Finite Group Databasebeta

← C22×#5661 #11702190

Subgroups — C22×#5661 #11702190

Order 768.

8798 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#123C211yesmaximal, characteristic, complemented
2C22×#938C211yesmaximal, characteristic, complemented
3C22×#939C211yesmaximal, characteristic, complemented
4C22×C4×#67C211yesmaximal, characteristic, complemented
5C22×C4×#67C211yesmaximal, characteristic, complemented
6C2×#5661C2148yesmaximal, direct product factor
7C22×D3×C4⋊C4C211yesmaximal, characteristic, complemented
8C22×#898C211yesmaximal, characteristic, complemented
9C22×#889C211yesmaximal, characteristic, complemented
10C22×#893C211yesmaximal, characteristic, complemented
11C22×#883C211yesmaximal, characteristic, complemented
12C22×#884C211yesmaximal, characteristic, complemented
13C22×#884C211yesmaximal, characteristic, complemented
14C22×#879C211yesmaximal, characteristic, complemented
15C22×#67⋊C4C211yesmaximal, characteristic, complemented
16C22×#877C211yesmaximal, characteristic, complemented
17C22×#553—31nomaximal, Sylow
18C23×C3×D4C2211yescharacteristic
19C24×C3×C4C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C23×#67C2211yescharacteristic
23C23×#67C2211yescharacteristic
24C24×Dic3C2211yescharacteristic
25C23×D12C2211yescharacteristic
26C23×C4×D3C2211yescharacteristic
27C23×C4×D3C2211yescharacteristic
28C23×C4×D3C2211yescharacteristic
29C23×C4×D3C2211yescharacteristic
30C2×C3×#123C22124yescomplemented
31C22×C3×C4⋊C4C2211yescharacteristic
32C22×C3×C4⋊C4C2211yescharacteristic
33C22×C3×C22⋊C4C2211yescharacteristic
34C22×C3×C22⋊C4C2211yescharacteristic
35C22×C3×C22⋊C4C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
39C2×#939C22124yescomplemented
40C2×#938C22124yescomplemented
41C2×C4×#67C22124yescomplemented
42C2×C4×#67C22124yescomplemented
43C22×(C2×D3)⋊C4C2211yescharacteristic
44C22×(C2×D3)⋊C4C2211yescharacteristic
45C22×(C2×D3)⋊C4C2211yescharacteristic
46C22×(C2×D3)⋊C4C2211yescharacteristic
47C22×C4⋊Dic3C2211yescharacteristic
48C22×C4⋊Dic3C2211yescharacteristic
49C22×Dic3⋊C4C2211yescharacteristic
50C22×Dic3⋊C4C2211yescharacteristic
51C22×Dic3⋊C4C2211yescharacteristic
52C22×Dic3⋊C4C2211yescharacteristic
53C22×Dic3⋊C4C2211yescharacteristic
54C22×Dic3⋊C4C2211yescharacteristic
55C22×C4×Dic3C2211yescharacteristic
56C22×C4×Dic3C2211yescharacteristic
57C22×C4×Dic3C2211yescharacteristic
58#5661C221256yesdirect product factor
59C2×#898C22124yescomplemented
60C2×#893C22124yescomplemented
61C2×D3×C4⋊C4C22124yescomplemented
62C2×#889C22124yescomplemented
63C2×#884C22124yescomplemented
64C2×#884C22124yescomplemented
65C2×#883C22124yescomplemented
