Finite Group Databasebeta

← #10956150

Subgroups — #10956150

Order 768.

2834 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5486C211yesmaximal, characteristic
2C3×#2315C211yesmaximal, characteristic, complemented
3#82121C211yesmaximal, characteristic
4C2×#4958C211yesmaximal, characteristic
5C2×#4950C211yesmaximal, characteristic, complemented
6#82083C211yesmaximal, characteristic, complemented
7C2×Dic3×C22⋊C4C211yesmaximal, characteristic, complemented
8#74595C214yesmaximal, complemented
9#74392C214yesmaximal, complemented
10#74383C214yesmaximal, complemented
11#74377C214yesmaximal, complemented
12#73884C214yesmaximal, complemented
13#73883C214yesmaximal, complemented
14#34251—31nomaximal, Sylow
15C23×#67C2211yescharacteristic
16C24×Dic3C2211yescharacteristic
17C22×C3×C22⋊C4C2211yescharacteristic
18C22×C3×C22⋊C4C2211yescharacteristic
19C22×C3×C22⋊C4C2211yescharacteristic
20C22×#217C2211yescharacteristic
21C22×#217C2211yescharacteristic
22C2×C4×#67C2214yes—
23C22×(C2×D3)⋊C4C2212yes—
24C22×C4⋊Dic3C2212yescomplemented
25C22×C4×Dic3C2212yescomplemented
26C2×#892C2214yescomplemented
27#5486C4116yescomplemented
28C2×#67⋊C4C2214yes—
29C2×D3×C22⋊C4C2212yes—
30C2×#877C2212yes—
31C3×#385C2214yes—
32C3×#385C2214yescomplemented
33C3×#380C2214yescomplemented
34#5213C2214yes—
35C4×#217C2214yes—
36C2×C3⋊#95C2212yes—
37C2×C3⋊#95C2212yescomplemented
38C2×C3⋊#95C2212yescomplemented
39#4990C2214yescomplemented
40#4990C2214yescomplemented
41#4987C2214yescomplemented
42#4978C2214yescomplemented
43#4978C2214yescomplemented
44#4977C2214yescomplemented
45Dic3×C4⋊C4C2214yescomplemented
46#4958C2212yes—
47#4958C2212yes—
48#4958C2212yes—
49#4958C2214yes—
50#4958C2212yes—
51#4955C2212yes—
52#4950C2214yes—
53#4950C2212yescomplemented
54#4950C2212yescomplemented
55#4943C2212yes—
56Dic3×C22⋊C4C2214yes—
57Dic3×C22⋊C4C2214yescomplemented
58Dic3×C22⋊C4C2212yescomplemented
59Dic3×C22⋊C4C2214yescomplemented
60Dic3×C22⋊C4C2212yescomplemented
61#4670C2214yescomplemented
62#4670C2214yescomplemented
63#4666C2214yescomplemented
64#4664C2214yescomplemented
65#4655C2214yescomplemented
66#4655C2214yescomplemented
67#4651C2214yescomplemented
68#4648C2214yescomplemented
69C2×#518—31no—
70#2353—34no—
71#2352—34no—
72#2343—34no—
73#2342—34no—
74#2318—34no—
75#2315D311yescharacteristic, complemented
76#2308—31no—
77#2290—34no—
78C2×#386—31no—
79C2×#385—31no—
80#2273—31no—
81C2×C4×C22⋊C4—31no—
82C25×C3C2311yescharacteristic
83C24×D3C2311yescharacteristic
84C23×C3×C4C2312yes—
85C23×C3×C4C2312yes—
86C23×C3×C4C2312yes—
87C22×#67—24no—
88C22×#67—24no—
89C22×#67C2×C418yes—
