Finite Group Databasebeta

← C3×#60469 #10679076

Subgroups — C3×#60469 #10679076

Order 768.

2628 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#575C212yesmaximal, complemented
2C2×C3×#575C211yesmaximal, characteristic, complemented
3C2×C3×#568C211yesmaximal, characteristic, complemented
4C3×#3069C218yesmaximal, complemented
5C3×#3068C218yesmaximal, complemented
6C3×#3067C218yesmaximal, complemented
7C2×C3×#430C211yesmaximal, characteristic, complemented
8C2×C3×#413C212yesmaximal, complemented
9#60469C311yesmaximal, characteristic, direct product factor, Sylow
10C22×C3×#41C2211yescharacteristic
11C22×C3×#41C2212yes—
12C3×#575—24no—
13C3×#575—24no—
14C3×#575—22no—
15C3×#575—22no—
16C3×#575—24no—
17C3×#575C2218yes—
18C3×#575C2218yescomplemented
19C2×C3×#137—22no—
20C2×C3×#137C2214yescomplemented
21C2×C3×#137C2214yescomplemented
22C2×C3×AGL(1,ℤ/8)—22no—
23C2×C3×AGL(1,ℤ/8)C2214yescomplemented
24C2×C3×AGL(1,ℤ/8)C2214yescomplemented
25C2×C3×#135—24no—
26C2×C3×#135C2214yescomplemented
27C3×#568—24no—
28C3×#568C2218yescomplemented
29C2×C3×#131—22no—
30C2×C3×#131C2214yescomplemented
31C22×C3×M16—22no—
32C22×C3×M16C2211yescharacteristic
33C22×C3×M16C2212yes—
34C22×C3×M16C2211yescharacteristic
35C3×#473C22116yescomplemented
36C3×#472C22116yescomplemented
37C3×#471C22132yescomplemented
38C3×#430C2218yescomplemented
39C2×C3×#108C2214yescomplemented
40C3×#413C2218yescomplemented
41C3×#413C2218yescomplemented
42C2×C3×#101C2214yescomplemented
43C2×C3×#100C2214yescomplemented
44C2×#575C2×C312yescomplemented
45C2×#575C2×C311yescharacteristic, complemented
46C2×#568C2×C311yescharacteristic, complemented
47#3069C2×C318yescomplemented
48#3068C2×C318yescomplemented
49#3067C2×C318yescomplemented
50C2×#430C2×C311yescharacteristic, complemented
51C2×#413C2×C312yescomplemented
52C2×C3×#41—21no—
53C2×C3×#41—22no—
54C2×C3×#41—22no—
55C2×C3×#41—21no—
56C2×C3×#41—22no—
57C2×C3×#41—22no—
58C2×C3×#41—22no—
59C2×C3×#41—22no—
60C2×C3×#41—22no—
61C2×C3×#41—22no—
62C2×C3×#41—22no—
63C2×C3×#41—22no—
64C2×C3×#41—22no—
65C2×C3×#41—22no—
66C2×C3×#41D414yes—
67C2×C3×#41D412yes—
68C2×C3×#41C2312yes—
69C2×C3×#41C2314yes—
70C2×C3×#41C2314yes—
71C2×C3×#41C2314yes—
72C22×C3×Q8D411yescharacteristic
73C22×C3×Q8C2312yes—
74C22×C3×D4—21no—
75C22×C3×D4—22no—
76C22×C3×D4D411yescharacteristic
77C22×C3×D4C2312yes—
78C23×C3×C4—21no—
79C23×C3×C4—22no—
80C23×C3×C4C2311yescharacteristic
81C3×#137—28no—
82C3×#137—28no—
83C3×#137—28no—
84C3×#137—28no—
85C3×#137—28no—
86C3×#137C23116yes—
87C3×AGL(1,ℤ/8)—28no—
88C3×AGL(1,ℤ/8)—28no—
89C3×AGL(1,ℤ/8)—28no—
90C3×AGL(1,ℤ/8)—28no—
91C3×AGL(1,ℤ/8)—28no—
92C3×AGL(1,ℤ/8)C23116yes—
93C3×#135—216no—
