Finite Group Databasebeta

← #10801766

Subgroups — #10801766

Order 768.

1098 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#4864C211yesmaximal, characteristic
2C2×#4710C211yesmaximal, characteristic, complemented
3C2×D3×#97C211yesmaximal, characteristic, complemented
4C4×#897C211yesmaximal, characteristic, complemented
5C4×#895C211yesmaximal, characteristic
6C3×#1776C211yesmaximal, characteristic, complemented
7#70630C211yesmaximal, characteristic, complemented
8#70629C211yesmaximal, characteristic, complemented
9#70562C211yesmaximal, characteristic, complemented
10#69475C211yesmaximal, characteristic, complemented
11#69474C211yesmaximal, characteristic, complemented
12#68883C211yesmaximal, characteristic
13#68882C211yesmaximal, characteristic, complemented
14#68857C211yesmaximal, characteristic, complemented
15#68855C211yesmaximal, characteristic, complemented
16#21528—31nomaximal, Sylow
17C22×#204C2211yescharacteristic
18C22×D3×C8C2211yescharacteristic
19C22×D3×C8C2211yescharacteristic
20C2×#897C2211yescharacteristic
21C2×#895C2211yescharacteristic
22C2×C4×D12—21no—
23C2×C4×D12C2211yescharacteristic
24C2×C42×D3C2211yescharacteristic
25C2×C4×Dic6C2211yescharacteristic
26C2×C3×#107C2211yescharacteristic
27C2×C3×#106C2211yescharacteristic
28C2×C3×#97C2211yescharacteristic
29C3×C4×C4⋊C4C2211yescharacteristic
30C3×C4×C4⋊C4C2211yescharacteristic
31C2×#821C2211yescharacteristic
32C2×#818C2211yescharacteristic
33C2×#816C2211yescharacteristic
34C2×#815C2211yescharacteristic
35C2×#815C2211yescharacteristic
36#4988C2211yescharacteristic
37#4987C2211yescharacteristic
38#4987C2211yescharacteristic
39#4984C2211yescharacteristic
40#4984C2211yescharacteristic
41#4973C2211yescharacteristic
42C2×#810C2211yescharacteristic
43C2×#810C2211yescharacteristic
44C2×#809C2211yescharacteristic
45C2×#809C2211yescharacteristic
46C4×(C2×D3)⋊C4—21no—
47C4×(C2×D3)⋊C4—21no—
48C4×C4⋊Dic3—21no—
49C2×#803C2211yescharacteristic
50#4864C418yescomplemented
51#4710—24no—
52D3×#97—24no—
53#4670—21no—
54#4668—21no—
55#4665—21no—
56#4653—21no—
57C3×#340C2211yescharacteristic
58C3×#340C2211yescharacteristic
59#4529C2211yescharacteristic
60#4529C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63C2×#465—31no—
64C2×#440—31no—
65C22×#97—31no—
66C4×C22⋊Q8—31no—
67C4×#121—31no—
68#1973—31no—
69#1944—31no—
70#1936—31no—
71#1935—31no—
72#1893—31no—
73#1892—31no—
74#1808—31no—
75#1776D311yescharacteristic, complemented
76#1763—31no—
77#1762—31no—
78C22×D12—21no—
79C22×D12C2311yescharacteristic
80C22×C4×D3—21no—
81C22×C4×D3D411yescharacteristic
82C22×C4×D3D411yescharacteristic
