Finite Group Databasebeta

← C3×#24675 #10643282

Subgroups — C3×#24675 #10643282

Order 768.

764 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
1C3×#3040C211yesmaximal, characteristic
2C2×C3×#464C211yesmaximal, characteristic, complemented
3C3×C4×#137C211yesmaximal, characteristic, complemented
4C3×#2925C211yesmaximal, characteristic, complemented
5C3×#2052C211yesmaximal, characteristic, complemented
6C3×#2051C211yesmaximal, characteristic
7C3×#2020C211yesmaximal, characteristic, complemented
8C3×#2019C211yesmaximal, characteristic
9C3×#1979C211yesmaximal, characteristic, complemented
10C3×#1977C211yesmaximal, characteristic, complemented
11C3×#1967C211yesmaximal, characteristic, complemented
12C3×#1950C211yesmaximal, characteristic, complemented
13C3×#1931C211yesmaximal, characteristic, complemented
14C3×#1930C211yesmaximal, characteristic, complemented
15C3×#1801C211yesmaximal, characteristic, complemented
16#24675C311yesmaximal, characteristic, direct product factor, Sylow
17C2×C3×#137C2211yescharacteristic
18C2×C3×#137C2211yescharacteristic
19C2×C3×AGL(1,ℤ/8)C2211yescharacteristic
20C22×C3×Q16C2211yescharacteristic
21C22×C3×SD16C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C3×C4×#41C2211yescharacteristic
24C2×C3×C4×Q8C2211yescharacteristic
25C3×#464—21no—
26C3×#464—21no—
27C3×#464—21no—
28C3×#464—21no—
29C3×#464—21no—
30C3×#464—21no—
31C3×#463—21no—
32C3×#463—21no—
33C3×#441—21no—
34C3×#440—21no—
35C3×C4×Q16—21no—
36C3×C4×SD16—21no—
37C3×#433—21no—
38C3×#433—21no—
39C3×#432—21no—
40C3×#431—21no—
41C2×C3×#108C2211yescharacteristic
42C2×C3×#108C2211yescharacteristic
43C3×#428C2211yescharacteristic
44C3×#423C2211yescharacteristic
45C3×#423C2211yescharacteristic
46C2×C3×C4⋊C8C2211yescharacteristic
47C3×#419C2211yescharacteristic
48C3×#419C2211yescharacteristic
49C3×#418C2211yescharacteristic
50C3×#417C2211yescharacteristic
51C2×C3×#103C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×#101C2211yescharacteristic
54C2×C3×#101C2211yescharacteristic
55C2×C3×#101C2211yescharacteristic
56C2×C3×#101C2211yescharacteristic
57C2×C3×#100C2211yescharacteristic
58C2×C3×#100C2211yescharacteristic
59C3×#408C2211yescharacteristic
60C3×#408C2211yescharacteristic
61C3×#405C2211yescharacteristic
62C3×#405C2211yescharacteristic
63C3×C4×M16C2211yescharacteristic
64C3×#343C2211yescharacteristic
65C3×#343C2211yescharacteristic
66C3×#341C2211yescharacteristic
67C3×#341C2211yescharacteristic
68#3040C2×C311yescharacteristic
69C2×#464C2×C311yescharacteristic, complemented
70C4×#137C2×C311yescharacteristic, complemented
71#2925C2×C311yescharacteristic, complemented
72#2052C2×C311yescharacteristic, complemented
73#2051C2×C311yescharacteristic
74#2020C2×C311yescharacteristic, complemented
75#2019C2×C311yescharacteristic
76#1979C2×C311yescharacteristic, complemented
77#1977C2×C311yescharacteristic, complemented
78#1967C2×C311yescharacteristic, complemented
79#1950C2×C311yescharacteristic, complemented
80#1931C2×C311yescharacteristic, complemented
81#1930C2×C311yescharacteristic, complemented
82#1801C2×C311yescharacteristic, complemented
83C2×C3×#41C2311yescharacteristic
84C22×C3×Q8C2311yescharacteristic
85C22×C3×Q8C2311yescharacteristic
86C22×C3×D4C2311yescharacteristic
87C3×#137—22no—
88C3×#137—22no—
