Finite Group Databasebeta

← C3×#21880 #10640487

Subgroups — C3×#21880 #10640487

Order 768.

1076 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#529C211yesmaximal, characteristic
2C3×#2920C211yesmaximal, characteristic, complemented
3C2×C3×#423C211yesmaximal, characteristic, complemented
4C3×#1998C212yesmaximal, complemented
5C3×#1967C212yesmaximal, complemented
6C3×#1901C212yesmaximal, complemented
7C3×#1900C212yesmaximal
8C3×#1801C212yesmaximal, complemented
9C3×#1800C212yesmaximal, complemented
10#21880C311yesmaximal, characteristic, direct product factor, Sylow
11C22×C3×M16C2212yes—
12C3×#529—21no—
13C3×#529—21no—
14C3×#529—21no—
15C3×#529—21no—
16C3×#529—21no—
17C3×#529—21no—
18C3×#529—21no—
19C3×#529—21no—
20C2×C3×#126C412yes—
21C2×C3×#125C2211yescharacteristic
22C2×C3×#124C2211yescharacteristic
23C2×C3×#123C412yes—
24C2×C3×C22⋊Q8C2211yescharacteristic
25C2×C3×#121C2211yescharacteristic
26C2×C3×C4×Q8C2211yescharacteristic
27C2×C3×C4×D4C412yes—
28C2×C3×C4×D4C2211yescharacteristic
29C2×C3×#117C412yes—
30C22×C3×C42C2211yescharacteristic
31C3×#432—21no—
32C3×#432—21no—
33C3×#431—21no—
34C3×#431—21no—
35C3×#423—21no—
36C3×#423—21no—
37C3×#423C2212yes—
38C3×#423C2212yes—
39C3×#423C2212yes—
40C2×C3×C4⋊C8—21no—
41C2×C3×C4⋊C8—21no—
42C2×C3×#101C2214yes—
43C2×C3×#100C2214yes—
44C3×#407C2212yes—
45C3×C4×M16C2212yes—
46C3×#343C2214yes—
47C3×#343C2214yes—
48C2×#529C2×C311yescharacteristic
49#2920C2×C311yescharacteristic, complemented
50C2×#423C2×C311yescharacteristic, complemented
51#1998C2×C312yescomplemented
52#1967C2×C312yescomplemented
53#1901C2×C312yescomplemented
54#1900C2×C312yes—
55#1801C2×C312yescomplemented
56#1800C2×C312yescomplemented
57C22×C3×Q8C2311yescharacteristic
58C22×C3×D4C2×C412yes—
59C22×C3×D4C2311yescharacteristic
60C23×C3×C4C2×C412yes—
61C23×C3×C4C2×C411yescharacteristic
62C23×C3×C4C2×C411yescharacteristic
63C23×C3×C4C2311yescharacteristic
64C2×C3×M16—22no—
65C2×C3×M16—44no—
66C2×C3×M16C2314yes—
67C2×C3×M16C2314yes—
68C22×C3×C8—22no—
69C3×#126—22no—
70C3×#126—22no—
71C3×#126—22no—
72C3×#126—22no—
73C3×#125—21no—
74C3×#125—21no—
75C3×#125—21no—
76C3×#125—21no—
77C3×#124—21no—
78C3×#124—21no—
79C3×#124—21no—
80C3×#124—21no—
81C3×#123—22no—
82C3×#123—22no—
83C3×#123—22no—
84C3×#123—22no—
85C3×C22⋊Q8—21no—
86C3×C22⋊Q8—21no—
87C3×C22⋊Q8—21no—
88C3×C22⋊Q8—21no—
89C3×#121—21no—
90C3×#121—21no—
91C3×#121—21no—
92C3×#121—21no—
93C3×C4×Q8—21no—
94C3×C4×Q8—21no—
95C3×C4×Q8—21no—
96C3×C4×Q8—21no—
97C3×C4×D4—22no—
98C3×C4×D4—22no—
99C3×C4×D4—22no—
100C3×C4×D4—22no—
101C3×C4×D4—21no—
102C3×C4×D4—21no—
103C3×C4×D4—21no—
104C3×C4×D4—21no—
105C3×#117—22no—
106C3×#117—22no—
107C3×#117—22no—
108C3×#117—22no—
109C2×C3×C4⋊C4C2×C412yes—
110C2×C3×C4⋊C4C2×C412yes—
111C2×C3×C4⋊C4C2×C412yes—
112C2×C3×C4⋊C4C2×C412yes—
113C2×C3×C4⋊C4C2311yescharacteristic
114C2×C3×C4⋊C4C2311yescharacteristic
115C2×C3×C22⋊C4C2×C412yes—
116C2×C3×C22⋊C4C2×C412yes—
117C2×C3×C22⋊C4C2×C412yes—
118C2×C3×C22⋊C4C2×C412yes—
