Finite Group Databasebeta

← #13150678

Subgroups — #13150678

Order 1728.

1201 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×(C3⋊D3)⋊C3C211yesmaximal, characteristic
2C2×((C3⋊D3)⋊C3)⋊Q8C211yesmaximal, characteristic, complemented
3#11721824C211yesmaximal, characteristic, complemented
4#64133⋊C3C211yesmaximal, characteristic, complemented
5#11721310C212yesmaximal
6#11721299C212yesmaximal, complemented
7#11721129C211yesmaximal, characteristic, complemented
8#11721119C212yesmaximal, complemented
9#11721107C211yesmaximal, characteristic, complemented
10#11721106C211yesmaximal, characteristic, complemented
11#11721101C212yesmaximal, complemented
12#10594925—31nomaximal
13D3×#924—31nomaximal
14C23×(C3⋊D3)⋊C3C2211yescharacteristic
15C22×C4×H(3,𝔽3)C2211yescharacteristic
16C2×#6229C2211yescharacteristic, complemented
17C22×(C3⋊Dic3)⋊C3C2211yescharacteristic
18C2×C4×(C3⋊D3)⋊C3—24no—
19C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
20C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
21C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
22C2×C4×(C3⋊D3)⋊C3C2211yescharacteristic
23C2×#634⋊C3C2211yescharacteristic, complemented
24C2×((C3⋊D3)⋊C3)⋊C4C2212yes—
25C2×((C3⋊D3)⋊C3)⋊C4C2212yes—
26C2×#6196C2212yescomplemented
27((C3⋊D3)⋊C3)⋊Q8—24no—
28#88552C2212yes—
29C4⋊#1084C2211yescharacteristic, complemented
30#88540C2212yescomplemented
31#3757⋊C3C2212yes—
32C4⋊((C3⋊Dic3)⋊C3)C2211yescharacteristic, complemented
33#3750⋊C3C2212yescomplemented
34#88450C2212yes—
35#88450C2212yes—
36#88449C2212yescomplemented
37#88448C2212yescomplemented
38#88448C2212yescomplemented
39C22×C4×C3⋊D3D311yescharacteristic
40C22×C3×C4×D3—31no—
41C2×#3797—31no—
42C2×D3×Dic6—31no—
43#64133D311yescharacteristic, complemented
44C3×#924—31no—
45C3×#924—31no—
46C3×#924—31no—
47C3×#924—61no—
48#63982—32no—
49#63974—32no—
50D3×#217—32no—
51#63964—32no—
52#63900—31no—
53D3×C4⋊Dic3—31no—
54#63883—32no—
55D3×Dic3⋊C4—32no—
56#63871—31no—
57#63871—31no—
58#63865—32no—
59#63857—31no—
60#63856—31no—
61#63851—32no—
62C23×H(3,𝔽3)C2311yescharacteristic
63C22×(C3⋊D3)⋊C3—22no—
64C22×(C3⋊D3)⋊C3—22no—
65C22×(C3⋊D3)⋊C3Q814yescomplemented
66C22×(C3⋊D3)⋊C3C2311yescharacteristic
67C22×(C3⋊D3)⋊C3C2311yescharacteristic
68C2×C4×H(3,𝔽3)—22no—
69C2×C4×H(3,𝔽3)C2311yescharacteristic
70C2×C4×H(3,𝔽3)C2311yescharacteristic
71C2×#1084C2312yes—
72C2×#1084C2312yes—
73#6229—22no—
74C2×(C3⋊Dic3)⋊C3—22no—
75C2×(C3⋊Dic3)⋊C3C2312yes—
76C2×(C3⋊Dic3)⋊C3C2312yes—
77C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
78C2×(C3⋊Dic3)⋊C3C2311yescharacteristic
79C4×(C3⋊D3)⋊C3—22no—
