Finite Group Databasebeta

← C3×#26420 #10645027

Subgroups — C3×#26420 #10645027

Order 768.

858 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#2442C211yesmaximal, characteristic, complemented
2C3×#2361C211yesmaximal, characteristic
3C3×#2101C211yesmaximal, characteristic, complemented
4C3×#2087C211yesmaximal, characteristic, complemented
5C3×#2067C211yesmaximal, characteristic, complemented
6C3×#2025C211yesmaximal, characteristic, complemented
7C3×#1989C211yesmaximal, characteristic, complemented
8C3×#1921C211yesmaximal, characteristic, complemented
9C3×#1893C211yesmaximal, characteristic
10C3×#1874C211yesmaximal, characteristic
11C3×#1862C211yesmaximal, characteristic, complemented
12C3×#1852C211yesmaximal, characteristic, complemented
13C3×#1850C211yesmaximal, characteristic, complemented
14C3×#1804C211yesmaximal, characteristic, complemented
15C2×C3×#340C211yesmaximal, characteristic, complemented
16#26420C311yesmaximal, characteristic, direct product factor, Sylow
17C23×C3×C8C2211yescharacteristic
18C2×C3×#125C2211yescharacteristic
19C2×C3×#121C2211yescharacteristic
20C2×C3×C4×D4—21no—
21C2×C3×C4×D4C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic
23C22×C3×C4⋊C4C2211yescharacteristic
24C2×C3×#107C2211yescharacteristic
25C2×C3×#107C2211yescharacteristic
26C2×C3×C4⋊C8C2211yescharacteristic
27C2×C3×C4⋊C8C2211yescharacteristic
28C2×C3×#102C2211yescharacteristic
29C2×C3×#102C2211yescharacteristic
30C2×C3×#102C2211yescharacteristic
31C2×C3×#102C2211yescharacteristic
32C2×C3×C22⋊C8C2211yescharacteristic
33C3×#400—21no—
34C3×#398—21no—
35C3×#390C2211yescharacteristic
36C3×#389C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C3×#389C2211yescharacteristic
39C3×#388—21no—
40C3×#386—21no—
41C3×#385—21no—
42C3×#385—21no—
43C3×#382C2211yescharacteristic
44C3×#380—21no—
45C3×#380C2211yescharacteristic
46C3×C4×C4⋊C4C2211yescharacteristic
47C3×C4×C22⋊C4C2211yescharacteristic
48C3×#340C2211yescharacteristic
49C3×#340C2211yescharacteristic
50C3×#340C2211yescharacteristic
51C3×#340C2211yescharacteristic
52C3×#340C2211yescharacteristic
53C3×#340C2211yescharacteristic
54C3×#340C2211yescharacteristic
55C3×#340C2211yescharacteristic
56C3×#340C2211yescharacteristic
57C3×#340C2211yescharacteristic
58C3×#336C2211yescharacteristic
59C3×#336C2211yescharacteristic
60#2442C2×C311yescharacteristic, complemented
61#2361C2×C311yescharacteristic
62#2101C2×C311yescharacteristic, complemented
63#2087C2×C311yescharacteristic, complemented
64#2067C2×C311yescharacteristic, complemented
65#2025C2×C311yescharacteristic, complemented
66#1989C2×C311yescharacteristic, complemented
67#1921C2×C311yescharacteristic, complemented
68#1893C2×C311yescharacteristic
69#1874C2×C311yescharacteristic
70#1862C2×C311yescharacteristic, complemented
71#1852C2×C311yescharacteristic, complemented
72#1850C2×C311yescharacteristic, complemented
73#1804C2×C311yescharacteristic, complemented
74C2×#340C2×C311yescharacteristic, complemented
