Finite Group Databasebeta

← #10846308

Subgroups — #10846308

Order 768.

970 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#83254C211yesmaximal, characteristic
2C2×#5092C211yesmaximal, characteristic, complemented
3C2×#4813C211yesmaximal, characteristic
4C2×#4813C211yesmaximal, characteristic
5C2×#4790C211yesmaximal, characteristic, complemented
6#76221C211yesmaximal, characteristic
7C3×#2043C211yesmaximal, characteristic, complemented
8#70281C211yesmaximal, characteristic, complemented
9#70273C211yesmaximal, characteristic
10#70273C211yesmaximal, characteristic
11#70258C211yesmaximal, characteristic, complemented
12#70239C211yesmaximal, characteristic, complemented
13#69619C211yesmaximal, characteristic, complemented
14#68647C211yesmaximal, characteristic
15#68631C211yesmaximal, characteristic, complemented
16#25415—31nomaximal, Sylow
17C2×C3×C4⋊Q8C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×#946C2211yescharacteristic
20C2×Q8×Dic3C2211yescharacteristic
21C22×#216C2211yescharacteristic
22C22×#216C2211yescharacteristic
23C22×#216C2211yescharacteristic
24C22×#216C2211yescharacteristic
25C22×D3×C8C2211yescharacteristic
26C2×#897C2211yescharacteristic
27C2×#897C2211yescharacteristic
28C2×#887C2211yescharacteristic
29C2×#869C2211yescharacteristic
30C2×C3×#103C2211yescharacteristic
31C2×C3×#103C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C3×#389C2211yescharacteristic
35#5229C2211yescharacteristic
36C2×(C2×D3)⋊C8C2211yescharacteristic
37C2×#816C2211yescharacteristic
38C2×#816C2211yescharacteristic
39C2×#816C2211yescharacteristic
40C2×#816C2211yescharacteristic
41C2×C8×Dic3C2211yescharacteristic
42#5092—24no—
43#4994—21no—
44#4994—21no—
45#4990—21no—
46#4984—21no—
47#4982—21no—
48#4976—21no—
49#4973C2211yescharacteristic
50C2×#807C2211yescharacteristic
51C2×#807C2211yescharacteristic
52C4×(C2×D3)⋊C4C2211yescharacteristic
53#4928C2211yescharacteristic
54C2×C4×C3⋊C8C2211yescharacteristic
55#4813—24no—
56#4813—24no—
57#4790—24no—
58#4670—21no—
59#4661—21no—
60C3×#336C2211yescharacteristic
61#4550C2211yescharacteristic
62#4529C2211yescharacteristic
63#4529C2211yescharacteristic
64C2×#494—31no—
65C2×#467—31no—
66C2×#467—31no—
67C2×C4×Q16—31no—
68#2429—31no—
69#2429—31no—
70#2043—31no—
71#2043D311yescharacteristic, complemented
72#2001—31no—
73#2001—31no—
74#1969—31no—
75#1942—31no—
76#1878—31no—
77#1878—31no—
78C8×C22⋊C4—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×Q8C2311yescharacteristic
81C22×C4×D3C2311yescharacteristic
82C22×Dic6C2311yescharacteristic
83C22×Dic6C2311yescharacteristic
84C22×C3×C8C2311yescharacteristic
85C22×C3×C8C2311yescharacteristic
86C3×C4⋊Q8—22no—
87C3×C4⋊Q8—41no—
88C2×C3×C4⋊C4—21no—
89C2×C3×C4⋊C4—21no—
90C2×C3×C4⋊C4—21no—
91C2×C3×C4⋊C4C2311yescharacteristic
92C2×C3×C4⋊C4C2311yescharacteristic
93C2×C3×C42C2311yescharacteristic
94#946—22no—
95#946—22no—
96#946—41no—
97#946—41no—
98Q8×Dic3—22no—