90C22×#67C2312yes—
91C22×#67C2312yes—
92C23×Dic3—24no—
93C23×Dic3—44no—
94C23×Dic3C2311yescharacteristic
95C23×Dic3C2312yes—
96C23×Dic3C2312yes—
97C23×Dic3C2311yescharacteristic
98C23×Dic3C2311yescharacteristic
99C23×Dic3C2311yescharacteristic
100C23×Dic3C2311yescharacteristic
101C23×Dic3C2312yes—
102C22×C4×D3C2314yes—
103C2×C3×C4⋊C4C2314yes—
104C2×C3×C4⋊C4C2314yes—
105C2×C3×C22⋊C4—24no—
106C2×C3×C22⋊C4—24no—
107C2×C3×C22⋊C4C2×C418yes—
108C2×C3×C22⋊C4C2312yes—
109C2×C3×C22⋊C4C2312yes—
110C2×C3×C22⋊C4C2312yes—
111C2×C3×C22⋊C4C2312yes—
112C2×C3×C22⋊C4C2312yes—
113C2×C3×C22⋊C4C2312yes—
114C2×#217—24no—
115C2×#217C2×C418yes—
116C2×#217C2312yes—
117C2×#217C2312yes—
118C2×#217C2312yes—
119C2×#217C2312yes—
120C4×#67C2×C4132yescomplemented
121C2×(C2×D3)⋊C4—44no—
122C2×(C2×D3)⋊C4C2314yes—
123C2×(C2×D3)⋊C4C2314yes—
124C2×(C2×D3)⋊C4C2314yes—
125C2×(C2×D3)⋊C4C2314yes—
126C2×(C2×D3)⋊C4C2314yes—
127C2×C4⋊Dic3—44no—
128C2×C4⋊Dic3C2314yes—
129C2×C4⋊Dic3C2314yes—
130C2×Dic3⋊C4C2314yes—
131C2×C4×Dic3—44no—
132C2×C4×Dic3C2314yes—
133C2×C4×Dic3C2314yes—
134C2×C4×Dic3C2314yes—
135C2×C4×Dic3C2314yes—
136C2×C4×Dic3C2314yes—
137#892—48no—
138#67⋊C4C2×C4132yescomplemented
139D3×C22⋊C4C2×C4116yescomplemented
140#877C2×C4116yescomplemented
141C3×#95C2314yes—
142C3×#95C2314yes—
143C3⋊#95C2314yes—
144C3⋊#95C2314yes—
145C3⋊#95C2314yes—
146C3⋊#95C2314yes—
147C3⋊#95C2314yes—
148C3⋊#95C2314yes—
149C3⋊#95C2314yes—
150C3⋊#95C2314yes—
151C3⋊#95C2314yes—
152C3⋊#95C2314yes—
153C23×D4—31no—
154C24×C4—31no—
155#518—316no—
156C2×C4×D4—34no—
157C2×C4×D4—34no—
158C2×#117—34no—
159C2×#117—32no—
160C22×C4⋊C4—32no—
161C22×C22⋊C4—31no—
162C22×C22⋊C4—32no—
163C22×C22⋊C4—31no—
164C22×C22⋊C4—32no—
165C22×C22⋊C4C2×D311yescharacteristic
166C22×C22⋊C4C2×D311yescharacteristic
167C22×C22⋊C4C2×D311yescharacteristic
168C22×C42—32no—
169#388—34no—
170#388—34no—
171#388—34no—
172#388—34no—
173#387—34no—
174#387—34no—
175#387—34no—
176#387—34no—
177#386—34no—
178#386—32no—
179#386—32no—
180#386—32no—
181#386—34no—
182#386—32no—
183#385—32no—
184#385—34no—
185#385—32no—
186#385C2×D314yes—
187#385C2×D314yescomplemented
188#383—34no—
189#382—34no—
190#381—32no—
191#381—34no—
192#380—34no—
193#380C2×D314yescomplemented
194#379—32no—
195C4×C4⋊C4—34no—
196C4×C22⋊C4—34no—
197C4×C22⋊C4—34no—
198C4×C22⋊C4—34no—
199C4×C22⋊C4—32no—
200C4×C22⋊C4—34no—
201C4×C22⋊C4—32no—
202C4×C22⋊C4—34no—
203#376—34no—
204C2×#95—32no—
205C2×#95—32no—
206C2×#95—32no—
207C24×C3—42no—
208C24×C3—42no—
209C24×C3C22×C414yes—
210C24×C3#4114yes—
211C24×C3#4114yes—
212C24×C3C2411yescharacteristic
213C24×C3C2411yescharacteristic