75C22×C3×D4—21no—
76C22×C3×D4C2311yescharacteristic
77C23×C3×C4—21no—
78C23×C3×C4—21no—
79C23×C3×C4—21no—
80C23×C3×C4C2311yescharacteristic
81C22×C3×C8—22no—
82C22×C3×C8—41no—
83C22×C3×C8—41no—
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C22×C3×C8C2311yescharacteristic
88C3×#125—22no—
89C3×#125—41no—
90C3×#121—22no—
91C3×#121Q814yes—
92C3×C4×D4—22no—
93C3×C4×D4—41no—
94C3×C4×D4—44no—
95C2×C3×C4⋊C4—22no—
96C2×C3×C4⋊C4—22no—
97C2×C3×C4⋊C4—21no—
98C2×C3×C4⋊C4—21no—
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—41no—
105C2×C3×C4⋊C4—41no—
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C4⋊C4C2311yescharacteristic
109C2×C3×C4⋊C4C2311yescharacteristic
110C2×C3×C4⋊C4C2311yescharacteristic
111C2×C3×C4⋊C4C2311yescharacteristic
112C2×C3×C4⋊C4C2311yescharacteristic
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⋊C4D411yescharacteristic
119C2×C3×C22⋊C4D411yescharacteristic
120C2×C3×C42—21no—
121C2×C3×C42C2311yescharacteristic
122C2×C3×C42C2311yescharacteristic
123C3×#107—22no—
124C3×#107—41no—
125C3×C4⋊C8—41no—
126C3×C4⋊C8—41no—
127C3×#102—22no—
128C3×#102—41no—
129C3×#102—41no—
130C3×#102—41no—
131C3×C22⋊C8—22no—
132C3×#95—21no—
133C3×#95—21no—
134C3×#95—21no—
135C3×#95—21no—
136C3×#95—21no—
137C3×#95—21no—
138C3×#95—21no—
139C3×#95D411yescharacteristic
140C3×#95D411yescharacteristic
141C23×C8C22×C311yescharacteristic
142C2×#125C22×C311yescharacteristic
143C2×#121C22×C311yescharacteristic
144C2×C4×D4—21no—
145C2×C4×D4C22×C311yescharacteristic
146C22×C4⋊C4C22×C311yescharacteristic
147C22×C4⋊C4C22×C311yescharacteristic
148C2×#107C22×C311yescharacteristic
149C2×#107C22×C311yescharacteristic
150C2×C4⋊C8C22×C311yescharacteristic
151C2×C4⋊C8C22×C311yescharacteristic
152C2×#102C22×C311yescharacteristic
153C2×#102C22×C311yescharacteristic
154C2×#102C22×C311yescharacteristic
155C2×#102C22×C311yescharacteristic
156C2×C22⋊C8C22×C311yescharacteristic
157#400—21no—
158#398—21no—
159#390C22×C311yescharacteristic
160#389C22×C311yescharacteristic
161#389C22×C311yescharacteristic
162#389C22×C311yescharacteristic
163#388—21no—
164#386—21no—
165#385—21no—
166#385—21no—
167#382C22×C311yescharacteristic
168#380—21no—
169#380C22×C311yescharacteristic
170C4×C4⋊C4C22×C311yescharacteristic
171C4×C22⋊C4C22×C311yescharacteristic
172#340C22×C311yescharacteristic
173#340C22×C311yescharacteristic
174#340C22×C311yescharacteristic
175#340C22×C311yescharacteristic
176#340C22×C311yescharacteristic
177#340C22×C311yescharacteristic
178#340C22×C311yescharacteristic
179#340C22×C311yescharacteristic
180#340C22×C311yescharacteristic
181#340C22×C311yescharacteristic
182#336C22×C311yescharacteristic
183#336C22×C311yescharacteristic
184C24×C3—21no—
185C24×C3C2×D411yescharacteristic
186C2×C3×D4—24no—
187C2×C3×D4—21no—
188C2×C3×D4—21no—
189C2×C3×D4—21no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—42no—
193C2×C3×D4—42no—
194C2×C3×D4C2×Q812yes—
195C22×C3×C4—21no—
196C22×C3×C4—21no—