99Q8×Dic3—41no—
100C2×#216—22no—
101C2×#216—22no—
102C2×#216—22no—
103C2×#216—22no—
104C2×#216—22no—
105C2×#216—22no—
106C2×#216—22no—
107C2×#216—22no—
108C2×#216—22no—
109C2×#216—41no—
110C2×#216—41no—
111C2×#216D414yes—
112C2×(C2×D3)⋊C4—21no—
113C2×(C2×D3)⋊C4—21no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4D411yescharacteristic
117C2×(C2×D3)⋊C4D411yescharacteristic
118C2×C4⋊Dic3—21no—
119C2×C4⋊Dic3—21no—
120C2×C4⋊Dic3—21no—
121C2×C4⋊Dic3—21no—
122C2×C4⋊Dic3—21no—
123C2×C4⋊Dic3C2311yescharacteristic
124C2×C4⋊Dic3C2311yescharacteristic
125C2×Dic3⋊C4—21no—
126C2×Dic3⋊C4—21no—
127C2×Dic3⋊C4—21no—
128C2×Dic3⋊C4—21no—
129C2×C4×Dic3—21no—
130C2×C4×Dic3—21no—
131C2×C4×Dic3C2311yescharacteristic
132C22×C3⋊C8C2311yescharacteristic
133C22×C3⋊C8C2311yescharacteristic
134C2×D3×C8—22no—
135C2×D3×C8—22no—
136C2×D3×C8—22no—
137#897—22no—
138#897—22no—
139#897—41no—
140#897—41no—
141#887—22no—
142#887—41no—
143#869—22no—
144#869—41no—
145C3×#103—22no—
146C3×#103—22no—
147C3×#103—22no—
148C3×#103—41no—
149C3×#95—21no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153C3⋊#95—21no—
154C3⋊#95—21no—
155C3⋊#95D411yescharacteristic
156C3⋊#95D411yescharacteristic
157(C2×D3)⋊C8—22no—
158#816—22no—
159#816—22no—
160#816—22no—
161#816—41no—
162C8×Dic3—22no—
163#807—22no—
164#807D414yes—
165C4×C3⋊C8—22no—
166C22×Q16—31no—
167C22×Q16—31no—
168C22×Q16—31no—
169C22×Q16—31no—
170C23×C8—31no—
171C2×C4⋊Q8—31no—
172C2×C4⋊Q8C2×D311yescharacteristic
173C2×C22⋊Q8—31no—
174C2×C22⋊Q8—31no—
175C2×C22⋊Q8—31no—
176C2×C22⋊Q8—31no—
177C2×C4×Q8—31no—
178C2×C4×Q8—31no—
179#494—64no—
180#467—64no—
181#467—64no—
182C4×Q16—64no—
183C2×#107—31no—
184C2×#107—31no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#103C2×D311yescharacteristic
191C2×#103C2×D311yescharacteristic
192C2×#103C2×D311yescharacteristic
193C2×C22⋊C8—31no—
194C2×C4×C8—31no—
195C2×C4×C8—31no—
196#398—61no—
197#398—61no—
198#396—61no—
199#396—61no—
200#391—31no—
201#391—31no—
202#389—31no—
203#389—61no—
204#389—61no—
205#389C2×D311yescharacteristic
206#388—61no—
207#388—61no—
208C4×C22⋊C4—31no—
209#340—31no—
210#340—31no—
211#336—31no—
212#336C2×D311yescharacteristic
213C23×D3C2×D411yescharacteristic
214C2×C3×Q8—21no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—21no—
225C2×C3×Q8C2×D412yes—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—21no—
229C22×C3×C4—21no—
230C22×C3×C4C2×D411yescharacteristic
231C22×C3×C4C2×D411yescharacteristic
232C22×C3×C4C2411yescharacteristic
233C22×Dic3—21no—
234C22×Dic3—21no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3C2×D411yescharacteristic
238C22×Dic3C2×D411yescharacteristic
239C22×Dic3C2×D411yescharacteristic
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—21no—
244C2×C4×D3—21no—
245C2×C4×D3—21no—
246C2×Dic6—21no—
247C2×Dic6—21no—
248C2×Dic6—21no—
249C2×Dic6—21no—
250C2×Dic6—21no—
251C2×Dic6—21no—
252C2×Dic6—21no—
253C2×Dic6—21no—
254C2×Dic6—21no—
255C2×Dic6—21no—
