Finite Group Databasebeta

← C32×#5696 #13179063

Subgroups — C32×#5696 #13179063

Order 1728.

1376 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C33×#125C211yesmaximal, characteristic, complemented
2C32×#898C211yesmaximal, characteristic
3C32×#898C211yesmaximal, characteristic
4C32×#898C211yesmaximal, characteristic
5C32×#896C211yesmaximal, characteristic
6C32×#896C211yesmaximal, characteristic
7C32×#892C211yesmaximal, characteristic
8C32×#890C211yesmaximal, characteristic, complemented
9C32×#889C211yesmaximal, characteristic, complemented
10C32×#889C211yesmaximal, characteristic, complemented
11C32×#889C211yesmaximal, characteristic, complemented
12C32×#888C211yesmaximal, characteristic, complemented
13C32×#887C211yesmaximal, characteristic, complemented
14C32×#876C211yesmaximal, characteristic
15C32×C4×Dic6C211yesmaximal, characteristic, complemented
16C32×#541—31nomaximal
17C3×#5696C314yesmaximal, direct product factor
18C2×C32×C4×D3C2211yescharacteristic
19C2×C32×Dic6C2211yescharacteristic
20C2×C32×Dic6C2211yescharacteristic
21C33×C4⋊C4C2211yescharacteristic
22C33×C4⋊C4C2211yescharacteristic
23C33×C4⋊C4C2211yescharacteristic
24C33×C4⋊C4C2211yescharacteristic
25C33×C4⋊C4C2211yescharacteristic
26C33×C4⋊C4C2211yescharacteristic
27C33×C42C2211yescharacteristic
28C32×(C2×D3)⋊C4C2211yescharacteristic
29C32×(C2×D3)⋊C4C2211yescharacteristic
30C32×(C2×D3)⋊C4C2211yescharacteristic
31C32×(C2×D3)⋊C4C2211yescharacteristic
32C32×(C2×D3)⋊C4C2211yescharacteristic
33C32×(C2×D3)⋊C4C2211yescharacteristic
34C32×C4⋊Dic3C2211yescharacteristic
35C32×C4⋊Dic3C2211yescharacteristic
36C32×C4⋊Dic3C2211yescharacteristic
37C32×C4⋊Dic3C2211yescharacteristic
38C32×Dic3⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic
40C32×Dic3⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic
42C32×Dic3⋊C4C2211yescharacteristic
43C32×Dic3⋊C4C2211yescharacteristic
44C32×Dic3⋊C4C2211yescharacteristic
45C32×Dic3⋊C4C2211yescharacteristic
46C32×Dic3⋊C4C2211yescharacteristic
47C32×Dic3⋊C4C2211yescharacteristic
48C32×C4×Dic3C2211yescharacteristic
49C32×C4×Dic3C2211yescharacteristic
50C32×C4×Dic3C2211yescharacteristic
51C32×C4×Dic3C2211yescharacteristic
52C32×C4×Dic3C2211yescharacteristic
53C32×C4⋊Q8—31no—
54C32×#126—31no—
55C32×#126—31no—
56C32×#126—31no—
57C32×#126—31no—
58C32×#125—24no—
59C32×#125—31no—
60C32×#125—31no—
61C32×#125—31no—
62C32×#125—31no—
63C32×#125D311yescharacteristic, complemented
64C32×#125C2×C314yescomplemented
65C32×C22⋊Q8—31no—
66C32×C22⋊Q8—31no—
67C32×C4×Q8—31no—
68C32×C4×Q8—31no—
69C32×#117—31no—
70C3×#898C2×C314yes—
71C3×#898C2×C314yes—
72C3×#898C2×C314yes—
73C3×#896C2×C314yes—
74C3×#896C2×C314yes—
75C3×#892C2×C314yes—
76C3×#890C2×C314yescomplemented
77C3×#889C2×C314yescomplemented