94C3×#135—216no—
95C3×#135—28no—
96C3×#135—28no—
97C2×C3×Q16—24no—
98C2×C3×Q16C2314yescomplemented
99C2×C3×SD16—24no—
100C2×C3×SD16—24no—
101C2×C3×SD16C2318yescomplemented
102C2×C3×D8—24no—
103C2×C3×D8C2314yescomplemented
104C3×#131—216no—
105C3×#131—28no—
106C3×#131C23116yes—
107C2×C3×M16—21no—
108C2×C3×M16—22no—
109C2×C3×M16—22no—
110C2×C3×M16—22no—
111C2×C3×M16—22no—
112C2×C3×M16—216no—
113C2×C3×M16—24no—
114C2×C3×M16D412yes—
115C2×C3×M16D412yes—
116C2×C3×M16D414yes—
117C2×C3×M16C2312yes—
118C2×C3×M16C2314yes—
119C2×C3×M16C2314yes—
120C2×C3×M16C2314yes—
121C2×C3×M16C2314yes—
122C2×C3×M16C2314yes—
123C22×C3×C8—21no—
124C22×C3×C8—22no—
125C22×C3×C8—24no—
126C22×C3×C8C2312yes—
127C3×#108C23116yescomplemented
128C3×#101C23116yescomplemented
129C3×#100C23116yescomplemented
130C22×#41C22×C311yescharacteristic
131C22×#41C22×C312yes—
132#575—24no—
133#575—24no—
134#575—22no—
135#575—22no—
136#575—24no—
137#575C22×C318yes—
138#575C22×C318yescomplemented
139C2×#137—22no—
140C2×#137C22×C314yescomplemented
141C2×#137C22×C314yescomplemented
142C2×AGL(1,ℤ/8)—22no—
143C2×AGL(1,ℤ/8)C22×C314yescomplemented
144C2×AGL(1,ℤ/8)C22×C314yescomplemented
145C2×#135—24no—
146C2×#135C22×C314yescomplemented
147#568—24no—
148#568C22×C318yescomplemented
149C2×#131—22no—
150C2×#131C22×C314yescomplemented
151C22×M16—22no—
152C22×M16C22×C311yescharacteristic
153C22×M16C22×C312yes—
154C22×M16C22×C311yescharacteristic
155#473C22×C3116yescomplemented
156#472C22×C3116yescomplemented
157#471C22×C3132yescomplemented
158#430C22×C318yescomplemented
159C2×#108C22×C314yescomplemented
160#413C22×C318yescomplemented
161#413C22×C318yescomplemented
162C2×#101C22×C314yescomplemented
163C2×#100C22×C314yescomplemented
164C24×C3—21no—
165C24×C3—22no—
166C24×C3#4111yescharacteristic
167C3×#41—24no—
168C3×#41—24no—
169C3×#41—24no—
170C3×#41—24no—
171C3×#41—22no—
172C3×#41—24no—
173C3×#41—22no—
174C3×#41—24no—
175C3×#41—24no—
176C3×#41—24no—
177C3×#41—24no—
178C3×#41—24no—
179C3×#41—24no—
180C3×#41—24no—
181C3×#41—24no—
182C3×#41—42no—
183C3×#41—42no—
184C3×#41—42no—
185C3×#41—42no—
186C3×#41—42no—
187C3×#41—42no—
188C3×#41—42no—
189C3×#41—42no—
190C3×#41C2×D414yes—
191C3×#41C2×D418yes—
192C3×#41C2414yes—
193C2×C3×Q8—22no—
194C2×C3×Q8—21no—
195C2×C3×Q8—22no—
196C2×C3×Q8—22no—
197C2×C3×Q8—22no—
198C2×C3×Q8—22no—
199C2×C3×Q8—22no—
200C2×C3×Q8C2×D414yes—
201C2×C3×Q8C2×D412yes—
202C2×C3×Q8C2414yes—
203C2×C3×D4—22no—
204C2×C3×D4—24no—
205C2×C3×D4—22no—
206C2×C3×D4—24no—
207C2×C3×D4—24no—
208C2×C3×D4—24no—
209C2×C3×D4—22no—
210C2×C3×D4—21no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—22no—
214C2×C3×D4—22no—
215C2×C3×D4—22no—
216C2×C3×D4—42no—