256C2×Dic6—21no—
257C2×Dic6C2×D412yes—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C2×C3×C8—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—21no—
267C3×C4⋊C4—42no—
268C3×C4⋊C4—42no—
269C3×C4⋊C4—42no—
270C3×C4⋊C4C2×D412yes—
271C3×C42—21no—
272C3×C42—21no—
273#216—28no—
274#216—44no—
275#216—44no—
276#216—44no—
277(C2×D3)⋊C4—22no—
278(C2×D3)⋊C4—42no—
279(C2×D3)⋊C4—42no—
280(C2×D3)⋊C4—42no—
281(C2×D3)⋊C4—42no—
282(C2×D3)⋊C4Q1614yescomplemented
283C4⋊Dic3—21no—
284C4⋊Dic3—21no—
285C4⋊Dic3—21no—
286C4⋊Dic3—42no—
287C4⋊Dic3—42no—
288C4⋊Dic3—42no—
289C4⋊Dic3—42no—
290C4⋊Dic3—42no—
291C4⋊Dic3C2×D412yes—
292Dic3⋊C4—42no—
293Dic3⋊C4—42no—
294Dic3⋊C4—42no—
295Dic3⋊C4—42no—
296C4×Dic3—21no—
297C4×Dic3—21no—
298C4×Dic3—42no—
299C4×Dic3—42no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8C2×D412yes—
303C2×C3⋊C8C2×D412yes—
304C2×C3⋊C8#4112yes—
305C2×C3⋊C8#4112yes—
306D3×C8—44no—
307C22×Q8—31no—
308C22×Q8—31no—
309C22×Q8C22×D311yescharacteristic
310C22×Q8C22×D311yescharacteristic
311C23×C4—31no—
312C2×Q16—34no—
313C2×Q16—62no—
314C2×Q16—62no—
315C2×Q16—62no—
316C2×Q16—62no—
317C2×Q16—62no—
318C2×Q16—62no—
319C2×Q16—62no—
320C2×Q16—62no—
321C2×Q16—62no—
322C2×Q16—121no—
323C2×Q16—121no—
324C22×C8—31no—
325C22×C8—31no—
326C22×C8—62no—
327C22×C8—62no—
328C22×C8—62no—
329C22×C8C22×D311yescharacteristic
330C22×C8C22×D311yescharacteristic
331C4⋊Q8—22no—
332C4⋊Q8—41no—
333C4⋊Q8—62no—
334C4⋊Q8—121no—
335C22⋊Q8—62no—
336C22⋊Q8—62no—
337C22⋊Q8—62no—
338C22⋊Q8—62no—
339C22⋊Q8—121no—
340C22⋊Q8—121no—
341C22⋊Q8—121no—
342C22⋊Q8—121no—
343C4×Q8—62no—
344C4×Q8—62no—
345C4×Q8—121no—
346C4×Q8—121no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—21no—
350C2×C4⋊C4—31no—
351C2×C4⋊C4—31no—
352C2×C4⋊C4—61no—
353C2×C4⋊C4—61no—
354C2×C4⋊C4—61no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—61no—
357C2×C4⋊C4—61no—
358C2×C4⋊C4—61no—
359C2×C4⋊C4—61no—
360C2×C4⋊C4—61no—
361C2×C4⋊C4C22×D311yescharacteristic
362C2×C4⋊C4C22×D311yescharacteristic
363C2×C22⋊C4—31no—
364C2×C22⋊C4—31no—
365C2×C22⋊C4—61no—
366C2×C22⋊C4—61no—
367C2×C22⋊C4—61no—
368C2×C22⋊C4—61no—
369C2×C42—31no—
370C2×C42—61no—
371C2×C42—61no—
372C2×C42C22×D311yescharacteristic
373#107—34no—
374#107—62no—
375#103—22no—
376#103—22no—
377#103—22no—
378#103—41no—
379#103—62no—
380#103—62no—
381#103—62no—
382#103—121no—
383C22⋊C8—62no—
384C4×C8—62no—
385C4×C8—62no—
386#95—21no—
387#95—31no—
388#95—31no—
389#95—61no—
390#95—61no—
391#95—61no—
392#95—61no—
393#95—61no—
394C23×C3C22×D411yescharacteristic
395C22×D3—21no—
396C22×D3—21no—
397C22×D3—21no—
398C22×D3—21no—
399C22×D3—21no—
400C22×D3—21no—
401C22×D3C2×Q1612yes—
402C3×Q8—22no—
403C3×Q8—22no—
404C3×Q8—41no—
405C3×Q8—41no—
406C3×Q8—41no—
407C3×Q8—41no—
408C3×Q8—41no—
409C3×Q8—41no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—22no—
415C2×C3×C4—22no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4—41no—
422C2×C3×C4—41no—