80C4×(C3⋊D3)⋊C3—22no—
81C4×(C3⋊D3)⋊C3—22no—
82C4×(C3⋊D3)⋊C3D414yes—
83#634⋊C3—22no—
84((C3⋊D3)⋊C3)⋊C4—24no—
85((C3⋊D3)⋊C3)⋊C4—24no—
86#6196—24no—
87C2×#924—91no—
88D3×C22⋊Q8—91no—
89D3×C22⋊Q8—91no—
90C23×C3⋊D3C2×D311yescharacteristic
91C23×C3×D3—31no—
92C22×C32×C4—21no—
93C22×C32×C4C2×D311yescharacteristic
94C22×C32×C4C2×D311yescharacteristic
95C22×C3⋊Dic3C2×D311yescharacteristic
96C2×C4×C3⋊D3—24no—
97C2×C4×C3⋊D3C2×D311yescharacteristic
98C2×C4×C3⋊D3C2×D311yescharacteristic
99C2×C4×C3⋊D3C2×D311yescharacteristic
100C2×C4×C3⋊D3C2×D311yescharacteristic
101C2×#634C2×D311yescharacteristic, complemented
102C22×C3×Dic3—31no—
103C2×C3×C4×D3—31no—
104C2×C3×C4×D3—31no—
105C2×C3×C4×D3—31no—
106C2×C3×C4×D3—31no—
107C2×C3×C4×D3—64no—
108C2×C3×Dic6—31no—
109C2×C3×Dic6—31no—
110C2×C3×Dic6—31no—
111C2×C3×Dic6—61no—
112C2×#627—32no—
113C2×#627—32no—
114C2×#624—32no—
115C2×#624—32no—
116C2×D3×Dic3—32no—
117C2×D3×Dic3—32no—
118#3797—64no—
119D3×Dic6—64no—
120#3757C2×D312yes—
121C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
122#3750C2×D312yescomplemented
123C3×#217—32no—
124C3×#217—32no—
125C3×#217—32no—
126C3×#217—62no—
127C3×C4⋊Dic3—31no—
128C3×C4⋊Dic3—31no—
129C3×C4⋊Dic3—31no—
130C3×C4⋊Dic3—61no—
131C3×Dic3⋊C4—32no—
132C3×Dic3⋊C4—32no—
133C3×Dic3⋊C4—32no—
134C3×Dic3⋊C4—62no—
135#3724—32no—
136#3724—32no—
137Dic3⋊Dic3—32no—
138Dic3⋊Dic3—32no—
139Dic3⋊Dic3—32no—
140Dic3⋊Dic3—32no—
141#3722—32no—
142#3722—32no—
143(C2×D3)⋊Dic3—32no—
144(C2×D3)⋊Dic3—32no—
145C22×H(3,𝔽3)—21no—
146C22×H(3,𝔽3)—21no—
147C22×H(3,𝔽3)C2×Q812yescomplemented
148C22×H(3,𝔽3)C2411yescharacteristic
149C2×(C3⋊D3)⋊C3—21no—
150C2×(C3⋊D3)⋊C3—21no—
151C2×(C3⋊D3)⋊C3—28no—
152C2×(C3⋊D3)⋊C3C2×D412yes—
153C2×(C3⋊D3)⋊C3C2×Q812yes—
154C2×(C3⋊D3)⋊C3C2×Q812yescomplemented
155C2×(C3⋊D3)⋊C3#4112yes—
156C4×H(3,𝔽3)—21no—
157C4×H(3,𝔽3)C2×D412yes—
158#1084—22no—
159#1084—22no—
160(C3⋊Dic3)⋊C3—22no—
161(C3⋊Dic3)⋊C3—21no—
162(C3⋊Dic3)⋊C3—22no—
163(C3⋊Dic3)⋊C3C2×D412yes—
164C23×C3×C4—91no—
165C2×D3×Q8—91no—
166C2×D3×Q8—91no—
167C22×C4×D3—31no—
168C22×C4×D3—91no—
169C22×Dic6—91no—
170C3×C22⋊Q8—91no—
171C3×C22⋊Q8—91no—
172C2×#217—92no—
173#946—91no—
174#946—91no—
175C2×C4⋊Dic3—91no—
176#924—31no—
177#924—31no—
178#924—31no—
179#924—61no—
180#924—91no—
181#924—92no—
182#924—91no—
183#924—92no—
184#924—91no—
185C2×Dic3⋊C4—92no—
186#897—91no—
187#897—91no—
188#896—92no—
189#896—92no—
190D3×C4⋊C4—92no—
191D3×C4⋊C4—92no—
192D3×C4⋊C4—91no—
193D3×C4⋊C4—91no—
194D3×C22⋊C4—92no—
195D3×C22⋊C4—92no—
196#878—92no—
197#878—92no—
198C23×C32—21no—
199C23×C32C22×D311yescharacteristic
200C23×C32C22×D311yescharacteristic