78C3×#889C2×C314yescomplemented
79C3×#889C2×C314yescomplemented
80C3×#888C2×C314yescomplemented
81C3×#887C2×C314yescomplemented
82C3×#876C2×C314yes—
83C3×C4×Dic6C2×C314yescomplemented
84C22×C32×D3C2311yescharacteristic
85C2×C33×C4C2311yescharacteristic
86C2×C33×C4C2311yescharacteristic
87C2×C33×C4C2311yescharacteristic
88C2×C33×C4C2311yescharacteristic
89C2×C33×C4C2311yescharacteristic
90C2×C33×C4C2311yescharacteristic
91C2×C33×C4C2311yescharacteristic
92C2×C32×Dic3C2311yescharacteristic
93C2×C32×Dic3C2311yescharacteristic
94C2×C32×Dic3C2311yescharacteristic
95C2×C32×Dic3C2311yescharacteristic
96C2×C32×Dic3C2311yescharacteristic
97C2×C32×Dic3C2311yescharacteristic
98C2×C32×Dic3C2311yescharacteristic
99C32×C4×D3—22no—
100C32×Dic6—22no—
101C32×Dic6—22no—
102C3×#541—34no—
103#5696C3211yescharacteristic, direct product factor
104C2×C32×Q8—31no—
105C2×C32×Q8—31no—
106C22×C32×C4—31no—
107C2×C3×C4×D3C22×C314yes—
108C2×C3×Dic6C22×C314yes—
109C2×C3×Dic6C22×C314yes—
110C32×C4⋊C4—24no—
111C32×C4⋊C4—24no—
112C32×C4⋊C4—24no—
113C32×C4⋊C4—24no—
114C32×C4⋊C4—24no—
115C32×C4⋊C4—24no—
116C32×C4⋊C4—31no—
117C32×C4⋊C4—31no—
118C32×C4⋊C4—31no—
119C32×C4⋊C4—31no—
120C32×C4⋊C4—31no—
121C32×C4⋊C4—31no—
122C32×C4⋊C4—31no—
123C32×C4⋊C4—31no—
124C32×C4⋊C4—31no—
125C32×C4⋊C4—31no—
126C32×C4⋊C4—31no—
127C32×C4⋊C4—31no—
128C32×C4⋊C4—31no—
129C32×C4⋊C4—31no—
130C32×C4⋊C4C2×D311yescharacteristic
131C32×C4⋊C4C2×D311yescharacteristic
132C32×C4⋊C4C2×D311yescharacteristic
133C32×C4⋊C4C2×D311yescharacteristic
134C32×C4⋊C4C2×D311yescharacteristic
135C32×C4⋊C4C2×D311yescharacteristic
136C32×C4⋊C4C22×C314yes—
137C32×C4⋊C4C22×C314yes—
138C32×C4⋊C4C22×C314yes—
139C32×C4⋊C4C22×C314yes—
140C32×C4⋊C4C22×C314yes—
141C32×C4⋊C4C22×C314yes—
142C32×C22⋊C4—31no—
143C32×C22⋊C4—31no—
144C32×C22⋊C4—31no—
145C32×C22⋊C4—31no—
146C32×C22⋊C4—31no—
147C32×C22⋊C4—31no—
148C32×C42—24no—
149C32×C42—31no—
150C32×C42—31no—
151C32×C42—31no—
152C32×C42—31no—
153C32×C42—31no—
154C32×C42C2×D311yescharacteristic
155C32×C42C22×C314yes—
156C3×(C2×D3)⋊C4C22×C314yes—
157C3×(C2×D3)⋊C4C22×C314yes—
158C3×(C2×D3)⋊C4C22×C314yes—
159C3×(C2×D3)⋊C4C22×C314yes—
160C3×(C2×D3)⋊C4C22×C314yes—
161C3×(C2×D3)⋊C4C22×C314yes—
162C3×C4⋊Dic3C22×C314yes—
163C3×C4⋊Dic3C22×C314yes—
164C3×C4⋊Dic3C22×C314yes—
165C3×C4⋊Dic3C22×C314yes—
166C3×Dic3⋊C4C22×C314yes—
167C3×Dic3⋊C4C22×C314yes—
168C3×Dic3⋊C4C22×C314yes—
169C3×Dic3⋊C4C22×C314yes—
170C3×Dic3⋊C4C22×C314yes—
171C3×Dic3⋊C4C22×C314yes—
172C3×Dic3⋊C4C22×C314yes—
173C3×Dic3⋊C4C22×C314yes—
174C3×Dic3⋊C4C22×C314yes—
175C3×Dic3⋊C4C22×C314yes—
176C3×C4×Dic3C22×C314yes—
177C3×C4×Dic3C22×C314yes—
178C3×C4×Dic3C22×C314yes—
179C3×C4×Dic3C22×C314yes—
180C3×C4×Dic3C22×C314yes—
181C22×C33C2411yescharacteristic
182C2×C32×D3—21no—
183C2×C32×D3—21no—