214C24×C3C2411yescharacteristic
215C23×D3—22no—
216C23×D3—22no—
217C23×D3—42no—
218C23×D3—42no—
219C23×D3C22×C414yes—
220C23×D3C2412yes—
221C22×C3×C4—24no—
222C22×C3×C4—24no—
223C22×C3×C4—42no—
224C22×C3×C4—42no—
225C22×C3×C4—42no—
226C22×C3×C4—42no—
227C22×C3×C4—42no—
228C22×C3×C4—42no—
229C22×C3×C4C22×C418yes—
230C22×C3×C4C2414yes—
231C22×C3×C4C2414yes—
232C22×C3×C4C2414yes—
233C2×#67—232no—
234C2×#67—24no—
235C2×#67—24no—
236C2×#67—24no—
237C2×#67—24no—
238C2×#67C22×C418yes—
239C2×#67C22×C418yes—
240C22×Dic3—22no—
241C22×Dic3—22no—
242C22×Dic3—22no—
243C22×Dic3—24no—
244C22×Dic3—24no—
245C22×Dic3—24no—
246C22×Dic3—22no—
247C22×Dic3—22no—
248C22×Dic3—22no—
249C22×Dic3—24no—
250C22×Dic3—24no—
251C22×Dic3—42no—
252C22×Dic3—42no—
253C22×Dic3—42no—
254C22×Dic3—42no—
255C22×Dic3—42no—
256C22×Dic3—42no—
257C22×Dic3—42no—
258C22×Dic3—416no—
259C22×Dic3C22×C414yes—
260C22×Dic3C22×C418yes—
261C22×Dic3C2412yes—
262C22×Dic3C2412yes—
263C22×Dic3C2412yes—
264C22×Dic3C2412yes—
265C22×Dic3C2414yes—
266C22×Dic3C2412yes—
267C2×C4×D3—44no—
268C2×C4×D3—44no—
269C2×C4×D3C22×C4116yescomplemented
270C3×C4⋊C4—44no—
271C3×C4⋊C4—44no—
272C3×C22⋊C4—24no—
273C3×C22⋊C4—24no—
274C3×C22⋊C4—24no—
275C3×C22⋊C4—24no—
276C3×C22⋊C4C22×C418yes—
277C3×C22⋊C4C22×C418yes—
278#217—24no—
279#217—24no—
280#217C22×C418yes—
281#217C22×C418yes—
282(C2×D3)⋊C4—28no—
283(C2×D3)⋊C4—44no—
284(C2×D3)⋊C4—44no—
285(C2×D3)⋊C4—44no—
286(C2×D3)⋊C4C22×C4116yescomplemented
287C4⋊Dic3—28no—
288C4⋊Dic3—44no—
289Dic3⋊C4C22×C4116yescomplemented
290C4×Dic3—28no—
291C4×Dic3—44no—
292C4×Dic3—44no—
293C4×Dic3—44no—
294C4×Dic3C22×C4116yescomplemented
295C25—31no—
296C25C22×D311yescharacteristic
297C22×D4—38no—
298C22×D4—32no—
299C22×D4—32no—
300C22×D4—64no—
301C22×D4—64no—
302C23×C4—31no—
303C23×C4—32no—
304C23×C4—34no—
305C23×C4—31no—
306C23×C4—32no—
307C23×C4—32no—
308C23×C4—31no—
309C23×C4—31no—
310C23×C4—31no—
311C23×C4—64no—
312C23×C4—124no—
313C23×C4C22×D312yes—
314C23×C4C22×D312yes—
315C23×C4C22×D312yes—
316C4×D4—332no—
317C4×D4—332no—
318#117—316no—
319#117—128no—
320C2×C4⋊C4—34no—
321C2×C4⋊C4—34no—
322C2×C4⋊C4—34no—
323C2×C4⋊C4—124no—
324C2×C4⋊C4C22×D314yes—
325C2×C4⋊C4C22×D314yes—
326C2×C22⋊C4—24no—
327C2×C22⋊C4—24no—
328C2×C22⋊C4—38no—
329C2×C22⋊C4—32no—
330C2×C22⋊C4—32no—
331C2×C22⋊C4—34no—
332C2×C22⋊C4—316no—
333C2×C22⋊C4—32no—
334C2×C22⋊C4—32no—
335C2×C22⋊C4—34no—
336C2×C22⋊C4—34no—
337C2×C22⋊C4—34no—
338C2×C22⋊C4—34no—
339C2×C22⋊C4—64no—
340C2×C22⋊C4—124no—
341C2×C22⋊C4C4×D318yes—
342C2×C22⋊C4C22×D312yes—
343C2×C22⋊C4C22×D312yes—
344C2×C22⋊C4C22×D312yes—