66C2×#67⋊C4C22124yescomplemented
67C2×#879C22124yescomplemented
68C2×#877C22124yescomplemented
69C2×#553—348no—
70C22×#126—31no—
71C22×#126—31no—
72C22×#125—31no—
73C22×#123—31no—
74C22×#123D311yescharacteristic, complemented
75C22×#121—31no—
76C22×#121—31no—
77C22×#121—31no—
78C22×#121—31no—
79C22×C4×D4—31no—
80C22×C4×D4—31no—
81C22×C4×D4—31no—
82C22×C4×D4—31no—
83C22×#117—31no—
84C23×C4⋊C4—31no—
85C25×C3C2311yescharacteristic
86C25×C3C2311yescharacteristic
87C24×D3C2311yescharacteristic
88C24×D3C2311yescharacteristic
89C22×C3×D4—44no—
90C22×C3×D4C23112yes—
91C23×C3×C4—44no—
92C23×C3×C4C2311yescharacteristic
93C23×C3×C4C2311yescharacteristic
94C23×C3×C4C2311yescharacteristic
95C23×C3×C4C2311yescharacteristic
96C23×C3×C4C2311yescharacteristic
97C23×C3×C4C23112yes—
98C22×#67—28no—
99C22×#67—28no—
100C22×#67—28no—
101C22×#67—44no—
102C22×#67C23112yes—
103C22×#67C23112yes—
104C22×#67C23112yes—
105C22×#67C23112yes—
106C23×Dic3—28no—
107C23×Dic3C2311yescharacteristic
108C23×Dic3C2311yescharacteristic
109C23×Dic3C23112yes—
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C23×Dic3C2311yescharacteristic
114C22×D12—28no—
115C22×D12C23112yes—
116C22×C4×D3—28no—
117C22×C4×D3—44no—
118C22×C4×D3—44no—
119C22×C4×D3—44no—
120C22×C4×D3C23112yes—
121C22×C4×D3C23112yes—
122C22×C4×D3C23112yes—
123C22×C4×D3C23112yes—
124C3×#123C23164yescomplemented
125C2×C3×C4⋊C4C23112yes—
126C2×C3×C4⋊C4C23112yes—
127C2×C3×C22⋊C4C23112yes—
128C2×C3×C22⋊C4C23112yes—
129C2×C3×C22⋊C4C23112yes—
130C2×#217C23112yes—
131C2×#217C23112yes—
132C2×#217C23112yes—
133#939C23164yescomplemented
134#938C23164yescomplemented
135C4×#67C23164yescomplemented
136C4×#67C23164yescomplemented
137C2×(C2×D3)⋊C4C23112yes—
138C2×(C2×D3)⋊C4C23112yes—
139C2×(C2×D3)⋊C4C23112yes—
140C2×(C2×D3)⋊C4C23112yes—
141C2×C4⋊Dic3C23112yes—
142C2×C4⋊Dic3C23112yes—
143C2×Dic3⋊C4C23112yes—
144C2×Dic3⋊C4C23112yes—
145C2×Dic3⋊C4C23112yes—
146C2×Dic3⋊C4C23112yes—
147C2×Dic3⋊C4C23112yes—
148C2×Dic3⋊C4C23112yes—
149C2×C4×Dic3C23112yes—
150C2×C4×Dic3C23112yes—
151C2×C4×Dic3C23112yes—
152#898C23164yescomplemented
153#893C23164yescomplemented
154D3×C4⋊C4C23164yescomplemented
155#889C23164yescomplemented
156#884C23164yescomplemented
157#884C23164yescomplemented
158#883C23164yescomplemented
159#67⋊C4C23164yescomplemented
160#879C23164yescomplemented
161#877C23164yescomplemented
162C23×D4—31no—
163C23×D4—31no—
164C23×D4—31no—
165C23×D4—31no—
166C23×D4—31no—
167C23×D4C2×D311yescharacteristic
168C24×C4—31no—
169C24×C4—31no—
170C24×C4—31no—
171C24×C4—31no—
172C24×C4—31no—
173C24×C4C2×D311yescharacteristic
174#553—3256no—
175C2×#126—324no—
176C2×#126—324no—
177C2×#125—324no—