89C3×#137—41no—
90C3×#137—41no—
91C3×AGL(1,ℤ/8)—41no—
92C3×AGL(1,ℤ/8)—41no—
93C2×C3×Q16—21no—
94C2×C3×Q16—21no—
95C2×C3×Q16—22no—
96C2×C3×Q16—21no—
97C2×C3×Q16—21no—
98C2×C3×Q16—41no—
99C2×C3×SD16—21no—
100C2×C3×SD16—21no—
101C2×C3×SD16—22no—
102C2×C3×SD16—21no—
103C2×C3×SD16—21no—
104C2×C3×SD16—21no—
105C2×C3×SD16—41no—
106C2×C3×D8—21no—
107C2×C3×M16C2311yescharacteristic
108C2×C3×M16C2311yescharacteristic
109C2×C3×M16C2311yescharacteristic
110C2×C3×M16C2311yescharacteristic
111C2×C3×M16C2311yescharacteristic
112C2×C3×M16C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C3×#124—21no—
116C3×#124—21no—
117C3×#124—21no—
118C3×#124—21no—
119C3×C4×Q8—21no—
120C3×C4×Q8—21no—
121C3×C4×Q8—21no—
122C3×C4×Q8—21no—
123C3×C4×Q8D411yescharacteristic
124C3×C4×Q8D411yescharacteristic
125C3×C4×D4—21no—
126C3×C4×D4—21no—
127C3×C4×D4D411yescharacteristic
128C3×C4×D4D411yescharacteristic
129C3×#117—21no—
130C3×#117C2311yescharacteristic
131C2×C3×C4⋊C4—21no—
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C42—21no—
136C2×C3×C42—21no—
137C2×C3×C42C2311yescharacteristic
138C3×#108—41no—
139C3×#108—41no—
140C3×#107—21no—
141C3×#106—21no—
142C3×C4⋊C8—21no—
143C3×C4⋊C8—21no—
144C3×C4⋊C8—21no—
145C3×C4⋊C8—21no—
146C3×C4⋊C8D411yescharacteristic
147C3×C4⋊C8D411yescharacteristic
148C3×C4⋊C8D411yescharacteristic
149C3×C4⋊C8D411yescharacteristic
150C3×#103—21no—
151C3×#103—21no—
152C3×#103—21no—
153C3×#103—21no—
154C3×#103—21no—
155C3×#103—21no—
156C3×#103—21no—
157C3×#102—21no—
158C3×#102—21no—
159C3×#102—21no—
160C3×#102—21no—
161C3×#102—21no—
162C3×#101—22no—
163C3×#101—41no—
164C3×#101—41no—
165C3×#101—41no—
166C3×#100—22no—
167C3×#100—41no—
168C3×C22⋊C8—21no—
169C3×C22⋊C8—21no—
170C3×C22⋊C8—21no—
171C3×C22⋊C8—21no—
172C3×#97—21no—
173C3×#97—21no—
174C3×#97—21no—
175C3×C4×C8—21no—
176C3×C4×C8—21no—
177C3×C4×C8—21no—
178C2×#137C22×C311yescharacteristic
179C2×#137C22×C311yescharacteristic
180C2×AGL(1,ℤ/8)C22×C311yescharacteristic
181C22×Q16C22×C311yescharacteristic
182C22×SD16C22×C311yescharacteristic
183C2×#124C22×C311yescharacteristic
184C4×#41C22×C311yescharacteristic
185C2×C4×Q8C22×C311yescharacteristic
186#464—21no—
187#464—21no—
188#464—21no—
189#464—21no—
190#464—21no—
191#464—21no—
192#463—21no—
193#463—21no—
194#441—21no—
195#440—21no—
196C4×Q16—21no—
197C4×SD16—21no—
198#433—21no—
199#433—21no—
200#432—21no—
201#431—21no—
202C2×#108C22×C311yescharacteristic
203C2×#108C22×C311yescharacteristic
204#428C22×C311yescharacteristic
205#423C22×C311yescharacteristic
206#423C22×C311yescharacteristic
207C2×C4⋊C8C22×C311yescharacteristic
208#419C22×C311yescharacteristic
209#419C22×C311yescharacteristic
210#418C22×C311yescharacteristic
211#417C22×C311yescharacteristic
212C2×#103C22×C311yescharacteristic
213C2×#102C22×C311yescharacteristic
214C2×#101C22×C311yescharacteristic
215C2×#101C22×C311yescharacteristic
216C2×#101C22×C311yescharacteristic
217C2×#101C22×C311yescharacteristic
218C2×#100C22×C311yescharacteristic
219C2×#100C22×C311yescharacteristic
220#408C22×C311yescharacteristic
221#408C22×C311yescharacteristic
222#405C22×C311yescharacteristic
223#405C22×C311yescharacteristic
224C4×M16C22×C311yescharacteristic
225#343C22×C311yescharacteristic
226#343C22×C311yescharacteristic
227#341C22×C311yescharacteristic