345C2×C22⋊C4C22×D312yes—
346C2×C22⋊C4C22×D312yes—
347C2×C22⋊C4C22×D312yes—
348C2×C42—34no—
349C2×C42—34no—
350C2×C42—34no—
351C2×C42—34no—
352C2×C42—34no—
353C2×C42—124no—
354#95—34no—
355#95—34no—
356#95—34no—
357#95—34no—
358#95—34no—
359#95—34no—
360#95—34no—
361#95—34no—
362#95—34no—
363#95—34no—
364#95C22×D314yes—
365#95C22×D314yes—
366C23×C3—22no—
367C23×C3—22no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—22no—
371C23×C3—22no—
372C23×C3—44no—
373C23×C3—48no—
374C23×C3—48no—
375C23×C3—44no—
376C23×C3#117116yescomplemented
377C23×C3C23×C412yes—
378C23×C3C23×C412yes—
379C23×C3C23×C412yes—
380C23×C3C2×#4112yes—
381C23×C3C2×#4112yes—
382C23×C3C2×#4112yes—
383C23×C3C2×#4112yes—
384C23×C3C2×#4112yes—
385C23×C3C2×#4112yes—
386C23×C3C2511yescharacteristic
387C22×D3—22no—
388C22×D3—22no—
389C22×D3—24no—
390C22×D3—24no—
391C22×D3—28no—
392C22×D3—48no—
393C22×D3—82no—
394C22×D3—82no—
395C22×D3—84no—
396C22×D3C23×C414yes—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—24no—
400C2×C3×C4—24no—
401C2×C3×C4—24no—
402C2×C3×C4—24no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—48no—
406C2×C3×C4—48no—
407C2×C3×C4—84no—
408C2×C3×C4C23×C418yes—
409#67—216no—
410#67—216no—
411C2×Dic3—28no—
412C2×Dic3—28no—
413C2×Dic3—22no—
414C2×Dic3—22no—
415C2×Dic3—22no—
416C2×Dic3—24no—
417C2×Dic3—22no—
418C2×Dic3—24no—
419C2×Dic3—22no—
420C2×Dic3—22no—
421C2×Dic3—22no—
422C2×Dic3—24no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—24no—
426C2×Dic3—48no—
427C2×Dic3—48no—
428C2×Dic3—48no—
429C2×Dic3—44no—
430C2×Dic3—82no—
431C2×Dic3—82no—
432C2×Dic3C23×C414yes—
433C2×Dic3C23×C418yes—
434C2×Dic3H(5,𝔽2)14yes—
435C4×D3—416no—
436C24—32no—
437C24—34no—
438C24—42no—
439C24—42no—
440C24—62no—
441C24—62no—
442C24—122no—
443C24—122no—
444C24C2×C4×D314yes—
445C24#23714yes—
446C24#23914yes—
447C24C23×D311yescharacteristic
448C24C23×D311yescharacteristic
449C24C23×D311yescharacteristic
450C2×D4—38no—
451C2×D4—38no—
452C2×D4—632no—
453C2×D4—64no—
454C2×D4—64no—
455C2×D4—64no—
456C2×D4—64no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—34no—
460C22×C4—32no—
461C22×C4—34no—
462C22×C4—32no—
463C22×C4—38no—
464C22×C4—316no—
465C22×C4—32no—
466C22×C4—32no—
467C22×C4—32no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—64no—
475C22×C4—64no—
476C22×C4—64no—
477C22×C4—62no—
478C22×C4—62no—
479C22×C4—62no—
480C22×C4—64no—
481C22×C4—64no—
482C22×C4—62no—
483C22×C4—62no—
484C22×C4—62no—
485C22×C4—124no—
486C22×C4—124no—
487C22×C4—122no—
488C22×C4—122no—
489C22×C4—122no—
490C22×C4—122no—
491C22×C4—122no—
492C22×C4—122no—
493C22×C4—122no—