83C22×C4×D3C2311yescharacteristic
84C22×Dic6C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C22×C3×C8C2311yescharacteristic
87C2×C3×C4⋊C4C2311yescharacteristic
88C2×C3×C4⋊C4C2311yescharacteristic
89C2×C3×C4⋊C4C2311yescharacteristic
90C2×C3×C4⋊C4C2311yescharacteristic
91C2×C3×C42—21no—
92C2×C3×C42—21no—
93C2×C3×C42C2311yescharacteristic
94C2×(C2×D3)⋊C4—21no—
95C2×(C2×D3)⋊C4—21no—
96C2×(C2×D3)⋊C4—21no—
97C2×(C2×D3)⋊C4—21no—
98C2×(C2×D3)⋊C4—21no—
99C2×(C2×D3)⋊C4—21no—
100C2×(C2×D3)⋊C4—21no—
101C2×C4⋊Dic3—21no—
102C2×C4⋊Dic3—21no—
103C2×C4⋊Dic3—21no—
104C2×C4⋊Dic3C2311yescharacteristic
105C2×C4⋊Dic3C2311yescharacteristic
106C2×Dic3⋊C4—21no—
107C2×C4×Dic3—21no—
108C2×C4×Dic3D411yescharacteristic
109C2×C4×Dic3D411yescharacteristic
110C2×C4×Dic3C2311yescharacteristic
111C22×C3⋊C8C2311yescharacteristic
112C22×C3⋊C8C2311yescharacteristic
113C2×#204—22no—
114C2×#204—22no—
115C2×#204C2×C414yescomplemented
116C2×D3×C8—22no—
117C2×D3×C8—22no—
118C2×D3×C8—22no—
119C2×D3×C8—22no—
120C2×D3×C8—22no—
121C2×D3×C8C2×C414yescomplemented
122#897—22no—
123#897C2×C414yescomplemented
124#895—22no—
125#895C2×C414yes—
126C4×D12—22no—
127C4×D12—22no—
128C4×D12—44no—
129C42×D3—22no—
130C42×D3—22no—
131C4×Dic6—22no—
132C4×Dic6—22no—
133C3×#107—22no—
134C3×#106C2×C414yescomplemented
135C3×#97D414yescomplemented
136C3×#95—21no—
137C3×#95—21no—
138C3⋊#95—21no—
139C3⋊#95—21no—
140C3⋊#95—21no—
141C3⋊#95—21no—
142C3⋊#95—21no—
143C3⋊#95—21no—
144#821—22no—
145#818—22no—
146#816—22no—
147#815—22no—
148#815—22no—
149#810—22no—
150#810C2×C414yescomplemented
151#809—22no—
152#809C2×C414yescomplemented
153#803—22no—
154C22×SD16—31no—
155C23×C8—31no—
156C23×C8—31no—
157C2×C22⋊Q8—31no—
158C2×#121—31no—
159C2×C4×Q8—31no—
160C2×C4×D4—31no—
161C2×C4×D4—61no—
162C22×C42—31no—
163#465—38no—
164#440—64no—
165C2×#107—31no—
166C2×#107C2×D311yescharacteristic
167C2×#106C2×D311yescharacteristic
168C2×#103—31no—
169C2×#103—31no—
170C2×#103—31no—
171C2×#102—31no—
172C2×#102—31no—
173C2×#102—31no—
174C2×#97—31no—
175C2×#97—31no—
176C2×#97—31no—
177C2×#97—64no—
178C2×#97C2×D311yescharacteristic
179#391—31no—
180#390—31no—
181#389—31no—
182#389—31no—
183#388—61no—
184#387—61no—
185#386—61no—
186#385—61no—
187#380—31no—
188#380—31no—
189C4×C4⋊C4—61no—
190C4×C4⋊C4C2×D311yescharacteristic
191C4×C4⋊C4C2×D311yescharacteristic
192C4×C22⋊C4—61no—
193C4×C22⋊C4—61no—
194#340—31no—
195#340—31no—
196#340—31no—
197#340—31no—
198#340C2×D311yescharacteristic
199#340C2×D311yescharacteristic
200C23×D3—21no—
201C23×D3C2×D411yescharacteristic
202C22×C3×C4—21no—
203C22×C3×C4—21no—
204C22×C3×C4—21no—
