Finite Group Databasebeta

← C3×#23955 #10642562

Subgroups — C3×#23955 #10642562

Order 768.

1234 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3494C211yesmaximal, characteristic
2C3×#3004C211yesmaximal, characteristic, complemented
3C2×C3×#419C211yesmaximal, characteristic, complemented
4C3×#2436C211yesmaximal, characteristic, complemented
5C3×#2028C212yesmaximal, complemented
6C3×#2004C212yesmaximal, complemented
7C3×#1900C211yesmaximal, characteristic, complemented
8C3×#1885C212yesmaximal, complemented
9C3×#1882C212yesmaximal, complemented
10C3×#1871C211yesmaximal, characteristic, complemented
11C3×#1826C211yesmaximal, characteristic, complemented
12#23955C311yesmaximal, characteristic, direct product factor, Sylow
13C23×C3×Q8C2211yescharacteristic
14C2×C3×#137C2212yes—
15C22×C3×M16C2211yescharacteristic
16C3×#555—21no—
17C3×#553—21no—
18C3×#553—21no—
19C3×#551—22no—
20C3×#547—21no—
21C3×#546—22no—
22C3×#544C2211yescharacteristic
23C3×#542—21no—
24C3×#540—21no—
25C3×#535C2211yescharacteristic
26C3×#532—21no—
27C3×#529—21no—
28C2×C3×#124C2212yes—
29C3×#525C2211yescharacteristic
30C2×C3×#121C2211yescharacteristic
31C3×#520C2211yescharacteristic
32C3×#518C2211yescharacteristic
33C2×C3×#117C2211yescharacteristic
34C3×#451—21no—
35C3×#451—21no—
36C3×#448—21no—
37C3×#448—21no—
38C2×C3×#104C2212yes—
39C3×#419—21no—
40C3×#419—21no—
41C3×#419C2212yes—
42C3×#419C2212yes—
43C3×#419C2212yes—
44C2×C3×#103—21no—
45C2×C3×#103—21no—
46C2×C3×#100C2212yes—
47C3×#407C2211yescharacteristic
48C3×#393—22no—
49C3×#391C2212yes—
50C3×#386—22no—
51C3×C4×C22⋊C4C2211yescharacteristic
52C3×#343C2212yes—
53C3×#339C2212yes—
54C3×#339C2212yes—
55C3×#339C2212yes—
56#3494C2×C311yescharacteristic
57#3004C2×C311yescharacteristic, complemented
58C2×#419C2×C311yescharacteristic, complemented
59#2436C2×C311yescharacteristic, complemented
60#2028C2×C312yescomplemented
61#2004C2×C312yescomplemented
62#1900C2×C311yescharacteristic, complemented
63#1885C2×C312yescomplemented
64#1882C2×C312yescomplemented
65#1871C2×C311yescharacteristic, complemented
66#1826C2×C311yescharacteristic, complemented
67C2×C3×#41—22no—
68C2×C3×#41C2311yescharacteristic
69C22×C3×Q8—21no—
70C22×C3×Q8—24no—
71C22×C3×Q8—21no—
72C22×C3×Q8—21no—
73C22×C3×Q8—21no—
74C22×C3×Q8—21no—
75C22×C3×Q8—42no—
76C22×C3×Q8C2312yes—
77C22×C3×D4D412yes—
78C22×C3×D4C2311yescharacteristic
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C3×#137—24no—
82C3×#137—42no—
83C2×C3×Q16—22no—
84C2×C3×SD16—22no—
85C2×C3×M16—21no—
86C2×C3×M16—42no—
87C2×C3×M16C2312yes—
88C2×C3×M16C2312yes—
89C22×C3×C8—21no—
90C3×C4⋊Q8—21no—
91C3×C4⋊Q8—21no—
