Finite Group Databasebeta

← C3×#10591352 #13158299

Subgroups — C3×#10591352 #13158299

Order 1728.

1026 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic
2C2×C32×C4⋊Dic3C211yesmaximal, characteristic
3C2×C32×C4×Dic3C211yesmaximal, characteristic
4C2×C3×Dic3⋊Dic3C212yesmaximal
5C3×#63579C212yesmaximal
6C3×#4984—31nomaximal
7C3×#4928—31nomaximal
8#10591352C311yesmaximal, characteristic, direct product factor
9C22×C33×C4C2211yescharacteristic
10C22×C3×C3⋊Dic3C2212yes—
11C22×C32×Dic3C2212yes—
12C22×C32×Dic3C2211yescharacteristic
13C22×C32×Dic3C2211yescharacteristic
14C3×C4⋊(C3⋊Dic3)—22no—
15C32×C4⋊Dic3C414yescomplemented
16C32×C4×Dic3—22no—
17C3×Dic3⋊Dic3—24no—
18C2×C32×C4⋊C4—31no—
19C2×C32×C42—31no—
20C2×C4⋊(C3⋊Dic3)C2×C311yescharacteristic
21C2×C3×C4⋊Dic3—21no—
22C2×C3×C4⋊Dic3—31no—
23C2×C3×C4⋊Dic3—31no—
24C2×C3×C4⋊Dic3—32no—
25C2×C3×C4⋊Dic3—61no—
26C2×C3×C4⋊Dic3D311yescharacteristic
27C2×C3×C4⋊Dic3C2×C311yescharacteristic
28C2×C3×Dic3⋊C4—32no—
29C2×C3×C4×Dic3—21no—
30C2×C3×C4×Dic3D311yescharacteristic
31C2×C3×C4×Dic3C2×C311yescharacteristic
32C2×Dic3⋊Dic3C2×C312yes—
33C3×C3⋊#95—32no—
34C3×C3⋊#95—32no—
35#63579C2×C312yes—
36C23×C33C2311yescharacteristic
37C2×C33×C4C2×C412yes—
38C2×C33×C4D412yes—
39C2×C33×C4Q812yes—
40C2×C3×C3⋊Dic3—22no—
41C2×C3×C3⋊Dic3—22no—
42C2×C3×C3⋊Dic3—22no—
43C2×C32×Dic3—21no—
44C2×C32×Dic3—21no—
45C2×C32×Dic3—22no—
46C2×C32×Dic3—21no—
47C2×C32×Dic3—21no—
48C2×C32×Dic3—22no—
49C2×C32×Dic3C2×C414yes—
50C2×C32×Dic3D412yes—
51C2×C32×Dic3Q812yes—
52C3×#389—91no—
53#4984—31no—
54#4928—31no—
55C22×C32×C4—21no—
56C22×C32×C4—21no—
57C22×C32×C4—21no—
58C22×C32×C4—31no—
59C22×C32×C4—32no—
60C22×C32×C4—31no—
61C22×C32×C4—41no—
62C22×C32×C4C2×D311yescharacteristic
63C22×C32×C4C2×D311yescharacteristic
64C22×C32×C4C22×C311yescharacteristic
65C22×C3⋊Dic3C22×C312yes—
66C22×C3×Dic3—21no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—22no—
69C22×C3×Dic3—32no—
70C22×C3×Dic3—32no—
71C22×C3×Dic3—62no—
72C22×C3×Dic3C2×D311yescharacteristic
73C22×C3×Dic3C2×D311yescharacteristic
74C22×C3×Dic3C2×D312yes—
75C22×C3×Dic3C22×C312yes—
76C22×C3×Dic3C22×C311yescharacteristic
77C22×C3×Dic3C22×C311yescharacteristic
78C32×C4⋊C4—34no—
79C32×C42—62no—
80C4⋊(C3⋊Dic3)—22no—
81C3×C4⋊Dic3—24no—
82C3×C4⋊Dic3—64no—
83C3×C4⋊Dic3—62no—
84C3×C4⋊Dic3—62no—
85C3×C4⋊Dic3—64no—
86C3×C4⋊Dic3Dic314yescomplemented
87C3×C4⋊Dic3C3×C414yescomplemented
88C3×Dic3⋊C4—64no—
89C3×C4×Dic3—24no—
90C3×C4×Dic3—22no—
91C3×C4×Dic3—22no—
92Dic3⋊Dic3—24no—
93C22×C33C22×C411yescharacteristic
94C22×C33C2×D411yescharacteristic
95C22×C33C2×D411yescharacteristic
96C22×C33C2×Q811yescharacteristic