201C22×C3⋊D3—22no—
202C22×C3⋊D3—22no—
203C22×C3⋊D3Dic614yescomplemented
204C22×C3⋊D3C22×D311yescharacteristic
205C22×C3⋊D3C22×D311yescharacteristic
206C22×C3×D3—31no—
207C22×C3×D3—34no—
208C22×C3×D3—31no—
209C22×C3×D3—62no—
210C22×C3×D3—62no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4—42no—
216C2×C32×C4C22×D311yescharacteristic
217C2×C32×C4C22×D311yescharacteristic
218C2×C32×C4C22×D311yescharacteristic
219C2×C32×C4C22×D311yescharacteristic
220C2×C3⋊Dic3—22no—
221C2×C3⋊Dic3C22×D312yes—
222C2×C3⋊Dic3C22×D312yes—
223C2×C3⋊Dic3C22×D311yescharacteristic
224C2×C3⋊Dic3C22×D311yescharacteristic
225C4×C3⋊D3—22no—
226C4×C3⋊D3—22no—
227C4×C3⋊D3—22no—
228C4×C3⋊D3#6714yes—
229#634—22no—
230C2×C3×Dic3—31no—
231C2×C3×Dic3—32no—
232C2×C3×Dic3—32no—
233C2×C3×Dic3—31no—
234C2×C3×Dic3—32no—
235C2×C3×Dic3—32no—
236C2×C3×Dic3—32no—
237C2×C3×Dic3—32no—
238C2×C3×Dic3—62no—
239C2×C3×Dic3—62no—
240C2×C3×Dic3—62no—
241C3×C4×D3—34no—
242C3×C4×D3—62no—
243C3×C4×D3—62no—
244C3×C4×D3—62no—
245C3×Dic6—62no—
246C3×Dic6—62no—
247C3×Dic6—62no—
248C3×Dic6—122no—
249#627—64no—
250#627—64no—
251#624—64no—
252#624—64no—
253D3×Dic3—64no—
254D3×Dic3—64no—
255C2×C22⋊Q8—271noSylow
256C2×H(3,𝔽3)—22no—
257C2×H(3,𝔽3)C22×D411yescharacteristic
258C2×H(3,𝔽3)C22×Q811yescharacteristic
259C2×H(3,𝔽3)C2×#4111yescharacteristic
260(C3⋊D3)⋊C3—22no—
261(C3⋊D3)⋊C3C22⋊Q814yescomplemented
262C24×C3—91no—
263C23×D3—31no—
264C23×D3—91no—
265C2×C3×Q8—91no—
266C2×C3×Q8—91no—
267C22×C3×C4—31no—
268C22×C3×C4—31no—
269C22×C3×C4—61no—
270C22×C3×C4—91no—
271C22×C3×C4—91no—
272C22×C3×C4—91no—
273C22×C3×C4—91no—
274C22×C3×C4—91no—
275C22×C3×C4—184no—
276C22×C3×C4D3211yescharacteristic
277C22×Dic3—31no—
278C22×Dic3—91no—
279C22×Dic3—92no—
280C22×Dic3—92no—
281D3×Q8—184no—
282D3×Q8—184no—
283C2×C4×D3—31no—
284C2×C4×D3—31no—
285C2×C4×D3—31no—
286C2×C4×D3—31no—
287C2×C4×D3—64no—
288C2×C4×D3—91no—
289C2×C4×D3—91no—
290C2×C4×D3—91no—
291C2×C4×D3—91no—
292C2×C4×D3—92no—
293C2×C4×D3—92no—
294C2×C4×D3—92no—
295C2×C4×D3—92no—
296C2×C4×D3—184no—
297C2×Dic6—31no—
298C2×Dic6—31no—
299C2×Dic6—31no—
300C2×Dic6—61no—
301C2×Dic6—91no—
302C2×Dic6—92no—
303C2×Dic6—92no—
304C2×Dic6—92no—
305C2×Dic6—184no—
306C3×C4⋊C4—92no—
307C3×C4⋊C4—91no—
308C3×C4⋊C4—92no—
309C3×C4⋊C4—91no—
310C3×C22⋊C4—92no—
311C3×C22⋊C4—92no—
312#217—32no—
313#217—32no—
314#217—32no—
315#217—62no—
316#217—92no—
317#217—92no—
318#217—92no—
319(C2×D3)⋊C4—92no—
320(C2×D3)⋊C4—92no—
321(C2×D3)⋊C4—92no—
322(C2×D3)⋊C4—92no—
323C4⋊Dic3—31no—
324C4⋊Dic3—31no—
325C4⋊Dic3—31no—
326C4⋊Dic3—61no—
327C4⋊Dic3—91no—
328C4⋊Dic3—92no—
