×Q8C2×D311yescharacteristic
97C2×C32×Q8C2×D311yescharacteristic
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×#634C2×D311yescharacteristic
100C2×C3×C4×D3—31no—
101C2×C3×C4×D3—31no—
102C2×C3×C4×D3—61no—
103C2×C3×Dic6—31no—
104C2×C3×Dic6—31no—
105C2×C3×Dic6—61no—
106#3752C2×D312yes—
107C4⋊(C3⋊Dic3)C2×D311yescharacteristic
108C4⋊(C3⋊Dic3)C2×D312yes—
109C4⋊(C3⋊Dic3)C2×D311yescharacteristic
110#3750C2×D312yes—
111#3750C2×D312yes—
112#3750C2×D312yes—
113C4×C3⋊Dic3C2×D311yescharacteristic
114C4×C3⋊Dic3C2×D311yescharacteristic
115C4×C3⋊Dic3C2×D312yes—
116C3×(C2×D3)⋊C4—32no—
117C3×(C2×D3)⋊C4—32no—
118C3×(C2×D3)⋊C4—62no—
119C3×C4⋊Dic3—32no—
120C3×C4⋊Dic3—32no—
121C3×C4⋊Dic3—31no—
122C3×C4⋊Dic3—31no—
123C3×C4⋊Dic3—31no—
124C3×C4⋊Dic3—31no—
125C3×C4⋊Dic3—62no—
126C3×C4⋊Dic3—61no—
127C3×C4⋊Dic3—61no—
128C3×Dic3⋊C4—32no—
129C3×Dic3⋊C4—32no—
130C3×Dic3⋊C4—32no—
131C3×Dic3⋊C4—32no—
132C3×Dic3⋊C4—32no—
133C3×Dic3⋊C4—32no—
134C3×Dic3⋊C4—62no—
135C3×Dic3⋊C4—62no—
136C3×Dic3⋊C4—62no—
137C3×C4×Dic3—31no—
138C3×C4×Dic3—31no—
139C3×C4×Dic3—31no—
140C3×C4×Dic3—31no—
141C3×C4×Dic3—32no—
142C3×C4×Dic3—32no—
143C3×C4×Dic3—61no—
144C3×C4×Dic3—61no—
145C3×C4×Dic3—62no—
146#3724—32no—
147#3724—32no—
148#3724—31no—
149#3724—32no—
150#3724—32no—
151#3724—31no—
152Dic3⋊Dic3—32no—
153Dic3⋊Dic3—32no—
154Dic3⋊Dic3—31no—
155Dic3⋊Dic3—32no—
156Dic3⋊Dic3—31no—
157Dic3⋊Dic3—32no—
158Dic3⋊Dic3—32no—
159Dic3⋊Dic3—32no—
160Dic3⋊Dic3—32no—
161Dic3⋊Dic3—31no—
162Dic3⋊Dic3—31no—
163Dic3⋊Dic3—32no—
164#3722—31no—
165#3722—32no—
166#3722—31no—
167(C2×D3)⋊Dic3—31no—
168(C2×D3)⋊Dic3—31no—
169(C2×D3)⋊Dic3—31no—
170(C2×D3)⋊Dic3—31no—
171(C2×D3)⋊Dic3—32no—
172(C2×D3)⋊Dic3—32no—
173Dic32—32no—
174Dic32—32no—
175Dic32—32no—
176C22×C33C2411yescharacteristic
177C2×C3×C3⋊D3—21no—
178C2×C3×C3⋊D3—21no—
179C2×C3×C3⋊D3—21no—
180C33×C4—22no—
181C33×C4#4112yes—
182C3×C3⋊Dic3—22no—
183C3×C3⋊Dic3—21no—
184C3×C3⋊Dic3—21no—
185C3×C3⋊Dic3—21no—
186C3×C3⋊Dic3—21no—
187C3×C3⋊Dic3—21no—
188C3×C3⋊Dic3—22no—
189C3×C3⋊Dic3—22no—
190C3×C4⋊Q8—91no—
191C3×C22⋊Q8—91no—
192C3×C4×Q8—91no—
193#946—31no—
194#946—31no—
195#946—61no—
196#946—91no—
197Q8×Dic3—31no—
198Q8×Dic3—31no—
199Q8×Dic3—61no—
200Q8×Dic3—91no—
201#944—31no—
202#944—31no—
203#944—61no—
204#926—91no—
205#924—91no—
206#898—92no—
207#898—92no—
208#898—92no—
209#897—91no—
210#890—91no—
211#890—91no—
212#890—92no—
213#889—92no—
214#889—92no—
215#889—92no—
216#889—92no—
217#887—91no—
218#879—92no—
219#879—92no—
220#876—92no—
221#872—91no—
222#872—91no—