97C22×C33C2×Q811yescharacteristic
98C22×C33#4111yescharacteristic
99C22×C33#4111yescharacteristic
100C33×C4C4⋊C414yescomplemented
101C3×C3⋊Dic3—42no—
102C32×Dic3—24no—
103C32×Dic3—22no—
104C32×Dic3—22no—
105C2×C3×C4⋊C4—31no—
106C2×C3×C4⋊C4—31no—
107C2×C3×C4⋊C4—61no—
108C2×C3×C4⋊C4—92no—
109C2×C3×C4⋊C4—91no—
110C2×C3×C42—31no—
111C2×C3×C42—31no—
112C2×C3×C42—61no—
113C2×C4⋊Dic3—31no—
114C2×C4⋊Dic3—31no—
115C2×C4⋊Dic3—32no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3C3×D311yescharacteristic
118C2×Dic3⋊C4—32no—
119C2×C4×Dic3C3×D311yescharacteristic
120C3×#95—92no—
121C3⋊#95—32no—
122C3⋊#95—32no—
123C23×C32—21no—
124C23×C32—21no—
125C23×C32—21no—
126C23×C32—41no—
127C23×C32C22×D311yescharacteristic
128C23×C32C22×D311yescharacteristic
129C23×C32C23×C311yescharacteristic
130C2×C32×C4—22no—
131C2×C32×C4—22no—
132C2×C32×C4—22no—
133C2×C32×C4—22no—
134C2×C32×C4—22no—
135C2×C32×C4—22no—
136C2×C32×C4—22no—
137C2×C32×C4—22no—
138C2×C32×C4—22no—
139C2×C32×C4—34no—
140C2×C32×C4—32no—
141C2×C32×C4—32no—
142C2×C32×C4—42no—
143C2×C32×C4—42no—
144C2×C32×C4—42no—
145C2×C32×C4—61no—
146C2×C32×C4—61no—
147C2×C32×C4—61no—
148C2×C32×C4—61no—
149C2×C32×C4—62no—
150C2×C32×C4—62no—
151C2×C32×C4Dic612yes—
152C2×C32×C4Dic612yes—
153C2×C32×C4C4×D312yes—
154C2×C32×C4D1212yes—
155C2×C32×C4C2×Dic312yes—
156C2×C32×C4#6712yes—
157C2×C32×C4C2×C3×C412yes—
158C2×C32×C4C3×D412yes—
159C2×C32×C4C3×Q812yes—
160C2×C3⋊Dic3—22no—
161C2×C3⋊Dic3—22no—
162C2×C3⋊Dic3—22no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3—22no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—21no—
169C2×C3×Dic3—22no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—21no—
172C2×C3×Dic3—21no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3—42no—
183C2×C3×Dic3—42no—
184C2×C3×Dic3—64no—
185C2×C3×Dic3—62no—
186C2×C3×Dic3—62no—
187C2×C3×Dic3—62no—
188C2×C3×Dic3—62no—
189C2×C3×Dic3—62no—
190C2×C3×Dic3—62no—
191C2×C3×Dic3—122no—
192C2×C3×Dic3—122no—
193C2×C3×Dic3Dic612yes—
194C2×C3×Dic3D1212yes—
195C2×C3×Dic3C2×Dic314yes—
196C2×C3×Dic3C2×C3×C414yes—
197C2×C3×Dic3C3×D412yes—
198C2×C3×Dic3C3×Q812yes—
199#389—91noSylow
200C2×C33C2×C4⋊C411yescharacteristic
201C2×C33C4×D411yescharacteristic
202C2×C33C4×Q811yescharacteristic
203C2×C33#12111yescharacteristic
204C2×C33C22⋊Q811yescharacteristic
205C2×C33#12511yescharacteristic
206C2×C33C4⋊Q811yescharacteristic
207C22×C3×C4—21no—
208C22×C3×C4—21no—
209C22×C3×C4—21no—
210C22×C3×C4—31no—
211C22×C3×C4—32no—
212C22×C3×C4—31no—
213C22×C3×C4—31no—
214C22×C3×C4—32no—
215C22×C3×C4—31no—
216C22×C3×C4—41no—
217C22×C3×C4—61no—
218C22×C3×C4—61no—
219C22×C3×C4—62no—