217C2×C3×D4—42no—
218C2×C3×D4—42no—
219C2×C3×D4—42no—
220C2×C3×D4C2×D414yes—
221C2×C3×D4C2×D412yes—
222C2×C3×D4C2414yes—
223C22×C3×C4—21no—
224C22×C3×C4—22no—
225C22×C3×C4—24no—
226C22×C3×C4—22no—
227C22×C3×C4—24no—
228C22×C3×C4—22no—
229C22×C3×C4—24no—
230C22×C3×C4—24no—
231C22×C3×C4—42no—
232C22×C3×C4—42no—
233C22×C3×C4—42no—
234C22×C3×C4—42no—
235C22×C3×C4C2×D412yes—
236C22×C3×C4C2×D411yescharacteristic
237C22×C3×C4C2×D411yescharacteristic
238C22×C3×C4C2×D411yescharacteristic
239C22×C3×C4C2×D411yescharacteristic
240C22×C3×C4C2×D412yes—
241C22×C3×C4#4112yes—
242C22×C3×C4#4111yescharacteristic
243C22×C3×C4C2411yescharacteristic
244C22×C3×C4C2412yes—
245C3×Q16—216no—
246C3×Q16—28no—
247C3×SD16—216no—
248C3×SD16—216no—
249C3×SD16—216no—
250C3×D8—216no—
251C3×D8—28no—
252C3×M16—24no—
253C3×M16—22no—
254C3×M16—24no—
255C3×M16—24no—
256C3×M16—24no—
257C3×M16—216no—
258C3×M16C2×D418yes—
259C3×M16C2×D418yes—
260C3×M16C2414yes—
261C3×M16C2418yes—
262C2×C3×C8—22no—
263C2×C3×C8—24no—
264C2×C3×C8—24no—
265C2×C3×C8—24no—
266C2×C3×C8—24no—
267C2×C3×C8—216no—
268C2×C3×C8C2×D414yes—
269C2×C3×C8C2×D414yes—
270C2×C3×C8C2414yes—
271C2×#41—21no—
272C2×#41—22no—
273C2×#41—22no—
274C2×#41—21no—
275C2×#41—22no—
276C2×#41—22no—
277C2×#41—22no—
278C2×#41—22no—
279C2×#41—22no—
280C2×#41—22no—
281C2×#41—22no—
282C2×#41—22no—
283C2×#41—22no—
284C2×#41—22no—
285C2×#41C3×D414yes—
286C2×#41C3×D412yes—
287C2×#41C23×C312yes—
288C2×#41C23×C314yes—
289C2×#41C23×C314yes—
290C2×#41C23×C314yes—
291C22×Q8C3×D411yescharacteristic
292C22×Q8C23×C312yes—
293C22×D4—21no—
294C22×D4—22no—
295C22×D4C3×D411yescharacteristic
296C22×D4C23×C312yes—
297C23×C4—21no—
298C23×C4—22no—
299C23×C4C23×C311yescharacteristic
300#137—28no—
301#137—28no—
302#137—28no—
303#137—28no—
304#137—28no—
305#137C23×C3116yes—
306AGL(1,ℤ/8)—28no—
307AGL(1,ℤ/8)—28no—
308AGL(1,ℤ/8)—28no—
309AGL(1,ℤ/8)—28no—
310AGL(1,ℤ/8)—28no—
311AGL(1,ℤ/8)C23×C3116yes—
312#135—216no—
313#135—216no—
314#135—28no—
315#135—28no—
316C2×Q16—24no—
317C2×Q16C23×C314yescomplemented
318C2×SD16—24no—
319C2×SD16—24no—
320C2×SD16C23×C318yescomplemented
321C2×D8—24no—
322C2×D8C23×C314yescomplemented
323#131—216no—
324#131—28no—
325#131C23×C3116yes—
326C2×M16—21no—
327C2×M16—22no—
328C2×M16—22no—
329C2×M16—22no—
330C2×M16—22no—
331C2×M16—216no—
332C2×M16—24no—
333C2×M16C3×D412yes—
334C2×M16C3×D412yes—
335C2×M16C3×D414yes—
336C2×M16C23×C312yes—
337C2×M16C23×C314yes—
338C2×M16C23×C314yes—
339C2×M16C23×C314yes—
340C2×M16C23×C314yes—
341C2×M16C23×C314yes—
342C22×C8—21no—
343C22×C8—22no—
344C22×C8—24no—
345C22×C8C23×C312yes—
346#108C23×C3116yescomplemented
347#101C23×C3116yescomplemented