205C22×C3×C4—21no—
206C22×C3×C4C2×D411yescharacteristic
207C22×C3×C4C2×D411yescharacteristic
208C22×C3×C4C2411yescharacteristic
209C22×Dic3—21no—
210C22×Dic3—21no—
211C22×Dic3—21no—
212C22×Dic3C2×D411yescharacteristic
213C22×Dic3C2×D411yescharacteristic
214C22×Dic3C2×D411yescharacteristic
215C2×D12—21no—
216C2×D12—21no—
217C2×D12—21no—
218C2×D12—21no—
219C2×D12—24no—
220C2×D12—21no—
221C2×D12—42no—
222C2×D12—42no—
223C2×D12C22×C412yes—
224C2×C4×D3—21no—
225C2×C4×D3—21no—
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—22no—
229C2×C4×D3—22no—
230C2×C4×D3—22no—
231C2×C4×D3—22no—
232C2×C4×D3—41no—
233C2×C4×D3—41no—
234C2×C4×D3—42no—
235C2×C4×D3—42no—
236C2×C4×D3—42no—
237C2×C4×D3C22×C412yes—
238C2×C4×D3#4112yes—
239C2×Dic6—21no—
240C2×Dic6—21no—
241C2×Dic6—21no—
242C2×Dic6—21no—
243C2×Dic6—21no—
244C2×Dic6C22×C412yes—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8C22×C412yes—
248C2×C3×C8C2×D412yes—
249C2×C3×C8C2×D412yes—
250C2×C3×C8#4112yes—
251C3×C4⋊C4—21no—
252C3×C4⋊C4—21no—
253C3×C4⋊C4—21no—
254C3×C4⋊C4—21no—
255C3×C4⋊C4—21no—
256C3×C4⋊C4—21no—
257C3×C4⋊C4C22×C412yes—
258C3×C4⋊C4C22×C412yes—
259C3×C42—42no—
260C3×C42—42no—
261C3×C42C2×D412yes—
262C3×C42#4112yes—
263(C2×D3)⋊C4—24no—
264(C2×D3)⋊C4—24no—
265(C2×D3)⋊C4—42no—
266(C2×D3)⋊C4—42no—
267(C2×D3)⋊C4—42no—
268(C2×D3)⋊C4—42no—
269(C2×D3)⋊C4—42no—
270C4⋊Dic3—24no—
271C4⋊Dic3—21no—
272C4⋊Dic3—21no—
273C4⋊Dic3—21no—
274C4⋊Dic3—21no—
275C4⋊Dic3—42no—
276C4⋊Dic3—42no—
277Dic3⋊C4—42no—
278C4×Dic3—22no—
279C4×Dic3—22no—
280C4×Dic3—21no—
281C4×Dic3—21no—
282C4×Dic3—42no—
283C2×C3⋊C8—21no—
284C2×C3⋊C8—21no—
285C2×C3⋊C8—21no—
286C2×C3⋊C8—21no—
287C2×C3⋊C8C22×C412yes—
288C2×C3⋊C8#4112yes—
289#204—28no—
290D3×C8—28no—
291D3×C8—28no—
292C22×Q8—31no—
293C22×D4—31no—
294C22×D4—61no—
295C23×C4—31no—
296C23×C4—31no—
297C23×C4—31no—
298C23×C4—61no—
299C2×SD16—34no—
300C2×SD16—62no—
301C2×SD16—62no—
302C22×C8—31no—
303C22×C8—31no—
304C22×C8—34no—
305C22×C8—62no—
306C22×C8—62no—
307C22×C8—62no—
308C22×C8—62no—
309C22×C8—62no—
310C22×C8C22×D311yescharacteristic
311C22×C8C22×D311yescharacteristic
312C22⋊Q8—34no—
313C22⋊Q8—62no—
314#121—34no—
315#121—62no—
316C4×Q8—62no—
317C4×Q8—62no—
318C4×D4—62no—
319C4×D4—62no—
320C4×D4—124no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—31no—
323C2×C4⋊C4—61no—
324C2×C4⋊C4—61no—
325C2×C4⋊C4—61no—
326C2×C4⋊C4—61no—
327C2×C4⋊C4C22×D311yescharacteristic
328C2×C4⋊C4C22×D311yescharacteristic
329C2×C4⋊C4C22×D311yescharacteristic
330C2×C4⋊C4C22×D311yescharacteristic
331C2×C22⋊C4—61no—
332C2×C22⋊C4—61no—
333C2×C22⋊C4—61no—
334C2×C22⋊C4—61no—