329C4⋊Dic3—92no—
330C4⋊Dic3—92no—
331Dic3⋊C4—32no—
332Dic3⋊C4—32no—
333Dic3⋊C4—32no—
334Dic3⋊C4—62no—
335Dic3⋊C4—92no—
336Dic3⋊C4—92no—
337Dic3⋊C4—92no—
338Dic3⋊C4—92no—
339Dic3⋊C4—92no—
340Dic3⋊C4—92no—
341Dic3⋊C4—92no—
342C22×C32—21no—
343C22×C32—21no—
344C22×C32—21no—
345C22×C32—21no—
346C22×C32—21no—
347C22×C32—22no—
348C22×C32—41no—
349C22×C32—41no—
350C22×C32C2×Dic612yescomplemented
351C22×C32D3×Q812yescomplemented
352C22×C32C23×D311yescharacteristic
353C22×C32C23×D311yescharacteristic
354C2×C3⋊D3—21no—
355C2×C3⋊D3—21no—
356C2×C3⋊D3—28no—
357C2×C3⋊D3C2×Dic612yes—
358C2×C3⋊D3C2×Dic612yescomplemented
359C2×C3⋊D3#23512yes—
360C2×C3⋊D3C2×#6712yes—
361C2×C3×D3—32no—
362C2×C3×D3—32no—
363C2×C3×D3—32no—
364C2×C3×D3—32no—
365C2×C3×D3—68no—
366C2×C3×D3—61no—
367C2×C3×D3—61no—
368C32×C4—21no—
369C32×C4—21no—
370C32×C4—22no—
371C32×C4—41no—
372C32×C4D3×D412yes—
373C32×C4C2×#6712yes—
374C3⋊Dic3—22no—
375C3⋊Dic3—22no—
376C3⋊Dic3—21no—
377C3⋊Dic3C2×#6712yes—
378C3×Dic3—32no—
379C3×Dic3—62no—
380C3×Dic3—62no—
381C3×Dic3—61no—
382C3×Dic3—62no—
383C3×Dic3—62no—
384C3×Dic3—62no—
385C3×Dic3—62no—
386C3×Dic3—122no—
387C3×Dic3—122no—
388C22×Q8—271no—
389C23×C4—91no—
390C22⋊Q8—91no—
391C22⋊Q8—91no—
392C22⋊Q8—272no—
393C22⋊Q8—272no—
394C22⋊Q8—271no—
395C22⋊Q8—271no—
396C2×C4⋊C4—272no—
397C2×C4⋊C4—271no—
398C2×C22⋊C4—272no—
399H(3,𝔽3)C2×C22⋊Q811yescharacteristic, complemented, Sylow
400C23×C3—31no—
401C23×C3—31no—
402C23×C3—61no—
403C23×C3—91no—
404C23×C3—91no—
405C23×C3—94no—
406C23×C3—182no—
407C23×C3—182no—
408C23×C3C2×D3211yescharacteristic
409C22×D3—31no—
410C22×D3—31no—
411C22×D3—34no—
412C22×D3—62no—
413C22×D3—62no—
414C22×D3—91no—
415C22×D3—94no—
416C22×D3—91no—
417C22×D3—182no—
418C22×D3—182no—
419C3×Q8—182no—
420C3×Q8—182no—
421C2×C3×C4—22no—
422C2×C3×C4—31no—
423C2×C3×C4—31no—
424C2×C3×C4—31no—
425C2×C3×C4—31no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4—94no—
431C2×C3×C4—91no—
432C2×C3×C4—91no—
433C2×C3×C4—92no—
434C2×C3×C4—92no—
435C2×C3×C4—92no—
436C2×C3×C4—92no—
437C2×C3×C4—122no—
438C2×C3×C4—182no—
439C2×C3×C4—182no—
440C2×C3×C4—182no—
441C2×C3×C4—182no—
442C2×C3×C4C2×D3211yescharacteristic
443C2×C3×C4C2×D3211yescharacteristic
444C2×Dic3—31no—
445C2×Dic3—32no—
446C2×Dic3—32no—
447C2×Dic3—32no—
448C2×Dic3—32no—
449C2×Dic3—32no—
450C2×Dic3—32no—
451C2×Dic3—31no—
452C2×Dic3—62no—
453C2×Dic3—62no—
454C2×Dic3—62no—
455C2×Dic3—91no—
456C2×Dic3—92no—
457C2×Dic3—91no—
458C2×Dic3—92no—
459C2×Dic3—182no—
460C2×Dic3—184no—
461C2×Dic3—184no—
462C4×D3—34no—
463C4×D3—62no—
464C4×D3—62no—
465C4×D3—62no—
466C4×D3—94no—