119C2×C3×C22⋊C4C2×C412yes—
120C2×C3×C42C2×C412yes—
121C2×C3×C42C2×C411yescharacteristic
122C2×C3×C42C2×C411yescharacteristic
123C2×C3×C42D411yescharacteristic
124C2×C3×C42D411yescharacteristic
125C2×C3×C42D411yescharacteristic
126C2×C3×C42D411yescharacteristic
127C2×C3×C42D411yescharacteristic
128C2×C3×C42D411yescharacteristic
129C2×C3×C42D411yescharacteristic
130C2×C3×C42D411yescharacteristic
131C2×C3×C42C2311yescharacteristic
132C2×C3×C42C2311yescharacteristic
133C3×C4⋊C8—22no—
134C3×C4⋊C8—22no—
135C3×C4⋊C8—22no—
136C3×C4⋊C8—22no—
137C3×C4⋊C8—22no—
138C3×C4⋊C8—22no—
139C3×#101—44no—
140C3×#100—44no—
141C3×C22⋊C8—22no—
142C3×C22⋊C8—22no—
143C3×#97—22no—
144C3×C4×C8—22no—
145C22×M16C22×C312yes—
146#529—21no—
147#529—21no—
148#529—21no—
149#529—21no—
150#529—21no—
151#529—21no—
152#529—21no—
153#529—21no—
154C2×#126C3×C412yes—
155C2×#125C22×C311yescharacteristic
156C2×#124C22×C311yescharacteristic
157C2×#123C3×C412yes—
158C2×C22⋊Q8C22×C311yescharacteristic
159C2×#121C22×C311yescharacteristic
160C2×C4×Q8C22×C311yescharacteristic
161C2×C4×D4C3×C412yes—
162C2×C4×D4C22×C311yescharacteristic
163C2×#117C3×C412yes—
164C22×C42C22×C311yescharacteristic
165#432—21no—
166#432—21no—
167#431—21no—
168#431—21no—
169#423—21no—
170#423—21no—
171#423C22×C312yes—
172#423C22×C312yes—
173#423C22×C312yes—
174C2×C4⋊C8—21no—
175C2×C4⋊C8—21no—
176C2×#101C22×C314yes—
177C2×#100C22×C314yes—
178#407C22×C312yes—
179C4×M16C22×C312yes—
180#343C22×C314yes—
181#343C22×C314yes—
182C24×C3C22×C411yescharacteristic
183C24×C3C22×C412yes—
184C2×C3×Q8—21no—
185C2×C3×Q8—21no—
186C2×C3×Q8—22no—
187C2×C3×Q8—22no—
188C2×C3×D4—22no—
189C2×C3×D4—22no—
190C2×C3×D4—21no—
191C2×C3×D4—21no—
192C2×C3×D4—22no—
193C2×C3×D4—22no—
194C2×C3×D4—44no—
195C22×C3×C4—22no—
196C22×C3×C4—22no—
197C22×C3×C4—22no—
198C22×C3×C4—22no—
199C22×C3×C4—42no—
200C22×C3×C4—42no—
201C22×C3×C4—44no—
202C22×C3×C4C22⋊C411yescharacteristic
203C22×C3×C4C22⋊C411yescharacteristic
204C22×C3×C4C22⋊C411yescharacteristic
205C22×C3×C4C22⋊C411yescharacteristic
206C22×C3×C4C22⋊C411yescharacteristic
207C22×C3×C4C22⋊C411yescharacteristic
208C22×C3×C4C22⋊C411yescharacteristic
209C22×C3×C4C22⋊C411yescharacteristic
210C22×C3×C4C22×C412yes—
211C22×C3×C4C22×C411yescharacteristic
212C22×C3×C4C22×C411yescharacteristic
213C22×C3×C4C22×C412yes—
214C22×C3×C4C22×C412yes—
215C22×C3×C4C22×C411yescharacteristic
216C22×C3×C4C22×C411yescharacteristic
217C22×C3×C4C22×C411yescharacteristic
218C22×C3×C4C2×D411yescharacteristic
219C22×C3×C4C2×D411yescharacteristic
220C22×C3×C4C2×D411yescharacteristic
221C22×C3×C4C2×D411yescharacteristic
222C22×C3×C4C2411yescharacteristic
223C3×M16—24no—
224C3×M16—24no—
225C3×M16—24no—
226C3×M16—24no—
227C3×M16—44no—
228C2×C3×C8—24no—
229C2×C3×C8—24no—
230C2×C3×C8—44no—
231C3×C4⋊C4—22no—
232C3×C4⋊C4—22no—
233C3×C4⋊C4—22no—
234C3×C4⋊C4—22no—
235C3×C4⋊C4—22no—
236C3×C4⋊C4—22no—
237C3×C4⋊C4—22no—
238C3×C4⋊C4—22no—
239C3×C4⋊C4—21no—
240C3×C4⋊C4—21no—
