Finite Group Databasebeta

← C3×#27786 #10646393

Subgroups — C3×#27786 #10646393

Order 768.

834 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#489C211yesmaximal, characteristic, complemented
2C2×C3×#488C211yesmaximal, characteristic, complemented
3C3×#2550C211yesmaximal, characteristic, complemented
4C3×#2548C211yesmaximal, characteristic
5C3×#2042C211yesmaximal, characteristic, complemented
6C3×#2042C211yesmaximal, characteristic, complemented
7C3×#2025C211yesmaximal, characteristic, complemented
8C3×#2023C211yesmaximal, characteristic, complemented
9C3×#1982C211yesmaximal, characteristic
10C3×#1961C211yesmaximal, characteristic
11C3×#1936C211yesmaximal, characteristic, complemented
12C3×#1934C211yesmaximal, characteristic, complemented
13C3×#1805C211yesmaximal, characteristic, complemented
14C3×#1771C211yesmaximal, characteristic, complemented
15C3×#1763C211yesmaximal, characteristic, complemented
16#27786C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×C4⋊Q8C2211yescharacteristic
18C2×C3×#127C2211yescharacteristic
19C2×C3×#125C2211yescharacteristic
20C2×C3×#124C2211yescharacteristic
21C2×C3×#124C2211yescharacteristic
22C2×C3×C4×Q8C2211yescharacteristic
23C3×#489—24no—
24C3×#488—24no—
25C2×C3×C4⋊C8C2211yescharacteristic
26C2×C3×#103C2211yescharacteristic
27C2×C3×#103C2211yescharacteristic
28C2×C3×#103C2211yescharacteristic
29C2×C3×#103C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×#102C2211yescharacteristic
33C2×C3×#102C2211yescharacteristic
34C2×C3×#102C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#97C2211yescharacteristic
39C2×C3×#97C2211yescharacteristic
40C2×C3×C4×C8C2211yescharacteristic
41C3×#398—21no—
42C3×#395—21no—
43C3×#394—21no—
44C3×#394—21no—
45C3×#391—21no—
46C3×#390—21no—
47C3×#390—21no—
48C3×#390C2211yescharacteristic
49C3×#390C2211yescharacteristic
50C3×#389—21no—
51C3×#389C2211yescharacteristic
52C3×#389C2211yescharacteristic
53C3×#382C2211yescharacteristic
54C3×C4×C4⋊C4C2211yescharacteristic
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#336C2211yescharacteristic
61C3×#336C2211yescharacteristic
62C2×#489C2×C311yescharacteristic, complemented
63C2×#488C2×C311yescharacteristic, complemented
64#2550C2×C311yescharacteristic, complemented
65#2548C2×C311yescharacteristic
66#2042C2×C311yescharacteristic, complemented
67#2042C2×C311yescharacteristic, complemented
68#2025C2×C311yescharacteristic, complemented
69#2023C2×C311yescharacteristic, complemented
70#1982C2×C311yescharacteristic
71#1961C2×C311yescharacteristic
72#1936C2×C311yescharacteristic, complemented
73#1934C2×C311yescharacteristic, complemented
74#1805C2×C311yescharacteristic, complemented
75#1771C2×C311yescharacteristic, complemented
76#1763C2×C311yescharacteristic, complemented
77C22×C3×Q8—21no—
78C22×C3×Q8C2311yescharacteristic
79C22×C3×D4—21no—
80C22×C3×D4—21no—
81C22×C3×D4C2311yescharacteristic
82C22×C3×D4C2311yescharacteristic
83C22×C3×C8C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C3×C4⋊Q8—22no—
88C3×C4⋊Q8—41no—
89C3×#127—22no—
90C3×#127—22no—
91C3×#125—22no—
92C3×#125—41no—
93C3×#124—22no—
94C3×#124—22no—
95C3×#124—41no—
96C3×#124—41no—
97C3×C4×Q8—22no—
98C3×C4×Q8—22no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4—21no—
103C2×C3×C4⋊C4—21no—
104C2×C3×C4⋊C4—21no—
105C2×C3×C4⋊C4D411yescharacteristic
106C2×C3×C4⋊C4D411yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C22⋊C4—21no—
113C2×C3×C22⋊C4—21no—
114C2×C3×C22⋊C4—21no—
115C2×C3×C22⋊C4—21no—
116C2×C3×C22⋊C4—21no—
117C2×C3×C22⋊C4—21no—
