Finite Group Databasebeta

← C3×#23927 #10642534

Subgroups — C3×#23927 #10642534

Order 768.

1760 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#537C211yesmaximal, characteristic
2C2×C3×#536C211yesmaximal, characteristic, complemented
3C2×C3×#452C212yesmaximal, complemented
4C2×C3×#451C211yesmaximal, characteristic, complemented
5C2×C3×#448C211yesmaximal, characteristic, complemented
6C3×#2001C212yesmaximal, complemented
7C3×#2000C212yesmaximal, complemented
8C3×#1875C211yesmaximal, characteristic, complemented
9C3×#1873C211yesmaximal, characteristic, complemented
10C3×#1872C212yesmaximal, complemented
11C3×#1780C211yesmaximal, characteristic, complemented
12#23927C311yesmaximal, characteristic, direct product factor, Sylow
13C22×C3×#41C2211yescharacteristic
14C22×C3×#41C2211yescharacteristic
15C23×C3×Q8C2211yescharacteristic
16C22×C3×Q16C2212yes—
17C22×C3×SD16C2212yes—
18C3×#537—24no—
19C3×#537—24no—
20C3×#536—28no—
21C2×C3×C4⋊Q8—21no—
22C2×C3×#124—21no—
23C2×C3×#123—21no—
24C2×C3×#123—21no—
25C2×C3×C22⋊Q8—21no—
26C2×C3×C22⋊Q8C2212yes—
27C2×C3×C22⋊Q8C2211yescharacteristic
28C2×C3×C22⋊Q8C2211yescharacteristic
29C2×C3×C22⋊Q8C2212yes—
30C2×C3×#121—21no—
31C2×C3×#121—21no—
32C2×C3×#121—21no—
33C2×C3×#121C2211yescharacteristic
34C2×C3×#121C2211yescharacteristic
35C2×C3×#117C2211yescharacteristic
36C22×C3×C4⋊C4C2211yescharacteristic
37C3×#452—28no—
38C3×#451—24no—
39C3×#448—24no—
40C2×C3×#103C2212yes—
41C2×C3×#103C2212yes—
42C2×C3×#103C2212yes—
43C2×C3×#102C2212yes—
44C2×C3×C22⋊C8C2211yescharacteristic
45C2×C3×C22⋊C8C2211yescharacteristic
46C2×C3×C22⋊C8C2212yes—
47C2×C3×C22⋊C8C2212yes—
48C3×#340C2212yes—
49C3×#340C2212yes—
50C2×#537C2×C311yescharacteristic
51C2×#536C2×C311yescharacteristic, complemented
52C2×#452C2×C312yescomplemented
53C2×#451C2×C311yescharacteristic, complemented
54C2×#448C2×C311yescharacteristic, complemented
55#2001C2×C312yescomplemented
56#2000C2×C312yescomplemented
57#1875C2×C311yescharacteristic, complemented
58#1873C2×C311yescharacteristic, complemented
59#1872C2×C312yescomplemented
60#1780C2×C311yescharacteristic, complemented
61C2×C3×#41—22no—
62C2×C3×#41—22no—
63C2×C3×#41—24no—
64C2×C3×#41—22no—
65C2×C3×#41—22no—
66C2×C3×#41—24no—
67C2×C3×#41—42no—
68C2×C3×#41—42no—
69C22×C3×Q8—24no—
70C22×C3×Q8—21no—
71C22×C3×Q8—22no—
72C22×C3×Q8—22no—
73C22×C3×Q8—42no—
74C22×C3×Q8D411yescharacteristic
75C22×C3×Q8C2312yes—
76C22×C3×Q8C2311yescharacteristic
77C22×C3×D4—21no—
78C22×C3×D4—21no—
79C22×C3×D4—21no—
80C22×C3×D4D411yescharacteristic
81C22×C3×D4D411yescharacteristic
82C22×C3×D4D411yescharacteristic
83C22×C3×D4C2311yescharacteristic
84C23×C3×C4—21no—
85C23×C3×C4—21no—
86C23×C3×C4—21no—
87C23×C3×C4C2311yescharacteristic
88C23×C3×C4C2311yescharacteristic
89C23×C3×C4C2311yescharacteristic
90C2×C3×Q16—24no—
91C2×C3×Q16—24no—
92C2×C3×Q16—42no—
93C2×C3×SD16—24no—
94C2×C3×SD16—24no—
95C2×C3×SD16—42no—
96C22×C3×C8C2312yes—
97C22×C3×C8C2312yes—
98C3×C4⋊Q8—28no—
99C3×#124—28no—
100C3×#123—28no—
101C3×#123—28no—
