Finite Group Databasebeta

← C3×#10595140 #13174703

Subgroups — C3×#10595140 #13174703

Order 1728.

1512 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C212yesmaximal, complemented
2C3×#64147C211yesmaximal, characteristic, complemented
3C32×#939C212yesmaximal, complemented
4C3×#63970C212yesmaximal, complemented
5C3×#63964C212yesmaximal, complemented
6C3×#63958C212yesmaximal, complemented
7C3×#63912C211yesmaximal, characteristic, complemented
8C3×#63893C212yesmaximal, complemented
9C3×#63883C211yesmaximal, characteristic, complemented
10C3×#5608—32nomaximal
11#10595140C311yesmaximal, characteristic, direct product factor
12C2×C33×D4C2211yescharacteristic
13C2×C3×#638C2212yes—
14C2×C3×C4×C3⋊D3C2211yescharacteristic
15C2×C32×#67C2212yes—
16C2×C32×#67C2212yes—
17C22×C32×Dic3C2212yes—
18C2×C3×#627C2212yes—
19C2×C3×#626C2212yes—
20C2×C3×#625C2211yescharacteristic
21C2×C3×#624C2211yescharacteristic
22C2×C3×#624C2211yescharacteristic
23C3×#3804—28no—
24C2×C3×D3×Dic3C2212yes—
25C3×#3757C2212yes—
26C3×C4⋊(C3⋊Dic3)C2211yescharacteristic
27C32×#217C2212yes—
28C32×(C2×D3)⋊C4C2212yes—
29C32×Dic3⋊C4C2212yes—
30C3×#3724C2211yescharacteristic
31C3×Dic3⋊Dic3C2212yes—
32C3×Dic3⋊Dic3C2212yes—
33C3×(C2×D3)⋊Dic3C2212yes—
34C2×C3×#237—32no—
35C2×C3×#235—32no—
36C2×#3804C2×C312yescomplemented
37C32×#121—32no—
38#64147C2×C311yescharacteristic, complemented
39C3×#939—22no—
40C3×#939—32no—
41C3×#939D312yescomplemented
42C3×#939C2×C312yescomplemented
43C3×#938—32no—
44C3×#938—32no—
45C3×#938—32no—
46C3×#938—61no—
47C3×#924—32no—
48C3×#897—32no—
49C3×D3×C4⋊C4—32no—
50C3×#884—32no—
51C3×#884—32no—
52C3×#878—32no—
53C3×#878—32no—
54#63970C2×C312yescomplemented
55#63964C2×C312yescomplemented
56#63958C2×C312yescomplemented
57#63912C2×C311yescharacteristic, complemented
58#63893C2×C312yescomplemented
59#63883C2×C311yescharacteristic, complemented
60C23×C33C2312yes—
61C22×C3×C3⋊D3C2311yescharacteristic
62C22×C32×D3C2312yes—
63C33×D4—41no—
64C2×C33×C4C2311yescharacteristic
65C3×#638—24no—
66C2×C3×C3⋊Dic3C2312yes—
67C2×C3×C3⋊Dic3C2311yescharacteristic
68C3×C4×C3⋊D3—41no—
69C32×#67—24no—
70C32×#67—42no—
71C2×C32×Dic3—24no—
72C2×C32×Dic3C2312yes—
73C2×C32×Dic3C2312yes—
74C2×C32×Dic3C2312yes—
75C3×#627—24no—
76C3×#626—24no—
77C3×#625—41no—
78C3×#624—41no—
79C3×#624D414yescomplemented
80C3×D3×Dic3—24no—
81C3×#537—91no—
82#5608—32no—
83C2×C32×D4—21no—
84C2×C32×D4—22no—
85C2×C32×D4—32no—
86C2×C32×D4—32no—
87C2×C32×D4—41no—
88C2×C32×D4C2×D312yes—
89C2×C32×D4C22×C311yescharacteristic