220C22×C3×C4—92no—
221C22×C3×C4D3211yescharacteristic
222C22×C3×C4C2×C3×D311yescharacteristic
223C22×C3×C4C2×C3×D311yescharacteristic
224C22×Dic3—32no—
225C22×Dic3—32no—
226C22×Dic3—62no—
227C22×Dic3C2×C3×D311yescharacteristic
228C22×Dic3C2×C3×D311yescharacteristic
229C22×Dic3C2×C3×D312yes—
230C3×C4⋊C4—34no—
231C3×C4⋊C4—34no—
232C3×C4⋊C4—64no—
233C3×C4⋊C4—184no—
234C3×C4⋊C4—182no—
235C3×C42—64no—
236C3×C42—62no—
237C3×C42—62no—
238C4⋊Dic3—64no—
239C4⋊Dic3—62no—
240C4⋊Dic3—62no—
241C4⋊Dic3—64no—
242C4⋊Dic3C3×Dic314yescomplemented
243Dic3⋊C4—64no—
244C4×Dic3—22no—
245C22×C32—21no—
246C22×C32—21no—
247C22×C32—21no—
248C22×C32—21no—
249C22×C32—21no—
250C22×C32—21no—
251C22×C32—21no—
252C22×C32—21no—
253C22×C32—21no—
254C22×C32—21no—
255C22×C32—21no—
256C22×C32—21no—
257C22×C32—21no—
258C22×C32—21no—
259C22×C32—21no—
260C22×C32—21no—
261C22×C32—21no—
262C22×C32—21no—
263C22×C32—21no—
264C22×C32—21no—
265C22×C32—21no—
266C22×C32—41no—
267C22×C32—41no—
268C22×C32—41no—
269C22×C32—41no—
270C22×C32—41no—
271C22×C32—41no—
272C22×C32—41no—
273C22×C32C2×Dic611yescharacteristic
274C22×C32C2×Dic611yescharacteristic
275C22×C32C2×Dic611yescharacteristic
276C22×C32C2×C4×D311yescharacteristic
277C22×C32C2×D1211yescharacteristic
278C22×C32C2×D1211yescharacteristic
279C22×C32#23511yescharacteristic
280C22×C32#23511yescharacteristic
281C22×C32D3×D411yescharacteristic
282C22×C32#23711yescharacteristic
283C22×C32D3×Q811yescharacteristic
284C22×C32#23911yescharacteristic
285C22×C32C22×Dic311yescharacteristic
286C22×C32C2×#6711yescharacteristic
287C22×C32C22×C3×C411yescharacteristic
288C22×C32C2×C3×D411yescharacteristic
289C22×C32C2×C3×D411yescharacteristic
290C22×C32C2×C3×Q811yescharacteristic
291C22×C32C2×C3×Q811yescharacteristic
292C22×C32C3×#4111yescharacteristic
293C22×C32C3×#4111yescharacteristic
294C32×C4—24no—
295C32×C4—24no—
296C32×C4—24no—
297C32×C4—44no—
298C32×C4—62no—
299C32×C4—62no—
300C32×C4—64no—
301C32×C4Dic3⋊C414yescomplemented
302C32×C4C4⋊Dic314yescomplemented
303C32×C4C3×C4⋊C414yescomplemented
304C3⋊Dic3—42no—
305C3×Dic3—24no—
306C3×Dic3—24no—
307C3×Dic3—22no—
308C3×Dic3—22no—
309C3×Dic3—24no—
310C3×Dic3—24no—
311C3×Dic3—22no—
312C3×Dic3—22no—
313C3×Dic3—44no—
314C3×Dic3—124no—
315C3×Dic3—122no—
316C3×Dic3—122no—
317C2×C4⋊C4—31no—
318C2×C4⋊C4—92no—
319C2×C4⋊C4—91no—
320C2×C42—31no—
321#95—92no—
322C33#38911yescharacteristic, complemented, Sylow
323C23×C3—21no—
324C23×C3—21no—
325C23×C3—21no—
326C23×C3—41no—
327C23×C3C2×D3211yescharacteristic
328C23×C3C22×C3×D311yescharacteristic
329C23×C3C22×C3×D311yescharacteristic
330C2×C3×C4—22no—