102C3×C22⋊Q8—28no—
103C3×C22⋊Q8—24no—
104C3×C22⋊Q8—22no—
105C3×C22⋊Q8—24no—
106C3×C22⋊Q8—22no—
107C3×C22⋊Q8—24no—
108C3×C22⋊Q8—22no—
109C3×C22⋊Q8D414yes—
110C3×C22⋊Q8D418yescomplemented
111C3×#121—28no—
112C3×#121—28no—
113C3×#121—28no—
114C3×#121—22no—
115C3×#121—22no—
116C3×#121—22no—
117C3×#121D414yes—
118C3×#117—24no—
119C2×C3×C4⋊C4—21no—
120C2×C3×C4⋊C4—21no—
121C2×C3×C4⋊C4—21no—
122C2×C3×C4⋊C4—22no—
123C2×C3×C4⋊C4—22no—
124C2×C3×C4⋊C4—22no—
125C2×C3×C4⋊C4—22no—
126C2×C3×C4⋊C4C2312yes—
127C2×C3×C4⋊C4C2311yescharacteristic
128C2×C3×C4⋊C4C2311yescharacteristic
129C2×C3×C22⋊C4—21no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—21no—
132C2×C3×C22⋊C4—22no—
133C2×C3×C22⋊C4—22no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C22⋊C4—21no—
136C2×C3×C42—21no—
137C3×#103—24no—
138C3×#103—24no—
139C3×#103—24no—
140C3×#102—24no—
141C3×C22⋊C8—22no—
142C3×C22⋊C8—22no—
143C3×C22⋊C8—24no—
144C3×C22⋊C8—42no—
145C22×#41C22×C311yescharacteristic
146C22×#41C22×C311yescharacteristic
147C23×Q8C22×C311yescharacteristic
148C22×Q16C22×C312yes—
149C22×SD16C22×C312yes—
150#537—24no—
151#537—24no—
152#536—28no—
153C2×C4⋊Q8—21no—
154C2×#124—21no—
155C2×#123—21no—
156C2×#123—21no—
157C2×C22⋊Q8—21no—
158C2×C22⋊Q8C22×C312yes—
159C2×C22⋊Q8C22×C311yescharacteristic
160C2×C22⋊Q8C22×C311yescharacteristic
161C2×C22⋊Q8C22×C312yes—
162C2×#121—21no—
163C2×#121—21no—
164C2×#121—21no—
165C2×#121C22×C311yescharacteristic
166C2×#121C22×C311yescharacteristic
167C2×#117C22×C311yescharacteristic
168C22×C4⋊C4C22×C311yescharacteristic
169#452—28no—
170#451—24no—
171#448—24no—
172C2×#103C22×C312yes—
173C2×#103C22×C312yes—
174C2×#103C22×C312yes—
175C2×#102C22×C312yes—
176C2×C22⋊C8C22×C312yes—
177C2×C22⋊C8C22×C311yescharacteristic
178C2×C22⋊C8C22×C311yescharacteristic
179C2×C22⋊C8C22×C312yes—
180#340C22×C312yes—
181#340C22×C312yes—
182C24×C3—21no—
183C24×C3C2×D411yescharacteristic
184C24×C3C2×D411yescharacteristic
185C24×C3C2×D411yescharacteristic
186C3×#41—48no—
187C3×#41—48no—
188C3×#41—48no—
189C3×#41—48no—
190C2×C3×Q8—24no—
191C2×C3×Q8—22no—
192C2×C3×Q8—22no—
193C2×C3×Q8—22no—
194C2×C3×Q8—21no—
195C2×C3×Q8—22no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8—22no—
200C2×C3×Q8—22no—
201C2×C3×Q8—41no—
202C2×C3×Q8—48no—
203C2×C3×Q8—48no—
204C2×C3×Q8—42no—
205C2×C3×Q8—42no—
206C2×C3×Q8C2×D412yes—
207C2×C3×Q8C2×D414yes—
208C2×C3×D4—24no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—24no—
214C2×C3×D4—24no—
215C2×C3×D4—22no—
216C2×C3×D4—22no—
217C2×C3×D4—22no—
218C2×C3×D4—21no—
219C2×C3×D4—22no—
220C2×C3×D4—41no—
221C2×C3×D4—41no—
222C2×C3×D4—41no—
223C2×C3×D4—42no—
224C2×C3×D4—42no—
225C2×C3×D4—82no—
226C2×C3×D4—82no—
227C2×C3×D4C2×D412yes—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—22no—
233C22×C3×C4—24no—
234C22×C3×C4—24no—
235C22×C3×C4—22no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—22no—
240C22×C3×C4—24no—
241C22×C3×C4—21no—
242C22×C3×C4—21no—
243C22×C3×C4—22no—
244C22×C3×C4—22no—
245C22×C3×C4—42no—
246C22×C3×C4—42no—