90C22×C32×C4—32no—
91C2×#638C22×C312yes—
92C2×C4×C3⋊D3C22×C311yescharacteristic
93C2×C3×#67—22no—
94C2×C3×#67—22no—
95C2×C3×#67—32no—
96C2×C3×#67—32no—
97C2×C3×#67—32no—
98C2×C3×#67—32no—
99C2×C3×#67—62no—
100C2×C3×#67C2×D312yes—
101C2×C3×#67C2×D312yes—
102C2×C3×#67C22×C312yes—
103C2×C3×#67C22×C312yes—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—32no—
106C22×C3×Dic3C2×D312yes—
107C22×C3×Dic3C22×C312yes—
108C3×#237—68no—
109C3×#235—68no—
110C2×C3×D12—32no—
111C2×C3×C4×D3—32no—
112C2×C3×C4×D3—32no—
113C2×C3×C4×D3—32no—
114C2×C3×C4×D3—32no—
115C2×C3×C4×D3—61no—
116C2×C3×Dic6—32no—
117C2×C3×Dic6—32no—
118C2×#627C22×C312yes—
119C2×#626C22×C312yes—
120C2×#625C22×C311yescharacteristic
121C2×#624C22×C311yescharacteristic
122C2×#624C22×C311yescharacteristic
123#3804—28no—
124C2×D3×Dic3C22×C312yes—
125C32×C4⋊C4—32no—
126C32×C22⋊C4—32no—
127C32×C22⋊C4—32no—
128#3757C22×C312yes—
129C4⋊(C3⋊Dic3)C22×C311yescharacteristic
130C3×#217—22no—
131C3×#217—32no—
132C3×#217—32no—
133C3×#217—32no—
134C3×#217—62no—
135C3×#217C2×D312yes—
136C3×#217C22×C312yes—
137C3×(C2×D3)⋊C4—22no—
138C3×(C2×D3)⋊C4—32no—
139C3×(C2×D3)⋊C4C2×D312yes—
140C3×(C2×D3)⋊C4C22×C312yes—
141C3×C4⋊Dic3—32no—
142C3×C4⋊Dic3—32no—
143C3×C4⋊Dic3—32no—
144C3×C4⋊Dic3—61no—
145C3×Dic3⋊C4—22no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4—32no—
149C3×Dic3⋊C4C2×D312yes—
150C3×Dic3⋊C4C22×C312yes—
151#3724C22×C311yescharacteristic
152Dic3⋊Dic3C22×C312yes—
153Dic3⋊Dic3C22×C312yes—
154(C2×D3)⋊Dic3C22×C312yes—
155C22×C33—22no—
156C22×C33—22no—
157C22×C33—22no—
158C22×C33C2411yescharacteristic
159C2×C3×C3⋊D3—21no—
160C2×C3×C3⋊D3—21no—
161C2×C3×C3⋊D3C2×D412yes—
162C2×C32×D3—22no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C33×C4—21no—
166C3×C3⋊Dic3—22no—
167C3×C3⋊Dic3—21no—
168C32×Dic3—22no—
169C32×Dic3—22no—
170C32×Dic3C2×D414yes—
171C2×C3×#41—92no—
172C2×#237—32no—
173C2×#235—32no—
174C3×C22⋊Q8—92no—
175C3×C22⋊Q8—92no—
176C3×#121—32no—
177C3×#121—32no—
178C3×#121—62no—
179C3×#121—91no—
180C3×#121—92no—
181C3×#121—92no—
182C3×#121—91no—
183C2×C3×C4⋊C4—91no—
184#939—32no—
185#939C3×D312yescomplemented
186#938—32no—
187#938—32no—
188#938—32no—
189#938—61no—
190#924—32no—
191#897—32no—
192D3×C4⋊C4—32no—
193#884—32no—
194#884—32no—
195#878—32no—
196#878—32no—
197C23×C32—22no—
198C23×C32—22no—
199C23×C32—22no—
200C23×C32—32no—
201C23×C32—42no—
202C23×C32C22×D312yes—
203C23×C32C22×D312yes—
204C23×C32C23×C312yes—
205C22×C3⋊D3C23×C311yescharacteristic
206C22×C3×D3—22no—
207C22×C3×D3—32no—
208C22×C3×D3—61no—