178C2×#123—324no—
179C2×#123C2×D3124yescomplemented
180C2×#121—324no—
181C2×#121—324no—
182C2×#121—324no—
183C2×#121—324no—
184C2×C4×D4—324no—
185C2×C4×D4—324no—
186C2×C4×D4—324no—
187C2×C4×D4—324no—
188C2×#117—324no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4—31no—
195C22×C4⋊C4—31no—
196C22×C4⋊C4—31no—
197C22×C4⋊C4—324no—
198C22×C4⋊C4C2×D311yescharacteristic
199C22×C4⋊C4C2×D311yescharacteristic
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4C2×D311yescharacteristic
208C22×C22⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C42—31no—
211C22×C42—31no—
212C22×C42—31no—
213C24×C3—24no—
214C24×C3—24no—
215C24×C3—24no—
216C24×C3—24no—
217C24×C3—24no—
218C24×C3—24no—
219C24×C3C2416yes—
220C24×C3C2416yes—
221C24×C3C2411yescharacteristic
222C23×D3—24no—
223C23×D3—24no—
224C23×D3—24no—
225C23×D3—24no—
226C23×D3—24no—
227C23×D3#4118yes—
228C23×D3C2416yes—
229C23×D3C2416yes—
230C2×C3×D4—424no—
231C2×C3×D4C24116yes—
232C22×C3×C4—24no—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C22×C3×C4—24no—
236C22×C3×C4—24no—
237C22×C3×C4—424no—
238C22×C3×C4C2416yes—
239C22×C3×C4C2416yes—
240C22×C3×C4C2416yes—
241C22×C3×C4C2416yes—
242C22×C3×C4C2416yes—
243C22×C3×C4C24116yes—
244C2×#67—248no—
245C2×#67—248no—
246C2×#67—248no—
247C2×#67—424no—
248C2×#67C24116yes—
249C2×#67C24116yes—
250C2×#67C24116yes—
251C2×#67C24116yes—
252C22×Dic3—24no—
253C22×Dic3—24no—
254C22×Dic3—24no—
255C22×Dic3—24no—
256C22×Dic3—24no—
257C22×Dic3—248no—
258C22×Dic3#4118yes—
259C22×Dic3C24116yes—
260C22×Dic3C2416yes—
261C22×Dic3C2416yes—
262C22×Dic3C2416yes—
263C22×Dic3C2416yes—
264C22×Dic3C2416yes—
265C22×Dic3C2416yes—
266C2×D12—248no—
267C2×D12C24116yes—
268C2×C4×D3—248no—
269C2×C4×D3—424no—
270C2×C4×D3—424no—
271C2×C4×D3—424no—
272C2×C4×D3C24116yes—
273C2×C4×D3C24116yes—
274C2×C4×D3C24116yes—
275C2×C4×D3C24116yes—
276C3×C4⋊C4C24116yes—
277C3×C4⋊C4C24116yes—
278C3×C22⋊C4C24116yes—
279C3×C22⋊C4C24116yes—
280C3×C22⋊C4C24116yes—
281#217C24116yes—
282#217C24116yes—
283#217C24116yes—
284(C2×D3)⋊C4C24116yes—
285(C2×D3)⋊C4C24116yes—
286(C2×D3)⋊C4C24116yes—
287(C2×D3)⋊C4C24116yes—
288C4⋊Dic3C24116yes—
289C4⋊Dic3C24116yes—
290Dic3⋊C4C24116yes—
291Dic3⋊C4C24116yes—
292Dic3⋊C4C24116yes—
293Dic3⋊C4C24116yes—
294Dic3⋊C4C24116yes—
295Dic3⋊C4C24116yes—
296C4×Dic3C24116yes—
297C4×Dic3C24116yes—
298C4×Dic3C24116yes—
299C25—31no—
300C25—31no—
301C25C22×D311yescharacteristic
302C25C22×D311yescharacteristic
303C22×D4—312no—
304C22×D4—312no—
305C22×D4—312no—
306C22×D4—312no—
307C22×D4—312no—
308C22×D4—44no—
309C22×D4—68no—
310C22×D4—68no—
311C22×D4—68no—
312C22×D4—68no—
313C22×D4—124no—
314C22×D4C22×D3112yes—