184C2×C32×D3—21no—
185C33×C4—21no—
186C33×C4—21no—
187C33×C4—21no—
188C33×C4—21no—
189C33×C4—21no—
190C33×C4—21no—
191C33×C4—21no—
192C32×Dic3—21no—
193C32×Dic3—21no—
194C32×Dic3—21no—
195C32×Dic3—21no—
196C32×Dic3—21no—
197C32×Dic3—21no—
198C32×Dic3#4112yes—
199C3×C4⋊Q8—34no—
200C3×#126—34no—
201C3×#126—34no—
202C3×#126—34no—
203C3×#126—34no—
204C3×#125—24no—
205C3×#125—34no—
206C3×#125—34no—
207C3×#125—34no—
208C3×#125—34no—
209C3×#125C3×D314yescomplemented
210C3×#125C2×C3211yescharacteristic, complemented
211C3×C22⋊Q8—34no—
212C3×C22⋊Q8—34no—
213C3×C4×Q8—34no—
214C3×C4×Q8—34no—
215C3×#117—34no—
216#898C2×C3211yescharacteristic
217#898C2×C3211yescharacteristic
218#898C2×C3211yescharacteristic
219#896C2×C3211yescharacteristic
220#896C2×C3211yescharacteristic
221#892C2×C3211yescharacteristic
222#890C2×C3211yescharacteristic, complemented
223#889C2×C3211yescharacteristic, complemented
224#889C2×C3211yescharacteristic, complemented
225#889C2×C3211yescharacteristic, complemented
226#888C2×C3211yescharacteristic, complemented
227#887C2×C3211yescharacteristic, complemented
228#876C2×C3211yescharacteristic
229C4×Dic6C2×C3211yescharacteristic, complemented
230C23×C32—31no—
231C22×C3×D3C23×C314yes—
232C32×Q8—62no—
233C32×Q8—62no—
234C2×C32×C4—24no—
235C2×C32×C4—24no—
236C2×C32×C4—24no—
237C2×C32×C4—24no—
238C2×C32×C4—24no—
239C2×C32×C4—24no—
240C2×C32×C4—24no—
241C2×C32×C4—31no—
242C2×C32×C4—31no—
243C2×C32×C4—31no—
244C2×C32×C4—31no—
245C2×C32×C4—31no—
246C2×C32×C4—31no—
247C2×C32×C4—31no—
248C2×C32×C4—62no—
249C2×C32×C4C22×D311yescharacteristic
250C2×C32×C4C22×D311yescharacteristic
251C2×C32×C4C22×D311yescharacteristic
252C2×C32×C4C22×D311yescharacteristic
253C2×C32×C4C22×D311yescharacteristic
254C2×C32×C4C22×D311yescharacteristic
255C2×C32×C4C22×D311yescharacteristic
256C2×C32×C4C23×C314yes—
257C2×C32×C4C23×C314yes—
258C2×C32×C4C23×C314yes—
259C2×C32×C4C23×C314yes—
260C2×C32×C4C23×C314yes—
261C2×C32×C4C23×C314yes—
262C2×C32×C4C23×C314yes—
263C2×C3×Dic3C23×C314yes—
264C2×C3×Dic3C23×C314yes—
265C2×C3×Dic3C23×C314yes—
266C2×C3×Dic3C23×C314yes—
267C2×C3×Dic3C23×C314yes—
268C2×C3×Dic3C23×C314yes—
269C2×C3×Dic3C23×C314yes—
270C3×C4×D3—28no—
271C3×Dic6—28no—
272C3×Dic6—28no—
273#541—31noSylow
274C2×C33C2×#4111yescharacteristic
275C2×C332−1+411yescharacteristic
276C2×C332−1+411yescharacteristic
277C32×D3—41no—
278C2×C3×Q8—34no—
279C2×C3×Q8—34no—
280C22×C3×C4—34no—
281C2×C4×D3C22×C3211yescharacteristic
282C2×Dic6C22×C3211yescharacteristic
283C2×Dic6C22×C3211yescharacteristic
284C3×C4⋊C4—24no—
285C3×C4⋊C4—24no—
286C3×C4⋊C4—24no—
287C3×C4⋊C4—24no—
288C3×C4⋊C4—24no—
289C3×C4⋊C4—24no—
290C3×C4⋊C4—34no—
291C3×C4⋊C4—34no—
292C3×C4⋊C4—34no—
293C3×C4⋊C4—34no—
294C3×C4⋊C4—34no—
295C3×C4⋊C4—34no—
