Finite Group Databasebeta

← #11872592

Subgroups — #11872592

Order 1152.

814 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5643C211yesmaximal, characteristic
2#10594828C211yesmaximal, characteristic, complemented
3#10592749C211yesmaximal, characteristic, complemented
4C3×#5045C211yesmaximal, characteristic, complemented
5#10591577C211yesmaximal, characteristic, complemented
6#10591577C211yesmaximal, characteristic, complemented
7#10591541C211yesmaximal, characteristic, complemented
8#10591537C211yesmaximal, characteristic, complemented
9#10591181C211yesmaximal, characteristic
10#10591090C211yesmaximal, characteristic
11#10591056C211yesmaximal, characteristic, complemented
12#10590590C211yesmaximal, characteristic, complemented
13#10590488C211yesmaximal, characteristic, complemented
14#10590487C211yesmaximal, characteristic, complemented
15#10590479C211yesmaximal, characteristic, complemented
16#83467—31nomaximal
17#81497—31nomaximal
18C22×#634C2211yescharacteristic
19C32×C22⋊Q8C2211yescharacteristic
20C2×#3756C2211yescharacteristic
21C2×#3756C2211yescharacteristic
22C3×#947C2211yescharacteristic
23C3×Q8×Dic3C2211yescharacteristic
24C3×#930C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C3×#898—21no—
28C3×#897—21no—
29C3×#893C2211yescharacteristic
30C3×#888C2211yescharacteristic
31C3×#885—21no—
32C3×#883—21no—
33#63957—21no—
34#63957—21no—
35#63844—21no—
36#63844—21no—
37#63844C2211yescharacteristic
38#63844C2211yescharacteristic
39#63844C2211yescharacteristic
40#63844C2211yescharacteristic
41C2×#3716C2211yescharacteristic
42C2×#3716C2211yescharacteristic
43#63657C2211yescharacteristic
44#63637C2211yescharacteristic
45#63637C2211yescharacteristic
46C3×#835C2211yescharacteristic
47C3×#835C2211yescharacteristic
48C3×#830C2211yescharacteristic
49C3×#808C2211yescharacteristic
50C3×#807C2211yescharacteristic
51#63576C2211yescharacteristic
52#63574C2211yescharacteristic
53Dic3⋊(C3⋊C8)C2211yescharacteristic
54Dic3⋊(C3⋊C8)C2211yescharacteristic
55#63567C2211yescharacteristic
56#63567C2211yescharacteristic
57#63562C2211yescharacteristic
58#63562C2211yescharacteristic
59#63554C2211yescharacteristic
60Dic3×C3⋊C8C2211yescharacteristic
61C3×#542—31no—
62#5643D311yescharacteristic
63#5516—31no—
64#5516—31no—
65C3×#485—31no—
66#5094—31no—
67#5091—31no—
68#5054—31no—
69#5054—31no—
70#5050—31no—
71#5050—31no—
72#5050—61no—
73#5045D311yescharacteristic, complemented
74#5040—31no—
75#5035—31no—
76#5030—31no—
77C4×#216—31no—
78#5018—31no—
79C4×#214—31no—
80#5003—31no—
81#5000—31no—
82#4889—31no—
83#4875—31no—