423C2×C3×C4—41no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4C2×Q1612yes—
427C2×C3×C4#13512yes—
428C2×C3×C4C22×D411yescharacteristic
429C2×C3×C4C22×D411yescharacteristic
430C2×C3×C4C2×#4111yescharacteristic
431C2×C3×C4C2×#4111yescharacteristic
432C2×C3×C4H(5,𝔽2)11yescharacteristic
433C2×C3×C4H(5,𝔽2)11yescharacteristic
434C2×Dic3—21no—
435C2×Dic3—21no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—22no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—22no—
442C2×Dic3—21no—
443C2×Dic3—21no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3—41no—
449C2×Dic3—41no—
450C2×Dic3—41no—
451C2×Dic3—41no—
452C2×Dic3—41no—
453C2×Dic3—41no—
454C2×Dic3C2×Q1612yes—
455C4×D3—41no—
456C4×D3—41no—
457C4×D3—41no—
458C4×D3—41no—
459Dic6—22no—
460Dic6—22no—
461Dic6—41no—
462Dic6—41no—
463Dic6—41no—
464Dic6—41no—
465Dic6—41no—
466Dic6—41no—
467C3×C8—41no—
468C3×C8—41no—
469C3⋊C8—22no—
470C3⋊C8#12114yes—
471C24—31no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—32no—
484C2×Q8—61no—
485C2×Q8—61no—
486C2×Q8—61no—
487C2×Q8—61no—
488C2×Q8—61no—
489C2×Q8—61no—
490C2×Q8—61no—
491C2×Q8—61no—
492C2×Q8—61no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8D3×D412yes—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—31no—
501C22×C4—31no—
502C22×C4—31no—
503C22×C4—61no—
504C22×C4—61no—
505C22×C4—61no—
506C22×C4—61no—
507C22×C4—61no—
508C22×C4—61no—
509C22×C4—61no—
510C22×C4—61no—
511C22×C4—61no—
512C22×C4—61no—
513C22×C4D3×D411yescharacteristic
514C22×C4D3×D411yescharacteristic
515C22×C4C23×D311yescharacteristic
516Q16—68no—
517Q16—124no—
518Q16—124no—
519Q16—124no—
520C2×C8—21no—
521C2×C8—21no—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—32no—
527C2×C8—32no—
528C2×C8—32no—
529C2×C8—32no—
530C2×C8—61no—
531C2×C8—61no—
532C2×C8—124no—
533C4⋊C4—21no—
534C4⋊C4—21no—
535C4⋊C4—21no—
536C4⋊C4—32no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—42no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—61no—
543C4⋊C4—122no—
544C4⋊C4—122no—
545C4⋊C4—122no—
546C4⋊C4—122no—
547C4⋊C4—122no—
548C4⋊C4—122no—
549C4⋊C4—122no—
550C4⋊C4—122no—
551C4⋊C4—122no—
552C4⋊C4D3×D412yes—
553C22⋊C4—34no—
554C22⋊C4—62no—
555C22⋊C4—122no—
556C22⋊C4—122no—
557C22⋊C4—122no—
558C22⋊C4—122no—
559C42—21no—
560C42—21no—
561C42—61no—
562C42—61no—
563C42—122no—
564C42—122no—
565C22×C3#53211yescharacteristic
566C22×C3D4211yescharacteristic
567C22×C3D4211yescharacteristic
568C22×C3C22×Q1611yescharacteristic
569C22×C3C2×#13511yescharacteristic
570C22×C3#57811yescharacteristic
571C22×C3#57811yescharacteristic
572C2×D3—22no—
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—41no—
576C2×D3—41no—
577C2×D3—41no—
578C2×D3—41no—
579C3×C4—22no—
580C3×C4—22no—
581C3×C4—42no—
582C3×C4—42no—
583C3×C4—81no—
584C3×C4—81no—
585C3×C4C2×#12111yescharacteristic
586C3×C4#54011yescharacteristic
587C3×C4#54611yescharacteristic
588C3×C4#55011yescharacteristic
589Dic3—22no—
590Dic3—42no—
591Dic3—41no—
