Finite Group Databasebeta

← C3×#29832 #10648439

Subgroups — C3×#29832 #10648439

Order 768.

852 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#478C211yesmaximal, characteristic, complemented
2C2×C3×#463C211yesmaximal, characteristic
3C3×#2861C211yesmaximal, characteristic, complemented
4C3×#2293C211yesmaximal, characteristic, complemented
5C3×#2068C211yesmaximal, characteristic, complemented
6C3×#2067C211yesmaximal, characteristic, complemented
7C3×#2066C211yesmaximal, characteristic, complemented
8C3×#2065C211yesmaximal, characteristic, complemented
9C3×#2055C211yesmaximal, characteristic, complemented
10C3×#2055C211yesmaximal, characteristic, complemented
11C3×#2054C211yesmaximal, characteristic
12C3×#2054C211yesmaximal, characteristic
13C3×#1989C211yesmaximal, characteristic, complemented
14C3×#1983C211yesmaximal, characteristic, complemented
15C3×#1842C211yesmaximal, characteristic, complemented
16#29832C311yesmaximal, characteristic, direct product factor, Sylow
17C22×C3×SD16C2211yescharacteristic
18C22×C3×D8C2211yescharacteristic
19C2×C3×#125C2211yescharacteristic
20C2×C3×#124C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×C3×#117—21no—
23C3×#478—24no—
24C3×#463—24no—
25C2×C3×#107C2211yescharacteristic
26C2×C3×#106C2211yescharacteristic
27C2×C3×C4⋊C8C2211yescharacteristic
28C2×C3×C4⋊C8C2211yescharacteristic
29C2×C3×C4⋊C8C2211yescharacteristic
30C2×C3×C4⋊C8C2211yescharacteristic
31C2×C3×C4⋊C8C2211yescharacteristic
32C2×C3×C4⋊C8C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#103C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C2×C3×#102C2211yescharacteristic
38C2×C3×#102C2211yescharacteristic
39C2×C3×#102C2211yescharacteristic
40C2×C3×#102C2211yescharacteristic
41C3×#391C2211yescharacteristic
42C3×#391C2211yescharacteristic
43C3×#390C2211yescharacteristic
44C3×#390C2211yescharacteristic
45C3×#390C2211yescharacteristic
46C3×#390C2211yescharacteristic
47C3×#389C2211yescharacteristic
48C3×#389C2211yescharacteristic
49C3×#388—21no—
50C3×#388—21no—
51C3×#388—21no—
52C3×#388—21no—
53C3×#388—21no—
54C3×#388—21no—
55C3×C4×C4⋊C4C2211yescharacteristic
56C3×C4×C22⋊C4—21no—
57C3×C43C2211yescharacteristic
58C3×#340C2211yescharacteristic
59C3×#340C2211yescharacteristic
60C3×#340C2211yescharacteristic
61C3×#340C2211yescharacteristic
62C2×#478C2×C311yescharacteristic, complemented
63C2×#463C2×C311yescharacteristic
64#2861C2×C311yescharacteristic, complemented
65#2293C2×C311yescharacteristic, complemented
66#2068C2×C311yescharacteristic, complemented
67#2067C2×C311yescharacteristic, complemented
68#2066C2×C311yescharacteristic, complemented
69#2065C2×C311yescharacteristic, complemented
70#2055C2×C311yescharacteristic, complemented
71#2055C2×C311yescharacteristic, complemented
72#2054C2×C311yescharacteristic
73#2054C2×C311yescharacteristic
74#1989C2×C311yescharacteristic, complemented
75#1983C2×C311yescharacteristic, complemented
76#1842C2×C311yescharacteristic, complemented
77C22×C3×Q8C2311yescharacteristic
78C22×C3×D4C2311yescharacteristic
79C22×C3×D4C2311yescharacteristic
80C23×C3×C4—21no—
81C2×C3×SD16—22no—
82C2×C3×SD16—41no—
83C2×C3×SD16—41no—
84C2×C3×D8—22no—
85C2×C3×D8—41no—
86C2×C3×D8—41no—
87C22×C3×C8C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C22×C3×C8C2311yescharacteristic
91C3×#125—22no—
92C3×#125—22no—
93C3×#124—22no—
94C3×#124—22no—
95C3×C4×D4—22no—
96C3×C4×D4D414yes—
97C3×#117—44no—
98C2×C3×C4⋊C4—21no—
99C2×C3×C4⋊C4—21no—
100C2×C3×C4⋊C4—21no—
101C2×C3×C4⋊C4—21no—
102C2×C3×C4⋊C4C2311yescharacteristic
103C2×C3×C4⋊C4C2311yescharacteristic