209C22×C3×D3C22×D312yes—
210C22×C3×D3C23×C312yes—
211C32×D4—42no—
212C32×D4—41no—
213C32×D4—42no—
214C32×D4—44no—
215C32×D4—44no—
216C32×D4—64no—
217C32×D4—122no—
218C2×C32×C4—21no—
219C2×C32×C4—22no—
220C2×C32×C4—32no—
221C2×C32×C4—32no—
222C2×C32×C4—32no—
223C2×C32×C4—41no—
224C2×C32×C4—64no—
225C2×C32×C4C22×D312yes—
226C2×C32×C4C23×C311yescharacteristic
227#638—24no—
228C2×C3⋊Dic3C23×C312yes—
229C2×C3⋊Dic3C23×C311yescharacteristic
230C4×C3⋊D3—41no—
231C3×#67—24no—
232C3×#67—24no—
233C3×#67—44no—
234C3×#67—42no—
235C3×#67—42no—
236C3×#67—44no—
237C3×#67—64no—
238C3×#67—64no—
239C3×#67—64no—
240C3×#67—124no—
241C3×#67—122no—
242C2×C3×Dic3—24no—
243C2×C3×Dic3—24no—
244C2×C3×Dic3—22no—
245C2×C3×Dic3—22no—
246C2×C3×Dic3—22no—
247C2×C3×Dic3—32no—
248C2×C3×Dic3—32no—
249C2×C3×Dic3—32no—
250C2×C3×Dic3—44no—
251C2×C3×Dic3—62no—
252C2×C3×Dic3—61no—
253C2×C3×Dic3—64no—
254C2×C3×Dic3C22×D312yes—
255C2×C3×Dic3C22×D312yes—
256C2×C3×Dic3C22×D312yes—
257C2×C3×Dic3C23×C312yes—
258C2×C3×Dic3C23×C312yes—
259C2×C3×Dic3C23×C312yes—
260C3×D12—64no—
261C3×C4×D3—38no—
262C3×C4×D3—64no—
263C3×C4×D3—122no—
264C3×C4×D3—122no—
265C3×C4×D3—122no—
266C3×Dic6—64no—
267C3×Dic6—64no—
268#627—24no—
269#626—24no—
270#625—41no—
271#624—41no—
272#624C3×D414yescomplemented
273D3×Dic3—24no—
274#537—91noSylow
275C2×C33—42no—
276C2×C33C22×D411yescharacteristic
277C2×C33H(5,𝔽2)11yescharacteristic
278C2×C332−1+411yescharacteristic
279C3×C3⋊D3—22no—
280C32×D3—42no—
281C3×#41—188no—
282C2×C3×Q8—92no—
283C2×C3×D4—21no—
284C2×C3×D4—22no—
285C2×C3×D4—32no—
286C2×C3×D4—32no—
287C2×C3×D4—32no—
288C2×C3×D4—32no—
289C2×C3×D4—41no—
290C2×C3×D4—62no—
291C2×C3×D4—62no—
292C2×C3×D4—92no—
293C2×C3×D4—92no—
294C2×C3×D4—91no—
295C2×C3×D4D3211yescharacteristic
296C2×C3×D4C2×C3×D312yes—
297C22×C3×C4—32no—
298C22×C3×C4—32no—
299C22×C3×C4—62no—
300C22×C3×C4—91no—
301C22×C3×C4—91no—
302C22×C3×C4—92no—
303C22×C3×C4—91no—
304C2×#67—32no—
305C2×#67—32no—
306C2×#67—32no—
307C2×#67—32no—
308C2×#67—62no—
309C2×#67C2×C3×D312yes—
310C2×#67C2×C3×D312yes—
311C22×Dic3—32no—
312C22×Dic3C2×C3×D312yes—
313#237—68no—
314#235—68no—
315C2×D12—32no—
316C2×C4×D3—32no—
317C2×C4×D3—32no—
318C2×C4×D3—32no—
319C2×C4×D3—32no—
320C2×C4×D3—61no—
321C2×Dic6—32no—
322C2×Dic6—32no—
323C3×C4⋊C4—32no—
324C3×C4⋊C4—32no—
325C3×C4⋊C4—62no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—92no—
328C3×C4⋊C4—92no—
329C3×C4⋊C4—91no—
330C3×C22⋊C4—32no—
331C3×C22⋊C4—32no—
332C3×C22⋊C4—32no—
333C3×C22⋊C4—32no—
334C3×C22⋊C4—62no—
335C3×C22⋊C4—62no—
336C3×C22⋊C4—92no—