331C2×C3×C4—22no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—22no—
335C2×C3×C4—22no—
336C2×C3×C4—22no—
337C2×C3×C4—22no—
338C2×C3×C4—22no—
339C2×C3×C4—32no—
340C2×C3×C4—32no—
341C2×C3×C4—34no—
342C2×C3×C4—34no—
343C2×C3×C4—32no—
344C2×C3×C4—32no—
345C2×C3×C4—42no—
346C2×C3×C4—42no—
347C2×C3×C4—42no—
348C2×C3×C4—62no—
349C2×C3×C4—62no—
350C2×C3×C4—64no—
351C2×C3×C4—62no—
352C2×C3×C4—62no—
353C2×C3×C4—62no—
354C2×C3×C4—62no—
355C2×C3×C4—61no—
356C2×C3×C4—62no—
357C2×C3×C4—61no—
358C2×C3×C4—62no—
359C2×C3×C4—61no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—61no—
363C2×C3×C4—61no—
364C2×C3×C4—62no—
365C2×C3×C4—61no—
366C2×C3×C4—61no—
367C2×C3×C4—122no—
368C2×C3×C4—122no—
369C2×C3×C4—182no—
370C2×C3×C4—182no—
371C2×C3×C4—182no—
372C2×C3×C4D3×Dic312yes—
373C2×C3×C4#62612yes—
374C2×C3×C4#62712yes—
375C2×C3×C4C3×Dic612yes—
376C2×C3×C4C3×Dic612yes—
377C2×C3×C4C3×C4×D312yes—
378C2×C3×C4C3×D1212yes—
379C2×C3×C4C2×C3×Dic312yes—
380C2×C3×C4C3×#6712yes—
381C2×Dic3—21no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384C2×Dic3—22no—
385C2×Dic3—21no—
386C2×Dic3—21no—
387C2×Dic3—64no—
388C2×Dic3—62no—
389C2×Dic3—62no—
390C2×Dic3—62no—
391C2×Dic3—62no—
392C2×Dic3—62no—
393C2×Dic3—62no—
394C2×Dic3—122no—
395C2×Dic3—122no—
396C2×Dic3C3×Dic612yes—
397C2×Dic3C3×D1212yes—
398C2×Dic3C2×C3×Dic314yes—
399C2×C32—21no—
400C2×C32—21no—
401C2×C32—21no—
402C2×C32—21no—
403C2×C32—21no—
404C2×C32—21no—
405C2×C32—21no—
406C2×C32—21no—
407C2×C32—21no—
408C2×C32—21no—
409C2×C32—21no—
410C2×C32—21no—
411C2×C32—21no—
412C2×C32—21no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—21no—
416C2×C32—21no—
417C2×C32—21no—
418C2×C32—21no—
419C2×C32—21no—
420C2×C32—41no—
421C2×C32—41no—
422C2×C32—41no—
423C2×C32—41no—
424C2×C32—41no—
425C2×C32—41no—
426C2×C32—41no—
427C2×C32C4×Dic611yescharacteristic
428C2×C32#86911yescharacteristic
429C2×C32#87011yescharacteristic
430C2×C32C4×D1211yescharacteristic
431C2×C32#88811yescharacteristic
432C2×C32#89011yescharacteristic
433C2×C32#89511yescharacteristic
434C2×C32#89711yescharacteristic
435C2×C32C2×Dic3⋊C411yescharacteristic
436C2×C32#92411yescharacteristic
437C2×C32C2×C4⋊Dic311yescharacteristic
438C2×C32#93011yescharacteristic
439C2×C32D4×Dic311yescharacteristic
440C2×C32Q8×Dic311yescharacteristic
441C2×C32C2×C3×C4⋊C411yescharacteristic
442C2×C32C3×C4×D411yescharacteristic
443C2×C32C3×C4×Q811yescharacteristic
444C2×C32C3×#12111yescharacteristic
445C2×C32C3×C22⋊Q811yescharacteristic
446C2×C32C3×#12511yescharacteristic
447C2×C32C3×C4⋊Q811yescharacteristic
448C22×C4—31no—
449C22×C4—32no—
450C22×C4—31no—
451C22×C4—92no—
452C22×C4C3×D3211yescharacteristic