84#4854—31no—
85#4852—31no—
86#4798—31no—
87#4798—31no—
88#4790—31no—
89#4789—31no—
90#4738—31no—
91#4720—31no—
92C2×C32×Q8C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3—21no—
95C2×#634—21no—
96C2×#634—22no—
97C2×#634—22no—
98C2×#634C2311yescharacteristic
99C2×#634C2311yescharacteristic
100C2×C3×#67—21no—
101C2×C3×D12C2311yescharacteristic
102C2×C3×C4×D3—21no—
103C2×C3×Dic6—21no—
104C32×C4⋊C4—21no—
105C32×C4⋊C4C2311yescharacteristic
106C32×C22⋊C4—21no—
107#3756—22no—
108#3756—22no—
109C2×C3⋊(C3⋊C8)C2311yescharacteristic
110C2×C3⋊(C3⋊C8)C2311yescharacteristic
111C3×#217—21no—
112C3×#217D411yescharacteristic
113C3×#217D411yescharacteristic
114C3×(C2×D3)⋊C4—21no—
115C3×(C2×D3)⋊C4—21no—
116C3×(C2×D3)⋊C4—21no—
117C3×(C2×D3)⋊C4—21no—
118C3×C4⋊Dic3—21no—
119C3×C4⋊Dic3D411yescharacteristic
120C3×C4⋊Dic3D411yescharacteristic
121C3×C4⋊Dic3C2311yescharacteristic
122C3×C4⋊Dic3C2311yescharacteristic
123C3×C4⋊Dic3C2311yescharacteristic
124C3×Dic3⋊C4—21no—
125C3×C4×Dic3—21no—
126C3×C4×Dic3—21no—
127C3×C4×Dic3C2311yescharacteristic
128C3×C4×Dic3C2311yescharacteristic
129C2×C3×C3⋊C8C2311yescharacteristic
130C2×C3×C3⋊C8C2311yescharacteristic
131#3724—21no—
132#3724—21no—
133#3724—21no—
134#3724—21no—
135Dic32—21no—
136Dic32—21no—
137Dic32—21no—
138Dic32—21no—
139#3716—22no—
140#3716—22no—
141#3121—91noSylow
142C22×Dic6—31no—
143C22×Dic6—31no—
144C22×Dic6—61no—
145C3×C4⋊Q8—31no—
146C3×#126—61no—
147C3×#124—31no—
148C3×#124—61no—
149C3×#123—61no—
150C3×C22⋊Q8—21no—
151C3×C22⋊Q8—61no—
152C3×C22⋊Q8C2×D311yescharacteristic
153C3×C22⋊Q8C2×D311yescharacteristic
154C3×#121—31no—
155C3×C4×Q8—31no—
156C3×C4×D4—31no—
157C3×#117—31no—
158C3×#117—31no—
159#947C2×D311yescharacteristic
160Q8×Dic3C2×D311yescharacteristic
161C2×#216—31no—
162C2×#216—31no—
163C2×#216—31no—
164C2×#216—31no—
165C2×#216—61no—
166C2×#216—61no—
167C2×#214—31no—
168C2×#214—31no—
169#930C2×D311yescharacteristic
170#926C2×D311yescharacteristic
171#926C2×D311yescharacteristic
172C2×#204—31no—
173C2×#204—31no—
174#898—21no—
175#897—21no—
176#893C2×D311yescharacteristic
177#888C2×D311yescharacteristic
178#887—31no—
179#887—31no—
180#887—31no—
181#887—31no—
182#887—61no—
183#887—61no—
184#885—21no—
185#883—21no—
186#877—61no—
187#877—61no—
188#877—61no—
189#877—61no—
190C4×Dic6—31no—
191C4×Dic6—31no—
192C4×Dic6—31no—
193C4×Dic6—31no—
194C4×Dic6—61no—
195C4×Dic6—61no—
196C3×#107—31no—
197C3×#106—31no—
198C3×#103—31no—
199C3×#103—31no—
200C3×C22⋊C8—31no—
201#835C2×D311yescharacteristic
202#835C2×D311yescharacteristic
203#832—31no—
204#832—31no—
205#830—31no—