197C22×C3×C4—21no—
198C22×C3×C4—21no—
199C22×C3×C4—21no—
200C22×C3×C4—21no—
201C22×C3×C4—21no—
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4—42no—
207C22×C3×C4—42no—
208C22×C3×C4—42no—
209C22×C3×C4—42no—
210C22×C3×C4—42no—
211C22×C3×C4—42no—
212C22×C3×C4—81no—
213C22×C3×C4—81no—
214C22×C3×C4—81no—
215C22×C3×C4C2×D411yescharacteristic
216C22×C3×C4C2×D411yescharacteristic
217C22×C3×C4C2×D411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×Q812yes—
221C22×C3×C4#4112yes—
222C22×C3×C4C2411yescharacteristic
223C2×C3×C8—21no—
224C2×C3×C8—21no—
225C2×C3×C8—21no—
226C2×C3×C8—21no—
227C2×C3×C8—21no—
228C2×C3×C8—21no—
229C2×C3×C8—21no—
230C2×C3×C8—21no—
231C2×C3×C8—21no—
232C2×C3×C8—21no—
233C2×C3×C8—21no—
234C2×C3×C8—21no—
235C2×C3×C8—44no—
236C3×C4⋊C4—21no—
237C3×C4⋊C4—21no—
238C3×C4⋊C4—21no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C4⋊C4—21no—
244C3×C4⋊C4—21no—
245C3×C4⋊C4—21no—
246C3×C4⋊C4—21no—
247C3×C4⋊C4—42no—
248C3×C4⋊C4—42no—
249C3×C4⋊C4—42no—
250C3×C4⋊C4—42no—
251C3×C4⋊C4—42no—
252C3×C4⋊C4—81no—
253C3×C4⋊C4—81no—
254C3×C4⋊C4C2×Q812yes—
255C3×C4⋊C4#4112yes—
256C3×C4⋊C4#4112yes—
257C3×C22⋊C4—22no—
258C3×C22⋊C4—22no—
259C3×C22⋊C4—24no—
260C3×C22⋊C4—42no—
261C3×C22⋊C4—42no—
262C3×C22⋊C4—42no—
263C3×C22⋊C4—81no—
264C3×C42—21no—
265C3×C42—21no—
266C3×C42—21no—
267C3×C42—21no—
268C3×C42—42no—
269C22×D4—21no—
270C22×D4C23×C311yescharacteristic
271C23×C4—21no—
272C23×C4—21no—
273C23×C4—21no—
274C23×C4C23×C311yescharacteristic
275C22×C8—22no—
276C22×C8—41no—
277C22×C8—41no—
278C22×C8C23×C311yescharacteristic
279C22×C8C23×C311yescharacteristic
280C22×C8C23×C311yescharacteristic
281C22×C8C23×C311yescharacteristic
282#125—22no—
283#125—41no—
284#121—22no—
285#121C3×Q814yes—
286C4×D4—22no—
287C4×D4—41no—
288C4×D4—44no—
289C2×C4⋊C4—22no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—41no—
299C2×C4⋊C4—41no—
300C2×C4⋊C4C23×C311yescharacteristic
301C2×C4⋊C4C23×C311yescharacteristic
302C2×C4⋊C4C23×C311yescharacteristic
303C2×C4⋊C4C23×C311yescharacteristic
304C2×C4⋊C4C23×C311yescharacteristic
305C2×C4⋊C4C23×C311yescharacteristic
306C2×C4⋊C4C23×C311yescharacteristic
307C2×C22⋊C4—21no—
308C2×C22⋊C4—21no—
309C2×C22⋊C4—21no—
310C2×C22⋊C4—21no—
311C2×C22⋊C4—21no—
312C2×C22⋊C4C3×D411yescharacteristic
313C2×C22⋊C4C3×D411yescharacteristic
314C2×C42—21no—
315C2×C42C23×C311yescharacteristic
316C2×C42C23×C311yescharacteristic
317#107—22no—
318#107—41no—
319C4⋊C8—41no—
320C4⋊C8—41no—
321#102—22no—
322#102—41no—
323#102—41no—
324#102—41no—
325C22⋊C8—22no—
326#95—21no—
327#95—21no—
328#95—21no—
329#95—21no—
330#95—21no—
331#95—21no—
332#95—21no—
333#95C3×D411yescharacteristic
334#95C3×D411yescharacteristic
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—21no—
339C23×C3—22no—
340C23×C3—41no—
341C23×C3—41no—
342C23×C3—41no—
343C23×C3—41no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3C22⋊Q812yes—
347C23×C3#13512yes—
348C23×C3AGL(1,ℤ/8)12yes—
349C23×C3C22×D411yescharacteristic