453C4⋊C4—34no—
454C4⋊C4—184no—
455C4⋊C4—182no—
456C42—62no—
457C22×C3—21no—
458C22×C3—21no—
459C22×C3—21no—
460C22×C3—21no—
461C22×C3—21no—
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—21no—
466C22×C3—21no—
467C22×C3—21no—
468C22×C3—21no—
469C22×C3—21no—
470C22×C3—21no—
471C22×C3—21no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—21no—
476C22×C3—21no—
477C22×C3—21no—
478C22×C3—41no—
479C22×C3—41no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—41no—
483C22×C3—41no—
484C22×C3—41no—
485C22×C3D3×Dic611yescharacteristic
486C22×C3#379511yescharacteristic
487C22×C3#379911yescharacteristic
488C22×C3D3×D1211yescharacteristic
489C22×C3C2×D3×Dic311yescharacteristic
490C22×C3C2×#62611yescharacteristic
491C22×C3C2×#62711yescharacteristic
492C22×C3C2×C3×Dic611yescharacteristic
493C22×C3C2×C3×Dic611yescharacteristic
494C22×C3C2×C3×Dic611yescharacteristic
495C22×C3C2×C3×C4×D311yescharacteristic
496C22×C3C2×C3×D1211yescharacteristic
497C22×C3C2×C3×D1211yescharacteristic
498C22×C3C3×#23511yescharacteristic
499C22×C3C3×#23511yescharacteristic
500C22×C3C3×D3×D411yescharacteristic
501C22×C3C3×#23711yescharacteristic
502C22×C3C3×D3×Q811yescharacteristic
503C22×C3C3×#23911yescharacteristic
504C22×C3C22×C3×Dic311yescharacteristic
505C22×C3C2×C3×#6711yescharacteristic
506C3×C4—24no—
507C3×C4—24no—
508C3×C4—24no—
509C3×C4—44no—
510C3×C4—64no—
511C3×C4—64no—
512C3×C4—62no—
513C3×C4—62no—
514C3×C4—62no—
515C3×C4—64no—
516C3×C4—62no—
517C3×C4—64no—
518C3×C4—124no—
519C3×C4—362no—
520C3×C4Dic3⋊Dic314yescomplemented
521C3×C4C3×Dic3⋊C414yescomplemented
522C3×C4C3×C4⋊Dic314yescomplemented
523Dic3—22no—
524Dic3—22no—
525Dic3—24no—
526Dic3—124no—
527Dic3—122no—
528Dic3—122no—
529C32—21no—
530C32—21no—
531C32—21no—
532C32—41no—
533C32#492811yescharacteristic, complemented
534C32#498411yescharacteristic, complemented
535C32C3×#38911yescharacteristic, complemented
536C23C2×C3×D3211yescharacteristic
537C2×C4—32no—
538C2×C4—32no—
539C2×C4—34no—
540C2×C4—61no—
541C2×C4—62no—
542C2×C4—61no—
543C2×C4—62no—
544C2×C4—61no—
545C2×C4—61no—
546C2×C4—182no—
547C2×C4—182no—
548C2×C4—182no—
549C2×C4C3×D3×Dic312yes—
550C2×C4C3×#62612yes—
551C2×C4C3×#62712yes—
552C2×C3—21no—
553C2×C3—21no—
554C2×C3—21no—
555C2×C3—21no—
556C2×C3—21no—
557C2×C3—21no—
558C2×C3—21no—
559C2×C3—21no—
560C2×C3—21no—
561C2×C3—21no—
562C2×C3—21no—
563C2×C3—21no—
564C2×C3—21no—
565C2×C3—21no—
566C2×C3—21no—
567C2×C3—21no—
568C2×C3—21no—
569C2×C3—21no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—21no—
573C2×C3—41no—
574C2×C3—41no—
575C2×C3—41no—
576C2×C3—41no—
577C2×C3—41no—
578C2×C3—41no—
579C2×C3—41no—