118C2×C3×C22⋊C4—21no—
119C2×C3×C22⋊C4—21no—
120C2×C3×C42—21no—
121C2×C3×C42—21no—
122C2×C3×C42C2311yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C3×C4⋊C8—22no—
126C3×#103—22no—
127C3×#103—22no—
128C3×#103—22no—
129C3×#103D414yescomplemented
130C3×#102—22no—
131C3×#102—22no—
132C3×#102—22no—
133C3×#102—22no—
134C3×#102—22no—
135C3×#102—22no—
136C3×#102—41no—
137C3×#102—41no—
138C3×#97—22no—
139C3×#97—22no—
140C3×C4×C8—22no—
141C3×#95—21no—
142C3×#95—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95D411yescharacteristic
147C3×#95D411yescharacteristic
148C2×C4⋊Q8C22×C311yescharacteristic
149C2×#127C22×C311yescharacteristic
150C2×#125C22×C311yescharacteristic
151C2×#124C22×C311yescharacteristic
152C2×#124C22×C311yescharacteristic
153C2×C4×Q8C22×C311yescharacteristic
154#489—24no—
155#488—24no—
156C2×C4⋊C8C22×C311yescharacteristic
157C2×#103C22×C311yescharacteristic
158C2×#103C22×C311yescharacteristic
159C2×#103C22×C311yescharacteristic
160C2×#103C22×C311yescharacteristic
161C2×#102C22×C311yescharacteristic
162C2×#102C22×C311yescharacteristic
163C2×#102C22×C311yescharacteristic
164C2×#102C22×C311yescharacteristic
165C2×#102C22×C311yescharacteristic
166C2×#102C22×C311yescharacteristic
167C2×#102C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#97C22×C311yescharacteristic
170C2×#97C22×C311yescharacteristic
171C2×C4×C8C22×C311yescharacteristic
172#398—21no—
173#395—21no—
174#394—21no—
175#394—21no—
176#391—21no—
177#390—21no—
178#390—21no—
179#390C22×C311yescharacteristic
180#390C22×C311yescharacteristic
181#389—21no—
182#389C22×C311yescharacteristic
183#389C22×C311yescharacteristic
184#382C22×C311yescharacteristic
185C4×C4⋊C4C22×C311yescharacteristic
186C4×C4⋊C4C22×C311yescharacteristic
187#340C22×C311yescharacteristic
188#340C22×C311yescharacteristic
189#340C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#336C22×C311yescharacteristic
192#336C22×C311yescharacteristic
193C24×C3—21no—
194C24×C3—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—42no—
201C2×C3×Q8—42no—
202C2×C3×Q8—81no—
203C2×C3×Q8C2×D412yes—
204C2×C3×D4—21no—
205C2×C3×D4—21no—
206C2×C3×D4—21no—
207C2×C3×D4—21no—
208C2×C3×D4—21no—
209C2×C3×D4—21no—
210C2×C3×D4—21no—
211C2×C3×D4—21no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4—81no—
221C2×C3×D4—81no—
222C22×C3×C4—21no—
223C22×C3×C4—21no—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2×D411yescharacteristic
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2×D411yescharacteristic
233C22×C3×C4C2×D411yescharacteristic
234C22×C3×C4C2411yescharacteristic
235C2×C3×C8—21no—
236C2×C3×C8—21no—
237C2×C3×C8—21no—
238C2×C3×C8—21no—
239C2×C3×C8—21no—
240C2×C3×C8—21no—
241C2×C3×C8—21no—
242C2×C3×C8—21no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8C2×D412yes—
247C3×C4⋊C4—21no—
248C3×C4⋊C4—21no—
249C3×C4⋊C4—21no—
250C3×C4⋊C4—21no—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—41no—
256C3×C4⋊C4—41no—
257C3×C4⋊C4—42no—
258C3×C4⋊C4—42no—
259C3×C4⋊C4—42no—
260C3×C4⋊C4—42no—
261C3×C4⋊C4—42no—
262C3×C4⋊C4—81no—
263C3×C4⋊C4C2×D412yes—
264C3×C4⋊C4#4112yes—
265C3×C22⋊C4—42no—
266C3×C22⋊C4—42no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—42no—
269C3×C22⋊C4—81no—
270C3×C22⋊C4—81no—
271C3×C22⋊C4—81no—
272C3×C22⋊C4—81no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—21no—
276C3×C42—21no—
277C3×C42—42no—
278C3×C42—81no—
279C3×C42#4112yes—
280C3×C42#4112yes—
281C22×Q8—21no—
282C22×Q8C23×C311yescharacteristic
283C22×D4—21no—
284C22×D4—21no—
285C22×D4C23×C311yescharacteristic