348#100C23×C3116yescomplemented
349C23×C3—22no—
350C23×C3—24no—
351C23×C3—24no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—81no—
355C23×C3—82no—
356C23×C3—84no—
357C23×C3#12111yescharacteristic
358C23×C3#12112yes—
359C23×C3#12111yescharacteristic
360C23×C3C2×#4112yes—
361C23×C3C2×#4111yescharacteristic
362C3×Q8—22no—
363C3×Q8—24no—
364C3×Q8—24no—
365C3×Q8—24no—
366C3×Q8—42no—
367C3×Q8—42no—
368C3×Q8C22×D414yes—
369C3×D4—28no—
370C3×D4—24no—
371C3×D4—24no—
372C3×D4—22no—
373C3×D4—24no—
374C3×D4—24no—
375C3×D4—24no—
376C3×D4—44no—
377C3×D4—44no—
378C3×D4—44no—
379C3×D4—44no—
380C3×D4—42no—
381C3×D4—42no—
382C3×D4C22×D414yes—
383C2×C3×C4—24no—
384C2×C3×C4—22no—
385C2×C3×C4—28no—
386C2×C3×C4—24no—
387C2×C3×C4—24no—
388C2×C3×C4—24no—
389C2×C3×C4—42no—
390C2×C3×C4—42no—
391C2×C3×C4—44no—
392C2×C3×C4—44no—
393C2×C3×C4—44no—
394C2×C3×C4—44no—
395C2×C3×C4#12111yescharacteristic
396C2×C3×C4#12112yes—
397C2×C3×C4#12112yes—
398C2×C3×C4#12111yescharacteristic
399C2×C3×C4#12112yes—
400C2×C3×C4#12112yes—
401C2×C3×C4#12112yes—
402C2×C3×C4C22×D412yes—
403C2×C3×C4C22×D412yes—
404C2×C3×C4C22×D412yes—
405C2×C3×C4C22×D411yescharacteristic
406C2×C3×C4C22×D411yescharacteristic
407C2×C3×C4C22×D412yes—
408C2×C3×C4C22×D411yescharacteristic
409C2×C3×C4C22×D411yescharacteristic
410C2×C3×C4C2×#4112yes—
411C2×C3×C4C2×#4111yescharacteristic
412C2×C3×C4C2511yescharacteristic
413C3×C8—24no—
414C3×C8—28no—
415C3×C8C22×D418yes—
416C24—21no—
417C24—22no—
418C24C3×#4111yescharacteristic
419#41—24no—
420#41—24no—
421#41—24no—
422#41—24no—
423#41—22no—
424#41—22no—
425#41—24no—
426#41—24no—
427#41—24no—
428#41—24no—
429#41—24no—
430#41—24no—
431#41—24no—
432#41—24no—
433#41—24no—
434#41—42no—
435#41—42no—
436#41—42no—
437#41—42no—
438#41—42no—
439#41—42no—
440#41—42no—
441#41—42no—
442#41C2×C3×D414yes—
443#41C2×C3×D418yes—
444#41C24×C314yes—
445C2×Q8—22no—
446C2×Q8—21no—
447C2×Q8—22no—
448C2×Q8—22no—
449C2×Q8—22no—
450C2×Q8—22no—
451C2×Q8—22no—
452C2×Q8C2×C3×D414yes—
453C2×Q8C2×C3×D412yes—
454C2×Q8C24×C314yes—
455C2×D4—22no—
456C2×D4—24no—
457C2×D4—22no—
458C2×D4—24no—
459C2×D4—24no—
460C2×D4—24no—
461C2×D4—22no—
462C2×D4—21no—
463C2×D4—22no—
464C2×D4—22no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—42no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—42no—
472C2×D4C2×C3×D414yes—
473C2×D4C2×C3×D412yes—
474C2×D4C24×C314yes—
475C22×C4—21no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—42no—
484C22×C4—42no—
485C22×C4—42no—
486C22×C4—42no—
487C22×C4C2×C3×D412yes—
488C22×C4C2×C3×D411yescharacteristic
489C22×C4C2×C3×D411yescharacteristic
490C22×C4C2×C3×D411yescharacteristic
491C22×C4C2×C3×D411yescharacteristic