315C23×C4—31no—
316C23×C4—312no—
317C23×C4—31no—
318C23×C4—31no—
319C23×C4—31no—
320C23×C4—31no—
321C23×C4—31no—
322C23×C4—312no—
323C23×C4—312no—
324C23×C4—312no—
325C23×C4—312no—
326C23×C4—44no—
327C23×C4—68no—
328C23×C4—68no—
329C23×C4—124no—
330C23×C4—124no—
331C23×C4—124no—
332C23×C4C22×D311yescharacteristic
333C23×C4C22×D311yescharacteristic
334C23×C4C22×D311yescharacteristic
335C23×C4C22×D311yescharacteristic
336C23×C4C22×D311yescharacteristic
337C23×C4C22×D3112yes—
338#126—364no—
339#126—364no—
340#125—364no—
341#123—364no—
342#123C22×D3164yescomplemented
343#121—364no—
344#121—364no—
345#121—364no—
346#121—364no—
347C4×D4—364no—
348C4×D4—364no—
349C4×D4—364no—
350C4×D4—364no—
351#117—364no—
352C2×C4⋊C4—312no—
353C2×C4⋊C4—312no—
354C2×C4⋊C4—312no—
355C2×C4⋊C4—312no—
356C2×C4⋊C4—312no—
357C2×C4⋊C4—312no—
358C2×C4⋊C4—312no—
359C2×C4⋊C4—312no—
360C2×C4⋊C4—364no—
361C2×C4⋊C4C22×D3112yes—
362C2×C4⋊C4C22×D3112yes—
363C2×C22⋊C4—312no—
364C2×C22⋊C4—312no—
365C2×C22⋊C4—312no—
366C2×C22⋊C4—312no—
367C2×C22⋊C4—312no—
368C2×C22⋊C4—312no—
369C2×C22⋊C4—312no—
370C2×C22⋊C4C22×D3112yes—
371C2×C22⋊C4C22×D3112yes—
372C2×C22⋊C4C22×D3112yes—
373C2×C42—312no—
374C2×C42—312no—
375C2×C42—312no—
376C23×C3—212no—
377C23×C3—212no—
378C23×C3—212no—
379C23×C3—212no—
380C23×C3—212no—
381C23×C3—212no—
382C23×C3—416no—
383C23×C3—416no—
384C23×C3C2×#4114yes—
385C23×C3C2×#4114yes—
386C23×C3H(5,𝔽2)14yes—
387C23×C3C2514yes—
388C23×C3C2514yes—
389C23×C3C2513yes—
390C22×D3—232no—
391C22×D3—212no—
392C22×D3—212no—
393C22×D3—212no—
394C22×D3—212no—
395C22×D3—212no—
396C22×D3—416no—
397C22×D3C2×#41124yes—
398C22×D3C2514yes—
399C22×D3C2514yes—
400C3×D4—416no—
401C2×C3×C4—212no—
402C2×C3×C4—212no—
403C2×C3×C4—212no—
404C2×C3×C4—212no—
405C2×C3×C4—212no—
406C2×C3×C4—416no—
407C2×C3×C4C2514yes—
408C2×C3×C4C2514yes—
409C2×C3×C4C2514yes—
410C2×C3×C4C2514yes—
411C2×C3×C4C2514yes—
412#67—232no—
413#67—232no—
414#67—232no—
415#67—416no—
416C2×Dic3—212no—
417C2×Dic3—212no—
418C2×Dic3—212no—
419C2×Dic3—212no—
420C2×Dic3—212no—
421C2×Dic3—232no—
422C2×Dic3C2×#41124yes—
423C2×Dic3C2514yes—
424C2×Dic3C2514yes—
425C2×Dic3C2514yes—
426C2×Dic3C2514yes—
427C2×Dic3C2514yes—
428C2×Dic3C2514yes—
429D12—232no—
430C4×D3—232no—
431C4×D3—416no—
432C4×D3—416no—
433C4×D3—416no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24—24no—
439C24—24no—
440C24—38no—
441C24—36no—
442C24—36no—
443C24—64no—
444C24—64no—
445C24—64no—
446C24—64no—
447C24—64no—
448C24C23×D316yes—
449C24C23×D316yes—
450C24C23×D311yescharacteristic
451C2×D4—316no—
452C2×D4—316no—
453C2×D4—316no—
454C2×D4—316no—
455C2×D4—316no—
456C2×D4—424no—
457C2×D4—648no—