223#870—92no—
224#870—91no—
225C4×Dic6—91no—
226C22×C3⋊D3C22×D311yescharacteristic
227C22×C3×D3—31no—
228C22×C3×D3—31no—
229C22×C3×D3—61no—
230C32×Q8—22no—
231C32×Q8—24no—
232C32×Q8—22no—
233C32×Q8—22no—
234C32×Q8—42no—
235C32×Q8—42no—
236C32×Q8—44no—
237C2×C32×C4—22no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—22no—
242C2×C32×C4—22no—
243C2×C32×C4—41no—
244C2×C32×C4—42no—
245C2×C32×C4C22×D312yes—
246C2×C32×C4C22×D312yes—
247C2×C32×C4C22×D312yes—
248C2×C32×C4C22×D311yescharacteristic
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C3⋊Dic3C22×D311yescharacteristic
252C2×C3⋊Dic3C22×D312yes—
253C2×C3⋊Dic3C22×D312yes—
254C2×C3⋊Dic3C22×D311yescharacteristic
255C2×C3⋊Dic3C22×D311yescharacteristic
256C2×C3⋊Dic3C22×D311yescharacteristic
257C2×C3⋊Dic3C22×D312yes—
258C2×C3⋊Dic3C22×D311yescharacteristic
259C4×C3⋊D3—22no—
260#634—22no—
261C2×C3×Dic3—31no—
262C2×C3×Dic3—31no—
263C2×C3×Dic3—32no—
264C2×C3×Dic3—32no—
265C2×C3×Dic3—32no—
266C2×C3×Dic3—32no—
267C2×C3×Dic3—31no—
268C2×C3×Dic3—32no—
269C2×C3×Dic3—31no—
270C2×C3×Dic3—31no—
271C2×C3×Dic3—31no—
272C2×C3×Dic3—31no—
273C2×C3×Dic3—32no—
274C2×C3×Dic3—31no—
275C2×C3×Dic3—31no—
276C2×C3×Dic3—31no—
277C2×C3×Dic3—61no—
278C2×C3×Dic3—61no—
279C2×C3×Dic3—61no—
280C2×C3×Dic3—61no—
281C2×C3×Dic3—62no—
282C2×C3×Dic3—62no—
283C2×C3×Dic3—61no—
284C2×C3×Dic3—62no—
285C3×C4×D3—62no—
286C3×C4×D3—62no—
287C3×C4×D3—122no—
288C3×Dic6—62no—
289C3×Dic6—62no—
290C3×Dic6—122no—
291#541—271noSylow
292C2×C33C2×#4111yescharacteristic
293C2×C332−1+411yescharacteristic
294C2×C332−1+411yescharacteristic
295C3×C3⋊D3—41no—
296C2×C3×Q8—21no—
297C2×C3×Q8—21no—
298C2×C3×Q8—21no—
299C2×C3×Q8—41no—
300C2×C3×Q8—91no—
301C2×C3×Q8D3211yescharacteristic
302C2×C3×Q8D3211yescharacteristic
303C2×C3×Q8D3211yescharacteristic
304C22×C3×C4—91no—
305C2×C4×D3—31no—
306C2×C4×D3—31no—
307C2×C4×D3—61no—
308C2×Dic6—31no—
309C2×Dic6—31no—
310C2×Dic6—61no—
311C3×C4⋊C4—91no—
312C3×C4⋊C4—92no—
313C3×C4⋊C4—92no—
314C3×C4⋊C4—92no—
315C3×C4⋊C4—92no—
316C3×C4⋊C4—91no—
317C3×C22⋊C4—92no—
318C3×C42—91no—
319C3×C42—91no—
320C3×C42—92no—
321#217—92no—
322#217—91no—
323#217—91no—
324(C2×D3)⋊C4—32no—
325(C2×D3)⋊C4—32no—
326(C2×D3)⋊C4—62no—
327(C2×D3)⋊C4—91no—
328(C2×D3)⋊C4—91no—
329(C2×D3)⋊C4—91no—
330(C2×D3)⋊C4—91no—
331(C2×D3)⋊C4—92no—
332(C2×D3)⋊C4—92no—
333C4⋊Dic3—31no—
334C4⋊Dic3—31no—
335C4⋊Dic3—31no—
336C4⋊Dic3—32no—
337C4⋊Dic3—32no—
338C4⋊Dic3—31no—
339C4⋊Dic3—61no—
340C4⋊Dic3—62no—
341C4⋊Dic3—61no—
342C4⋊Dic3—92no—
343C4⋊Dic3—92no—