92C3×#127—21no—
93C3×#126—22no—
94C3×#126—22no—
95C3×#125—21no—
96C3×#125—21no—
97C3×#124—22no—
98C3×#124—22no—
99C3×#124—21no—
100C3×#124—24no—
101C3×#124—42no—
102C3×#123—22no—
103C3×#123—22no—
104C3×#123—22no—
105C3×#123—22no—
106C3×#123—21no—
107C3×C22⋊Q8—22no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8D411yescharacteristic
110C3×C22⋊Q8D411yescharacteristic
111C3×#121—22no—
112C3×#121—22no—
113C3×#121—22no—
114C3×#121—21no—
115C3×#121—21no—
116C3×#121—21no—
117C3×#121—21no—
118C3×#121—21no—
119C3×#121—21no—
120C3×#121D411yescharacteristic
121C3×#121D411yescharacteristic
122C3×#120—21no—
123C3×#120—22no—
124C3×C4×Q8—21no—
125C3×C4×D4—22no—
126C3×C4×D4—22no—
127C3×C4×D4—21no—
128C3×C4×D4—22no—
129C3×C4×D4—21no—
130C3×C4×D4—21no—
131C3×C4×D4—21no—
132C3×C4×D4—21no—
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×#117—22no—
136C3×#117—21no—
137C3×#117—21no—
138C3×#117—21no—
139C3×#117D411yescharacteristic
140C3×#117D411yescharacteristic
141C3×#117C2311yescharacteristic
142C3×#117C2311yescharacteristic
143C3×#117C2311yescharacteristic
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4D411yescharacteristic
146C2×C3×C4⋊C4D411yescharacteristic
147C2×C3×C4⋊C4C2311yescharacteristic
148C2×C3×C22⋊C4—21no—
149C2×C3×C22⋊C4—22no—
150C2×C3×C22⋊C4—21no—
151C2×C3×C22⋊C4—24no—
152C2×C3×C22⋊C4D412yes—
153C2×C3×C42—21no—
154C2×C3×C42C2312yes—
155C3×#104—42no—
156C3×#103—22no—
157C3×#103—22no—
158C3×#103—22no—
159C3×#103—22no—
160C3×#103—22no—
161C3×#103—22no—
162C3×#100—42no—
163C3×C22⋊C8—21no—
164C3×C22⋊C8—21no—
165C3×#95—21no—
166C3×#95—24no—
167C23×Q8C22×C311yescharacteristic
168C2×#137C22×C312yes—
169C22×M16C22×C311yescharacteristic
170#555—21no—
171#553—21no—
172#553—21no—
173#551—22no—
174#547—21no—
175#546—22no—
176#544C22×C311yescharacteristic
177#542—21no—
178#540—21no—
179#535C22×C311yescharacteristic
180#532—21no—
181#529—21no—
182C2×#124C22×C312yes—
183#525C22×C311yescharacteristic
184C2×#121C22×C311yescharacteristic
185#520C22×C311yescharacteristic
186#518C22×C311yescharacteristic
187C2×#117C22×C311yescharacteristic
188#451—21no—
189#451—21no—
190#448—21no—
191#448—21no—
192C2×#104C22×C312yes—
193#419—21no—
194#419—21no—
195#419C22×C312yes—
196#419C22×C312yes—
197#419C22×C312yes—
198C2×#103—21no—
199C2×#103—21no—
200C2×#100C22×C312yes—
201#407C22×C311yescharacteristic
202#393—22no—
203#391C22×C312yes—
204#386—22no—
205C4×C22⋊C4C22×C311yescharacteristic
206#343C22×C312yes—
207#339C22×C312yes—
208#339C22×C312yes—
209#339C22×C312yes—
210C24×C3C2×D411yescharacteristic
211C24×C3C2×D412yes—
212C3×#41—22no—
213C3×#41—22no—
214C3×#41—84no—
215C2×C3×Q8—22no—
