Finite Group Databasebeta

← C3×#10594519 #13173934

Subgroups — C3×#10594519 #13173934

Order 1728.

1444 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3799C212yesmaximal, complemented
2C3×#64104C211yesmaximal, characteristic, complemented
3C32×#896C212yesmaximal, complemented
4C3×#63912C211yesmaximal, characteristic, complemented
5C3×#63910C212yesmaximal, complemented
6C3×#63910C212yesmaximal, complemented
7C3×#63906C212yesmaximal, complemented
8C3×#63888C212yesmaximal, complemented
9C3×#63883C211yesmaximal, characteristic, complemented
10C3×#5629—32nomaximal
11#10594519C311yesmaximal, characteristic, direct product factor
12C2×C3×C4⋊(C3⋊D3)C2212yes—
13C2×C3×C4⋊(C3⋊D3)C2211yescharacteristic
14C2×C3×C4×C3⋊D3C2211yescharacteristic
15C2×C32×C4×D3C2212yes—
16C2×C32×Dic6C2212yes—
17C2×C3×#626C2212yes—
18C2×C3×#626C2212yes—
19C2×C3×#626C2212yes—
20C2×C3×#625C2211yescharacteristic
21C2×C3×#624C2212yes—
22C2×C3×#624C2211yescharacteristic
23C2×C3×#624C2211yescharacteristic
24C3×#3799—28no—
25C33×C4⋊C4C2211yescharacteristic
26C3×#3752C2212yes—
27C32×(C2×D3)⋊C4C2212yes—
28C32×(C2×D3)⋊C4C2212yes—
29C32×Dic3⋊C4C2212yes—
30C32×Dic3⋊C4C2212yes—
31C3×#3724C2211yescharacteristic
32C3×Dic3⋊Dic3C2212yes—
33C3×#3722C2212yes—
34C2×C3×#239—32no—
35C2×C3×#235—32no—
36C2×#3799C2×C312yescomplemented
37C32×C22⋊Q8—32no—
38#64104C2×C311yescharacteristic, complemented
39C3×#946—32no—
40C3×#930—32no—
41C3×#896—22no—
42C3×#896—32no—
43C3×#896D312yescomplemented
44C3×#896C2×C312yescomplemented
45C3×#895—32no—
46C3×#895—32no—
47C3×#895—32no—
48C3×#895—61no—
49C3×D3×C4⋊C4—32no—
50C3×#884—32no—
51C3×#884—32no—
52C3×#884—32no—
53C3×#884—32no—
54#63912C2×C311yescharacteristic, complemented
55#63910C2×C312yescomplemented
56#63910C2×C312yescomplemented
57#63906C2×C312yescomplemented
58#63888C2×C312yescomplemented
59#63883C2×C311yescharacteristic, complemented
60C22×C3×C3⋊D3C2312yes—
61C22×C3×C3⋊D3C2311yescharacteristic
62C22×C32×D3C2312yes—
63C2×C33×C4C2312yes—
64C2×C33×C4C2311yescharacteristic
65C2×C3×C3⋊Dic3C2311yescharacteristic
66C3×C4⋊(C3⋊D3)—24no—
67C3×C4⋊(C3⋊D3)—41no—
68C3×C4×C3⋊D3—41no—
69C2×C32×Dic3C2312yes—
70C2×C32×Dic3C2312yes—
71C2×C32×Dic3C2312yes—
72C32×C4×D3—24no—
73C32×Dic6—24no—
74C3×#626—24no—
75C3×#626—24no—
76C3×#626—42no—
77C3×#625—41no—
78C3×#624—24no—
79C3×#624—41no—
80C3×#624D414yescomplemented
81C3×#537—91no—
82#5629—32no—
83C2×C32×Q8—32no—
84C22×C32×C4—32no—
85C2×C4⋊(C3⋊D3)C22×C312yes—
86C2×C4⋊(C3⋊D3)C22×C311yescharacteristic