344C4⋊Dic3—92no—
345C4⋊Dic3—91no—
346C4⋊Dic3—92no—
347C4⋊Dic3—91no—
348Dic3⋊C4—32no—
349Dic3⋊C4—32no—
350Dic3⋊C4—32no—
351Dic3⋊C4—32no—
352Dic3⋊C4—32no—
353Dic3⋊C4—32no—
354Dic3⋊C4—62no—
355Dic3⋊C4—62no—
356Dic3⋊C4—62no—
357Dic3⋊C4—92no—
358Dic3⋊C4—91no—
359Dic3⋊C4—92no—
360Dic3⋊C4—92no—
361Dic3⋊C4—91no—
362Dic3⋊C4—91no—
363Dic3⋊C4—91no—
364Dic3⋊C4—92no—
365Dic3⋊C4—92no—
366Dic3⋊C4—92no—
367Dic3⋊C4—92no—
368Dic3⋊C4—92no—
369C4×Dic3—31no—
370C4×Dic3—31no—
371C4×Dic3—32no—
372C4×Dic3—31no—
373C4×Dic3—32no—
374C4×Dic3—31no—
375C4×Dic3—61no—
376C4×Dic3—61no—
377C4×Dic3—62no—
378C4×Dic3—92no—
379C4×Dic3—92no—
380C4×Dic3—92no—
381C22×C32—21no—
382C22×C32—21no—
383C22×C32—21no—
384C22×C32—41no—
385C22×C32C23×D311yescharacteristic
386C22×C32C23×D311yescharacteristic
387C22×C32C23×D311yescharacteristic
388C2×C3⋊D3—21no—
389C2×C3⋊D3—21no—
390C2×C3⋊D3—21no—
391C2×C3×D3—62no—
392C2×C3×D3—61no—
393C2×C3×D3—61no—
394C2×C3×D3—61no—
395C2×C3×D3—61no—
396C2×C3×D3—61no—
397C2×C3×D3—61no—
398C2×C3×D3—121no—
399C2×C3×D3—121no—
400C32×C4—22no—
401C32×C4—24no—
402C32×C4—22no—
403C32×C4—22no—
404C32×C4—22no—
405C32×C4—22no—
406C32×C4—22no—
407C32×C4—42no—
408C32×C4—42no—
409C32×C4—42no—
410C32×C4—44no—
411C32×C4#23512yes—
412C32×C4#23712yes—
413C32×C4#23712yes—
414C3⋊Dic3—21no—
415C3⋊Dic3—21no—
416C3⋊Dic3—21no—
417C3⋊Dic3—22no—
418C3⋊Dic3—21no—
419C3⋊Dic3—21no—
420C3⋊Dic3—22no—
421C3⋊Dic3—22no—
422C3×Dic3—62no—
423C3×Dic3—62no—
424C3×Dic3—62no—
425C3×Dic3—62no—
426C3×Dic3—61no—
427C3×Dic3—62no—
428C3×Dic3—61no—
429C3×Dic3—61no—
430C3×Dic3—62no—
431C3×Dic3—62no—
432C3×Dic3—62no—
433C3×Dic3—61no—
434C3×Dic3—62no—
435C3×Dic3—61no—
436C3×Dic3—61no—
437C3×Dic3—61no—
438C3×Dic3—61no—
439C3×Dic3—61no—
440C3×Dic3—61no—
441C3×Dic3—122no—
442C3×Dic3—121no—
443C3×Dic3—121no—
444C3×Dic3—122no—
445C3×Dic3—122no—
446C4⋊Q8—91no—
447#126—272no—
448#126—272no—
449#125—272no—
450#125—271no—
451#125—272no—
452C22⋊Q8—91no—
453C22⋊Q8—271no—
454C4×Q8—91no—
455C4×Q8—271no—
456#117—271no—
457C33#54111yescharacteristic, complemented, Sylow
458C23×C3—91no—
459C22×D3—31no—
460C22×D3—31no—
461C22×D3—61no—
462C3×Q8—24no—
463C3×Q8—22no—
464C3×Q8—22no—
465C3×Q8—22no—
466C3×Q8—42no—
467C3×Q8—42no—
468C3×Q8—44no—
469C3×Q8—182no—
470C2×C3×C4—22no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—42no—
477C2×C3×C4—41no—
478C2×C3×C4—91no—
479C2×C3×C4—92no—
480C2×C3×C4—92no—
481C2×C3×C4—91no—
482C2×C3×C4—91no—
483C2×C3×C4—91no—
484C2×C3×C4—91no—
485C2×C3×C4—92no—
486C2×C3×C4—182no—
487C2×C3×C4C2×D3212yes—