296C3×C4⋊C4—34no—
297C3×C4⋊C4—34no—
298C3×C4⋊C4—34no—
299C3×C4⋊C4—34no—
300C3×C4⋊C4—34no—
301C3×C4⋊C4—34no—
302C3×C4⋊C4—34no—
303C3×C4⋊C4—34no—
304C3×C4⋊C4C2×C3×D314yes—
305C3×C4⋊C4C2×C3×D314yes—
306C3×C4⋊C4C2×C3×D314yes—
307C3×C4⋊C4C2×C3×D314yes—
308C3×C4⋊C4C2×C3×D314yes—
309C3×C4⋊C4C2×C3×D314yes—
310C3×C4⋊C4C22×C3211yescharacteristic
311C3×C4⋊C4C22×C3211yescharacteristic
312C3×C4⋊C4C22×C3211yescharacteristic
313C3×C4⋊C4C22×C3211yescharacteristic
314C3×C4⋊C4C22×C3211yescharacteristic
315C3×C4⋊C4C22×C3211yescharacteristic
316C3×C22⋊C4—34no—
317C3×C22⋊C4—34no—
318C3×C22⋊C4—34no—
319C3×C22⋊C4—34no—
320C3×C22⋊C4—34no—
321C3×C22⋊C4—34no—
322C3×C42—24no—
323C3×C42—34no—
324C3×C42—34no—
325C3×C42—34no—
326C3×C42—34no—
327C3×C42—34no—
328C3×C42C2×C3×D314yes—
329C3×C42C22×C3211yescharacteristic
330(C2×D3)⋊C4C22×C3211yescharacteristic
331(C2×D3)⋊C4C22×C3211yescharacteristic
332(C2×D3)⋊C4C22×C3211yescharacteristic
333(C2×D3)⋊C4C22×C3211yescharacteristic
334(C2×D3)⋊C4C22×C3211yescharacteristic
335(C2×D3)⋊C4C22×C3211yescharacteristic
336C4⋊Dic3C22×C3211yescharacteristic
337C4⋊Dic3C22×C3211yescharacteristic
338C4⋊Dic3C22×C3211yescharacteristic
339C4⋊Dic3C22×C3211yescharacteristic
340Dic3⋊C4C22×C3211yescharacteristic
341Dic3⋊C4C22×C3211yescharacteristic
342Dic3⋊C4C22×C3211yescharacteristic
343Dic3⋊C4C22×C3211yescharacteristic
344Dic3⋊C4C22×C3211yescharacteristic
345Dic3⋊C4C22×C3211yescharacteristic
346Dic3⋊C4C22×C3211yescharacteristic
347Dic3⋊C4C22×C3211yescharacteristic
348Dic3⋊C4C22×C3211yescharacteristic
349Dic3⋊C4C22×C3211yescharacteristic
350C4×Dic3C22×C3211yescharacteristic
351C4×Dic3C22×C3211yescharacteristic
352C4×Dic3C22×C3211yescharacteristic
353C4×Dic3C22×C3211yescharacteristic
354C4×Dic3C22×C3211yescharacteristic
355C22×C32—24no—
356C22×C32—61no—
357C22×C32—61no—
358C22×C32—61no—
359C22×C32C23×D311yescharacteristic
360C22×C32C24×C314yes—
361C2×C3×D3—24no—
362C2×C3×D3—24no—
363C2×C3×D3—24no—
364C32×C4—28no—
365C32×C4—21no—
366C32×C4—21no—
367C32×C4—21no—
368C32×C4—21no—
369C32×C4—21no—
370C32×C4—21no—
371C32×C4—21no—
372C32×C4—24no—
373C32×C4—24no—
374C32×C4—24no—
375C32×C4—24no—
376C32×C4—24no—
377C32×C4—24no—
378C32×C4—24no—
379C32×C4—32no—
380C32×C4—44no—
381C32×C4—44no—
382C32×C4—44no—
383C32×C4—44no—
384C32×C4—44no—
385C32×C4—44no—
386C32×C4—61no—
387C32×C4—61no—
388C32×C4—61no—
389C32×C4—61no—
390C32×C4—61no—
391C32×C4—61no—
392C3×Dic3—24no—
393C3×Dic3—24no—
394C3×Dic3—24no—
395C3×Dic3—24no—
396C3×Dic3—24no—
397C3×Dic3—24no—
398C3×Dic3C3×#4118yes—
399C4⋊Q8—31no—
400#126—31no—
401#126—31no—
402#126—31no—
403#126—31no—
404#125—31no—
405#125—31no—
406#125—31no—
407#125—31no—
408#125C32×D311yescharacteristic, complemented
409C22⋊Q8—31no—
410C22⋊Q8—31no—
411C4×Q8—31no—
412C4×Q8—31no—