104C2×C3×C4⋊C4C2311yescharacteristic
105C2×C3×C4⋊C4C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C22⋊C4—21no—
108C2×C3×C22⋊C4—21no—
109C2×C3×C22⋊C4—21no—
110C2×C3×C22⋊C4—21no—
111C2×C3×C22⋊C4—21no—
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×C42—21no—
119C2×C3×C42D411yescharacteristic
120C2×C3×C42D411yescharacteristic
121C2×C3×C42D411yescharacteristic
122C2×C3×C42D411yescharacteristic
123C2×C3×C42C2311yescharacteristic
124C2×C3×C42C2311yescharacteristic
125C2×C3×C42C2311yescharacteristic
126C3×#107—22no—
127C3×#106—22no—
128C3×C4⋊C8—22no—
129C3×C4⋊C8—22no—
130C3×C4⋊C8—41no—
131C3×C4⋊C8—41no—
132C3×C4⋊C8—41no—
133C3×C4⋊C8—41no—
134C3×#103—22no—
135C3×#103—41no—
136C3×#103—41no—
137C3×#102—22no—
138C3×#102—22no—
139C3×#102—22no—
140C3×#102—41no—
141C3×#102—41no—
142C3×#95—21no—
143C3×#95—21no—
144C3×#95—21no—
145C3×#95—21no—
146C3×#95—21no—
147C3×#95—21no—
148C3×#95—21no—
149C22×SD16C22×C311yescharacteristic
150C22×D8C22×C311yescharacteristic
151C2×#125C22×C311yescharacteristic
152C2×#124C22×C311yescharacteristic
153C2×C4×D4C22×C311yescharacteristic
154C2×#117—21no—
155#478—24no—
156#463—24no—
157C2×#107C22×C311yescharacteristic
158C2×#106C22×C311yescharacteristic
159C2×C4⋊C8C22×C311yescharacteristic
160C2×C4⋊C8C22×C311yescharacteristic
161C2×C4⋊C8C22×C311yescharacteristic
162C2×C4⋊C8C22×C311yescharacteristic
163C2×C4⋊C8C22×C311yescharacteristic
164C2×C4⋊C8C22×C311yescharacteristic
165C2×#103C22×C311yescharacteristic
166C2×#103C22×C311yescharacteristic
167C2×#103C22×C311yescharacteristic
168C2×#102C22×C311yescharacteristic
169C2×#102C22×C311yescharacteristic
170C2×#102C22×C311yescharacteristic
171C2×#102C22×C311yescharacteristic
172C2×#102C22×C311yescharacteristic
173#391C22×C311yescharacteristic
174#391C22×C311yescharacteristic
175#390C22×C311yescharacteristic
176#390C22×C311yescharacteristic
177#390C22×C311yescharacteristic
178#390C22×C311yescharacteristic
179#389C22×C311yescharacteristic
180#389C22×C311yescharacteristic
181#388—21no—
182#388—21no—
183#388—21no—
184#388—21no—
185#388—21no—
186#388—21no—
187C4×C4⋊C4C22×C311yescharacteristic
188C4×C22⋊C4—21no—
189C43C22×C311yescharacteristic
190#340C22×C311yescharacteristic
191#340C22×C311yescharacteristic
192#340C22×C311yescharacteristic
193#340C22×C311yescharacteristic
194C24×C3—21no—
195C24×C3—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—21no—
200C2×C3×Q8—21no—
201C2×C3×Q8—21no—
202C2×C3×D4—21no—
203C2×C3×D4—21no—
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×D4C2×D412yes—
214C22×C3×C4—21no—
215C22×C3×C4—24no—
216C22×C3×C4—21no—
217C22×C3×C4—21no—
218C22×C3×C4—21no—
219C22×C3×C4—21no—
220C22×C3×C4—21no—
221C22×C3×C4—42no—
222C22×C3×C4—42no—
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2×D411yescharacteristic
226C22×C3×C4C2×D411yescharacteristic
227C22×C3×C4C2×D411yescharacteristic
228C22×C3×C4C2×D411yescharacteristic
229C22×C3×C4C2411yescharacteristic
230C3×SD16—44no—
231C3×D8—44no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
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—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
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—42no—
254C3×C4⋊C4—42no—
255C3×C4⋊C4—42no—
256C3×C4⋊C4—42no—
257C3×C4⋊C4C2×D412yes—
258C3×C22⋊C4—24no—
259C3×C22⋊C4—42no—
260C3×C22⋊C4—42no—
261C3×C22⋊C4—42no—
262C3×C22⋊C4—42no—
263C3×C22⋊C4—42no—
264C3×C22⋊C4—42no—
265C3×C22⋊C4—42no—
266C3×C22⋊C4—42no—
267C3×C22⋊C4—42no—
268C3×C22⋊C4—42no—
269C3×C42—22no—
270C3×C42—22no—
271C3×C42—21no—
272C3×C42—21no—
273C3×C42—21no—