206#830—31no—
207#830—61no—
208#830C2×D311yescharacteristic
209#816—31no—
210#816—31no—
211#815—31no—
212Dic3⋊C8—31no—
213Dic3⋊C8—31no—
214C8×Dic3—31no—
215#810—31no—
216#810—31no—
217#810—31no—
218#810—31no—
219#810—31no—
220#810—31no—
221#810—61no—
222#810—61no—
223#809—31no—
224#809—31no—
225#808—31no—
226#808—31no—
227#808C2×D311yescharacteristic
228#807—31no—
229#807—31no—
230#807C2×D311yescharacteristic
231C4⋊(C3⋊C8)—31no—
232C4⋊(C3⋊C8)—31no—
233#803—31no—
234C4×C3⋊C8—31no—
235C23×C32C2×D411yescharacteristic
236C22×C3×D3—21no—
237C32×Q8—21no—
238C32×Q8—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4C2×D411yescharacteristic
244C2×C32×C4C2411yescharacteristic
245C2×C3⋊Dic3—24no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248#634—24no—
249#634—21no—
250#634—21no—
251#634#4112yes—
252#634#4112yes—
253C3×#67—81no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3C2×D411yescharacteristic
258C2×C3×Dic3C2×D411yescharacteristic
259C2×C3×Dic3C2×D411yescharacteristic
260C2×C3×Dic3C2×D411yescharacteristic
261C3×D12—21no—
262C3×D12—21no—
263C3×C4×D3—81no—
264C3×Dic6—81no—
265C3⋊(C3⋊C8)—21no—
266C3⋊(C3⋊C8)—21no—
267C3×C3⋊C8—21no—
268C3×C3⋊C8—21no—
269#542—31no—
270#519—91no—
271#485—31no—
272#482—91no—
273#477—91no—
274#475—91no—
275#464—91no—
276#464—91no—
277#451—91no—
278#448—91no—
279#441—91no—
280#440—91no—
281C4×Q16—91no—
282C4×SD16—91no—
283#433—91no—
284C2×C3×Q8—21no—
285C2×C3×Q8—61no—
286C2×C3×Q8C22×D311yescharacteristic
287C2×C3×Q8C22×D311yescharacteristic
288C2×C3×D4—31no—
289C2×C3×D4—61no—
290C22×C3×C4—21no—
291C22×C3×C4—61no—
292C22×C3×C4C22×D311yescharacteristic
293C22×C3×C4C22×D311yescharacteristic
294C2×#67—21no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3—121no—
298C2×D12C22×D311yescharacteristic
299C2×C4×D3—21no—
300C2×Dic6—21no—
301C2×Dic6—31no—
302C2×Dic6—31no—
303C2×Dic6—31no—
304C2×Dic6—31no—
305C2×Dic6—61no—
306C2×Dic6—61no—
307C2×Dic6—62no—
308C2×Dic6—62no—
309C2×Dic6—62no—
310C2×Dic6—62no—
311C2×Dic6—61no—
312C2×Dic6—61no—
313C2×Dic6—122no—
314C2×Dic6—122no—
315C2×Dic6—121no—
316C2×C3×C8—31no—
317C2×C3×C8—31no—
318C3×C4⋊C4—21no—
319C3×C4⋊C4—21no—
320C3×C4⋊C4—21no—
321C3×C4⋊C4—31no—
322C3×C4⋊C4—31no—
323C3×C4⋊C4—31no—
324C3×C4⋊C4—31no—
325C3×C4⋊C4—31no—
326C3×C4⋊C4—41no—
327C3×C4⋊C4—61no—
328C3×C4⋊C4—61no—
329C3×C4⋊C4C22×D311yescharacteristic
330C3×C4⋊C4C22×D311yescharacteristic
331C3×C22⋊C4—21no—
332C3×C22⋊C4—21no—
333C3×C22⋊C4—31no—
334C3×C22⋊C4—31no—
335C3×C22⋊C4—41no—
336C3×C22⋊C4—61no—
337C3×C22⋊C4—61no—
338C3×C22⋊C4—61no—
339C3×C22⋊C4—61no—