580C2×C3Dic3×Dic611yescharacteristic
581C2×C3#6385711yescharacteristic
582C2×C3#6386911yescharacteristic
583C2×C3Dic3×D1211yescharacteristic
584C2×C3#6390911yescharacteristic
585C2×C3#6391811yescharacteristic
586C2×C3C2×Dic3⋊Dic311yescharacteristic
587C2×C3C3×C4×Dic611yescharacteristic
588C2×C3C3×#86911yescharacteristic
589C2×C3C3×#87011yescharacteristic
590C2×C3C3×C4×D1211yescharacteristic
591C2×C3C3×#88811yescharacteristic
592C2×C3C3×#89011yescharacteristic
593C2×C3C3×#89511yescharacteristic
594C2×C3C3×#89711yescharacteristic
595C2×C3C2×C3×Dic3⋊C411yescharacteristic
596C2×C3C3×#92411yescharacteristic
597C2×C3C2×C3×C4⋊Dic311yescharacteristic
598C2×C3C3×#93011yescharacteristic
599C2×C3C3×D4×Dic311yescharacteristic
600C2×C3C3×Q8×Dic311yescharacteristic
601C22C3×D3×Dic611yescharacteristic
602C22C3×#379511yescharacteristic
603C22C3×#379911yescharacteristic
604C22C3×D3×D1211yescharacteristic
605C22C2×C3×D3×Dic311yescharacteristic
606C22C2×C3×#62611yescharacteristic
607C22C2×C3×#62711yescharacteristic
608C4—62no—
609C4—64no—
610C4—62no—
611C4—362no—
612C4C3×Dic3⋊Dic314yescomplemented
613C3—21no—
614C3—21no—
615C3—21no—
616C3—41no—
617C3#1059135211yescharacteristic, direct product factor
618C3C3×#492811yescharacteristic, complemented
619C3C3×#498411yescharacteristic, complemented
620C2C3×Dic3×Dic611yescharacteristic
621C2C3×#6385711yescharacteristic
622C2C3×#6386911yescharacteristic
623C2C3×Dic3×D1211yescharacteristic
624C2C3×#6390911yescharacteristic
625C2C3×#6391811yescharacteristic
626C2C2×C3×Dic3⋊Dic311yescharacteristic
subgroupG/H
centerC23×C3C2×D32
commutatorC22×C32C22×C3×C4
FrattiniC23C2×C3×D32
FittingC22×C33×C4C22
socle, prime radicalC23×C33C23
cosocleC23×C32C23×C3
hypercenterC22×C3×C4D32
hypocenterC32C3×#389
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23×C3 ◁ C22×C3×C4

Complements

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

NH ≅ G/Ntype
8. #10591352C3direct (N × H)
15. C32×C4⋊Dic3C4semidirect
86. C3×C4⋊Dic3Dic3semidirect
87. C3×C4⋊Dic3C3×C4semidirect
100. C33×C4C4⋊C4semidirect
242. C4⋊Dic3C3×Dic3semidirect
301. C32×C4Dic3⋊C4semidirect
302. C32×C4C4⋊Dic3semidirect
303. C32×C4C3×C4⋊C4semidirect
322. C33#389semidirect
520. C3×C4Dic3⋊Dic3semidirect
521. C3×C4C3×Dic3⋊C4semidirect
522. C3×C4C3×C4⋊Dic3semidirect
533. C32#4928semidirect
534. C32#4984semidirect
535. C32C3×#389semidirect
612. C4C3×Dic3⋊Dic3semidirect
617. C3#10591352direct (N × H)
618. C3C3×#4928semidirect
619. C3C3×#4984semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4⋊(C3⋊Dic3)2
C2×C32×C4⋊Dic32
C2×C32×C4×Dic32
C2×C3×Dic3⋊Dic32
C3×#635792
C3×#49843
C3×#49283
#105913523