87C2×C4×C3⋊D3C22×C311yescharacteristic
88C2×C3×#67—32no—
89C2×C3×#67—32no—
90C2×C3×#67—32no—
91C2×C3×#67—32no—
92C3×#239—68no—
93C3×#235—68no—
94C2×C3×D12—32no—
95C2×C3×D12—32no—
96C2×C3×D12—32no—
97C2×C3×D12—32no—
98C2×C3×D12—32no—
99C2×C3×D12—32no—
100C2×C3×D12—62no—
101C2×C3×D12—61no—
102C2×C3×C4×D3—22no—
103C2×C3×C4×D3—32no—
104C2×C3×C4×D3—32no—
105C2×C3×C4×D3—32no—
106C2×C3×C4×D3—32no—
107C2×C3×C4×D3—32no—
108C2×C3×C4×D3—61no—
109C2×C3×C4×D3C2×D312yes—
110C2×C3×C4×D3C22×C312yes—
111C2×C3×Dic6—22no—
112C2×C3×Dic6C2×D312yes—
113C2×C3×Dic6C22×C312yes—
114C2×#626C22×C312yes—
115C2×#626C22×C312yes—
116C2×#626C22×C312yes—
117C2×#625C22×C311yescharacteristic
118C2×#624C22×C312yes—
119C2×#624C22×C311yescharacteristic
120C2×#624C22×C311yescharacteristic
121#3799—28no—
122C32×C4⋊C4—21no—
123C32×C4⋊C4—22no—
124C32×C4⋊C4—32no—
125C32×C4⋊C4—32no—
126C32×C4⋊C4—41no—
127C32×C4⋊C4C2×D312yes—
128C32×C4⋊C4C22×C311yescharacteristic
129C32×C22⋊C4—32no—
130C32×C22⋊C4—32no—
131#3752C22×C312yes—
132C3×(C2×D3)⋊C4—22no—
133C3×(C2×D3)⋊C4—22no—
134C3×(C2×D3)⋊C4—32no—
135C3×(C2×D3)⋊C4—32no—
136C3×(C2×D3)⋊C4—32no—
137C3×(C2×D3)⋊C4—32no—
138C3×(C2×D3)⋊C4—62no—
139C3×(C2×D3)⋊C4C2×D312yes—
140C3×(C2×D3)⋊C4C2×D312yes—
141C3×(C2×D3)⋊C4C22×C312yes—
142C3×(C2×D3)⋊C4C22×C312yes—
143C3×C4⋊Dic3—32no—
144C3×Dic3⋊C4—22no—
145C3×Dic3⋊C4—22no—
146C3×Dic3⋊C4—32no—
147C3×Dic3⋊C4—32no—
148C3×Dic3⋊C4C2×D312yes—
149C3×Dic3⋊C4C2×D312yes—
150C3×Dic3⋊C4C22×C312yes—
151C3×Dic3⋊C4C22×C312yes—
152#3724C22×C311yescharacteristic
153Dic3⋊Dic3C22×C312yes—
154#3722C22×C312yes—
155C22×C33C2411yescharacteristic
156C2×C3×C3⋊D3—21no—
157C2×C3×C3⋊D3—21no—
158C2×C3×C3⋊D3—22no—
159C2×C3×C3⋊D3—22no—
160C2×C3×C3⋊D3—22no—
161C2×C3×C3⋊D3C2×D412yes—
162C2×C32×D3—22no—
163C2×C32×D3—22no—
164C2×C32×D3—22no—
165C33×C4—22no—
166C33×C4—21no—
167C3×C3⋊Dic3—21no—
168C32×Dic3—22no—
169C32×Dic3—22no—
170C32×Dic3C2×D414yes—
171C2×C3×#41—92no—
172C2×#239—32no—
173C2×#235—32no—
174C3×C22⋊Q8—32no—
175C3×C22⋊Q8—32no—
176C3×C22⋊Q8—62no—
177C3×C22⋊Q8—92no—
178C3×#121—91no—
179C3×#121—92no—
180C3×#121—92no—
181C3×#121—92no—
182C3×#121—91no—
183C2×C3×C4⋊C4—91no—
184#946—32no—
185#930—32no—
186#896—32no—
187#896C3×D312yescomplemented
188#895—32no—
189#895—32no—
190#895—32no—
191#895—61no—
192D3×C4⋊C4—32no—
193#884—32no—
194#884—32no—
195#884—32no—
196#884—32no—
197C23×C32—32no—
198C22×C3⋊D3C23×C312yes—
199C22×C3⋊D3C23×C311yescharacteristic
200C22×C3×D3—22no—
201C22×C3×D3—32no—