241C3×C4⋊C4—21no—
242C3×C4⋊C4—21no—
243C3×C22⋊C4—22no—
244C3×C22⋊C4—22no—
245C3×C22⋊C4—22no—
246C3×C22⋊C4—22no—
247C3×C22⋊C4—22no—
248C3×C22⋊C4—22no—
249C3×C22⋊C4—22no—
250C3×C22⋊C4—22no—
251C3×C22⋊C4—22no—
252C3×C22⋊C4—22no—
253C3×C42—22no—
254C3×C42—22no—
255C3×C42C22⋊C411yescharacteristic
256C3×C42C22⋊C411yescharacteristic
257C3×C42C22⋊C411yescharacteristic
258C3×C42C22⋊C411yescharacteristic
259C3×C42C22⋊C411yescharacteristic
260C3×C42C22⋊C411yescharacteristic
261C3×C42C22⋊C411yescharacteristic
262C3×C42C22⋊C411yescharacteristic
263C3×C42C2×D411yescharacteristic
264C3×C42C2×D411yescharacteristic
265C3×C42C2×D411yescharacteristic
266C3×C42C2×D411yescharacteristic
267C3×C42C2×D411yescharacteristic
268C3×C42C2×D411yescharacteristic
269C3×C42C2×D411yescharacteristic
270C3×C42C2×D411yescharacteristic
271C22×Q8C23×C311yescharacteristic
272C22×D4C2×C3×C412yes—
273C22×D4C23×C311yescharacteristic
274C23×C4C2×C3×C412yes—
275C23×C4C2×C3×C411yescharacteristic
276C23×C4C2×C3×C411yescharacteristic
277C23×C4C23×C311yescharacteristic
278C2×M16—22no—
279C2×M16—44no—
280C2×M16C23×C314yes—
281C2×M16C23×C314yes—
282C22×C8—22no—
283#126—22no—
284#126—22no—
285#126—22no—
286#126—22no—
287#125—21no—
288#125—21no—
289#125—21no—
290#125—21no—
291#124—21no—
292#124—21no—
293#124—21no—
294#124—21no—
295#123—22no—
296#123—22no—
297#123—22no—
298#123—22no—
299C22⋊Q8—21no—
300C22⋊Q8—21no—
301C22⋊Q8—21no—
302C22⋊Q8—21no—
303#121—21no—
304#121—21no—
305#121—21no—
306#121—21no—
307C4×Q8—21no—
308C4×Q8—21no—
309C4×Q8—21no—
310C4×Q8—21no—
311C4×D4—22no—
312C4×D4—22no—
313C4×D4—22no—
314C4×D4—22no—
315C4×D4—21no—
316C4×D4—21no—
317C4×D4—21no—
318C4×D4—21no—
319#117—22no—
320#117—22no—
321#117—22no—
322#117—22no—
323C2×C4⋊C4C2×C3×C412yes—
324C2×C4⋊C4C2×C3×C412yes—
325C2×C4⋊C4C2×C3×C412yes—
326C2×C4⋊C4C2×C3×C412yes—
327C2×C4⋊C4C23×C311yescharacteristic
328C2×C4⋊C4C23×C311yescharacteristic
329C2×C22⋊C4C2×C3×C412yes—
330C2×C22⋊C4C2×C3×C412yes—
331C2×C22⋊C4C2×C3×C412yes—
332C2×C22⋊C4C2×C3×C412yes—
333C2×C22⋊C4C2×C3×C412yes—
334C2×C42C2×C3×C412yes—
335C2×C42C2×C3×C411yescharacteristic
336C2×C42C2×C3×C411yescharacteristic
337C2×C42C3×D411yescharacteristic
338C2×C42C3×D411yescharacteristic
339C2×C42C3×D411yescharacteristic
340C2×C42C3×D411yescharacteristic
341C2×C42C3×D411yescharacteristic
342C2×C42C3×D411yescharacteristic
343C2×C42C3×D411yescharacteristic
344C2×C42C3×D411yescharacteristic
345C2×C42C23×C311yescharacteristic
346C2×C42C23×C311yescharacteristic
347C4⋊C8—22no—
348C4⋊C8—22no—
349C4⋊C8—22no—
350C4⋊C8—22no—
351C4⋊C8—22no—
352C4⋊C8—22no—
353#101—44no—
354#100—44no—
355C22⋊C8—22no—
356C22⋊C8—22no—
357#97—22no—
358C4×C8—22no—
359C23×C3—22no—
360C23×C3—22no—
361C23×C3—22no—
362C23×C3—24no—
363C23×C3—41no—
364C23×C3—42no—
365C23×C3—42no—
366C23×C3C2×C22⋊C411yescharacteristic
367C23×C3C2×C22⋊C411yescharacteristic
368C23×C3C23×C411yescharacteristic
369C3×Q8—41no—
370C3×Q8—41no—
371C3×Q8—42no—
372C3×D4—44no—
373C3×D4—44no—