467C4×D3—182no—
468C4×D3—182no—
469C4×D3—182no—
470C4×D3—184no—
471C4×D3—184no—
472C4×D3—184no—
473C4×D3—184no—
474Dic6—62no—
475Dic6—62no—
476Dic6—62no—
477Dic6—122no—
478Dic6—182no—
479Dic6—184no—
480Dic6—184no—
481Dic6—184no—
482C2×C32—22no—
483C2×C32—22no—
484C2×C32—21no—
485C2×C32—21no—
486C2×C32—21no—
487C2×C32—42no—
488C2×C32C22×Dic611yescharacteristic
489C2×C32C2×#23511yescharacteristic
490C2×C32C2×D3×D411yescharacteristic
491C2×C32C2×D3×Q811yescharacteristic
492C2×C32D3×#4111yescharacteristic
493C2×C32C22×#6711yescharacteristic
494C3⋊D3—22no—
495C3⋊D3#92414yescomplemented
496C3×D3—34no—
497C3×D3—62no—
498C24—91no—
499C2×Q8—91no—
500C2×Q8—91no—
501C2×Q8—272no—
502C2×Q8—544no—
503C22×C4—91no—
504C22×C4—91no—
505C22×C4—91no—
506C22×C4—91no—
507C22×C4—91no—
508C22×C4—184no—
509C22×C4—272no—
510C22×C4—272no—
511C22×C4((C3⋊D3)⋊C3)⋊C211yescharacteristic
512C4⋊C4—92no—
513C4⋊C4—92no—
514C4⋊C4—91no—
515C4⋊C4—91no—
516C4⋊C4—272no—
517C4⋊C4—272no—
518C4⋊C4—272no—
519C22⋊C4—92no—
520C22⋊C4—92no—
521C22⋊C4—272no—
522C22⋊C4—272no—
523C22×C3—21no—
524C22×C3—21no—
525C22×C3—31no—
526C22×C3—31no—
527C22×C3—32no—
528C22×C3—32no—
529C22×C3—61no—
530C22×C3—61no—
531C22×C3—61no—
532C22×C3—61no—
533C22×C3—61no—
534C22×C3—62no—
535C22×C3—92no—
536C22×C3—92no—
537C22×C3—92no—
538C22×C3—92no—
539C22×C3—121no—
540C22×C3—121no—
541C22×C3—181no—
542C22×C3—181no—
543C22×C3—188no—
544C22×C3D3×Dic612yes—
545C22×C3C22×D3211yescharacteristic
546C2×D3—32no—
547C2×D3—32no—
548C2×D3—32no—
549C2×D3—32no—
550C2×D3—68no—
551C2×D3—61no—
552C2×D3—61no—
553C2×D3—92no—
554C2×D3—92no—
555C2×D3—92no—
556C2×D3—92no—
557C2×D3—188no—
558C2×D3—181no—
559C2×D3—181no—
560C3×C4—21no—
561C3×C4—32no—
562C3×C4—32no—
563C3×C4—61no—
564C3×C4—61no—
565C3×C4—62no—
566C3×C4—92no—
567C3×C4—121no—
568C3×C4—182no—
569C3×C4—182no—
570C3×C4—181no—
571C3×C4—182no—
572C3×C4—182no—
573C3×C4D3×#6712yes—
574Dic3—32no—
575Dic3—62no—
576Dic3—62no—
577Dic3—62no—
578Dic3—62no—
579Dic3—62no—
580Dic3—62no—
581Dic3—61no—
582Dic3—92no—
583Dic3—122no—
584Dic3—122no—
585Dic3—182no—
586Dic3—181no—
587Dic3—182no—
588C32—21no—
589C32D3×C22⋊Q811yescharacteristic, complemented
590C32C2×#92411yescharacteristic, complemented
591C23—91no—
592C23—91no—
593C23—94no—
594C23—182no—
595C23—182no—
596C23C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
597Q8—182no—
598Q8—182no—
599Q8—544no—
600C2×C4—22no—
601C2×C4—91no—
602C2×C4—94no—
603C2×C4—92no—
604C2×C4—92no—
605C2×C4—92no—
606C2×C4—92no—
607C2×C4—91no—
608C2×C4—182no—
609C2×C4—182no—
610C2×C4—182no—
611C2×C4—182no—
612C2×C4—544no—
613C2×C4—544no—