274C3×C42—21no—
275C3×C42—41no—
276C3×C42—41no—
277C3×C42—42no—
278C3×C42C2×D412yes—
279C3×C42#4112yes—
280C22×Q8C23×C311yescharacteristic
281C22×D4C23×C311yescharacteristic
282C22×D4C23×C311yescharacteristic
283C23×C4—21no—
284C2×SD16—22no—
285C2×SD16—41no—
286C2×SD16—41no—
287C2×D8—22no—
288C2×D8—41no—
289C2×D8—41no—
290C22×C8C23×C311yescharacteristic
291C22×C8C23×C311yescharacteristic
292C22×C8C23×C311yescharacteristic
293C22×C8C23×C311yescharacteristic
294#125—22no—
295#125—22no—
296#124—22no—
297#124—22no—
298C4×D4—22no—
299C4×D4C3×D414yes—
300#117—44no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—21no—
305C2×C4⋊C4C23×C311yescharacteristic
306C2×C4⋊C4C23×C311yescharacteristic
307C2×C4⋊C4C23×C311yescharacteristic
308C2×C4⋊C4C23×C311yescharacteristic
309C2×C4⋊C4C23×C311yescharacteristic
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C22⋊C4—21no—
317C2×C22⋊C4—21no—
318C2×C22⋊C4—21no—
319C2×C22⋊C4—21no—
320C2×C22⋊C4—21no—
321C2×C42—21no—
322C2×C42C3×D411yescharacteristic
323C2×C42C3×D411yescharacteristic
324C2×C42C3×D411yescharacteristic
325C2×C42C3×D411yescharacteristic
326C2×C42C23×C311yescharacteristic
327C2×C42C23×C311yescharacteristic
328C2×C42C23×C311yescharacteristic
329#107—22no—
330#106—22no—
331C4⋊C8—22no—
332C4⋊C8—22no—
333C4⋊C8—41no—
334C4⋊C8—41no—
335C4⋊C8—41no—
336C4⋊C8—41no—
337#103—22no—
338#103—41no—
339#103—41no—
340#102—22no—
341#102—22no—
342#102—22no—
343#102—41no—
344#102—41no—
345#95—21no—
346#95—21no—
347#95—21no—
348#95—21no—
349#95—21no—
350#95—21no—
351#95—21no—
352C23×C3—22no—
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—41no—
368C3×Q8—41no—
369C3×Q8—41no—
370C3×Q8—41no—
371C3×D4—22no—
372C3×D4—22no—
373C3×D4—41no—
374C3×D4—41no—
375C3×D4—41no—
376C3×D4—41no—
377C3×D4—41no—
378C3×D4—41no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—48no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—41no—
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#12112yes—
413C2×C3×C4#12112yes—
414C2×C3×C4#13512yes—
415C2×C3×C4AGL(1,ℤ/8)12yes—
416C2×C3×C4C22×D411yescharacteristic
417C2×C3×C4C2×#4111yescharacteristic
418C2×C3×C4H(5,𝔽2)11yescharacteristic
419C2×C3×C4H(5,𝔽2)11yescharacteristic
420C2×C3×C42−1+411yescharacteristic
421C2×C3×C42−1+411yescharacteristic
422C3×C8—41no—
423C3×C8—41no—
424C3×C8—41no—
425C3×C8—41no—
426C24—21no—
427C24—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4C2×C3×D412yes—
446C22×C4—21no—
447C22×C4—24no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—42no—
454C22×C4—42no—
455C22×C4C2×C3×D411yescharacteristic
456C22×C4C2×C3×D411yescharacteristic
457C22×C4C2×C3×D411yescharacteristic
458C22×C4C2×C3×D411yescharacteristic
459C22×C4C2×C3×D411yescharacteristic
460C22×C4C2×C3×D411yescharacteristic
461C22×C4C24×C311yescharacteristic
462SD16—44no—
463D8—44no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—42no—
486C4⋊C4—42no—
487C4⋊C4—42no—
488C4⋊C4—42no—
489C4⋊C4C2×C3×D412yes—
490C22⋊C4—24no—
491C22⋊C4—42no—
492C22⋊C4—42no—
493C22⋊C4—42no—
494C22⋊C4—42no—
495C22⋊C4—42no—
496C22⋊C4—42no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C42—22no—
502C42—22no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42—41no—
509C42—42no—
510C42C2×C3×D412yes—
511C42C3×#4112yes—
512C22×C3—42no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—81no—
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×C3C2×#12111yescharacteristic
527C22×C3#53711yescharacteristic
528C22×C3#53711yescharacteristic
529C22×C3C2×#13511yescharacteristic
530C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