488C2×C3×C4C2×D3212yes—
489C2×C3×C4C2×D3212yes—
490C2×C3×C4C2×D3211yescharacteristic
491C2×C3×C4C2×D3211yescharacteristic
492C2×C3×C4C2×D3211yescharacteristic
493C2×Dic3—31no—
494C2×Dic3—31no—
495C2×Dic3—31no—
496C2×Dic3—31no—
497C2×Dic3—31no—
498C2×Dic3—31no—
499C2×Dic3—31no—
500C2×Dic3—31no—
501C2×Dic3—32no—
502C2×Dic3—32no—
503C2×Dic3—32no—
504C2×Dic3—32no—
505C2×Dic3—32no—
506C2×Dic3—32no—
507C2×Dic3—31no—
508C2×Dic3—31no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—62no—
514C2×Dic3—62no—
515C2×Dic3—61no—
516C2×Dic3—62no—
517C4×D3—62no—
518C4×D3—62no—
519C4×D3—122no—
520Dic6—62no—
521Dic6—62no—
522Dic6—122no—
523C2×C32—21no—
524C2×C32—21no—
525C2×C32—21no—
526C2×C32—21no—
527C2×C32—21no—
528C2×C32—21no—
529C2×C32—21no—
530C2×C32—21no—
531C2×C32—21no—
532C2×C32—41no—
533C2×C32—41no—
534C2×C32—41no—
535C2×C32C2×#23511yescharacteristic
536C2×C32C2×#23711yescharacteristic
537C2×C32C2×#23711yescharacteristic
538C2×C32#100711yescharacteristic
539C2×C32#100711yescharacteristic
540C2×C32#100711yescharacteristic
541C2×C32#100711yescharacteristic
542C2×C32#101011yescharacteristic
543C2×C32#101011yescharacteristic
544C3⋊D3—41no—
545C3×D3—122no—
546C3×D3—121no—
547C3×D3—121no—
548C2×Q8—91no—
549C2×Q8#111311yescharacteristic
550C22×C4—91no—
551C4⋊C4—91no—
552C4⋊C4—92no—
553C4⋊C4—91no—
554C4⋊C4—92no—
555C4⋊C4—92no—
556C4⋊C4—92no—
557C4⋊C4—271no—
558C4⋊C4—271no—
559C4⋊C4—272no—
560C4⋊C4—272no—
561C4⋊C4—272no—
562C4⋊C4—272no—
563C22⋊C4—92no—
564C22⋊C4—271no—
565C22⋊C4—271no—
566C22⋊C4—272no—
567C42—91no—
568C42—91no—
569C42—92no—
570C42—272no—
571C22×C3—21no—
572C22×C3—21no—
573C22×C3—21no—
574C22×C3—41no—
575C22×C3—181no—
576C22×C3—181no—
577C22×C3—181no—
578C22×C3C22×D3211yescharacteristic
579C22×C3C22×D3211yescharacteristic
580C22×C3C22×D3211yescharacteristic
581C2×D3—62no—
582C2×D3—61no—
583C2×D3—61no—
584C2×D3—61no—
585C2×D3—61no—
586C2×D3—61no—
587C2×D3—61no—
588C2×D3—121no—
589C2×D3—121no—
590C3×C4—24no—
591C3×C4—22no—
592C3×C4—22no—
593C3×C4—22no—
594C3×C4—22no—
595C3×C4—22no—
596C3×C4—22no—
597C3×C4—42no—
598C3×C4—42no—
599C3×C4—44no—
600C3×C4—42no—
601C3×C4—181no—
602C3×C4—181no—
603C3×C4—181no—
604C3×C4—181no—
605C3×C4—182no—
606C3×C4—182no—
607C3×C4—181no—
608C3×C4—182no—
609C3×C4#380412yes—
610C3×C4#380412yes—
611C3×C4#380512yes—
612Dic3—62no—
613Dic3—62no—
614Dic3—62no—
615Dic3—61no—
616Dic3—61no—
617Dic3—61no—
618Dic3—61no—
619Dic3—62no—
620Dic3—62no—
621Dic3—62no—
622Dic3—61no—
623Dic3—62no—
624Dic3—61no—
625Dic3—61no—