374C3×D4—41no—
375C3×D4—41no—
376C3×D4—42no—
377C2×C3×C4—22no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—21no—
384C2×C3×C4—22no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—22no—
392C2×C3×C4—24no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—41no—
396C2×C3×C4—41no—
397C2×C3×C4—41no—
398C2×C3×C4—41no—
399C2×C3×C4—41no—
400C2×C3×C4—44no—
401C2×C3×C4—44no—
402C2×C3×C4—42no—
403C2×C3×C4—42no—
404C2×C3×C4C2×C22⋊C411yescharacteristic
405C2×C3×C4C2×C22⋊C411yescharacteristic
406C2×C3×C4C2×C22⋊C411yescharacteristic
407C2×C3×C4C2×C22⋊C411yescharacteristic
408C2×C3×C4C2×C22⋊C411yescharacteristic
409C2×C3×C4C2×C22⋊C411yescharacteristic
410C2×C3×C4C2×C22⋊C411yescharacteristic
411C2×C3×C4C2×C22⋊C411yescharacteristic
412C2×C3×C4C2×C22⋊C411yescharacteristic
413C2×C3×C4C2×C22⋊C411yescharacteristic
414C2×C3×C4C22×D411yescharacteristic
415C2×C3×C4C22×D411yescharacteristic
416C2×C3×C4H(5,𝔽2)12yes—
417C2×C3×C42−1+412yes—
418C3×C8—44no—
419C3×C8—44no—
420C24C22×C3×C411yescharacteristic
421C24C22×C3×C412yes—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—22no—
425C2×Q8—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—44no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—42no—
438C22×C4—42no—
439C22×C4—44no—
440C22×C4C3×C22⋊C411yescharacteristic
441C22×C4C3×C22⋊C411yescharacteristic
442C22×C4C3×C22⋊C411yescharacteristic
443C22×C4C3×C22⋊C411yescharacteristic
444C22×C4C3×C22⋊C411yescharacteristic
445C22×C4C3×C22⋊C411yescharacteristic
446C22×C4C3×C22⋊C411yescharacteristic
447C22×C4C3×C22⋊C411yescharacteristic
448C22×C4C22×C3×C412yes—
449C22×C4C22×C3×C411yescharacteristic
450C22×C4C22×C3×C411yescharacteristic
451C22×C4C22×C3×C412yes—
452C22×C4C22×C3×C412yes—
453C22×C4C22×C3×C411yescharacteristic
454C22×C4C22×C3×C411yescharacteristic
455C22×C4C22×C3×C411yescharacteristic
456C22×C4C2×C3×D411yescharacteristic
457C22×C4C2×C3×D411yescharacteristic
458C22×C4C2×C3×D411yescharacteristic
459C22×C4C2×C3×D411yescharacteristic
460C22×C4C24×C311yescharacteristic
461M16—24no—
462M16—24no—
463M16—24no—
464M16—24no—
465M16—44no—
466C2×C8—24no—
467C2×C8—24no—
468C2×C8—44no—
469C4⋊C4—22no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—22no—
488C22⋊C4—22no—
489C22⋊C4—22no—
490C22⋊C4—22no—
491C42—22no—
492C42—22no—
493C42C3×C22⋊C411yescharacteristic
494C42C3×C22⋊C411yescharacteristic
495C42C3×C22⋊C411yescharacteristic
496C42C3×C22⋊C411yescharacteristic
497C42C3×C22⋊C411yescharacteristic
498C42C3×C22⋊C411yescharacteristic
499C42C3×C22⋊C411yescharacteristic
500C42C3×C22⋊C411yescharacteristic
501C42C2×C3×D411yescharacteristic
502C42C2×C3×D411yescharacteristic
503C42C2×C3×D411yescharacteristic
504C42C2×C3×D411yescharacteristic
505C42C2×C3×D411yescharacteristic
506C42C2×C3×D411yescharacteristic
507C42C2×C3×D411yescharacteristic
508C42C2×C3×D411yescharacteristic
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—44no—
517C22×C3—42no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—84no—