492C22×C4C2×C3×D412yes—
493C22×C4C3×#4112yes—
494C22×C4C3×#4111yescharacteristic
495C22×C4C24×C311yescharacteristic
496C22×C4C24×C312yes—
497Q16—216no—
498Q16—28no—
499SD16—216no—
500SD16—216no—
501SD16—216no—
502D8—216no—
503D8—28no—
504M16—24no—
505M16—22no—
506M16—24no—
507M16—24no—
508M16—24no—
509M16—216no—
510M16C2×C3×D418yes—
511M16C2×C3×D418yes—
512M16C24×C314yes—
513M16C24×C318yes—
514C2×C8—22no—
515C2×C8—24no—
516C2×C8—24no—
517C2×C8—24no—
518C2×C8—24no—
519C2×C8—216no—
520C2×C8C2×C3×D414yes—
521C2×C8C2×C3×D414yes—
522C2×C8C24×C314yes—
523C22×C3—24no—
524C22×C3—41no—
525C22×C3—42no—
526C22×C3—41no—
527C22×C3—42no—
528C22×C3—41no—
529C22×C3—44no—
530C22×C3—44no—
531C22×C3—84no—
532C22×C3—84no—
533C22×C3—84no—
534C22×C3—84no—
535C22×C3C2×#12112yes—
536C22×C3C2×#12111yescharacteristic
537C22×C3C2×#12112yes—
538C22×C3C2×#12111yescharacteristic
539C22×C3C22×#4111yescharacteristic
540C3×C4—24no—
541C3×C4—44no—
542C3×C4C2×#12112yes—
543C3×C4C2×#12111yescharacteristic
544C3×C4C2×#12112yes—
545C3×C4C2×#12111yescharacteristic
546C3×C4C23×D411yescharacteristic
547C3×C4C23×D411yescharacteristic
548C23—22no—
549C23—24no—
550C23—24no—
551C23—42no—
552C23—42no—
553C23—81no—
554C23—82no—
555C23—84no—
556C23C3×#12111yescharacteristic
557C23C3×#12112yes—
558C23C3×#12111yescharacteristic
559C23C2×C3×#4112yes—
560C23C2×C3×#4111yescharacteristic
561Q8—22no—
562Q8—24no—
563Q8—24no—
564Q8—24no—
565Q8—42no—
566Q8—42no—
567Q8C22×C3×D414yes—
568D4—24no—
569D4—28no—
570D4—24no—
571D4—24no—
572D4—24no—
573D4—22no—
574D4—24no—
575D4—44no—
576D4—44no—
577D4—44no—
578D4—44no—
579D4—42no—
580D4—42no—
581D4C22×C3×D414yes—
582C2×C4—24no—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—28no—
587C2×C4—24no—
588C2×C4—42no—
589C2×C4—42no—
590C2×C4—44no—
591C2×C4—44no—
592C2×C4—44no—
593C2×C4—44no—
594C2×C4C3×#12112yes—
595C2×C4C3×#12111yescharacteristic
596C2×C4C3×#12112yes—
597C2×C4C3×#12112yes—
598C2×C4C3×#12112yes—
599C2×C4C3×#12111yescharacteristic
600C2×C4C3×#12112yes—
601C2×C4C22×C3×D411yescharacteristic
602C2×C4C22×C3×D411yescharacteristic
603C2×C4C22×C3×D412yes—
604C2×C4C22×C3×D412yes—
605C2×C4C22×C3×D412yes—
606C2×C4C22×C3×D411yescharacteristic
607C2×C4C22×C3×D411yescharacteristic
608C2×C4C22×C3×D412yes—
609C2×C4C2×C3×#4111yescharacteristic
610C2×C4C2×C3×#4112yes—
611C2×C4C25×C311yescharacteristic
612C8—24no—
613C8—28no—
614C8C22×C3×D418yes—
615C2×C3—21no—
616C2×C3—22no—
617C2×C3—21no—
618C2×C3—22no—
619C2×C3—21no—
620C2×C3—44no—
621C2×C3—84no—
622C2×C3C22×#12111yescharacteristic
623C22—24no—
624C22—41no—
625C22—42no—
626C22—41no—
627C22—42no—
628C22—41no—
629C22—44no—
630C22—44no—
631C22—84no—
632C22—84no—