531C22×C3#57511yescharacteristic
532C22×C3#57511yescharacteristic
533C3×C4—22no—
534C3×C4—22no—
535C3×C4—22no—
536C3×C4—22no—
537C3×C4—41no—
538C3×C4—41no—
539C3×C4—42no—
540C3×C4—81no—
541C3×C4—81no—
542C3×C4—81no—
543C3×C4—81no—
544C3×C4—81no—
545C3×C4#53511yescharacteristic
546C3×C4#53611yescharacteristic
547C3×C4#54211yescharacteristic
548C3×C4#54211yescharacteristic
549C23—22no—
550C23—41no—
551C23—41no—
552C23—41no—
553C23—41no—
554C23—41no—
555C23—41no—
556C23—41no—
557C23—41no—
558C23—41no—
559C23—41no—
560C23—41no—
561C23—41no—
562C23—41no—
563C23C22×C3×D411yescharacteristic
564Q8—41no—
565Q8—41no—
566Q8—41no—
567Q8—41no—
568D4—22no—
569D4—22no—
570D4—41no—
571D4—41no—
572D4—41no—
573D4—41no—
574D4—41no—
575D4—41no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—21no—
587C2×C4—21no—
588C2×C4—22no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—48no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4C3×#12112yes—
610C2×C4C3×#12112yes—
611C2×C4C3×#13512yes—
612C2×C4C3×AGL(1,ℤ/8)12yes—
613C2×C4C22×C3×D411yescharacteristic
614C2×C4C2×C3×#4111yescharacteristic
615C2×C4C3×H(5,𝔽2)11yescharacteristic
616C2×C4C3×H(5,𝔽2)11yescharacteristic
617C2×C4C3×2−1+411yescharacteristic
618C2×C4C3×2−1+411yescharacteristic
619C8—41no—
620C8—41no—
621C8—41no—
622C8—41no—
623C2×C3—82no—
624C2×C3—161no—
625C2×C3#262011yescharacteristic
626C2×C3#303511yescharacteristic
627C2×C3#303611yescharacteristic
628C2×C3#324711yescharacteristic
629C2×C3#325011yescharacteristic
630C2×C3#325111yescharacteristic
631C2×C3#325611yescharacteristic
632C22—42no—
633C22—42no—
634C22—42no—
635C22—81no—
636C22—81no—
637C22—81no—
638C22—81no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22—81no—
646C22C2×C3×#12111yescharacteristic
647C22C3×#53711yescharacteristic
648C22C3×#53711yescharacteristic
649C22C2×C3×#13511yescharacteristic
650C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
651C22C3×#57511yescharacteristic
652C22C3×#57511yescharacteristic
653C4—22no—
654C4—22no—
655C4—22no—
656C4—22no—
657C4—41no—
658C4—41no—
659C4—42no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4—81no—
665C4C3×#53511yescharacteristic
666C4C3×#53611yescharacteristic
667C4C3×#54211yescharacteristic
668C4C3×#54211yescharacteristic
669C3#2983211yescharacteristic, direct product factor, Sylow
670C2—82no—
671C2—161no—
672C2C3×#262011yescharacteristic
673C2C3×#303511yescharacteristic
674C2C3×#303611yescharacteristic
675C2C3×#324711yescharacteristic
676C2C3×#325011yescharacteristic
677C2C3×#325111yescharacteristic
678C2C3×#325611yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC22×C3×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C43 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#478C2semidirect
3. C3×#2861C2semidirect
4. C3×#2293C2semidirect
5. C3×#2068C2semidirect
6. C3×#2067C2semidirect
7. C3×#2066C2semidirect
8. C3×#2065C2semidirect
9. C3×#2055C2semidirect
10. C3×#2055C2semidirect
13. C3×#1989C2semidirect
14. C3×#1983C2semidirect
15. C3×#1842C2semidirect
16. #29832C3direct (N × H)
62. C2×#478C2×C3semidirect
64. #2861C2×C3semidirect
65. #2293C2×C3semidirect
66. #2068C2×C3semidirect
67. #2067C2×C3semidirect
68. #2066C2×C3semidirect
69. #2065C2×C3semidirect
70. #2055C2×C3semidirect
71. #2055C2×C3semidirect
74. #1989C2×C3semidirect
75. #1983C2×C3semidirect
76. #1842C2×C3semidirect
669. C3#29832direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#4782
C2×C3×#4632
C3×#28612
C3×#22932
C3×#20682
C3×#20672
C3×#20662
C3×#20652
C3×#20552
C3×#20542
C3×#19892
C3×#19832
C3×#18422
#298323