202C22×C3×D3—32no—
203C22×C3×D3—32no—
204C22×C3×D3—61no—
205C22×C3×D3—62no—
206C22×C3×D3C22×D312yes—
207C22×C3×D3C23×C312yes—
208C32×Q8—64no—
209C2×C32×C4—21no—
210C2×C32×C4—22no—
211C2×C32×C4—22no—
212C2×C32×C4—22no—
213C2×C32×C4—22no—
214C2×C32×C4—32no—
215C2×C32×C4—32no—
216C2×C32×C4—32no—
217C2×C32×C4—41no—
218C2×C32×C4—42no—
219C2×C32×C4—64no—
220C2×C32×C4C22×D312yes—
221C2×C32×C4C22×D312yes—
222C2×C32×C4C22×D312yes—
223C2×C32×C4C23×C311yescharacteristic
224C2×C32×C4C23×C312yes—
225C2×C3⋊Dic3C23×C311yescharacteristic
226C4⋊(C3⋊D3)—24no—
227C4⋊(C3⋊D3)—41no—
228C4×C3⋊D3—41no—
229C3×#67—64no—
230C3×#67—64no—
231C3×#67—122no—
232C3×#67—122no—
233C2×C3×Dic3—22no—
234C2×C3×Dic3—22no—
235C2×C3×Dic3—22no—
236C2×C3×Dic3—32no—
237C2×C3×Dic3—61no—
238C2×C3×Dic3C22×D312yes—
239C2×C3×Dic3C22×D312yes—
240C2×C3×Dic3C22×D312yes—
241C2×C3×Dic3C23×C312yes—
242C2×C3×Dic3C23×C312yes—
243C2×C3×Dic3C23×C312yes—
244C3×D12—64no—
245C3×D12—64no—
246C3×D12—64no—
247C3×D12—64no—
248C3×D12—124no—
249C3×D12—122no—
250C3×D12—122no—
251C3×D12—122no—
252C3×C4×D3—24no—
253C3×C4×D3—24no—
254C3×C4×D3—38no—
255C3×C4×D3—44no—
256C3×C4×D3—64no—
257C3×C4×D3—64no—
258C3×C4×D3—122no—
259C3×C4×D3—122no—
260C3×C4×D3—122no—
261C3×Dic6—24no—
262C3×Dic6—24no—
263C3×Dic6—44no—
264#626—24no—
265#626—24no—
266#626—42no—
267#625—41no—
268#624—24no—
269#624—41no—
270#624C3×D414yescomplemented
271#537—91noSylow
272C2×C33C22×D411yescharacteristic
273C2×C33H(5,𝔽2)11yescharacteristic
274C2×C332−1+411yescharacteristic
275C3×C3⋊D3—22no—
276C3×C3⋊D3—42no—
277C32×D3—42no—
278C3×#41—188no—
279C2×C3×Q8—32no—
280C2×C3×Q8—32no—
281C2×C3×Q8—62no—
282C2×C3×D4—92no—
283C2×C3×D4—92no—
284C2×C3×D4—92no—
285C2×C3×D4—91no—
286C2×C3×D4—92no—
287C2×C3×D4—91no—
288C22×C3×C4—32no—
289C22×C3×C4—32no—
290C22×C3×C4—62no—
291C22×C3×C4—91no—
292C22×C3×C4—92no—
293C22×C3×C4—91no—
294C22×C3×C4—91no—
295C2×#67—32no—
296C2×#67—32no—
297C2×#67—32no—
298C2×#67—32no—
299#239—68no—
300#235—68no—
301C2×D12—32no—
302C2×D12—32no—
303C2×D12—32no—
304C2×D12—32no—
305C2×D12—32no—
306C2×D12—32no—
307C2×D12—62no—
308C2×D12—61no—
309C2×C4×D3—32no—
310C2×C4×D3—32no—
311C2×C4×D3—32no—
312C2×C4×D3—32no—
313C2×C4×D3—32no—
314C2×C4×D3—61no—
315C2×C4×D3C2×C3×D312yes—
316C2×Dic6C2×C3×D312yes—
317C3×C4⋊C4—21no—
318C3×C4⋊C4—22no—
319C3×C4⋊C4—32no—
320C3×C4⋊C4—32no—
321C3×C4⋊C4—32no—
322C3×C4⋊C4—32no—
323C3×C4⋊C4—41no—
324C3×C4⋊C4—62no—
325C3×C4⋊C4—62no—
326C3×C4⋊C4—91no—
327C3×C4⋊C4—92no—
328C3×C4⋊C4D3211yescharacteristic