335C2×C22⋊C4—61no—
336C2×C22⋊C4—61no—
337C2×C22⋊C4—61no—
338C2×C42—21no—
339C2×C42—21no—
340C2×C42—31no—
341C2×C42—31no—
342C2×C42—31no—
343C2×C42—62no—
344C2×C42—62no—
345C2×C42—61no—
346C2×C42C22×D311yescharacteristic
347#107—22no—
348#107—62no—
349#106C4×D314yescomplemented
350#103—34no—
351#103—62no—
352#103—62no—
353#102—34no—
354#102—62no—
355#102—62no—
356#97—62no—
357#97—62no—
358#97—62no—
359#97D1214yescomplemented
360#95—21no—
361#95—21no—
362#95—61no—
363#95—61no—
364#95—61no—
365#95—61no—
366#95—61no—
367#95—61no—
368C23×C3C22×D411yescharacteristic
369C22×D3—21no—
370C22×D3—21no—
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—22no—
374C22×D3—41no—
375C22×D3—41no—
376C22×D3—41no—
377C22×D3—41no—
378C22×D3—41no—
379C22×D3—41no—
380C22×D3C4×D412yes—
381C22×D3AGL(1,ℤ/8)12yes—
382C22×D3#13712yes—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—41no—
390C2×C3×C4—41no—
391C2×C3×C4—41no—
392C2×C3×C4—41no—
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#12112yes—
400C2×C3×C4#12112yes—
401C2×C3×C4C23×C411yescharacteristic
402C2×C3×C4C22×D411yescharacteristic
403C2×C3×C4C2×#4111yescharacteristic
404C2×C3×C4C2×#4111yescharacteristic
405C2×C3×C4C2×#4111yescharacteristic
406C2×C3×C4C2×#4111yescharacteristic
407C2×Dic3—21no—
408C2×Dic3—21no—
409C2×Dic3—22no—
410C2×Dic3—21no—
411C2×Dic3—21no—
412C2×Dic3—21no—
413C2×Dic3—21no—
414C2×Dic3—21no—
415C2×Dic3—21no—
416C2×Dic3—41no—
417C2×Dic3—41no—
418C2×Dic3—41no—
419C2×Dic3—41no—
420C2×Dic3—41no—
421C2×Dic3—41no—
422C2×Dic3—41no—
423C2×Dic3—41no—
424C2×Dic3C4×D412yes—
425D12—22no—
426D12—22no—
427D12—48no—
428D12—41no—
429D12—41no—
430C4×D3—22no—
431C4×D3—22no—
432C4×D3—22no—
433C4×D3—22no—
434C4×D3—44no—
435C4×D3—44no—
436C4×D3—84no—
437Dic6—22no—
438Dic6—22no—
439Dic6—41no—
440Dic6—41no—
441C3×C8—22no—
442C3×C8C4×D414yescomplemented
443C3⋊C8—22no—
444C3⋊C8—22no—
445C24—31no—
446C24—61no—
447C2×Q8—32no—
448C2×Q8—61no—
449C2×Q8—61no—
450C2×Q8—61no—
451C2×Q8—61no—
452C2×Q8—61no—
453C2×D4—32no—
454C2×D4—64no—
455C2×D4—61no—
456C2×D4—61no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4—61no—
460C2×D4—122no—
461C2×D4—122no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—31no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—31no—
470C22×C4—31no—
471C22×C4—62no—
472C22×C4—62no—
473C22×C4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4—61no—
477C22×C4—61no—
478C22×C4—62no—
479C22×C4—62no—
480C22×C4—61no—
481C22×C4—61no—
482C22×C4—121no—
483C22×C4—121no—
484C22×C4—122no—
485C22×C4—122no—
486C22×C4—122no—
487C22×C4D3×D411yescharacteristic
488C22×C4D3×D411yescharacteristic