286C22×D4C23×C311yescharacteristic
287C22×C8C23×C311yescharacteristic
288C22×C8C23×C311yescharacteristic
289C22×C8C23×C311yescharacteristic
290C22×C8C23×C311yescharacteristic
291C4⋊Q8—22no—
292C4⋊Q8—41no—
293#127—22no—
294#127—22no—
295#125—22no—
296#125—41no—
297#124—22no—
298#124—22no—
299#124—41no—
300#124—41no—
301C4×Q8—22no—
302C4×Q8—22no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C3×D411yescharacteristic
310C2×C4⋊C4C3×D411yescharacteristic
311C2×C4⋊C4C23×C311yescharacteristic
312C2×C4⋊C4C23×C311yescharacteristic
313C2×C4⋊C4C23×C311yescharacteristic
314C2×C4⋊C4C23×C311yescharacteristic
315C2×C4⋊C4C23×C311yescharacteristic
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C22⋊C4—21no—
322C2×C22⋊C4—21no—
323C2×C22⋊C4—21no—
324C2×C42—21no—
325C2×C42—21no—
326C2×C42C23×C311yescharacteristic
327C2×C42C23×C311yescharacteristic
328C2×C42C23×C311yescharacteristic
329C4⋊C8—22no—
330#103—22no—
331#103—22no—
332#103—22no—
333#103C3×D414yescomplemented
334#102—22no—
335#102—22no—
336#102—22no—
337#102—22no—
338#102—22no—
339#102—22no—
340#102—41no—
341#102—41no—
342#97—22no—
343#97—22no—
344C4×C8—22no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95C3×D411yescharacteristic
351#95C3×D411yescharacteristic
352C23×C3—41no—
353C23×C3—41no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—41no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3—41no—
362C23×C3—41no—
363C23×C3—41no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3C22×D411yescharacteristic
367C3×Q8—22no—
368C3×Q8—22no—
369C3×Q8—41no—
370C3×Q8—41no—
371C3×Q8—84no—
372C3×D4—41no—
373C3×D4—41no—
374C3×D4—41no—
375C3×D4—41no—
376C3×D4—41no—
377C3×D4—41no—
378C3×D4—41no—
379C3×D4—41no—
380C3×D4—84no—
381C3×D4—84no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—41no—
402C2×C3×C4—41no—
403C2×C3×C4—41no—
404C2×C3×C4—41no—
405C2×C3×C4—41no—
406C2×C3×C4—41no—
407C2×C3×C4—41no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4#12412yes—
417C2×C3×C4#12412yes—
418C2×C3×C4C22×D411yescharacteristic
419C2×C3×C4C2×#4111yescharacteristic
420C2×C3×C4C2×#4111yescharacteristic
421C2×C3×C4C2×#4111yescharacteristic
422C2×C3×C4H(5,𝔽2)11yescharacteristic
423C2×C3×C42−1+411yescharacteristic
424C3×C8—22no—
425C3×C8—41no—
426C3×C8—41no—
427C3×C8—41no—
428C24—21no—
429C24—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—42no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×Q8C2×C3×D412yes—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—42no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—42no—
455C2×D4—81no—
456C2×D4—81no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4C2×C3×D411yescharacteristic
464C22×C4C2×C3×D411yescharacteristic
465C22×C4C2×C3×D411yescharacteristic
466C22×C4C2×C3×D411yescharacteristic
467C22×C4C2×C3×D411yescharacteristic
468C22×C4C2×C3×D411yescharacteristic
469C22×C4C24×C311yescharacteristic
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8C2×C3×D412yes—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4—42no—
495C4⋊C4—42no—
496C4⋊C4—42no—
497C4⋊C4—81no—
498C4⋊C4C2×C3×D412yes—
499C4⋊C4C3×#4112yes—
500C22⋊C4—42no—
501C22⋊C4—42no—
502C22⋊C4—42no—
503C22⋊C4—42no—
504C22⋊C4—81no—
505C22⋊C4—81no—
506C22⋊C4—81no—
507C22⋊C4—81no—
508C42—21no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—42no—
513C42—81no—
514C42C3×#4112yes—
515C42C3×#4112yes—
516C22×C3—81no—
517C22×C3—81no—
518C22×C3—81no—
519C22×C3—81no—
520C22×C3—81no—
521C22×C3—81no—
522C22×C3—81no—
523C22×C3—81no—
524C22×C3—81no—
525C22×C3—81no—