247C22×C3×C4—42no—
248C22×C3×C4—42no—
249C22×C3×C4—82no—
250C22×C3×C4C2×D411yescharacteristic
251C22×C3×C4C2×D411yescharacteristic
252C22×C3×C4C2×D411yescharacteristic
253C22×C3×C4C2×D412yes—
254C22×C3×C4C2×D412yes—
255C22×C3×C4C2×D414yes—
256C22×C3×C4C2411yescharacteristic
257C3×Q16—48no—
258C3×SD16—48no—
259C2×C3×C8—22no—
260C2×C3×C8—22no—
261C2×C3×C8—22no—
262C2×C3×C8—22no—
263C2×C3×C8—22no—
264C2×C3×C8—22no—
265C3×C4⋊C4—24no—
266C3×C4⋊C4—24no—
267C3×C4⋊C4—28no—
268C3×C4⋊C4—24no—
269C3×C4⋊C4—28no—
270C3×C4⋊C4—21no—
271C3×C4⋊C4—21no—
272C3×C4⋊C4—22no—
273C3×C4⋊C4C2×D414yes—
274C3×C4⋊C4C2×D412yes—
275C3×C4⋊C4C2×D412yes—
276C3×C22⋊C4—24no—
277C3×C22⋊C4—24no—
278C3×C22⋊C4—24no—
279C3×C22⋊C4—28no—
280C3×C22⋊C4—24no—
281C3×C22⋊C4—28no—
282C3×C22⋊C4—24no—
283C3×C42—24no—
284C2×#41—22no—
285C2×#41—22no—
286C2×#41—24no—
287C2×#41—22no—
288C2×#41—22no—
289C2×#41—24no—
290C2×#41—42no—
291C2×#41—42no—
292C22×Q8—24no—
293C22×Q8—21no—
294C22×Q8—22no—
295C22×Q8—22no—
296C22×Q8—42no—
297C22×Q8C3×D411yescharacteristic
298C22×Q8C23×C312yes—
299C22×Q8C23×C311yescharacteristic
300C22×D4—21no—
301C22×D4—21no—
302C22×D4—21no—
303C22×D4C3×D411yescharacteristic
304C22×D4C3×D411yescharacteristic
305C22×D4C3×D411yescharacteristic
306C22×D4C23×C311yescharacteristic
307C23×C4—21no—
308C23×C4—21no—
309C23×C4—21no—
310C23×C4C23×C311yescharacteristic
311C23×C4C23×C311yescharacteristic
312C23×C4C23×C311yescharacteristic
313C2×Q16—24no—
314C2×Q16—24no—
315C2×Q16—42no—
316C2×SD16—24no—
317C2×SD16—24no—
318C2×SD16—42no—
319C22×C8C23×C312yes—
320C22×C8C23×C312yes—
321C4⋊Q8—28no—
322#124—28no—
323#123—28no—
324#123—28no—
325C22⋊Q8—28no—
326C22⋊Q8—24no—
327C22⋊Q8—22no—
328C22⋊Q8—24no—
329C22⋊Q8—22no—
330C22⋊Q8—24no—
331C22⋊Q8—22no—
332C22⋊Q8C3×D414yes—
333C22⋊Q8C3×D418yescomplemented
334#121—28no—
335#121—28no—
336#121—28no—
337#121—22no—
338#121—22no—
339#121—22no—
340#121C3×D414yes—
341#117—24no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—21no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—22no—
346C2×C4⋊C4—22no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4C23×C311yescharacteristic
350C2×C4⋊C4C23×C311yescharacteristic
351C2×C4⋊C4C23×C312yes—
352C2×C22⋊C4—21no—
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—22no—
356C2×C22⋊C4—22no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C42—21no—
360#103—24no—
361#103—24no—
362#103—24no—
363#102—24no—
364C22⋊C8—22no—
365C22⋊C8—22no—
366C22⋊C8—24no—
367C22⋊C8—42no—
368C23×C3—21no—
369C23×C3—21no—
370C23×C3—21no—
371C23×C3—21no—
372C23×C3—22no—
373C23×C3—22no—
374C23×C3—22no—
375C23×C3—22no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—22no—
379C23×C3—21no—
380C23×C3—22no—
381C23×C3—22no—
382C23×C3—41no—
383C23×C3—41no—
384C23×C3—42no—
385C23×C3—42no—
386C23×C3#12012yes—
387C23×C3#12012yes—
388C23×C3C22×D411yescharacteristic
389C3×Q8—24no—
390C3×Q8—24no—
391C3×Q8—24no—
392C3×Q8—44no—
393C3×Q8—48no—
394C3×Q8—42no—
395C3×Q8—42no—
396C3×Q8—42no—
397C3×D4—24no—
398C3×D4—44no—
399C3×D4—44no—