228#341C22×C311yescharacteristic
229C24×C3—21no—
230C3×#41—21no—
231C3×#41—21no—
232C3×#41—21no—
233C3×#41—21no—
234C2×C3×Q8—21no—
235C2×C3×Q8—21no—
236C2×C3×Q8—21no—
237C2×C3×Q8—21no—
238C2×C3×Q8—21no—
239C2×C3×Q8—21no—
240C2×C3×Q8—21no—
241C2×C3×Q8—21no—
242C2×C3×Q8—21no—
243C2×C3×Q8—21no—
244C2×C3×Q8—21no—
245C2×C3×Q8C2×D411yescharacteristic
246C2×C3×Q8#4112yes—
247C2×C3×D4—21no—
248C2×C3×D4—21no—
249C2×C3×D4—21no—
250C2×C3×D4—21no—
251C2×C3×D4—21no—
252C2×C3×D4—21no—
253C2×C3×D4—21no—
254C2×C3×D4C2×D411yescharacteristic
255C22×C3×C4—21no—
256C22×C3×C4—21no—
257C22×C3×C4—21no—
258C22×C3×C4—21no—
259C22×C3×C4—21no—
260C22×C3×C4—21no—
261C22×C3×C4#4111yescharacteristic
262C22×C3×C4#4111yescharacteristic
263C22×C3×C4C2411yescharacteristic
264C3×Q16—24no—
265C3×Q16—42no—
266C3×Q16—42no—
267C3×Q16—42no—
268C3×SD16—24no—
269C3×SD16—42no—
270C3×SD16—42no—
271C3×SD16—42no—
272C3×SD16—42no—
273C3×D8—42no—
274C3×M16—21no—
275C3×M16—21no—
276C3×M16—21no—
277C3×M16—21no—
278C3×M16—21no—
279C3×M16—21no—
280C3×M16—21no—
281C3×M16—21no—
282C3×M16—21no—
283C3×M16—21no—
284C3×M16—21no—
285C3×M16#4112yes—
286C2×C3×C8—21no—
287C2×C3×C8—21no—
288C2×C3×C8—21no—
289C2×C3×C8—21no—
290C2×C3×C8—21no—
291C2×C3×C8—21no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—21no—
295C2×C3×C8—21no—
296C2×C3×C8C2×D411yescharacteristic
297C2×C3×C8C2×D411yescharacteristic
298C2×C3×C8C2×D411yescharacteristic
299C2×C3×C8C2×D411yescharacteristic
300C3×C4⋊C4—21no—
301C3×C4⋊C4—21no—
302C3×C4⋊C4—21no—
303C3×C4⋊C4—21no—
304C3×C4⋊C4—41no—
305C3×C4⋊C4—41no—
306C3×C4⋊C4C2×D411yescharacteristic
307C3×C4⋊C4C2×D411yescharacteristic
308C3×C22⋊C4—21no—
309C3×C22⋊C4—21no—
310C3×C22⋊C4—21no—
311C3×C22⋊C4—41no—
312C3×C22⋊C4—41no—
313C3×C22⋊C4—41no—
314C3×C22⋊C4—41no—
315C3×C42—21no—
316C3×C42—21no—
317C3×C42—21no—
318C3×C42—41no—
319C3×C42—41no—
320C3×C42C2×D411yescharacteristic
321C3×C42C2×D411yescharacteristic
322C3×C42C2×D411yescharacteristic
323C3×C42C2×D411yescharacteristic
324C2×#41C23×C311yescharacteristic
325C22×Q8C23×C311yescharacteristic
326C22×Q8C23×C311yescharacteristic
327C22×D4C23×C311yescharacteristic
328#137—22no—
329#137—22no—
330#137—41no—
331#137—41no—
332AGL(1,ℤ/8)—41no—
333AGL(1,ℤ/8)—41no—
334C2×Q16—21no—
335C2×Q16—21no—
336C2×Q16—22no—
337C2×Q16—21no—
338C2×Q16—21no—
339C2×Q16—41no—
340C2×SD16—21no—
341C2×SD16—21no—
342C2×SD16—22no—
343C2×SD16—21no—
344C2×SD16—21no—
345C2×SD16—21no—
346C2×SD16—41no—
347C2×D8—21no—
348C2×M16C23×C311yescharacteristic
349C2×M16C23×C311yescharacteristic
350C2×M16C23×C311yescharacteristic
351C2×M16C23×C311yescharacteristic
352C2×M16C23×C311yescharacteristic
353C2×M16C23×C311yescharacteristic
354C22×C8C23×C311yescharacteristic
355C22×C8C23×C311yescharacteristic
356#124—21no—
357#124—21no—
358#124—21no—
359#124—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8C3×D411yescharacteristic
365C4×Q8C3×D411yescharacteristic
366C4×D4—21no—
367C4×D4—21no—
368C4×D4C3×D411yescharacteristic
369C4×D4C3×D411yescharacteristic
370#117—21no—
371#117C23×C311yescharacteristic
372C2×C4⋊C4—21no—
373C2×C4⋊C4C23×C311yescharacteristic
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42C23×C311yescharacteristic
379#108—41no—
380#108—41no—
381#107—21no—