340C3×C22⋊C4—61no—
341C3×C42—31no—
342C3×C42—31no—
343C3×C42—61no—
344C3×C42—61no—
345#217—21no—
346#217#6711yescharacteristic
347#217#6711yescharacteristic
348#216—62no—
349#216—62no—
350#216—62no—
351#216—62no—
352#216—122no—
353#216—122no—
354#214—62no—
355#214—62no—
356(C2×D3)⋊C4—21no—
357(C2×D3)⋊C4—21no—
358(C2×D3)⋊C4—21no—
359(C2×D3)⋊C4—21no—
360C4⋊Dic3—21no—
361C4⋊Dic3#6711yescharacteristic
362C4⋊Dic3#6711yescharacteristic
363C4⋊Dic3C22×D311yescharacteristic
364C4⋊Dic3C22×D311yescharacteristic
365C4⋊Dic3C22×D311yescharacteristic
366Dic3⋊C4—21no—
367Dic3⋊C4—61no—
368Dic3⋊C4—61no—
369Dic3⋊C4—61no—
370Dic3⋊C4—61no—
371Dic3⋊C4—61no—
372Dic3⋊C4—61no—
373Dic3⋊C4—61no—
374Dic3⋊C4—61no—
375C4×Dic3—21no—
376C4×Dic3—21no—
377C4×Dic3—61no—
378C4×Dic3—61no—
379C4×Dic3—61no—
380C4×Dic3—61no—
381C4×Dic3—61no—
382C4×Dic3—61no—
383C4×Dic3—61no—
384C4×Dic3—61no—
385C4×Dic3C22×D311yescharacteristic
386C4×Dic3C22×D311yescharacteristic
387C2×C3⋊C8—31no—
388C2×C3⋊C8—31no—
389C2×C3⋊C8—31no—
390C2×C3⋊C8—31no—
391C2×C3⋊C8—61no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8C22×D311yescharacteristic
394C2×C3⋊C8C22×D311yescharacteristic
395#204—62no—
396#204—62no—
397C22×C32—21no—
398C22×C32—21no—
399C22×C32—21no—
400C22×C32C22×D411yescharacteristic
401C2×C3×D3—41no—
402C2×C3×D3—41no—
403C2×C3×D3—41no—
404C32×C4—21no—
405C32×C4—41no—
406C32×C4—41no—
407C32×C4C2×#4111yescharacteristic
408C32×C4C2×#4111yescharacteristic
409C3⋊Dic3—22no—
410C3⋊Dic3—22no—
411C3×Dic3—21no—
412C3×Dic3—21no—
413C3×Dic3—21no—
414C3×Dic3—21no—
415C3×Dic3—41no—
416C3×Dic3—41no—
417C3×Dic3—41no—
418C22×Q8—91no—
419C2×Q16—91no—
420C2×Q16—91no—
421C2×SD16—91no—
422C2×SD16—91no—
423C4⋊Q8—31no—
424#126—61no—
425#124—31no—
426#124—61no—
427#123—61no—
428C22⋊Q8—61no—
429C22⋊Q8D3211yescharacteristic
430#121—31no—
431C4×Q8—31no—
432C4×Q8—91no—
433C4×Q8—91no—
434C4×Q8—91no—
435C4×Q8—91no—
436C4×Q8—181no—
437C4×Q8—181no—
438C4×D4—31no—
439#117—31no—
440#117—31no—
441#117—181no—
442#117—181no—
443#107—31no—
444#107—91no—
445#106—31no—
446#106—91no—
447C4⋊C8—91no—
448C4⋊C8—91no—
449#103—31no—
450#103—31no—
451#103—91no—
452#103—91no—
453#103—91no—
454#103—91no—
455#102—91no—
456#102—91no—
457C22⋊C8—31no—
458C22⋊C8—91no—
459#97—91no—
460C4×C8—91no—
461C23×C3—21no—
462C23×C3—61no—
463C23×C3D3×D411yescharacteristic
464C23×C3C2×#6711yescharacteristic
465C22×D3—21no—
466C3×Q8—21no—
467C3×Q8—21no—
468C3×Q8—21no—
469C3×Q8—21no—
470C3×Q8—41no—
471C3×Q8—41no—
472C3×Q8—241no—
473C3×D4—61no—
474C3×D4—61no—
475C3×D4—241no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—31no—