413#117—31no—
414C33#54111yescharacteristic, complemented, Sylow
415C23×C3—34no—
416C22×D3C23×C3211yescharacteristic
417C3×Q8—68no—
418C3×Q8—68no—
419C2×C3×C4—24no—
420C2×C3×C4—24no—
421C2×C3×C4—24no—
422C2×C3×C4—24no—
423C2×C3×C4—24no—
424C2×C3×C4—24no—
425C2×C3×C4—24no—
426C2×C3×C4—34no—
427C2×C3×C4—34no—
428C2×C3×C4—34no—
429C2×C3×C4—34no—
430C2×C3×C4—34no—
431C2×C3×C4—34no—
432C2×C3×C4—34no—
433C2×C3×C4—68no—
434C2×C3×C4C22×C3×D314yes—
435C2×C3×C4C22×C3×D314yes—
436C2×C3×C4C22×C3×D314yes—
437C2×C3×C4C22×C3×D314yes—
438C2×C3×C4C22×C3×D314yes—
439C2×C3×C4C22×C3×D314yes—
440C2×C3×C4C22×C3×D314yes—
441C2×C3×C4C23×C3211yescharacteristic
442C2×C3×C4C23×C3211yescharacteristic
443C2×C3×C4C23×C3211yescharacteristic
444C2×C3×C4C23×C3211yescharacteristic
445C2×C3×C4C23×C3211yescharacteristic
446C2×C3×C4C23×C3211yescharacteristic
447C2×C3×C4C23×C3211yescharacteristic
448C2×Dic3C23×C3211yescharacteristic
449C2×Dic3C23×C3211yescharacteristic
450C2×Dic3C23×C3211yescharacteristic
451C2×Dic3C23×C3211yescharacteristic
452C2×Dic3C23×C3211yescharacteristic
453C2×Dic3C23×C3211yescharacteristic
454C2×Dic3C23×C3211yescharacteristic
455C4×D3—22no—
456Dic6—22no—
457Dic6—22no—
458C2×C32—24no—
459C2×C32—24no—
460C2×C32—24no—
461C2×C32—121no—
462C2×C32#100711yescharacteristic
463C2×C32D3×#4111yescharacteristic
464C2×C32#101011yescharacteristic
465C2×C32C2×C3×#4114yes—
466C2×C32C3×2−1+414yes—
467C2×C32C3×2−1+414yes—
468C3×D3—44no—
469C2×Q8—31no—
470C2×Q8—31no—
471C22×C4—31no—
472C4⋊C4—31no—
473C4⋊C4—31no—
474C4⋊C4—31no—
475C4⋊C4—31no—
476C4⋊C4—31no—
477C4⋊C4—31no—
478C4⋊C4—31no—
479C4⋊C4—31no—
480C4⋊C4—31no—
481C4⋊C4—31no—
482C4⋊C4—31no—
483C4⋊C4—31no—
484C4⋊C4—31no—
485C4⋊C4—31no—
486C4⋊C4C2×C32×D311yescharacteristic
487C4⋊C4C2×C32×D311yescharacteristic
488C4⋊C4C2×C32×D311yescharacteristic
489C4⋊C4C2×C32×D311yescharacteristic
490C4⋊C4C2×C32×D311yescharacteristic
491C4⋊C4C2×C32×D311yescharacteristic
492C22⋊C4—31no—
493C22⋊C4—31no—
494C22⋊C4—31no—
495C22⋊C4—31no—
496C22⋊C4—31no—
497C22⋊C4—31no—
498C42—31no—
499C42—31no—
500C42—31no—
501C42—31no—
502C42—31no—
503C42C2×C32×D311yescharacteristic
504C22×C3—24no—
505C22×C3—64no—
506C22×C3—64no—
507C22×C3—64no—
508C22×C3C23×C3×D314yes—
509C22×C3C24×C3211yescharacteristic
510C2×D3—21no—
511C2×D3—21no—
512C2×D3—21no—
513C3×C4—28no—
514C3×C4—24no—
515C3×C4—24no—
516C3×C4—24no—
517C3×C4—24no—
518C3×C4—24no—
519C3×C4—24no—
520C3×C4—24no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—21no—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—38no—
529C3×C4—44no—
530C3×C4—44no—
531C3×C4—44no—
532C3×C4—44no—
533C3×C4—44no—
534C3×C4—44no—
535C3×C4—64no—
536C3×C4—64no—
537C3×C4—64no—
538C3×C4—64no—
539C3×C4—64no—
540C3×C4—64no—
541Dic3—21no—
542Dic3—21no—
543Dic3—21no—