458C2×D4—648no—
459C2×D4—648no—
460C2×D4—648no—
461C2×D4—1224no—
462C2×D4C23×D3116yes—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—38no—
469C22×C4—36no—
470C22×C4—36no—
471C22×C4—36no—
472C22×C4—36no—
473C22×C4—36no—
474C22×C4—36no—
475C22×C4—316no—
476C22×C4—316no—
477C22×C4—316no—
478C22×C4—316no—
479C22×C4—316no—
480C22×C4—424no—
481C22×C4—648no—
482C22×C4—648no—
483C22×C4—64no—
484C22×C4—64no—
485C22×C4—64no—
486C22×C4—64no—
487C22×C4—64no—
488C22×C4—1224no—
489C22×C4—1224no—
490C22×C4—1224no—
491C22×C4C23×D316yes—
492C22×C4C23×D316yes—
493C22×C4C23×D316yes—
494C22×C4C23×D316yes—
495C22×C4C23×D316yes—
496C22×C4C23×D3116yes—
497C4⋊C4—316no—
498C4⋊C4—316no—
499C4⋊C4—316no—
500C4⋊C4—316no—
501C4⋊C4—316no—
502C4⋊C4—316no—
503C4⋊C4—316no—
504C4⋊C4—316no—
505C4⋊C4C23×D3116yes—
506C4⋊C4C23×D3116yes—
507C22⋊C4—316no—
508C22⋊C4—316no—
509C22⋊C4—316no—
510C22⋊C4—316no—
511C22⋊C4—316no—
512C22⋊C4—316no—
513C22⋊C4—316no—
514C22⋊C4C23×D3116yes—
515C22⋊C4C23×D3116yes—
516C22⋊C4C23×D3116yes—
517C42—316no—
518C42—316no—
519C42—316no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—24no—
523C22×C3—24no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—424no—
527C22×C3—424no—
528C22×C3#553116yescomplemented
529C22×C3C22×#4116yes—
530C22×C3C22×#4116yes—
531C22×C3C2×H(5,𝔽2)16yes—
532C22×C3C2611yescharacteristic
533C2×D3—24no—
534C2×D3—24no—
535C2×D3—248no—
536C2×D3—24no—
537C2×D3—24no—
538C2×D3—24no—
539C2×D3—424no—
540C2×D3C22×#4118yes—
541C3×C4—24no—
542C3×C4—24no—
543C3×C4—24no—
544C3×C4—24no—
545C3×C4—24no—
546Dic3—24no—
547Dic3—24no—
548Dic3—24no—
549Dic3—24no—
550Dic3—24no—
551Dic3C22×#4118yes—
552C23—212no—
553C23—212no—
554C23—212no—
555C23—212no—
556C23—212no—
557C23—212no—
558C23—324no—
559C23—34no—
560C23—34no—
561C23—416no—
562C23—416no—
563C23—632no—
564C23—612no—
565C23—612no—
566C23—612no—
567C23—612no—
568C23—612no—
569C23—1216no—
570C23#100414yes—
571C23D3×#4114yes—
572C23D3×#4114yes—
573C23C24×D314yes—
574C23C24×D314yes—
575C23C24×D313yes—
576D4—416no—
577D4—632no—
578D4—632no—
579D4—632no—
580D4—632no—
581D4—1216no—
582C2×C4—212no—
583C2×C4—212no—
584C2×C4—212no—
585C2×C4—212no—
586C2×C4—212no—
587C2×C4—324no—
588C2×C4—34no—
589C2×C4—34no—
590C2×C4—34no—
591C2×C4—34no—
592C2×C4—34no—
593C2×C4—34no—
594C2×C4—416no—
595C2×C4—632no—
596C2×C4—632no—
597C2×C4—612no—
598C2×C4—612no—
599C2×C4—612no—
600C2×C4—612no—
601C2×C4—612no—
602C2×C4—1216no—
603C2×C4—1216no—
604C2×C4—1216no—
605C2×C4C24×D314yes—
606C2×C4C24×D314yes—
607C2×C4C24×D314yes—
608C2×C4C24×D314yes—
609C2×C4C24×D314yes—
610C2×C3—44no—
611C2×C3—44no—
612C2×C3C2×#553112yescomplemented
613C2×C3C23×#4111yescharacteristic