487C2×C3×C4—31no—
488C2×C3×C4—31no—
489C2×C3×C4—31no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—241no—
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4C2×#6711yescharacteristic
500C2×C3×C4C23×D311yescharacteristic
501C2×C3×C4C23×D311yescharacteristic
502#67—81no—
503C2×Dic3—21no—
504C2×Dic3—21no—
505C2×Dic3—21no—
506C2×Dic3—64no—
507C2×Dic3—64no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—121no—
513C2×Dic3—121no—
514C2×Dic3—124no—
515C2×Dic3C2×#6711yescharacteristic
516C2×Dic3C2×#6711yescharacteristic
517C2×Dic3C2×#6711yescharacteristic
518C2×Dic3C2×#6711yescharacteristic
519D12—21no—
520D12—21no—
521C4×D3—81no—
522Dic6—32no—
523Dic6—32no—
524Dic6—32no—
525Dic6—32no—
526Dic6—62no—
527Dic6—62no—
528Dic6—64no—
529Dic6—64no—
530Dic6—61no—
531Dic6—61no—
532Dic6—61no—
533Dic6—61no—
534Dic6—81no—
535Dic6—121no—
536Dic6—121no—
537Dic6—124no—
538C3×C8—61no—
539C3×C8—61no—
540C3⋊C8—21no—
541C3⋊C8—21no—
542C3⋊C8—61no—
543C3⋊C8—61no—
544C3⋊C8—61no—
545C3⋊C8—61no—
546C3⋊C8—121no—
547C3⋊C8—121no—
548C2×C32—41no—
549C2×C32#52511yescharacteristic
550C2×C32#57711yescharacteristic
551C2×C32#57811yescharacteristic
552C3×D3—81no—
553C2×Q8—61no—
554C2×Q8—91no—
555C2×Q8—91no—
556C2×Q8—182no—
557C2×Q8—182no—
558C2×Q8—181no—
559C2×Q8C2×D3211yescharacteristic
560C2×D4—31no—
561C2×D4—61no—
562C22×C4—61no—
563C22×C4—181no—
564C22×C4C2×D3211yescharacteristic
565Q16—182no—
566Q16—182no—
567SD16—182no—
568SD16—182no—
569C2×C8—31no—
570C2×C8—31no—
571C2×C8—91no—
572C2×C8—91no—
573C4⋊C4—21no—
574C4⋊C4—31no—
575C4⋊C4—31no—
576C4⋊C4—31no—
577C4⋊C4—31no—
578C4⋊C4—31no—
579C4⋊C4—61no—
580C4⋊C4—61no—
581C4⋊C4—181no—
582C4⋊C4—181no—
583C4⋊C4—181no—
584C4⋊C4—181no—
585C4⋊C4C2×D3211yescharacteristic
586C22⋊C4—21no—
587C22⋊C4—31no—
588C22⋊C4—31no—
589C22⋊C4—61no—
590C22⋊C4—61no—
591C22⋊C4—61no—
592C22⋊C4—61no—
593C22⋊C4—61no—
594C42—31no—
595C42—31no—
596C42—61no—
597C42—61no—
598C42—181no—
599C42—181no—
600C42—181no—
601C42—181no—
602C22×C3—22no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—21no—
610C22×C3—41no—
611C22×C3—41no—
612C22×C3—121no—
613C22×C3—121no—
614C22×C3—121no—
615C22×C3C2×D3×D411yescharacteristic
616C22×C3C22×#6711yescharacteristic
617C2×D3—41no—
618C2×D3—41no—
619C2×D3—41no—
620C3×C4—21no—
621C3×C4—21no—
622C3×C4—21no—
623C3×C4—21no—
624C3×C4—41no—
625C3×C4—41no—
626C3×C4—41no—
627C3×C4—41no—
628C3×C4—41no—
629C3×C4—61no—
630C3×C4—61no—
631C3×C4—61no—
632C3×C4—61no—
633C3×C4—81no—
634C3×C4—81no—
635C3×C4—121no—
636C3×C4—121no—
637C3×C4—121no—
638C3×C4D3×#4111yescharacteristic