489C22×C4C23×D311yescharacteristic
490SD16—68no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—32no—
494C2×C8—32no—
495C2×C8—68no—
496C2×C8—61no—
497C2×C8—61no—
498C2×C8—61no—
499C2×C8—61no—
500C2×C8—68no—
501C2×C8C2×C4×D312yes—
502C2×C8C2×D1212yes—
503C2×C8C2×D1212yes—
504C2×C8#23512yes—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—64no—
512C4⋊C4—61no—
513C4⋊C4—61no—
514C4⋊C4—61no—
515C4⋊C4—61no—
516C4⋊C4—122no—
517C4⋊C4—122no—
518C4⋊C4—122no—
519C4⋊C4C2×C4×D312yes—
520C4⋊C4C2×C4×D312yes—
521C22⋊C4—64no—
522C22⋊C4—64no—
523C22⋊C4—122no—
524C22⋊C4—122no—
525C22⋊C4—122no—
526C22⋊C4—122no—
527C22⋊C4—122no—
528C42—42no—
529C42—42no—
530C42—62no—
531C42—62no—
532C42—61no—
533C42—61no—
534C42—122no—
535C42C2×D1212yes—
536C42#23912yes—
537C22×C3C2×C4×D411yescharacteristic
538C22×C3C2×#12111yescharacteristic
539C22×C3#53211yescharacteristic
540C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
541C22×C3C2×#13711yescharacteristic
542C22×C3#57511yescharacteristic
543C22×C3#57511yescharacteristic
544C2×D3—22no—
545C2×D3—22no—
546C2×D3—22no—
547C2×D3—22no—
548C2×D3—22no—
549C2×D3—22no—
550C2×D3—42no—
551C2×D3—42no—
552C2×D3—42no—
553C2×D3—81no—
554C2×D3—81no—
555C2×D3—81no—
556C2×D3—81no—
557C2×D3#44014yescomplemented
558C3×C4—22no—
559C3×C4—22no—
560C3×C4—42no—
561C3×C4—42no—
562C3×C4—81no—
563C3×C4—81no—
564C3×C4C2×C4×D411yescharacteristic
565C3×C4C4×#4111yescharacteristic
566C3×C4#52511yescharacteristic
567C3×C4#52911yescharacteristic
568Dic3—22no—
569Dic3—41no—
570Dic3—41no—
571Dic3—42no—
572Dic3—81no—
573Dic3—81no—
574C23—32no—
575C23—32no—
576C23—32no—
577C23—61no—
578C23—61no—
579C23—61no—
580C23—61no—
581C23—62no—
582C23—121no—
583C23—121no—
584C23—121no—
585C23—121no—
586C23—121no—
587C23—121no—
588C23C2×D3×D411yescharacteristic
589Q8—62no—
590Q8—62no—
591Q8—121no—
592Q8—121no—
593D4—62no—
594D4—62no—
595D4—128no—
596D4—121no—
597D4—121no—
598C2×C4—21no—
599C2×C4—21no—
600C2×C4—21no—
601C2×C4—21no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—32no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—61no—
616C2×C4—61no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—62no—
621C2×C4—61no—
622C2×C4—61no—
623C2×C4—61no—
624C2×C4—61no—
625C2×C4—61no—
626C2×C4—61no—
627C2×C4—62no—
628C2×C4—124no—
629C2×C4—124no—
630C2×C4—121no—
631C2×C4—121no—
632C2×C4—121no—
633C2×C4—121no—
634C2×C4—121no—
635C2×C4—121no—
636C2×C4—121no—
637C2×C4—121no—
638C2×C4—244no—
639C2×C4#89512yes—
640C2×C4#89512yes—
641C2×C4C22×C4×D311yescharacteristic
642C2×C4C22×D1211yescharacteristic
643C2×C4C2×#23511yescharacteristic