382#106—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8C3×D411yescharacteristic
388C4⋊C8C3×D411yescharacteristic
389C4⋊C8C3×D411yescharacteristic
390C4⋊C8C3×D411yescharacteristic
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#102—21no—
399#102—21no—
400#102—21no—
401#102—21no—
402#102—21no—
403#101—22no—
404#101—41no—
405#101—41no—
406#101—41no—
407#100—22no—
408#100—41no—
409C22⋊C8—21no—
410C22⋊C8—21no—
411C22⋊C8—21no—
412C22⋊C8—21no—
413#97—21no—
414#97—21no—
415#97—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C23×C3—21no—
420C23×C3—41no—
421C23×C3—41no—
422C23×C3—41no—
423C23×C3—81no—
424C23×C3—81no—
425C23×C3C2×#4111yescharacteristic
426C3×Q8—22no—
427C3×Q8—21no—
428C3×Q8—21no—
429C3×Q8—22no—
430C3×Q8—41no—
431C3×Q8—41no—
432C3×Q8—41no—
433C3×Q8—41no—
434C3×Q8—41no—
435C3×Q8—41no—
436C3×D4—21no—
437C3×D4—21no—
438C3×D4—41no—
439C3×D4—41no—
440C3×D4—41no—
441C3×D4—41no—
442C3×D4—41no—
443C3×D4—41no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—22no—
448C2×C3×C4—41no—
449C2×C3×C4—41no—
450C2×C3×C4—42no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—81no—
460C2×C3×C4—81no—
461C2×C3×C4#12111yescharacteristic
462C2×C3×C4#12111yescharacteristic
463C2×C3×C4#12111yescharacteristic
464C2×C3×C4#12111yescharacteristic
465C2×C3×C4C22×D411yescharacteristic
466C2×C3×C4C22×D411yescharacteristic
467C2×C3×C4C2×#4111yescharacteristic
468C2×C3×C4C2×#4111yescharacteristic
469C2×C3×C4H(5,𝔽2)11yescharacteristic
470C2×C3×C4H(5,𝔽2)11yescharacteristic
471C3×C8—22no—
472C3×C8—21no—
473C3×C8—21no—
474C3×C8—21no—
475C3×C8—21no—
476C3×C8—41no—
477C3×C8—41no—
478C3×C8—41no—
479C3×C8—41no—
480C3×C8—41no—
481C24—21no—
482#41—21no—
483#41—21no—
484#41—21no—
485#41—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—21no—
490C2×Q8—21no—
491C2×Q8—21no—
492C2×Q8—21no—
493C2×Q8—21no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8C2×C3×D411yescharacteristic
498C2×Q8C3×#4112yes—
499C2×D4—21no—
500C2×D4—21no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—21no—
505C2×D4—21no—
506C2×D4C2×C3×D411yescharacteristic
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4C3×#4111yescharacteristic
514C22×C4C3×#4111yescharacteristic
515C22×C4C24×C311yescharacteristic
516Q16—24no—
517Q16—42no—
518Q16—42no—
519Q16—42no—
520SD16—24no—
521SD16—42no—
522SD16—42no—
523SD16—42no—
524SD16—42no—
525D8—42no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—21no—
534M16—21no—
535M16—21no—
536M16—21no—
537M16C3×#4112yes—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8C2×C3×D411yescharacteristic
549C2×C8C2×C3×D411yescharacteristic
550C2×C8C2×C3×D411yescharacteristic
551C2×C8C2×C3×D411yescharacteristic
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—41no—
557C4⋊C4—41no—
558C4⋊C4C2×C3×D411yescharacteristic
559C4⋊C4C2×C3×D411yescharacteristic
560C22⋊C4—21no—
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—41no—
564C22⋊C4—41no—
565C22⋊C4—41no—
566C22⋊C4—41no—
567C42—21no—
568C42—21no—
569C42—21no—
570C42—41no—
571C42—41no—
572C42C2×C3×D411yescharacteristic
573C42C2×C3×D411yescharacteristic
574C42C2×C3×D411yescharacteristic
575C42C2×C3×D411yescharacteristic
576C22×C3—21no—
577C22×C3—21no—
578C22×C3—41no—
579C22×C3—41no—
580C22×C3—41no—
581C22×C3—81no—
582C22×C3—81no—
583C22×C3—81no—
584C22×C3—161no—
585C22×C3—161no—