216C2×C3×Q8—22no—
217C2×C3×Q8—24no—
218C2×C3×Q8—24no—
219C2×C3×Q8—22no—
220C2×C3×Q8—22no—
221C2×C3×Q8—22no—
222C2×C3×Q8—22no—
223C2×C3×Q8—44no—
224C2×C3×Q8—44no—
225C2×C3×Q8—44no—
226C2×C3×Q8—42no—
227C2×C3×Q8—42no—
228C2×C3×Q8—41no—
229C2×C3×Q8—41no—
230C2×C3×Q8C2×D411yescharacteristic
231C2×C3×Q8#4114yescomplemented
232C2×C3×D4—21no—
233C2×C3×D4—22no—
234C2×C3×D4—21no—
235C2×C3×D4—22no—
236C2×C3×D4—22no—
237C2×C3×D4—21no—
238C2×C3×D4—22no—
239C2×C3×D4—21no—
240C2×C3×D4—21no—
241C2×C3×D4—22no—
242C2×C3×D4—22no—
243C2×C3×D4—44no—
244C2×C3×D4C2×D411yescharacteristic
245C22×C3×C4—22no—
246C22×C3×C4—22no—
247C22×C3×C4—21no—
248C22×C3×C4—22no—
249C22×C3×C4—22no—
250C22×C3×C4—22no—
251C22×C3×C4—22no—
252C22×C3×C4—21no—
253C22×C3×C4—21no—
254C22×C3×C4—22no—
255C22×C3×C4—44no—
256C22×C3×C4—41no—
257C22×C3×C4—41no—
258C22×C3×C4C2×D411yescharacteristic
259C22×C3×C4C2×D411yescharacteristic
260C22×C3×C4C2×D411yescharacteristic
261C22×C3×C4C2×D411yescharacteristic
262C22×C3×C4C2×D411yescharacteristic
263C22×C3×C4C2×D412yes—
264C22×C3×C4C2411yescharacteristic
265C3×Q16—44no—
266C3×SD16—44no—
267C3×M16—22no—
268C3×M16—22no—
269C3×M16—22no—
270C3×M16—22no—
271C3×M16—42no—
272C2×C3×C8—22no—
273C2×C3×C8—22no—
274C2×C3×C8—42no—
275C3×C4⋊C4—22no—
276C3×C4⋊C4—22no—
277C3×C4⋊C4—22no—
278C3×C4⋊C4—22no—
279C3×C4⋊C4—21no—
280C3×C4⋊C4—21no—
281C3×C4⋊C4—21no—
282C3×C4⋊C4—21no—
283C3×C4⋊C4—21no—
284C3×C4⋊C4—21no—
285C3×C4⋊C4C2×D411yescharacteristic
286C3×C4⋊C4C2×D411yescharacteristic
287C3×C4⋊C4C2×D411yescharacteristic
288C3×C4⋊C4C2×D411yescharacteristic
289C3×C4⋊C4C2×D411yescharacteristic
290C3×C4⋊C4C2×D411yescharacteristic
291C3×C22⋊C4—22no—
292C3×C22⋊C4—22no—
293C3×C22⋊C4—22no—
294C3×C22⋊C4—22no—
295C3×C22⋊C4—22no—
296C3×C22⋊C4—21no—
297C3×C22⋊C4—21no—
298C3×C22⋊C4—21no—
299C3×C22⋊C4—21no—
300C3×C22⋊C4—21no—
301C3×C22⋊C4—21no—
302C3×C22⋊C4—21no—
303C3×C22⋊C4—22no—
304C3×C22⋊C4—22no—
305C3×C22⋊C4—21no—
306C3×C22⋊C4—21no—
307C3×C22⋊C4—48no—
308C3×C22⋊C4—42no—
309C3×C42—22no—
310C3×C42—21no—
311C3×C42—21no—
312C3×C42—21no—
313C3×C42—21no—
314C3×C42—21no—
315C3×C42—22no—
316C3×C42—22no—
317C2×#41—22no—
318C2×#41C23×C311yescharacteristic
319C22×Q8—21no—
320C22×Q8—24no—
321C22×Q8—21no—
322C22×Q8—21no—
323C22×Q8—21no—
324C22×Q8—21no—
325C22×Q8—42no—
326C22×Q8C23×C312yes—
327C22×D4C3×D412yes—
328C22×D4C23×C311yescharacteristic
329C23×C4—21no—
330C23×C4C23×C311yescharacteristic
331#137—24no—
332#137—42no—
333C2×Q16—22no—
334C2×SD16—22no—
335C2×M16—21no—
336C2×M16—42no—
337C2×M16C23×C312yes—
338C2×M16C23×C312yes—
339C22×C8—21no—
340C4⋊Q8—21no—
341C4⋊Q8—21no—
342#127—21no—
343#126—22no—