626Dic3—61no—
627Dic3—62no—
628Dic3—61no—
629Dic3—62no—
630Dic3—61no—
631Dic3—122no—
632Dic3—121no—
633Dic3—121no—
634Dic3—122no—
635Dic3—122no—
636C32—21no—
637C32—21no—
638C32—21no—
639C32—41no—
640C32#558311yescharacteristic, complemented
641C32#562511yescharacteristic, complemented
642C32#573111yescharacteristic, complemented
643C23—91no—
644Q8—22no—
645Q8—182no—
646C2×C4—91no—
647C2×C4—91no—
648C2×C4—91no—
649C2×C4—91no—
650C2×C4—92no—
651C2×C4—92no—
652C2×C4—92no—
653C2×C4—91no—
654C2×C4—182no—
655C2×C4C2×#111312yes—
656C2×C4C2×#111311yescharacteristic
657C2×C3—21no—
658C2×C3—21no—
659C2×C3—21no—
660C2×C3—21no—
661C2×C3—21no—
662C2×C3—21no—
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—41no—
667C2×C3—41no—
668C2×C3—41no—
669C2×C3—361no—
670C2×C3#6431511yescharacteristic
671C2×C3#6431511yescharacteristic
672C2×C3#6431511yescharacteristic
673C2×C3#6431511yescharacteristic
674C2×C3#6431611yescharacteristic
675C2×C3#6431611yescharacteristic
676C2×C3C2×#380411yescharacteristic
677C2×C3C2×#380411yescharacteristic
678C2×C3C2×#380511yescharacteristic
679D3—122no—
680D3—121no—
681D3—121no—
682C22—181no—
683C22—181no—
684C22—181no—
685C22C22×#111311yescharacteristic
686C4—22no—
687C4—181no—
688C4—181no—
689C4—181no—
690C4—181no—
691C4—182no—
692C4—182no—
693C4—181no—
694C4—182no—
695C4#8904612yes—
696C3—21no—
697C3—21no—
698C3—21no—
699C3—41no—
700C3#1059534811yescharacteristic, complemented
701C3#1059534911yescharacteristic, complemented
702C3#1059535411yescharacteristic, complemented
703C2—361no—
704C2#1172462411yescharacteristic
705C2#1172462411yescharacteristic
706C2C2×#8904611yescharacteristic
subgroupG/H
center, FrattiniC22C22×#1113
commutator, socle, cosocleC22×C33C24
FittingC2×C33×Q8C22
prime radicalC22×C3×C3⋊D3C23
hypercenterC2×Q8#1113
hypocenterC33#541
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
2. C3×Q8×C3⋊Dic3C2semidirect
3. C3×#64153C2semidirect
4. #11723680C2semidirect
5. #11723679C2semidirect
10. #11723669C2semidirect
11. #11723668C2semidirect
39. Q8×C3⋊Dic3D3semidirect
40. #64153D3semidirect
457. C33#541semidirect
640. C32#5583semidirect
641. C32#5625semidirect
642. C32#5731semidirect
700. C3#10595348semidirect
701. C3#10595349semidirect
702. C3#10595354semidirect

Maximal subgroups

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

subgroupindex
C3×#641552
C3×Q8×C3⋊Dic32
C3×#641532
#117236802
#117236792
#117236762
#117236752
#117236742
#117236732
#117236692
#117236682
#105953543
#105953493
#105953483