337C3×C22⋊C4—92no—
338#217—32no—
339#217—32no—
340#217—32no—
341#217—62no—
342#217C2×C3×D312yes—
343(C2×D3)⋊C4—32no—
344(C2×D3)⋊C4C2×C3×D312yes—
345C4⋊Dic3—32no—
346C4⋊Dic3—32no—
347C4⋊Dic3—32no—
348C4⋊Dic3—61no—
349Dic3⋊C4—32no—
350Dic3⋊C4—32no—
351Dic3⋊C4—32no—
352Dic3⋊C4C2×C3×D312yes—
353C22×C32—22no—
354C22×C32—24no—
355C22×C32—22no—
356C22×C32—22no—
357C22×C32—22no—
358C22×C32—22no—
359C22×C32—22no—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—21no—
364C22×C32—22no—
365C22×C32—41no—
366C22×C32—42no—
367C22×C32—42no—
368C22×C32—44no—
369C22×C32—42no—
370C22×C32—42no—
371C22×C32—42no—
372C22×C32—42no—
373C22×C32—42no—
374C22×C32—42no—
375C22×C32—62no—
376C22×C32—62no—
377C22×C32—62no—
378C22×C32—82no—
379C22×C32—82no—
380C22×C32C23×D312yes—
381C22×C32C24×C311yescharacteristic
382C2×C3⋊D3—21no—
383C2×C3⋊D3—21no—
384C2×C3⋊D3C2×C3×D412yes—
385C2×C3×D3—22no—
386C2×C3×D3—22no—
387C2×C3×D3—22no—
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—34no—
392C2×C3×D3—42no—
393C2×C3×D3—42no—
394C2×C3×D3—42no—
395C2×C3×D3—62no—
396C2×C3×D3—62no—
397C2×C3×D3—62no—
398C2×C3×D3—121no—
399C2×C3×D3—121no—
400C32×C4—21no—
401C32×C4—22no—
402C32×C4—22no—
403C32×C4—34no—
404C32×C4—42no—
405C32×C4—42no—
406C32×C4—62no—
407C32×C4—62no—
408C3⋊Dic3—22no—
409C3⋊Dic3—21no—
410C3×Dic3—22no—
411C3×Dic3—22no—
412C3×Dic3—22no—
413C3×Dic3—22no—
414C3×Dic3—24no—
415C3×Dic3—42no—
416C3×Dic3—42no—
417C3×Dic3—62no—
418C3×Dic3—62no—
419C3×Dic3—62no—
420C3×Dic3—121no—
421C3×Dic3—122no—
422C3×Dic3D3×D414yes—
423C3×Dic3C2×C3×D414yes—
424C2×#41—92no—
425C22⋊Q8—92no—
426C22⋊Q8—92no—
427#121—32no—
428#121—91no—
429#121—92no—
430#121—92no—
431#121—91no—
432C2×C4⋊C4—91no—
433C33#53711yescharacteristic, complemented, Sylow
434C23×C3—22no—
435C23×C3—22no—
436C23×C3—22no—
437C23×C3—32no—
438C23×C3—32no—
439C23×C3—42no—
440C23×C3—62no—
441C23×C3—91no—
442C23×C3C2×D3212yes—
443C23×C3C22×C3×D312yes—
444C23×C3C22×C3×D312yes—
445C22×D3—32no—
446C22×D3—61no—
447C22×D3C22×C3×D312yes—
448C3×Q8—184no—
449C3×D4—41no—
450C3×D4—42no—
451C3×D4—42no—
452C3×D4—44no—
453C3×D4—44no—
454C3×D4—64no—
455C3×D4—64no—
456C3×D4—124no—
457C3×D4—122no—
458C3×D4—122no—
459C3×D4—124no—
460C3×D4—184no—
461C3×D4—184no—
462C3×D4—361no—
463C2×C3×C4—21no—
464C2×C3×C4—22no—
465C2×C3×C4—32no—
466C2×C3×C4—32no—
467C2×C3×C4—32no—
468C2×C3×C4—32no—
469C2×C3×C4—32no—
470C2×C3×C4—32no—
471C2×C3×C4—41no—
472C2×C3×C4—62no—
473C2×C3×C4—62no—
474C2×C3×C4—62no—
475C2×C3×C4—64no—
476C2×C3×C4—64no—
477C2×C3×C4—94no—