329C3×C4⋊C4C2×C3×D312yes—
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(C2×D3)⋊C4—32no—
339(C2×D3)⋊C4—32no—
340(C2×D3)⋊C4—32no—
341(C2×D3)⋊C4—32no—
342(C2×D3)⋊C4—62no—
343(C2×D3)⋊C4C2×C3×D312yes—
344(C2×D3)⋊C4C2×C3×D312yes—
345C4⋊Dic3—32no—
346Dic3⋊C4—32no—
347Dic3⋊C4—32no—
348Dic3⋊C4C2×C3×D312yes—
349Dic3⋊C4C2×C3×D312yes—
350C22×C32—21no—
351C22×C32—22no—
352C22×C32—41no—
353C22×C32—62no—
354C22×C32—62no—
355C22×C32—62no—
356C22×C32C23×D312yes—
357C22×C32C24×C311yescharacteristic
358C2×C3⋊D3—21no—
359C2×C3⋊D3—21no—
360C2×C3⋊D3—22no—
361C2×C3⋊D3—22no—
362C2×C3⋊D3—22no—
363C2×C3⋊D3C2×C3×D412yes—
364C2×C3×D3—24no—
365C2×C3×D3—22no—
366C2×C3×D3—22no—
367C2×C3×D3—22no—
368C2×C3×D3—22no—
369C2×C3×D3—22no—
370C2×C3×D3—22no—
371C2×C3×D3—34no—
372C2×C3×D3—42no—
373C2×C3×D3—42no—
374C2×C3×D3—62no—
375C2×C3×D3—62no—
376C2×C3×D3—62no—
377C2×C3×D3—62no—
378C2×C3×D3—62no—
379C2×C3×D3—62no—
380C2×C3×D3—62no—
381C2×C3×D3—62no—
382C2×C3×D3—62no—
383C2×C3×D3—121no—
384C2×C3×D3—121no—
385C2×C3×D3—122no—
386C2×C3×D3—122no—
387C2×C3×D3—122no—
388C32×C4—21no—
389C32×C4—22no—
390C32×C4—22no—
391C32×C4—22no—
392C32×C4—22no—
393C32×C4—22no—
394C32×C4—34no—
395C32×C4—42no—
396C32×C4—42no—
397C32×C4—42no—
398C32×C4—42no—
399C32×C4—42no—
400C32×C4—62no—
401C32×C4—62no—
402C32×C4—82no—
403C3⋊Dic3—21no—
404C3×Dic3—22no—
405C3×Dic3—22no—
406C3×Dic3—22no—
407C3×Dic3—22no—
408C3×Dic3—24no—
409C3×Dic3—42no—
410C3×Dic3—42no—
411C3×Dic3—62no—
412C3×Dic3—121no—
413C3×Dic3D3×D414yes—
414C3×Dic3C2×C3×D414yes—
415C2×#41—92no—
416C22⋊Q8—32no—
417C22⋊Q8—92no—
418#121—91no—
419#121—92no—
420#121—92no—
421#121—92no—
422#121—91no—
423C2×C4⋊C4—91no—
424C33#53711yescharacteristic, complemented, Sylow
425C23×C3—32no—
426C23×C3—32no—
427C23×C3—62no—
428C23×C3—91no—
429C23×C3—92no—
430C22×D3—32no—
431C22×D3—32no—
432C22×D3—32no—
433C22×D3—61no—
434C22×D3—62no—
435C22×D3C22×C3×D312yes—
436C3×Q8—64no—
437C3×Q8—64no—
438C3×Q8—124no—
439C3×D4—184no—
440C3×D4—184no—
441C3×D4—184no—
442C3×D4—361no—
443C3×D4—362no—
444C3×D4—361no—
445C2×C3×C4—21no—
446C2×C3×C4—22no—
447C2×C3×C4—22no—
448C2×C3×C4—22no—
449C2×C3×C4—22no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—32no—
454C2×C3×C4—32no—
455C2×C3×C4—32no—
456C2×C3×C4—41no—
457C2×C3×C4—42no—
458C2×C3×C4—62no—
459C2×C3×C4—62no—
460C2×C3×C4—62no—
461C2×C3×C4—64no—
462C2×C3×C4—64no—
463C2×C3×C4—94no—
464C2×C3×C4—91no—
465C2×C3×C4—124no—
466C2×C3×C4—184no—
467C2×C3×C4—361no—
468C2×C3×C4—361no—