350C3×D4—22no—
351C3×D4—22no—
352C3×D4—48no—
353C3×D4—41no—
354C3×D4—41no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—22no—
360C2×C3×C4—22no—
361C2×C3×C4—22no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—21no—
366C2×C3×C4—22no—
367C2×C3×C4—22no—
368C2×C3×C4—21no—
369C2×C3×C4—21no—
370C2×C3×C4—21no—
371C2×C3×C4—21no—
372C2×C3×C4—21no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—21no—
376C2×C3×C4—41no—
377C2×C3×C4—41no—
378C2×C3×C4—41no—
379C2×C3×C4—41no—
380C2×C3×C4—41no—
381C2×C3×C4—41no—
382C2×C3×C4—41no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—41no—
386C2×C3×C4—41no—
387C2×C3×C4—41no—
388C2×C3×C4—41no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
393C2×C3×C4—41no—
394C2×C3×C4—84no—
395C2×C3×C4—84no—
396C2×C3×C4—84no—
397C2×C3×C4C22⋊Q812yes—
398C2×C3×C4C22×Q811yescharacteristic
399C2×C3×C4C2×#4111yescharacteristic
400C2×C3×C4C2×#4111yescharacteristic
401C2×C3×C4C2×#4111yescharacteristic
402C2×C3×C4H(5,𝔽2)11yescharacteristic
403C2×C3×C4H(5,𝔽2)11yescharacteristic
404C3×C8—41no—
405C3×C8—41no—
406C3×C8—41no—
407C3×C8—41no—
408C24—21no—
409C24C2×C3×D411yescharacteristic
410C2×D4—24no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4C2×C3×Q812yes—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—42no—
435C22×C4—42no—
436C22×C4—81no—
437C22×C4—81no—
438C22×C4—81no—
439C22×C4C2×C3×D411yescharacteristic
440C22×C4C2×C3×D411yescharacteristic
441C22×C4C2×C3×D411yescharacteristic
442C22×C4C2×C3×D411yescharacteristic
443C22×C4C2×C3×D411yescharacteristic
444C22×C4C2×C3×Q812yes—
445C22×C4C3×#4112yes—
446C22×C4C24×C311yescharacteristic
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—44no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—42no—
472C4⋊C4—42no—
473C4⋊C4—42no—
474C4⋊C4—42no—
475C4⋊C4—42no—
476C4⋊C4—81no—
477C4⋊C4—81no—
478C4⋊C4C2×C3×Q812yes—
479C4⋊C4C3×#4112yes—
480C4⋊C4C3×#4112yes—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—24no—
484C22⋊C4—42no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—81no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—42no—
493C22×C3—22no—
494C22×C3—22no—
495C22×C3—22no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—22no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—42no—
502C22×C3—81no—
503C22×C3—81no—
504C22×C3—81no—
505C22×C3—81no—
506C22×C3#47814yes—
507C22×C3C2×C22⋊Q811yescharacteristic
508C22×C3#54611yescharacteristic
509C22×C3#54611yescharacteristic
510C22×C3C2×#13511yescharacteristic
511C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
512C22×C3#57611yescharacteristic
513C22×C3#57811yescharacteristic
514C3×C4—22no—
515C3×C4—42no—
516C3×C4—41no—
517C3×C4—42no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—42no—
522C3×C4—81no—
523C3×C4—81no—
524C3×C4—81no—
525C3×C4—81no—
526C3×C4#52911yescharacteristic
527C3×C4#53811yescharacteristic
528C3×C4#55411yescharacteristic
529C3×C4#55411yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—22no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C3×C22⋊Q812yes—