586C22×C3C2×#12111yescharacteristic
587C22×C3#55311yescharacteristic
588C22×C3#55511yescharacteristic
589C3×C4—21no—
590C3×C4—21no—
591C3×C4—21no—
592C3×C4—21no—
593C3×C4—41no—
594C3×C4—42no—
595C3×C4—41no—
596C3×C4—41no—
597C3×C4—81no—
598C3×C4—81no—
599C3×C4#52511yescharacteristic
600C3×C4#53511yescharacteristic
601C3×C4#54611yescharacteristic
602C3×C4#55011yescharacteristic
603C23—21no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—81no—
608C23—81no—
609C23C2×C3×#4111yescharacteristic
610Q8—22no—
611Q8—21no—
612Q8—21no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620D4—21no—
621D4—21no—
622D4—41no—
623D4—41no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—22no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—42no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—81no—
644C2×C4—81no—
645C2×C4C3×#12111yescharacteristic
646C2×C4C3×#12111yescharacteristic
647C2×C4C3×#12111yescharacteristic
648C2×C4C3×#12111yescharacteristic
649C2×C4C22×C3×D411yescharacteristic
650C2×C4C22×C3×D411yescharacteristic
651C2×C4C2×C3×#4111yescharacteristic
652C2×C4C2×C3×#4111yescharacteristic
653C2×C4C3×H(5,𝔽2)11yescharacteristic
654C2×C4C3×H(5,𝔽2)11yescharacteristic
655C8—22no—
656C8—21no—
657C8—21no—
658C8—21no—
659C8—21no—
660C8—41no—
661C8—41no—
662C8—41no—
663C8—41no—
664C8—41no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—81no—
668C2×C3—161no—
669C2×C3#241411yescharacteristic
670C2×C3#306711yescharacteristic
671C2×C3#306911yescharacteristic
672C22—21no—
673C22—21no—
674C22—41no—
675C22—41no—
676C22—41no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—161no—
681C22—161no—
682C22C2×C3×#12111yescharacteristic
683C22C3×#55311yescharacteristic
684C22C3×#55511yescharacteristic
685C4—21no—
686C4—21no—
687C4—21no—
688C4—21no—
689C4—41no—
690C4—42no—
691C4—41no—
692C4—41no—
693C4—81no—
694C4—81no—
695C4C3×#52511yescharacteristic
696C4C3×#53511yescharacteristic
697C4C3×#54611yescharacteristic
698C4C3×#55011yescharacteristic
699C3#2467511yescharacteristic, direct product factor, Sylow
700C2—21no—
701C2—21no—
702C2—81no—
703C2—161no—
704C2C3×#241411yescharacteristic
705C2C3×#306711yescharacteristic
706C2C3×#306911yescharacteristic
subgroupG/H
center, socleC22×C3C2×#121
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×AGL(1,ℤ/8)C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C2×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C3×#464C2semidirect
3. C3×C4×#137C2semidirect
4. C3×#2925C2semidirect
5. C3×#2052C2semidirect
7. C3×#2020C2semidirect
9. C3×#1979C2semidirect
10. C3×#1977C2semidirect
11. C3×#1967C2semidirect
12. C3×#1950C2semidirect
13. C3×#1931C2semidirect
14. C3×#1930C2semidirect
15. C3×#1801C2semidirect
16. #24675C3direct (N × H)
69. C2×#464C2×C3semidirect
70. C4×#137C2×C3semidirect
71. #2925C2×C3semidirect
72. #2052C2×C3semidirect
74. #2020C2×C3semidirect
76. #1979C2×C3semidirect
77. #1977C2×C3semidirect
78. #1967C2×C3semidirect
79. #1950C2×C3semidirect
80. #1931C2×C3semidirect
81. #1930C2×C3semidirect
82. #1801C2×C3semidirect
699. C3#24675direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#30402
C2×C3×#4642
C3×C4×#1372
C3×#29252
C3×#20522
C3×#20512
C3×#20202
C3×#20192
C3×#19792
C3×#19772
C3×#19672
C3×#19502
C3×#19312
C3×#19302
C3×#18012
#246753