494C22×C4—1216no—
495C22×C4C2×C4×D318yes—
496C22×C4C23×D314yes—
497C22×C4C23×D314yes—
498C22×C4C23×D314yes—
499C4⋊C4—316no—
500C4⋊C4—44no—
501C4⋊C4—44no—
502C4⋊C4—68no—
503C4⋊C4—124no—
504C22⋊C4—24no—
505C22⋊C4—24no—
506C22⋊C4—24no—
507C22⋊C4—24no—
508C22⋊C4—38no—
509C22⋊C4—38no—
510C22⋊C4—316no—
511C22⋊C4—68no—
512C22⋊C4—64no—
513C22⋊C4—64no—
514C22⋊C4—124no—
515C22⋊C4—124no—
516C22⋊C4—124no—
517C22⋊C4C2×C4×D318yes—
518C22⋊C4C2×C4×D318yes—
519C42—316no—
520C42—68no—
521C42—124no—
522C42—124no—
523C42—124no—
524C22×C3—24no—
525C22×C3—24no—
526C22×C3—24no—
527C22×C3—22no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—22no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—24no—
534C22×C3—24no—
535C22×C3—24no—
536C22×C3—416no—
537C22×C3C2×#11714yes—
538C22×C3C2×#11714yes—
539C22×C3C2×#11714yes—
540C22×C3C24×C411yescharacteristic
541C22×C3C22×#4111yescharacteristic
542C22×C3C22×#4111yescharacteristic
543C22×C3C2×H(5,𝔽2)12yes—
544C22×C3#58512yes—
545C2×D3—24no—
546C2×D3—28no—
547C2×D3—42no—
548C2×D3—42no—
549C2×D3—44no—
550C2×D3—88no—
551C3×C4—28no—
552C3×C4—44no—
553C3×C4—44no—
554Dic3—24no—
555Dic3—28no—
556Dic3—24no—
557Dic3—42no—
558Dic3—42no—
559Dic3—42no—
560C23—22no—
561C23—22no—
562C23—22no—
563C23—22no—
564C23—22no—
565C23—22no—
566C23—34no—
567C23—44no—
568C23—48no—
569C23—48no—
570C23—44no—
571C23—62no—
572C23—62no—
573C23—64no—
574C23—64no—
575C23—68no—
576C23—128no—
577C23—244no—
578C23—242no—
579C23—242no—
580C23#892116yescomplemented
581C23C22×C4×D312yes—
582C23C22×C4×D312yes—
583C23C22×C4×D312yes—
584C23C2×#23712yes—
585C23C2×#23712yes—
586C23C2×#23712yes—
587C23C2×#23912yes—
588C23C2×#23912yes—
589C23C2×#23912yes—
590C23C24×D311yescharacteristic
591D4—616no—
592D4—616no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—24no—
597C2×C4—24no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—34no—
602C2×C4—38no—
603C2×C4—34no—
604C2×C4—48no—
605C2×C4—48no—
606C2×C4—68no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—64no—
611C2×C4—62no—
612C2×C4—64no—
613C2×C4—68no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—64no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—64no—
621C2×C4—84no—
622C2×C4—1216no—
623C2×C4—128no—
624C2×C4—128no—
625C2×C4—128no—
626C2×C4—124no—
627C2×C4—242no—
628C2×C4—242no—
629C2×C4C22×C4×D318yes—
630C2×C3—24no—
631C2×C3—24no—
632C2×C3—24no—
633C2×C3C22×#11711yescharacteristic
634C2×C3C4×H(5,𝔽2)12yes—
635C2×C3#349011yescharacteristic
636C2×C3#349111yescharacteristic
637C2×C3#350512yes—
638D3—44no—
639C22—24no—
640C22—24no—
641C22—24no—
642C22—22no—
643C22—22no—
644C22—22no—