469C2×C3×C4C2×D3211yescharacteristic
470C2×C3×C4C2×D3212yes—
471C2×C3×C4C22×C3×D312yes—
472C2×C3×C4C22×C3×D312yes—
473C2×C3×C4C22×C3×D312yes—
474#67—64no—
475#67—64no—
476#67—122no—
477#67—122no—
478C2×Dic3—32no—
479C2×Dic3—61no—
480C2×Dic3C22×C3×D312yes—
481C2×Dic3C22×C3×D312yes—
482C2×Dic3C22×C3×D312yes—
483D12—64no—
484D12—64no—
485D12—64no—
486D12—64no—
487D12—124no—
488D12—122no—
489D12—122no—
490D12—122no—
491C4×D3—24no—
492C4×D3—38no—
493C4×D3—64no—
494C4×D3—64no—
495C4×D3—122no—
496C4×D3—122no—
497C4×D3—122no—
498Dic6—24no—
499C2×C32—21no—
500C2×C32—21no—
501C2×C32—21no—
502C2×C32—22no—
503C2×C32—22no—
504C2×C32—22no—
505C2×C32—41no—
506C2×C32—41no—
507C2×C32—41no—
508C2×C32—122no—
509C2×C32C2×D3×D412yes—
510C2×C32#100712yes—
511C2×C32#100912yes—
512C2×C32C22×C3×D411yescharacteristic
513C2×C32C3×H(5,𝔽2)11yescharacteristic
514C2×C32C3×2−1+411yescharacteristic
515C3⋊D3—22no—
516C3⋊D3—42no—
517C3×D3—44no—
518C3×D3—42no—
519C3×D3—42no—
520C3×D3—64no—
521C3×D3—122no—
522C3×D3—122no—
523C3×D3—122no—
524C3×D3—242no—
525#41—188no—
526C2×Q8—32no—
527C2×D4—92no—
528C2×D4—92no—
529C2×D4—92no—
530C2×D4—91no—
531C2×D4—92no—
532C2×D4—91no—
533C22×C4—32no—
534C22×C4—91no—
535C22×C4—92no—
536C22×C4—91no—
537C22×C4—91no—
538C4⋊C4—32no—
539C4⋊C4—32no—
540C4⋊C4—92no—
541C4⋊C4—91no—
542C4⋊C4C3×D3211yescharacteristic
543C22⋊C4—32no—
544C22⋊C4—32no—
545C22⋊C4—92no—
546C22⋊C4—92no—
547C22×C3—21no—
548C22×C3—22no—
549C22×C3—41no—
550C22×C3—64no—
551C22×C3—62no—
552C22×C3—62no—
553C22×C3—62no—
554C22×C3—62no—
555C22×C3—62no—
556C22×C3—62no—
557C22×C3—92no—
558C22×C3—122no—
559C22×C3—122no—
560C22×C3—181no—
561C22×C3—181no—
562C22×C3—182no—
563C22×C3—182no—
564C22×C3—182no—
565C22×C3C22×D3211yescharacteristic
566C22×C3C23×C3×D312yes—
567C2×D3—22no—
568C2×D3—22no—
569C2×D3—22no—
570C2×D3—34no—
571C2×D3—62no—
572C2×D3—62no—
573C2×D3—62no—
574C2×D3—62no—
575C2×D3—62no—
576C2×D3—62no—
577C2×D3—62no—
578C2×D3—62no—
579C2×D3—62no—
580C2×D3—121no—
581C2×D3—121no—
582C2×D3—122no—
583C2×D3—122no—
584C2×D3—122no—
585C3×C4—22no—
586C3×C4—21no—
587C3×C4—22no—
588C3×C4—22no—
589C3×C4—22no—
590C3×C4—22no—
591C3×C4—34no—
592C3×C4—34no—
593C3×C4—42no—
594C3×C4—42no—
595C3×C4—42no—
596C3×C4—42no—
597C3×C4—42no—
598C3×C4—64no—
599C3×C4—62no—
600C3×C4—62no—
601C3×C4—62no—
602C3×C4—62no—
603C3×C4—82no—
604C3×C4—122no—
605C3×C4—122no—
606C3×C4—181no—
607Dic3—22no—
608Dic3—22no—
609Dic3—62no—
610Dic3—121no—
611Dic3C3×D3×D414yes—
612C32—22no—
613C32—21no—