542C23C3×#13512yes—
543C23C3×AGL(1,ℤ/8)12yes—
544C23C22×C3×D411yescharacteristic
545D4—22no—
546D4—22no—
547D4—48no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—22no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—84no—
590C2×C4—84no—
591C2×C4—84no—
592C2×C4C3×C22⋊Q812yes—
593C2×C4C22×C3×Q811yescharacteristic
594C2×C4C2×C3×#4111yescharacteristic
595C2×C4C2×C3×#4111yescharacteristic
596C2×C4C2×C3×#4111yescharacteristic
597C2×C4C3×H(5,𝔽2)11yescharacteristic
598C2×C4C3×H(5,𝔽2)11yescharacteristic
599C8—41no—
600C8—41no—
601C8—41no—
602C8—41no—
603C2×C3—24no—
604C2×C3—82no—
605C2×C3#245011yescharacteristic
606C2×C3C2×#47811yescharacteristic
607C2×C3#308311yescharacteristic
608C2×C3#329711yescharacteristic
609C2×C3#330011yescharacteristic
610C2×C3#330811yescharacteristic
611C2×C3#331811yescharacteristic
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—42no—
619C22—42no—
620C22—42no—
621C22—81no—
622C22—81no—
623C22—81no—
624C22—81no—
625C22C3×#47814yes—
626C22C2×C3×C22⋊Q811yescharacteristic
627C22C3×#54611yescharacteristic
628C22C3×#54611yescharacteristic
629C22C2×C3×#13511yescharacteristic
630C22C2×C3×AGL(1,ℤ/8)11yescharacteristic
631C22C3×#57611yescharacteristic
632C22C3×#57811yescharacteristic
633C4—22no—
634C4—41no—
635C4—42no—
636C4—41no—
637C4—41no—
638C4—41no—
639C4—42no—
640C4—42no—
641C4—81no—
642C4—81no—
643C4—81no—
644C4—81no—
645C4C3×#52911yescharacteristic
646C4C3×#53811yescharacteristic
647C4C3×#55411yescharacteristic
648C4C3×#55411yescharacteristic
649C3#2642011yescharacteristic, direct product factor, Sylow
650C2—24no—
651C2—82no—
652C2C3×#245011yescharacteristic
653C2C2×C3×#47811yescharacteristic
654C2C3×#308311yescharacteristic
655C2C3×#329711yescharacteristic
656C2C3×#330011yescharacteristic
657C2C3×#330811yescharacteristic
658C2C3×#331811yescharacteristic
subgroupG/H
center, socleC23×C3C22×D4
commutator, Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C3 ◁ C3×C4×C22⋊C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C3×#2442C2semidirect
3. C3×#2101C2semidirect
4. C3×#2087C2semidirect
5. C3×#2067C2semidirect
6. C3×#2025C2semidirect
7. C3×#1989C2semidirect
8. C3×#1921C2semidirect
11. C3×#1862C2semidirect
12. C3×#1852C2semidirect
13. C3×#1850C2semidirect
14. C3×#1804C2semidirect
15. C2×C3×#340C2semidirect
16. #26420C3direct (N × H)
60. #2442C2×C3semidirect
62. #2101C2×C3semidirect
63. #2087C2×C3semidirect
64. #2067C2×C3semidirect
65. #2025C2×C3semidirect
66. #1989C2×C3semidirect
67. #1921C2×C3semidirect
70. #1862C2×C3semidirect
71. #1852C2×C3semidirect
72. #1850C2×C3semidirect
73. #1804C2×C3semidirect
74. C2×#340C2×C3semidirect
649. C3#26420direct (N × H)

Maximal subgroups

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

subgroupindex
C3×#24422
C3×#23612
C3×#21012
C3×#20872
C3×#20672
C3×#20252
C3×#19892
C3×#19212
C3×#18932
C3×#18742
C3×#18622
C3×#18522
C3×#18502
C3×#18042
C2×C3×#3402
#264203