400C3×D4—44no—
401C3×D4—48no—
402C3×D4—42no—
403C3×D4—84no—
404C3×D4—84no—
405C2×C3×C4—21no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—24no—
412C2×C3×C4—24no—
413C2×C3×C4—24no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—22no—
417C2×C3×C4—24no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—48no—
422C2×C3×C4—48no—
423C2×C3×C4—41no—
424C2×C3×C4—42no—
425C2×C3×C4—41no—
426C2×C3×C4—42no—
427C2×C3×C4—42no—
428C2×C3×C4—42no—
429C2×C3×C4—42no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4—42no—
433C2×C3×C4—84no—
434C2×C3×C4#12012yes—
435C2×C3×C4#12012yes—
436C2×C3×C4C22×D412yes—
437C2×C3×C4C22×D411yescharacteristic
438C2×C3×C4C22×D411yescharacteristic
439C2×C3×C4H(5,𝔽2)12yes—
440C3×C8—42no—
441C3×C8—42no—
442C24—21no—
443C24C2×C3×D411yescharacteristic
444C24C2×C3×D411yescharacteristic
445C24C2×C3×D411yescharacteristic
446#41—48no—
447#41—48no—
448#41—48no—
449#41—48no—
450C2×Q8—24no—
451C2×Q8—22no—
452C2×Q8—22no—
453C2×Q8—22no—
454C2×Q8—21no—
455C2×Q8—22no—
456C2×Q8—22no—
457C2×Q8—22no—
458C2×Q8—22no—
459C2×Q8—22no—
460C2×Q8—22no—
461C2×Q8—41no—
462C2×Q8—48no—
463C2×Q8—48no—
464C2×Q8—42no—
465C2×Q8—42no—
466C2×Q8C2×C3×D412yes—
467C2×Q8C2×C3×D414yes—
468C2×D4—24no—
469C2×D4—22no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—24no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—41no—
481C2×D4—41no—
482C2×D4—41no—
483C2×D4—42no—
484C2×D4—42no—
485C2×D4—82no—
486C2×D4—82no—
487C2×D4C2×C3×D412yes—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—22no—
500C22×C4—24no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—42no—
506C22×C4—42no—
507C22×C4—42no—
508C22×C4—42no—
509C22×C4—82no—
510C22×C4C2×C3×D411yescharacteristic
511C22×C4C2×C3×D411yescharacteristic
512C22×C4C2×C3×D411yescharacteristic
513C22×C4C2×C3×D412yes—
514C22×C4C2×C3×D412yes—
515C22×C4C2×C3×D414yes—
516C22×C4C24×C311yescharacteristic
517Q16—48no—
518SD16—48no—
519C2×C8—22no—
520C2×C8—22no—
521C2×C8—22no—
522C2×C8—22no—
523C2×C8—22no—
524C2×C8—22no—
525C4⋊C4—24no—
526C4⋊C4—24no—
527C4⋊C4—28no—
528C4⋊C4—24no—
529C4⋊C4—28no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—22no—
533C4⋊C4C2×C3×D414yes—
534C4⋊C4C2×C3×D412yes—
535C4⋊C4C2×C3×D412yes—
536C22⋊C4—24no—
537C22⋊C4—24no—
538C22⋊C4—24no—
539C22⋊C4—28no—
540C22⋊C4—24no—
541C22⋊C4—28no—
542C22⋊C4—24no—
543C42—24no—
544C22×C3—22no—
545C22×C3—22no—
546C22×C3—22no—
547C22×C3—22no—
548C22×C3—24no—
549C22×C3—42no—
550C22×C3—42no—
551C22×C3—41no—
552C22×C3—41no—
553C22×C3—42no—
554C22×C3—42no—
555C22×C3—41no—
556C22×C3—42no—
557C22×C3—41no—
558C22×C3—42no—
559C22×C3—41no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—82no—
563C22×C3—82no—
564C22×C3C2×#12011yescharacteristic
565C22×C3C2×#12011yescharacteristic
566C22×C3#53411yescharacteristic
567C22×C3#57712yes—
568C22×C3#57812yes—
569C3×C4—22no—
570C3×C4—22no—
571C3×C4—41no—
572C3×C4—42no—
573C3×C4—44no—
574C3×C4—42no—
575C3×C4—42no—
576C3×C4—44no—
577C3×C4D4212yes—
578C3×C4D4212yes—
579C23—22no—
580C23—22no—