344#126—22no—
345#125—21no—
346#125—21no—
347#124—22no—
348#124—22no—
349#124—21no—
350#124—24no—
351#124—42no—
352#123—22no—
353#123—22no—
354#123—22no—
355#123—22no—
356#123—21no—
357C22⋊Q8—22no—
358C22⋊Q8—22no—
359C22⋊Q8C3×D411yescharacteristic
360C22⋊Q8C3×D411yescharacteristic
361#121—22no—
362#121—22no—
363#121—22no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121—21no—
368#121—21no—
369#121—21no—
370#121C3×D411yescharacteristic
371#121C3×D411yescharacteristic
372#120—21no—
373#120—22no—
374C4×Q8—21no—
375C4×D4—22no—
376C4×D4—22no—
377C4×D4—21no—
378C4×D4—22no—
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—21no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385#117—22no—
386#117—21no—
387#117—21no—
388#117—21no—
389#117C3×D411yescharacteristic
390#117C3×D411yescharacteristic
391#117C23×C311yescharacteristic
392#117C23×C311yescharacteristic
393#117C23×C311yescharacteristic
394C2×C4⋊C4—21no—
395C2×C4⋊C4C3×D411yescharacteristic
396C2×C4⋊C4C3×D411yescharacteristic
397C2×C4⋊C4C23×C311yescharacteristic
398C2×C22⋊C4—21no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—24no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4C3×D412yes—
403C2×C42—21no—
404C2×C42C23×C312yes—
405#104—42no—
406#103—22no—
407#103—22no—
408#103—22no—
409#103—22no—
410#103—22no—
411#103—22no—
412#100—42no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415#95—21no—
416#95—24no—
417C23×C3—22no—
418C23×C3—22no—
419C23×C3—22no—
420C23×C3—21no—
421C23×C3—24no—
422C23×C3—41no—
423C23×C3—42no—
424C23×C3—42no—
425C23×C3#12011yescharacteristic
426C23×C3#12011yescharacteristic
427C23×C3C22×D411yescharacteristic
428C3×Q8—24no—
429C3×Q8—24no—
430C3×Q8—22no—
431C3×Q8—44no—
432C3×Q8—44no—
433C3×Q8—42no—
434C3×Q8—42no—
435C3×Q8—82no—
436C3×D4—22no—
437C3×D4—42no—
438C3×D4—44no—
439C3×D4—42no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—42no—
443C3×D4—81no—
444C3×D4—82no—
445C3×D4—82no—
446C3×D4—82no—
447C2×C3×C4—22no—
448C2×C3×C4—21no—
449C2×C3×C4—21no—
450C2×C3×C4—21no—
451C2×C3×C4—21no—
452C2×C3×C4—22no—
453C2×C3×C4—22no—
454C2×C3×C4—21no—
455C2×C3×C4—21no—
456C2×C3×C4—21no—
457C2×C3×C4—21no—
458C2×C3×C4—21no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—22no—
462C2×C3×C4—24no—
463C2×C3×C4—44no—
464C2×C3×C4—44no—
465C2×C3×C4—42no—
466C2×C3×C4—42no—
467C2×C3×C4—42no—
468C2×C3×C4—41no—
469C2×C3×C4—41no—
470C2×C3×C4—42no—
471C2×C3×C4—42no—
472C2×C3×C4—42no—
473C2×C3×C4—42no—
474C2×C3×C4—81no—
475C2×C3×C4—82no—
476C2×C3×C4—82no—
477C2×C3×C4—82no—
478C2×C3×C4#12011yescharacteristic
479C2×C3×C4#12011yescharacteristic
480C2×C3×C4C22×D411yescharacteristic