644C2×C4C2×#23911yescharacteristic
645C2×C4D3×#4111yescharacteristic
646C2×C4D3×#4111yescharacteristic
647C8—22no—
648C8—62no—
649C8—62no—
650C8C4×D1214yescomplemented
651C2×C3C4×#12111yescharacteristic
652C2×C3C2×#44011yescharacteristic
653C2×C3#294311yescharacteristic
654C2×C3#305511yescharacteristic
655C2×C3#305611yescharacteristic
656C2×C3#318011yescharacteristic
657C2×C3#318111yescharacteristic
658D3—24no—
659D3—82no—
660C22—34no—
661C22—62no—
662C22—62no—
663C22—62no—
664C22—62no—
665C22—62no—
666C22—62no—
667C22—122no—
668C22—122no—
669C22—122no—
670C22—241no—
671C22—241no—
672C22—241no—
673C22—241no—
674C22C2×#89511yescharacteristic
675C22C4×D3×D411yescharacteristic
676C22#554811yescharacteristic
677C22D3×AGL(1,ℤ/8)11yescharacteristic
678C22#577311yescharacteristic
679C22D3×#13711yescharacteristic
680C22#577711yescharacteristic
681C4—22no—
682C4—22no—
683C4—42no—
684C4—42no—
685C4—62no—
686C4—81no—
687C4—81no—
688C4—122no—
689C4—121no—
690C4—121no—
691C4—241no—
692C4—241no—
693C4C2×C4×D1211yescharacteristic
694C4#552411yescharacteristic
695C4C4×#23911yescharacteristic
696C4#558011yescharacteristic
697C3#2152811yescharacteristic, complemented, Sylow
698C2—64no—
699C2—242no—
700C2C4×#89511yescharacteristic
701C2#7921111yescharacteristic
702C2#7921211yescharacteristic
703C2D3×#44011yescharacteristic
704C2#7977211yescharacteristic
705C2#7983711yescharacteristic
706C2#7987611yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1776C2
socleC23×C3C22×D4
prime radicalC2×#895C22
cosocleC22×C3×C4C24
hypercenter#1776D3
hypocenterC3#21528
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1776

Complements

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

NH ≅ G/Ntype
2. C2×#4710C2semidirect
3. C2×D3×#97C2semidirect
4. C4×#897C2semidirect
6. C3×#1776C2semidirect
7. #70630C2semidirect
8. #70629C2semidirect
9. #70562C2semidirect
10. #69475C2semidirect
11. #69474C2semidirect
13. #68882C2semidirect
14. #68857C2semidirect
15. #68855C2semidirect
50. #4864C4semidirect
75. #1776D3semidirect
115. C2×#204C2×C4semidirect
121. C2×D3×C8C2×C4semidirect
123. #897C2×C4semidirect
134. C3×#106C2×C4semidirect
135. C3×#97D4semidirect
150. #810C2×C4semidirect
152. #809C2×C4semidirect
349. #106C4×D3semidirect
359. #97D12semidirect
442. C3×C8C4×D4semidirect
557. C2×D3#440semidirect
650. C8C4×D12semidirect
697. C3#21528semidirect

Maximal subgroups

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

subgroupindex
C2×#48642
C2×#47102
C2×D3×#972
C4×#8972
C4×#8952
C3×#17762
#706302
#706292
#705622
#694752
#694742
#688832
#688822
#688572
#688552
#215283