614C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
615C2×C4C2×((C3⋊D3)⋊C3)⋊C211yescharacteristic
616C2×C3—22no—
617C2×C3—31no—
618C2×C3—31no—
619C2×C3—31no—
620C2×C3—31no—
621C2×C3—31no—
622C2×C3—31no—
623C2×C3—62no—
624C2×C3—62no—
625C2×C3—61no—
626C2×C3—61no—
627C2×C3—61no—
628C2×C3—94no—
629C2×C3—122no—
630C2×C3—182no—
631C2×C3C2×D3×Dic611yescharacteristic
632C2×C3D3×#23511yescharacteristic
633C2×C3C2×D3×#6711yescharacteristic
634D3—34no—
635D3—62no—
636D3—94no—
637D3—182no—
638C22—21no—
639C22—21no—
640C22—92no—
641C22—92no—
642C22—92no—
643C22—92no—
644C22—188no—
645C22—181no—
646C22—181no—
647C22((C3⋊D3)⋊C3)⋊Q812yescomplemented
648C22C22×((C3⋊D3)⋊C3)⋊C211yescharacteristic
649C4—21no—
650C4—92no—
651C4—181no—
652C4—182no—
653C4—182no—
654C4—182no—
655C4—182no—
656C4#8867612yes—
657C3—31no—
658C3—31no—
659C3—61no—
660C3D3×#92411yescharacteristic
661C2—22no—
662C2—94no—
663C2—182no—
664C2C2×((C3⋊D3)⋊C3)⋊Q811yescharacteristic
665C2#1172249011yescharacteristic
666C2C2×#8867611yescharacteristic
subgroupG/H
centerC22C22×((C3⋊D3)⋊C3)⋊C2
commutator, cosocleC22×H(3,𝔽3)C24
Frattini, socleC22×C3C22×D32
FittingC22×C4×H(3,𝔽3)C22
prime radicalC23×(C3⋊D3)⋊C3C22
hypercenterC22×C4((C3⋊D3)⋊C3)⋊C2
hypocenterH(3,𝔽3)C2×C22⋊Q8
LCSG ▷ C22×H(3,𝔽3) ▷ H(3,𝔽3)
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
2. C2×((C3⋊D3)⋊C3)⋊Q8C2semidirect
3. #11721824C2semidirect
4. #64133⋊C3C2semidirect
6. #11721299C2semidirect
7. #11721129C2semidirect
8. #11721119C2semidirect
9. #11721107C2semidirect
10. #11721106C2semidirect
11. #11721101C2semidirect
16. C2×#6229C22semidirect
23. C2×#634⋊C3C22semidirect
26. C2×#6196C22semidirect
29. C4⋊#1084C22semidirect
30. #88540C22semidirect
32. C4⋊((C3⋊Dic3)⋊C3)C22semidirect
33. #3750⋊C3C22semidirect
36. #88449C22semidirect
37. #88448C22semidirect
38. #88448C22semidirect
43. #64133D3semidirect
65. C22×(C3⋊D3)⋊C3Q8semidirect
101. C2×#634C2×D3semidirect
121. C4⋊(C3⋊Dic3)C2×D3semidirect
122. #3750C2×D3semidirect
147. C22×H(3,𝔽3)C2×Q8semidirect
154. C2×(C3⋊D3)⋊C3C2×Q8semidirect
203. C22×C3⋊D3Dic6semidirect
261. (C3⋊D3)⋊C3C22⋊Q8semidirect
350. C22×C32C2×Dic6semidirect
351. C22×C32D3×Q8semidirect
358. C2×C3⋊D3C2×Dic6semidirect
399. H(3,𝔽3)C2×C22⋊Q8semidirect
495. C3⋊D3#924semidirect
589. C32D3×C22⋊Q8semidirect
590. C32C2×#924semidirect
647. C22((C3⋊D3)⋊C3)⋊Q8semidirect

Maximal subgroups

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

subgroupindex
C22×C4×(C3⋊D3)⋊C32
C2×((C3⋊D3)⋊C3)⋊Q82
#117218242
#64133⋊C32
#117213102
#117212992
#117211292
#117211192
#117211072
#117211062
#117211012
#105949253
D3×#9243