481C2×C3×C4C22×D411yescharacteristic
482C2×C3×C4C2×#4112yes—
483C2×C3×C4H(5,𝔽2)12yes—
484C3×C8—42no—
485C3×C8—42no—
486C24C2×C3×D411yescharacteristic
487C24C2×C3×D412yes—
488#41—22no—
489#41—22no—
490#41—84no—
491C2×Q8—22no—
492C2×Q8—22no—
493C2×Q8—24no—
494C2×Q8—24no—
495C2×Q8—22no—
496C2×Q8—22no—
497C2×Q8—22no—
498C2×Q8—22no—
499C2×Q8—44no—
500C2×Q8—44no—
501C2×Q8—44no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—41no—
505C2×Q8—41no—
506C2×Q8C2×C3×D411yescharacteristic
507C2×Q8C3×#4114yescomplemented
508C2×D4—21no—
509C2×D4—22no—
510C2×D4—21no—
511C2×D4—22no—
512C2×D4—22no—
513C2×D4—21no—
514C2×D4—22no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—44no—
520C2×D4C2×C3×D411yescharacteristic
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—21no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—44no—
532C22×C4—41no—
533C22×C4—41no—
534C22×C4C2×C3×D411yescharacteristic
535C22×C4C2×C3×D411yescharacteristic
536C22×C4C2×C3×D411yescharacteristic
537C22×C4C2×C3×D411yescharacteristic
538C22×C4C2×C3×D411yescharacteristic
539C22×C4C2×C3×D412yes—
540C22×C4C24×C311yescharacteristic
541Q16—44no—
542SD16—44no—
543M16—22no—
544M16—22no—
545M16—22no—
546M16—22no—
547M16—42no—
548C2×C8—22no—
549C2×C8—22no—
550C2×C8—42no—
551C4⋊C4—22no—
552C4⋊C4—22no—
553C4⋊C4—22no—
554C4⋊C4—22no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4C2×C3×D411yescharacteristic
562C4⋊C4C2×C3×D411yescharacteristic
563C4⋊C4C2×C3×D411yescharacteristic
564C4⋊C4C2×C3×D411yescharacteristic
565C4⋊C4C2×C3×D411yescharacteristic
566C4⋊C4C2×C3×D411yescharacteristic
567C22⋊C4—22no—
568C22⋊C4—22no—
569C22⋊C4—22no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C22⋊C4—21no—
573C22⋊C4—21no—
574C22⋊C4—21no—
575C22⋊C4—21no—
576C22⋊C4—21no—
577C22⋊C4—21no—
578C22⋊C4—21no—
579C22⋊C4—22no—
580C22⋊C4—22no—
581C22⋊C4—21no—
582C22⋊C4—21no—
583C22⋊C4—48no—
584C22⋊C4—42no—
585C42—22no—
586C42—21no—
587C42—21no—
588C42—21no—
589C42—21no—
590C42—21no—
591C42—22no—
592C42—22no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3—21no—
600C22×C3—44no—
601C22×C3—41no—
602C22×C3—42no—
603C22×C3—41no—
604C22×C3—42no—
605C22×C3—42no—
606C22×C3—41no—
607C22×C3—84no—
608C22×C3#45512yes—
609C22×C3C2×#12011yescharacteristic
610C22×C3#54612yes—
611C3×C4—21no—
612C3×C4—21no—
613C3×C4—44no—
614C3×C4—41no—
615C3×C4—41no—
616C3×C4—41no—
617C3×C4—42no—
618C3×C4—41no—
619C3×C4—41no—
620C3×C4—41no—
621C3×C4—41no—
622C3×C4—82no—
623C3×C4#52511yescharacteristic
624C3×C4#53511yescharacteristic
625C3×C4#54612yes—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—21no—
630C23—24no—
631C23—41no—
632C23—42no—
633C23—42no—