639C3×C4D3×#4111yescharacteristic
640C3×C4D3×#4111yescharacteristic
641C3×C4D3×#4111yescharacteristic
642Dic3—21no—
643Dic3—21no—
644Dic3—21no—
645Dic3—21no—
646Dic3—41no—
647Dic3—41no—
648Dic3—41no—
649Dic3—62no—
650Dic3—62no—
651Dic3—62no—
652Dic3—62no—
653Dic3—122no—
654Dic3—122no—
655C32#312111yescharacteristic, complemented, Sylow
656C23—61no—
657C23D3×#6711yescharacteristic
658Q8—21no—
659Q8—21no—
660Q8—92no—
661Q8—92no—
662Q8—184no—
663Q8—181no—
664Q8—181no—
665Q8—241no—
666D4—61no—
667D4—61no—
668D4—241no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—31no—
674C2×C4—31no—
675C2×C4—31no—
676C2×C4—31no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—184no—
681C2×C4—181no—
682C2×C4—181no—
683C2×C4—241no—
684C2×C4D3×#6711yescharacteristic
685C2×C4C22×D3211yescharacteristic
686C8—61no—
687C8—61no—
688C8—181no—
689C8—181no—
690C2×C3—21no—
691C2×C3—21no—
692C2×C3—21no—
693C2×C3—42no—
694C2×C3—41no—
695C2×C3—41no—
696C2×C3—241no—
697C2×C3#565611yescharacteristic
698C2×C3#577011yescharacteristic
699C2×C3#577911yescharacteristic
700C2×C3#582811yescharacteristic
701C2×C3#583611yescharacteristic
702C2×C3#583811yescharacteristic
703D3—81no—
704C22—21no—
705C22—21no—
706C22—21no—
707C22—121no—
708C22—121no—
709C22—121no—
710C22C2×D3×#6711yescharacteristic
711C4—21no—
712C4—41no—
713C4—41no—
714C4—61no—
715C4—61no—
716C4—61no—
717C4—61no—
718C4—121no—
719C4—121no—
720C4—121no—
721C4—182no—
722C4—182no—
723C4#6431211yescharacteristic
724C4#6431211yescharacteristic
725C3—21no—
726C3#8149711yescharacteristic, complemented
727C3#8346711yescharacteristic, complemented
728C2—41no—
729C2—241no—
730C2#1059515911yescharacteristic
731C2#1059532811yescharacteristic
732C2#1059546611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C22⋊Q8C22
socleC22×C32C22×D4
prime radicalC3×#930C22
hypercenterC22⋊Q8D32
hypocenterC32#3121
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10594828C2semidirect
3. #10592749C2semidirect
4. C3×#5045C2semidirect
5. #10591577C2semidirect
6. #10591577C2semidirect
7. #10591541C2semidirect
8. #10591537C2semidirect
11. #10591056C2semidirect
12. #10590590C2semidirect
13. #10590488C2semidirect
14. #10590487C2semidirect
15. #10590479C2semidirect
73. #5045D3semidirect
655. C32#3121semidirect
726. C3#81497semidirect
727. C3#83467semidirect

Maximal subgroups

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

subgroupindex
C3×#56432
#105948282
#105927492
C3×#50452
#105915772
#105915412
#105915372
#105911812
#105910902
#105910562
#105905902
#105904882
#105904872
#105904792
#834673
#814973