526C22×C3—81no—
527C22×C3—81no—
528C22×C3—81no—
529C22×C3—81no—
530C22×C3C2×#12411yescharacteristic
531C22×C3D4211yescharacteristic
532C22×C3#54811yescharacteristic
533C22×C3#57511yescharacteristic
534C22×C3#57511yescharacteristic
535C22×C3#57611yescharacteristic
536C22×C3#57711yescharacteristic
537C3×C4—22no—
538C3×C4—22no—
539C3×C4—42no—
540C3×C4—42no—
541C3×C4—41no—
542C3×C4—41no—
543C3×C4—42no—
544C3×C4—41no—
545C3×C4—41no—
546C3×C4—81no—
547C3×C4—81no—
548C3×C4—81no—
549C3×C4#53211yescharacteristic
550C3×C4#54211yescharacteristic
551C3×C4#54711yescharacteristic
552C3×C4#55511yescharacteristic
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23C22×C3×D411yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—41no—
571Q8—41no—
572Q8—84no—
573D4—41no—
574D4—41no—
575D4—41no—
576D4—41no—
577D4—41no—
578D4—41no—
579D4—41no—
580D4—41no—
581D4—84no—
582D4—84no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—41no—
617C2×C4C3×#12412yes—
618C2×C4C3×#12412yes—
619C2×C4C22×C3×D411yescharacteristic
620C2×C4C2×C3×#4111yescharacteristic
621C2×C4C2×C3×#4111yescharacteristic
622C2×C4C2×C3×#4111yescharacteristic
623C2×C4C3×H(5,𝔽2)11yescharacteristic
624C2×C4C3×2−1+411yescharacteristic
625C8—22no—
626C8—41no—
627C8—41no—
628C8—41no—
629C2×C3—161no—
630C2×C3—161no—
631C2×C3#249111yescharacteristic
632C2×C3#313611yescharacteristic
633C2×C3#314011yescharacteristic
634C2×C3#326811yescharacteristic
635C2×C3#327111yescharacteristic
636C2×C3#337011yescharacteristic
637C2×C3#337111yescharacteristic
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22—81no—
647C22—81no—
648C22—81no—
649C22—81no—
650C22—81no—
651C22—81no—
652C22C2×C3×#12411yescharacteristic
653C22C3×D4211yescharacteristic
654C22C3×#54811yescharacteristic
655C22C3×#57511yescharacteristic
656C22C3×#57511yescharacteristic
657C22C3×#57611yescharacteristic
658C22C3×#57711yescharacteristic
659C4—22no—
660C4—22no—
661C4—42no—
662C4—41no—
663C4—41no—
664C4—42no—
665C4—41no—
666C4—41no—
667C4—42no—
668C4—81no—
669C4—81no—
670C4—81no—
671C4C3×#53211yescharacteristic
672C4C3×#54211yescharacteristic
673C4C3×#54711yescharacteristic
674C4C3×#55511yescharacteristic
675C3#2778611yescharacteristic, direct product factor, Sylow
676C2—161no—
677C2—161no—
678C2C3×#249111yescharacteristic
679C2C3×#313611yescharacteristic
680C2C3×#314011yescharacteristic
681C2C3×#326811yescharacteristic
682C2C3×#327111yescharacteristic
683C2C3×#337011yescharacteristic
684C2C3×#337111yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#127C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C4⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#489C2semidirect
2. C2×C3×#488C2semidirect
3. C3×#2550C2semidirect
5. C3×#2042C2semidirect
6. C3×#2042C2semidirect
7. C3×#2025C2semidirect
8. C3×#2023C2semidirect
11. C3×#1936C2semidirect
12. C3×#1934C2semidirect
13. C3×#1805C2semidirect
14. C3×#1771C2semidirect
15. C3×#1763C2semidirect
16. #27786C3direct (N × H)
62. C2×#489C2×C3semidirect
63. C2×#488C2×C3semidirect
64. #2550C2×C3semidirect
66. #2042C2×C3semidirect
67. #2042C2×C3semidirect
68. #2025C2×C3semidirect
69. #2023C2×C3semidirect
72. #1936C2×C3semidirect
73. #1934C2×C3semidirect
74. #1805C2×C3semidirect
75. #1771C2×C3semidirect
76. #1763C2×C3semidirect
129. C3×#103D4semidirect
333. #103C3×D4semidirect
675. C3#27786direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4892
C2×C3×#4882
C3×#25502
C3×#25482
C3×#20422
C3×#20252
C3×#20232
C3×#19822
C3×#19612
C3×#19362
C3×#19342
C3×#18052
C3×#17712
C3×#17632
#277863