478C2×C3×C4—91no—
479C2×C3×C4—92no—
480C2×C3×C4—124no—
481C2×C3×C4—184no—
482C2×C3×C4—361no—
483C2×C3×C4—361no—
484C2×C3×C4C2×D3211yescharacteristic
485C2×C3×C4C22×C3×D312yes—
486#67—24no—
487#67—42no—
488#67—64no—
489#67—64no—
490#67—64no—
491#67—124no—
492#67—122no—
493C2×Dic3—24no—
494C2×Dic3—32no—
495C2×Dic3—32no—
496C2×Dic3—32no—
497C2×Dic3—62no—
498C2×Dic3—61no—
499C2×Dic3—64no—
500C2×Dic3C22×C3×D312yes—
501C2×Dic3C22×C3×D312yes—
502C2×Dic3C22×C3×D312yes—
503D12—64no—
504C4×D3—38no—
505C4×D3—64no—
506C4×D3—122no—
507C4×D3—122no—
508C4×D3—122no—
509Dic6—64no—
510Dic6—64no—
511C2×C32—21no—
512C2×C32—21no—
513C2×C32—21no—
514C2×C32—22no—
515C2×C32—22no—
516C2×C32—22no—
517C2×C32—41no—
518C2×C32—41no—
519C2×C32—41no—
520C2×C32—42no—
521C2×C32—44no—
522C2×C32—42no—
523C2×C32—42no—
524C2×C32—82no—
525C2×C32—82no—
526C2×C32—84no—
527C2×C32—122no—
528C2×C32C2×D3×D412yes—
529C2×C32#100412yes—
530C2×C32#101012yes—
531C2×C32C22×C3×D411yescharacteristic
532C2×C32C3×H(5,𝔽2)11yescharacteristic
533C2×C32C3×2−1+411yescharacteristic
534C3⋊D3—22no—
535C3×D3—42no—
536C3×D3—42no—
537C3×D3—64no—
538C3×D3—82no—
539C3×D3—122no—
540#41—188no—
541C2×Q8—92no—
542C2×D4—32no—
543C2×D4—32no—
544C2×D4—92no—
545C2×D4—92no—
546C2×D4—91no—
547C2×D4C3×D3211yescharacteristic
548C22×C4—32no—
549C22×C4—91no—
550C22×C4—91no—
551C22×C4—92no—
552C22×C4—91no—
553C4⋊C4—32no—
554C4⋊C4—92no—
555C4⋊C4—91no—
556C4⋊C4—92no—
557C4⋊C4—91no—
558C22⋊C4—32no—
559C22⋊C4—32no—
560C22⋊C4—92no—
561C22⋊C4—92no—
562C22×C3—24no—
563C22×C3—22no—
564C22×C3—22no—
565C22×C3—22no—
566C22×C3—22no—
567C22×C3—22no—
568C22×C3—22no—
569C22×C3—22no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—21no—
573C22×C3—22no—
574C22×C3—42no—
575C22×C3—42no—
576C22×C3—42no—
577C22×C3—42no—
578C22×C3—42no—
579C22×C3—42no—
580C22×C3—42no—
581C22×C3—42no—
582C22×C3—44no—
583C22×C3—41no—
584C22×C3—62no—
585C22×C3—62no—
586C22×C3—62no—
587C22×C3—62no—
588C22×C3—62no—
589C22×C3—62no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3—92no—
593C22×C3—122no—
594C22×C3—122no—
595C22×C3—122no—
596C22×C3—181no—
597C22×C3—181no—
598C22×C3C22×D3211yescharacteristic
599C22×C3C23×C3×D312yes—
600C2×D3—22no—
601C2×D3—22no—
602C2×D3—22no—
603C2×D3—34no—
604C2×D3—62no—
605C2×D3—62no—
606C2×D3—62no—
607C2×D3—121no—
608C2×D3—121no—
609C3×C4—22no—
610C3×C4—21no—
611C3×C4—22no—
612C3×C4—34no—
613C3×C4—34no—
614C3×C4—42no—
615C3×C4—42no—
616C3×C4—64no—
617C3×C4—62no—
618C3×C4—62no—
619C3×C4—62no—
620C3×C4—62no—
621C3×C4—122no—
622C3×C4—122no—
623C3×C4—182no—