634C23C3×#12011yescharacteristic
635C23C3×#12011yescharacteristic
636C23C22×C3×D411yescharacteristic
637Q8—24no—
638Q8—24no—
639Q8—22no—
640Q8—44no—
641Q8—44no—
642Q8—42no—
643Q8—42no—
644Q8—82no—
645D4—22no—
646D4—44no—
647D4—42no—
648D4—42no—
649D4—41no—
650D4—41no—
651D4—42no—
652D4—82no—
653D4—81no—
654D4—82no—
655D4—82no—
656C2×C4—22no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—22no—
671C2×C4—24no—
672C2×C4—44no—
673C2×C4—44no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—81no—
684C2×C4—82no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4C3×#12011yescharacteristic
688C2×C4C3×#12011yescharacteristic
689C2×C4C22×C3×D411yescharacteristic
690C2×C4C22×C3×D411yescharacteristic
691C2×C4C2×C3×#4112yes—
692C2×C4C3×H(5,𝔽2)12yes—
693C8—42no—
694C8—42no—
695C2×C3—22no—
696C2×C3—22no—
697C2×C3—41no—
698C2×C3—81no—
699C2×C3—82no—
700C2×C3#240411yescharacteristic
701C2×C3C2×#45511yescharacteristic
702C2×C3#302211yescharacteristic
703C22—21no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—21no—
708C22—21no—
709C22—21no—
710C22—44no—
711C22—41no—
712C22—42no—
713C22—41no—
714C22—42no—
715C22—42no—
716C22—41no—
717C22—84no—
718C22C3×#45512yes—
719C22C2×C3×#12011yescharacteristic
720C22C3×#54612yes—
721C4—21no—
722C4—21no—
723C4—44no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—42no—
728C4—41no—
729C4—41no—
730C4—41no—
731C4—41no—
732C4—82no—
733C4C3×#52511yescharacteristic
734C4C3×#53511yescharacteristic
735C4C3×#54612yes—
736C3#2395511yescharacteristic, direct product factor, Sylow
737C2—22no—
738C2—22no—
739C2—41no—
740C2—82no—
741C2—81no—
742C2C3×#240411yescharacteristic
743C2C2×C3×#45511yescharacteristic
744C2C3×#302211yescharacteristic
subgroupG/H
center, socleC22×C3C2×#120
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC3×#3494C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#3004C2semidirect
3. C2×C3×#419C2semidirect
4. C3×#2436C2semidirect
5. C3×#2028C2semidirect
6. C3×#2004C2semidirect
7. C3×#1900C2semidirect
8. C3×#1885C2semidirect
9. C3×#1882C2semidirect
10. C3×#1871C2semidirect
11. C3×#1826C2semidirect
12. #23955C3direct (N × H)
57. #3004C2×C3semidirect
58. C2×#419C2×C3semidirect
59. #2436C2×C3semidirect
60. #2028C2×C3semidirect
61. #2004C2×C3semidirect
62. #1900C2×C3semidirect
63. #1885C2×C3semidirect
64. #1882C2×C3semidirect
65. #1871C2×C3semidirect
66. #1826C2×C3semidirect
231. C2×C3×Q8#41semidirect
507. C2×Q8C3×#41semidirect
736. C3#23955direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#34942
C3×#30042
C2×C3×#4192
C3×#24362
C3×#20282
C3×#20042
C3×#19002
C3×#18852
C3×#18822
C3×#18712
C3×#18262
#239553