581C23—22no—
582C23—22no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—22no—
588C23—22no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—21no—
593C23—42no—
594C23—42no—
595C23—41no—
596C23—41no—
597C23C3×#12012yes—
598C23C3×#12012yes—
599C23C22×C3×D411yescharacteristic
600Q8—24no—
601Q8—24no—
602Q8—24no—
603Q8—44no—
604Q8—48no—
605Q8—42no—
606Q8—42no—
607Q8—42no—
608D4—24no—
609D4—44no—
610D4—44no—
611D4—44no—
612D4—48no—
613D4—42no—
614D4—84no—
615D4—84no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—24no—
623C2×C4—24no—
624C2×C4—24no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—24no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—48no—
633C2×C4—48no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—41no—
639C2×C4—42no—
640C2×C4—41no—
641C2×C4—42no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—84no—
645C2×C4C3×#12012yes—
646C2×C4C3×#12012yes—
647C2×C4C22×C3×D412yes—
648C2×C4C22×C3×D411yescharacteristic
649C2×C4C22×C3×D411yescharacteristic
650C2×C4C3×H(5,𝔽2)12yes—
651C8—42no—
652C8—42no—
653C2×C3—42no—
654C2×C3—42no—
655C2×C3—81no—
656C2×C3—82no—
657C2×C3#240311yescharacteristic
658C2×C3#300911yescharacteristic
659C2×C3#301111yescharacteristic
660C2×C3#301312yes—
661C2×C3#320112yes—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—24no—
667C22—42no—
668C22—42no—
669C22—41no—
670C22—41no—
671C22—42no—
672C22—42no—
673C22—41no—
674C22—42no—
675C22—41no—
676C22—42no—
677C22—41no—
678C22—42no—
679C22—42no—
680C22—82no—
681C22—82no—
682C22C2×C3×#12011yescharacteristic
683C22C2×C3×#12011yescharacteristic
684C22C3×#53411yescharacteristic
685C22C3×#57712yes—
686C22C3×#57812yes—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—42no—
691C4—44no—
692C4—42no—
693C4—42no—
694C4—44no—
695C4C3×D4212yes—
696C4C3×D4212yes—
697C3#2392711yescharacteristic, direct product factor, Sylow
698C2—42no—
699C2—42no—
700C2—81no—
701C2—82no—
702C2C3×#240311yescharacteristic
703C2C3×#300911yescharacteristic
704C2C3×#301111yescharacteristic
705C2C3×#301312yes—
706C2C3×#320112yes—
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#537C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C22×C3×#41 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#536C2semidirect
3. C2×C3×#452C2semidirect
4. C2×C3×#451C2semidirect
5. C2×C3×#448C2semidirect
6. C3×#2001C2semidirect
7. C3×#2000C2semidirect
8. C3×#1875C2semidirect
9. C3×#1873C2semidirect
10. C3×#1872C2semidirect
11. C3×#1780C2semidirect
12. #23927C3direct (N × H)
51. C2×#536C2×C3semidirect
52. C2×#452C2×C3semidirect
53. C2×#451C2×C3semidirect
54. C2×#448C2×C3semidirect
55. #2001C2×C3semidirect
56. #2000C2×C3semidirect
57. #1875C2×C3semidirect
58. #1873C2×C3semidirect
59. #1872C2×C3semidirect
60. #1780C2×C3semidirect
110. C3×C22⋊Q8D4semidirect
333. C22⋊Q8C3×D4semidirect
697. C3#23927direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5372
C2×C3×#5362
C2×C3×#4522
C2×C3×#4512
C2×C3×#4482
C3×#20012
C3×#20002
C3×#18752
C3×#18732
C3×#18722
C3×#17802
#239273