624C3×C4—181no—
625Dic3—22no—
626Dic3—22no—
627Dic3—62no—
628Dic3—62no—
629Dic3—62no—
630Dic3—121no—
631Dic3—122no—
632Dic3C3×D3×D414yes—
633C32—21no—
634C32—22no—
635C32—41no—
636C32#560812yescomplemented
637C32C3×#53711yescharacteristic, complemented
638C23—32no—
639C23—91no—
640C23C2×C3×D3212yes—
641Q8—184no—
642D4—41no—
643D4—64no—
644D4—122no—
645D4—184no—
646D4—184no—
647D4—361no—
648C2×C4—32no—
649C2×C4—32no—
650C2×C4—32no—
651C2×C4—64no—
652C2×C4—94no—
653C2×C4—91no—
654C2×C4—92no—
655C2×C4—184no—
656C2×C4—361no—
657C2×C4—361no—
658C2×C4C2×C3×D3211yescharacteristic
659C2×C3—21no—
660C2×C3—22no—
661C2×C3—21no—
662C2×C3—22no—
663C2×C3—21no—
664C2×C3—22no—
665C2×C3—44no—
666C2×C3—42no—
667C2×C3—42no—
668C2×C3—42no—
669C2×C3—41no—
670C2×C3—41no—
671C2×C3—41no—
672C2×C3—82no—
673C2×C3—82no—
674C2×C3—84no—
675C2×C3—122no—
676C2×C3—122no—
677C2×C3—182no—
678C2×C3—242no—
679C2×C3#6430911yescharacteristic
680C2×C3D32×D411yescharacteristic
681C2×C3#6433011yescharacteristic
682C2×C3C2×C3×D3×D412yes—
683C2×C3C3×#100412yes—
684C2×C3C3×#101012yes—
685D3—42no—
686D3—64no—
687D3—122no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—62no—
692C22—62no—
693C22—62no—
694C22—92no—
695C22—181no—
696C22—181no—
697C22C22×C3×D3211yescharacteristic
698C4—21no—
699C4—34no—
700C4—62no—
701C4—62no—
702C4—181no—
703C4—182no—
704C3—21no—
705C3—22no—
706C3—41no—
707C3#1059514011yescharacteristic, direct product factor
708C3C3×#560812yescomplemented
709C2—42no—
710C2—122no—
711C2—182no—
712C2C3×#6430911yescharacteristic
713C2C3×D32×D411yescharacteristic
714C2C3×#6433011yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3804C2semidirect
2. C3×#64147C2semidirect
3. C32×#939C2semidirect
4. C3×#63970C2semidirect
5. C3×#63964C2semidirect
6. C3×#63958C2semidirect
7. C3×#63912C2semidirect
8. C3×#63893C2semidirect
9. C3×#63883C2semidirect
11. #10595140C3direct (N × H)
36. C2×#3804C2×C3semidirect
38. #64147C2×C3semidirect
41. C3×#939D3semidirect
42. C3×#939C2×C3semidirect
54. #63970C2×C3semidirect
55. #63964C2×C3semidirect
56. #63958C2×C3semidirect
57. #63912C2×C3semidirect
58. #63893C2×C3semidirect
59. #63883C2×C3semidirect
79. C3×#624D4semidirect
185. #939C3×D3semidirect
272. #624C3×D4semidirect
433. C33#537semidirect
636. C32#5608semidirect
637. C32C3×#537semidirect
707. C3#10595140direct (N × H)
708. C3C3×#5608semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C3×#641472
C32×#9392
C3×#639702
C3×#639642
C3×#639582
C3×#639122
C3×#638932
C3×#638832
C3×#56083
#105951403