521C22×C3#41312yes—
522C22×C3C22×C22⋊C411yescharacteristic
523C22×C3#52012yes—
524C3×C4—21no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—21no—
533C3×C4—42no—
534C3×C4—42no—
535C3×C4—42no—
536C3×C4#41312yes—
537C3×C4#53511yescharacteristic
538C3×C4#53611yescharacteristic
539C3×C4#53712yes—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—24no—
544C23—41no—
545C23—42no—
546C23—42no—
547C23C2×C3×C22⋊C411yescharacteristic
548C23C2×C3×C22⋊C411yescharacteristic
549C23C23×C3×C411yescharacteristic
550Q8—41no—
551Q8—41no—
552Q8—42no—
553D4—44no—
554D4—44no—
555D4—41no—
556D4—41no—
557D4—42no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—44no—
582C2×C4—44no—
583C2×C4—42no—
584C2×C4—42no—
585C2×C4C2×C3×C22⋊C411yescharacteristic
586C2×C4C2×C3×C22⋊C411yescharacteristic
587C2×C4C2×C3×C22⋊C411yescharacteristic
588C2×C4C2×C3×C22⋊C411yescharacteristic
589C2×C4C2×C3×C22⋊C411yescharacteristic
590C2×C4C2×C3×C22⋊C411yescharacteristic
591C2×C4C2×C3×C22⋊C411yescharacteristic
592C2×C4C2×C3×C22⋊C411yescharacteristic
593C2×C4C2×C3×C22⋊C411yescharacteristic
594C2×C4C2×C3×C22⋊C411yescharacteristic
595C2×C4C22×C3×D411yescharacteristic
596C2×C4C22×C3×D411yescharacteristic
597C2×C4C3×H(5,𝔽2)12yes—
598C2×C4C3×2−1+412yes—
599C8—44no—
600C8—44no—
601C2×C3—22no—
602C2×C3—22no—
603C2×C3—41no—
604C2×C3—82no—
605C2×C3#231111yescharacteristic
606C2×C3C2×#41311yescharacteristic
607C2×C3C2×#41311yescharacteristic
608C22—21no—
609C22—21no—
610C22—21no—
611C22—21no—
612C22—21no—
613C22—21no—
614C22—21no—
615C22—44no—
616C22—42no—
617C22—42no—
618C22—42no—
619C22—84no—
620C22C3×#41312yes—
621C22C22×C3×C22⋊C411yescharacteristic
622C22C3×#52012yes—
623C4—21no—
624C4—21no—
625C4—21no—
626C4—21no—
627C4—21no—
628C4—21no—
629C4—21no—
630C4—21no—
631C4—21no—
632C4—42no—
633C4—42no—
634C4—42no—
635C4C3×#41312yes—
636C4C3×#53511yescharacteristic
637C4C3×#53611yescharacteristic
638C4C3×#53712yes—
639C3#2188011yescharacteristic, direct product factor, Sylow
640C2—22no—
641C2—22no—
642C2—41no—
643C2—82no—
644C2C3×#231111yescharacteristic
645C2C2×C3×#41311yescharacteristic
646C2C2×C3×#41311yescharacteristic
subgroupG/H
center, socleC22×C3C22×C22⋊C4
commutatorC23C23×C3×C4
Frattini, cosocleC22×C4C24×C3
prime radicalC2×C3×#121C22
LCSG ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C3 ◁ C22×C3×C42 ◁ G

Complements

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

NH ≅ G/Ntype
2. C3×#2920C2semidirect
3. C2×C3×#423C2semidirect
4. C3×#1998C2semidirect
5. C3×#1967C2semidirect
6. C3×#1901C2semidirect
8. C3×#1801C2semidirect
9. C3×#1800C2semidirect
10. #21880C3direct (N × H)
49. #2920C2×C3semidirect
50. C2×#423C2×C3semidirect
51. #1998C2×C3semidirect
52. #1967C2×C3semidirect
53. #1901C2×C3semidirect
55. #1801C2×C3semidirect
56. #1800C2×C3semidirect
639. C3#21880direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5292
C3×#29202
C2×C3×#4232
C3×#19982
C3×#19672
C3×#19012
C3×#19002
C3×#18012
C3×#18002
#218803