544Dic3—21no—
545Dic3—21no—
546Dic3—21no—
547Dic3C32×#4112yes—
548C32—24no—
549C32#569611yescharacteristic, direct product factor
550C32C3×#54114yescomplemented
551C23—31no—
552Q8—62no—
553Q8—62no—
554C2×C4—31no—
555C2×C4—31no—
556C2×C4—31no—
557C2×C4—31no—
558C2×C4—31no—
559C2×C4—31no—
560C2×C4—31no—
561C2×C4—62no—
562C2×C4C22×C32×D311yescharacteristic
563C2×C4C22×C32×D311yescharacteristic
564C2×C4C22×C32×D311yescharacteristic
565C2×C4C22×C32×D311yescharacteristic
566C2×C4C22×C32×D311yescharacteristic
567C2×C4C22×C32×D311yescharacteristic
568C2×C4C22×C32×D311yescharacteristic
569C2×C3—24no—
570C2×C3—24no—
571C2×C3—24no—
572C2×C3—124no—
573C2×C3C3×#100714yes—
574C2×C3C3×D3×#4114yes—
575C2×C3C3×#101014yes—
576C2×C3C2×C32×#4111yescharacteristic
577C2×C3C32×2−1+411yescharacteristic
578C2×C3C32×2−1+411yescharacteristic
579D3—41no—
580C22—61no—
581C22—61no—
582C22—61no—
583C22C23×C32×D311yescharacteristic
584C4—21no—
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—32no—
592C4—61no—
593C4—61no—
594C4—61no—
595C4—61no—
596C4—61no—
597C4—61no—
598C3—24no—
599C3C3×#569614yesdirect product factor
600C3C32×#54111yescharacteristic, complemented
601C2—121no—
602C2C32×#100711yescharacteristic
603C2C32×D3×#4111yescharacteristic
604C2C32×#101011yescharacteristic
subgroupG/H
centerC22×C32C23×D3
commutator, cosocleC22×C3C24×C32
FrattiniC22C23×C32×D3
FittingC33×#125C2
socleC22×C33C24
prime radicalC22×C32×D3C23
hypercenterC32×#125D3
hypocenterC3C32×#541
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C32 ◁ C32×#125

Complements

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

NH ≅ G/Ntype
1. C33×#125C2semidirect
8. C32×#890C2semidirect
9. C32×#889C2semidirect
10. C32×#889C2semidirect
11. C32×#889C2semidirect
12. C32×#888C2semidirect
13. C32×#887C2semidirect
15. C32×C4×Dic6C2semidirect
17. C3×#5696C3direct (N × H)
63. C32×#125D3semidirect
64. C32×#125C2×C3semidirect
76. C3×#890C2×C3semidirect
77. C3×#889C2×C3semidirect
78. C3×#889C2×C3semidirect
79. C3×#889C2×C3semidirect
80. C3×#888C2×C3semidirect
81. C3×#887C2×C3semidirect
83. C3×C4×Dic6C2×C3semidirect
103. #5696C32direct (N × H)
209. C3×#125C3×D3semidirect
210. C3×#125C2×C32semidirect
222. #890C2×C32semidirect
223. #889C2×C32semidirect
224. #889C2×C32semidirect
225. #889C2×C32semidirect
226. #888C2×C32semidirect
227. #887C2×C32semidirect
229. C4×Dic6C2×C32semidirect
408. #125C32×D3semidirect
414. C33#541semidirect
549. C32#5696direct (N × H)
550. C32C3×#541semidirect
599. C3C3×#5696direct (N × H)
600. C3C32×#541semidirect

Maximal subgroups

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

subgroupindex
C33×#1252
C32×#8982
C32×#8962
C32×#8922
C32×#8902
C32×#8892
C32×#8882
C32×#8872
C32×#8762
C32×C4×Dic62
C32×#5413
C3×#56963