614C32—41no—
615C32#562912yescomplemented
616C32C3×#53711yescharacteristic, complemented
617C23—32no—
618C23—91no—
619C23—92no—
620Q8—64no—
621D4—184no—
622D4—184no—
623D4—184no—
624D4—361no—
625D4—362no—
626D4—361no—
627C2×C4—32no—
628C2×C4—32no—
629C2×C4—32no—
630C2×C4—64no—
631C2×C4—94no—
632C2×C4—91no—
633C2×C4—184no—
634C2×C4—361no—
635C2×C4—361no—
636C2×C4C2×C3×D3211yescharacteristic
637C2×C4C2×C3×D3212yes—
638C2×C3—21no—
639C2×C3—22no—
640C2×C3—21no—
641C2×C3—22no—
642C2×C3—22no—
643C2×C3—21no—
644C2×C3—41no—
645C2×C3—41no—
646C2×C3—41no—
647C2×C3—124no—
648C2×C3—122no—
649C2×C3—122no—
650C2×C3—182no—
651C2×C3—362no—
652C2×C3#6430811yescharacteristic
653C2×C3D32×D411yescharacteristic
654C2×C3#6431611yescharacteristic
655C2×C3C2×C3×D3×D412yes—
656C2×C3C3×#100712yes—
657C2×C3C3×#100912yes—
658D3—42no—
659D3—64no—
660D3—122no—
661D3—122no—
662D3—122no—
663D3—242no—
664C22—62no—
665C22—62no—
666C22—62no—
667C22—92no—
668C22—181no—
669C22—181no—
670C22—182no—
671C22—182no—
672C22—182no—
673C22C22×C3×D3211yescharacteristic
674C4—21no—
675C4—22no—
676C4—34no—
677C4—62no—
678C4—62no—
679C4—181no—
680C3—21no—
681C3—22no—
682C3—41no—
683C3#1059451911yescharacteristic, direct product factor
684C3C3×#562912yescomplemented
685C2—122no—
686C2—182no—
687C2—362no—
688C2C3×#6430811yescharacteristic
689C2C3×D32×D411yescharacteristic
690C2C3×#6431611yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC33×C4⋊C4C22
socleC22×C33C24
hypercenterC3×C4⋊C4D32
hypocenterC32C3×#537
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C3×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3799C2semidirect
2. C3×#64104C2semidirect
3. C32×#896C2semidirect
4. C3×#63912C2semidirect
5. C3×#63910C2semidirect
6. C3×#63910C2semidirect
7. C3×#63906C2semidirect
8. C3×#63888C2semidirect
9. C3×#63883C2semidirect
11. #10594519C3direct (N × H)
36. C2×#3799C2×C3semidirect
38. #64104C2×C3semidirect
43. C3×#896D3semidirect
44. C3×#896C2×C3semidirect
54. #63912C2×C3semidirect
55. #63910C2×C3semidirect
56. #63910C2×C3semidirect
57. #63906C2×C3semidirect
58. #63888C2×C3semidirect
59. #63883C2×C3semidirect
80. C3×#624D4semidirect
187. #896C3×D3semidirect
270. #624C3×D4semidirect
424. C33#537semidirect
615. C32#5629semidirect
616. C32C3×#537semidirect
683. C3#10594519direct (N × H)
684. C3C3×#5629semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#37992
C3×#641042
C32×#8962
C3×#639122
C3×#639102
C3×#639062
C3×#638882
C3×#638832
C3×#56293
#105945193