614C2×C3C23×#4111yescharacteristic
615C2×C3C22×H(5,𝔽2)11yescharacteristic
616D3—28no—
617D3—44no—
618C22—24no—
619C22—24no—
620C22—24no—
621C22—24no—
622C22—24no—
623C22—24no—
624C22—38no—
625C22—424no—
626C22—424no—
627C22—64no—
628C22—64no—
629C22—648no—
630C22—64no—
631C22—64no—
632C22—64no—
633C22—1224no—
634C22#5661116yesdirect product factor
635C22C2×#100416yes—
636C22C2×D3×#4116yes—
637C22C2×D3×#4116yes—
638C22C25×D311yescharacteristic
639C4—24no—
640C4—24no—
641C4—24no—
642C4—24no—
643C4—24no—
644C4—38no—
645C4—64no—
646C4—64no—
647C4—64no—
648C4—64no—
649C4—64no—
650C3C22×#55311yescharacteristic, complemented, Sylow
651C2—44no—
652C2—44no—
653C2—68no—
654C2—124no—
655C2C2×#5661112yesdirect product factor
656C2C22×#100411yescharacteristic
657C2C22×D3×#4111yescharacteristic
658C2C22×D3×#4111yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC22×C3C26
FrattiniC22C25×D3
FittingC22×C3×#123C2
socleC24×C3C24
hypercenterC22×#123D3
hypocenterC3C22×#553
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×C3×#123C2semidirect
2. C22×#938C2semidirect
3. C22×#939C2semidirect
4. C22×C4×#67C2semidirect
5. C22×C4×#67C2semidirect
6. C2×#5661C2direct (N × H)
7. C22×D3×C4⋊C4C2semidirect
8. C22×#898C2semidirect
9. C22×#889C2semidirect
10. C22×#893C2semidirect
11. C22×#883C2semidirect
12. C22×#884C2semidirect
13. C22×#884C2semidirect
14. C22×#879C2semidirect
15. C22×#67⋊C4C2semidirect
16. C22×#877C2semidirect
30. C2×C3×#123C22semidirect
39. C2×#939C22semidirect
40. C2×#938C22semidirect
41. C2×C4×#67C22semidirect
42. C2×C4×#67C22semidirect
58. #5661C22direct (N × H)
59. C2×#898C22semidirect
60. C2×#893C22semidirect
61. C2×D3×C4⋊C4C22semidirect
62. C2×#889C22semidirect
63. C2×#884C22semidirect
64. C2×#884C22semidirect
65. C2×#883C22semidirect
66. C2×#67⋊C4C22semidirect
67. C2×#879C22semidirect
68. C2×#877C22semidirect
74. C22×#123D3semidirect
124. C3×#123C23semidirect
133. #939C23semidirect
134. #938C23semidirect
135. C4×#67C23semidirect
136. C4×#67C23semidirect
152. #898C23semidirect
153. #893C23semidirect
154. D3×C4⋊C4C23semidirect
155. #889C23semidirect
156. #884C23semidirect
157. #884C23semidirect
158. #883C23semidirect
159. #67⋊C4C23semidirect
160. #879C23semidirect
161. #877C23semidirect
179. C2×#123C2×D3semidirect
342. #123C22×D3semidirect
528. C22×C3#553semidirect
612. C2×C3C2×#553semidirect
634. C22#5661direct (N × H)
650. C3C22×#553semidirect
655. C2C2×#5661direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1232
C22×#9382
C22×#9392
C22×C4×#672
C2×#56612
C22×D3×C4⋊C42
C22×#8982
C22×#8892
C22×#8932
C22×#8832
C22×#8842
C22×#8792
C22×#67⋊C42
C22×#8772
C22×#5533