645C22—22no—
646C22—22no—
647C22—22no—
648C22—24no—
649C22—24no—
650C22—24no—
651C22—416no—
652C22—68no—
653C22—64no—
654C22—124no—
655C22—122no—
656C22—122no—
657C22—248no—
658C22C2×#89214yes—
659C22C2×#89214yes—
660C22C2×#89214yes—
661C22C23×C4×D311yescharacteristic
662C22C22×#23711yescharacteristic
663C22C22×#23911yescharacteristic
664C22D3×H(5,𝔽2)12yes—
665C22#596612yes—
666C4—28no—
667C4—44no—
668C4—44no—
669C4—64no—
670C4—68no—
671C4—64no—
672C4—122no—
673C4—122no—
674C4—122no—
675C3#3425111yescharacteristic, complemented, Sylow
676C2—24no—
677C2—24no—
678C2—24no—
679C2—124no—
680C2C22×#89211yescharacteristic
681C2#8585712yes—
682C2#8629912yes—
683C2#8657311yescharacteristic
684C2#8657911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutatorC22×C3C24×C4
FittingC3×#2315C2
socle, cosocleC23×C3C25
prime radicalC23×#67C22
hypercenter#2315D3
hypocenterC3#34251
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2315

Complements

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

NH ≅ G/Ntype
2. C3×#2315C2semidirect
5. C2×#4950C2semidirect
6. #82083C2semidirect
7. C2×Dic3×C22⋊C4C2semidirect
8. #74595C2semidirect
9. #74392C2semidirect
10. #74383C2semidirect
11. #74377C2semidirect
12. #73884C2semidirect
13. #73883C2semidirect
24. C22×C4⋊Dic3C22semidirect
25. C22×C4×Dic3C22semidirect
26. C2×#892C22semidirect
27. #5486C4semidirect
32. C3×#385C22semidirect
33. C3×#380C22semidirect
37. C2×C3⋊#95C22semidirect
38. C2×C3⋊#95C22semidirect
39. #4990C22semidirect
40. #4990C22semidirect
41. #4987C22semidirect
42. #4978C22semidirect
43. #4978C22semidirect
44. #4977C22semidirect
45. Dic3×C4⋊C4C22semidirect
53. #4950C22semidirect
54. #4950C22semidirect
57. Dic3×C22⋊C4C22semidirect
58. Dic3×C22⋊C4C22semidirect
59. Dic3×C22⋊C4C22semidirect
60. Dic3×C22⋊C4C22semidirect
61. #4670C22semidirect
62. #4670C22semidirect
63. #4666C22semidirect
64. #4664C22semidirect
65. #4655C22semidirect
66. #4655C22semidirect
67. #4651C22semidirect
68. #4648C22semidirect
75. #2315D3semidirect
120. C4×#67C2×C4semidirect
138. #67⋊C4C2×C4semidirect
139. D3×C22⋊C4C2×C4semidirect
140. #877C2×C4semidirect
187. #385C2×D3semidirect
193. #380C2×D3semidirect
269. C2×C4×D3C22×C4semidirect
286. (C2×D3)⋊C4C22×C4semidirect
289. Dic3⋊C4C22×C4semidirect
294. C4×Dic3C22×C4semidirect
376. C23×C3#117semidirect
580. C23#892semidirect
675. C3#34251semidirect

Maximal subgroups

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

subgroupindex
C2×#54862
C3×#23152
#821212
C2×#49582
C2×#49502
#820832
C2×Dic3×C22⋊C42
#745952
#743922
#743832
#743772
#738842
#738832
#342513