633C22—84no—
634C22—84no—
635C22C2×C3×#12112yes—
636C22C2×C3×#12111yescharacteristic
637C22C2×C3×#12112yes—
638C22C2×C3×#12111yescharacteristic
639C22C22×C3×#4111yescharacteristic
640C4—24no—
641C4—44no—
642C4C2×C3×#12111yescharacteristic
643C4C2×C3×#12112yes—
644C4C2×C3×#12111yescharacteristic
645C4C2×C3×#12112yes—
646C4C23×C3×D411yescharacteristic
647C4C23×C3×D411yescharacteristic
648C3#6046911yescharacteristic, direct product factor, Sylow
649C2—21no—
650C2—21no—
651C2—22no—
652C2—22no—
653C2—21no—
654C2—44no—
655C2—84no—
656C2C22×C3×#12111yescharacteristic
subgroupG/H
centerC3×C4C2×#121
commutator, Frattini, cosocleC2×C4C25×C3
socleC2×C3C22×#121
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C3×C4 ◁ C23×C3×C4 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C3×#575C2semidirect
2. C2×C3×#575C2semidirect
3. C2×C3×#568C2semidirect
4. C3×#3069C2semidirect
5. C3×#3068C2semidirect
6. C3×#3067C2semidirect
7. C2×C3×#430C2semidirect
8. C2×C3×#413C2semidirect
9. #60469C3direct (N × H)
18. C3×#575C22semidirect
20. C2×C3×#137C22semidirect
21. C2×C3×#137C22semidirect
23. C2×C3×AGL(1,ℤ/8)C22semidirect
24. C2×C3×AGL(1,ℤ/8)C22semidirect
26. C2×C3×#135C22semidirect
28. C3×#568C22semidirect
30. C2×C3×#131C22semidirect
35. C3×#473C22semidirect
36. C3×#472C22semidirect
37. C3×#471C22semidirect
38. C3×#430C22semidirect
39. C2×C3×#108C22semidirect
40. C3×#413C22semidirect
41. C3×#413C22semidirect
42. C2×C3×#101C22semidirect
43. C2×C3×#100C22semidirect
44. C2×#575C2×C3semidirect
45. C2×#575C2×C3semidirect
46. C2×#568C2×C3semidirect
47. #3069C2×C3semidirect
48. #3068C2×C3semidirect
49. #3067C2×C3semidirect
50. C2×#430C2×C3semidirect
51. C2×#413C2×C3semidirect
98. C2×C3×Q16C23semidirect
101. C2×C3×SD16C23semidirect
103. C2×C3×D8C23semidirect
127. C3×#108C23semidirect
128. C3×#101C23semidirect
129. C3×#100C23semidirect
138. #575C22×C3semidirect
140. C2×#137C22×C3semidirect
141. C2×#137C22×C3semidirect
143. C2×AGL(1,ℤ/8)C22×C3semidirect
144. C2×AGL(1,ℤ/8)C22×C3semidirect
146. C2×#135C22×C3semidirect
148. #568C22×C3semidirect
150. C2×#131C22×C3semidirect
155. #473C22×C3semidirect
156. #472C22×C3semidirect
157. #471C22×C3semidirect
158. #430C22×C3semidirect
159. C2×#108C22×C3semidirect
160. #413C22×C3semidirect
161. #413C22×C3semidirect
162. C2×#101C22×C3semidirect
163. C2×#100C22×C3semidirect
317. C2×Q16C23×C3semidirect
320. C2×SD16C23×C3semidirect
322. C2×D8C23×C3semidirect
346. #108C23×C3semidirect
347. #101C23×C3semidirect
348. #100C23×C3semidirect
648. C3#60469direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#5752
C2×C3×#5682
C3×#30692
C3×#30682
C3×#30672
C2×C3×#4302
C2×C3×#4132
#604693