592Dic3—41no—
593Dic3—42no—
594Dic3—81no—
595Dic3—81no—
596C23—32no—
597C23—61no—
598C23—61no—
599C23—61no—
600C23—61no—
601C23—61no—
602C23—61no—
603C23C2×D3×D411yescharacteristic
604Q8—22no—
605Q8—22no—
606Q8—41no—
607Q8—41no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8—62no—
613Q8—62no—
614Q8—121no—
615Q8—121no—
616Q8—121no—
617Q8—121no—
618Q8—121no—
619Q8—121no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—32no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—61no—
638C2×C4—61no—
639C2×C4—61no—
640C2×C4—61no—
641C2×C4—61no—
642C2×C4—62no—
643C2×C4—61no—
644C2×C4—61no—
645C2×C4—62no—
646C2×C4—61no—
647C2×C4—121no—
648C2×C4—121no—
649C2×C4—121no—
650C2×C4—121no—
651C2×C4—121no—
652C2×C4—121no—
653C2×C4—121no—
654C2×C4—121no—
655C2×C4—121no—
656C2×C4—121no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—121no—
660C2×C4—121no—
661C2×C4#91612yes—
662C2×C4D3×Q1612yes—
663C2×C4C2×D3×D411yescharacteristic
664C2×C4C2×D3×D411yescharacteristic
665C2×C4#100411yescharacteristic
666C2×C4D3×#4111yescharacteristic
667C2×C4D3×#4111yescharacteristic
668C2×C4#100911yescharacteristic
669C8—34no—
670C8—41no—
671C8—41no—
672C8—62no—
673C2×C3#242811yescharacteristic
674C2×C3#317011yescharacteristic
675C2×C3#317711yescharacteristic
676C2×C3#328311yescharacteristic
677C2×C3#328511yescharacteristic
678C2×C3D4×Q1611yescharacteristic
679C2×C3D4×Q1611yescharacteristic
680D3—42no—
681C22—62no—
682C22—62no—
683C22—62no—
684C22—121no—
685C22—121no—
686C22—121no—
687C22—121no—
688C22#559011yescharacteristic
689C22#560911yescharacteristic
690C22#566811yescharacteristic
691C22C2×#91611yescharacteristic
692C22C2×D3×Q1611yescharacteristic
693C22#577911yescharacteristic
694C22#577911yescharacteristic
695C4—22no—
696C4—22no—
697C4—42no—
698C4—42no—
699C4—62no—
700C4—81no—
701C4—81no—
702C4—121no—
703C4—122no—
704C4—121no—
705C4—122no—
706C4—241no—
707C4—241no—
708C4#559911yescharacteristic
709C4D3×#12111yescharacteristic
710C4#565411yescharacteristic
711C4#566311yescharacteristic
712C3#2541511yescharacteristic, complemented, Sylow
713C2—122no—
714C2#7690311yescharacteristic
715C2#8006711yescharacteristic
716C2#8021111yescharacteristic
717C2#8044911yescharacteristic
718C2#8049011yescharacteristic
719C2#8159311yescharacteristic
720C2#8173011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2043C2
socleC23×C3C22×D4
prime radicalC23×D3C2×D4
hypercenter#2043D3
hypocenterC3#25415
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2043

Complements

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

NH ≅ G/Ntype
2. C2×#5092C2semidirect
5. C2×#4790C2semidirect
7. C3×#2043C2semidirect
8. #70281C2semidirect
11. #70258C2semidirect
12. #70239C2semidirect
13. #69619C2semidirect
15. #68631C2semidirect
71. #2043D3semidirect
282. (C2×D3)⋊C4Q16semidirect
712. C3#25415semidirect

Maximal subgroups

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

subgroupindex
#832542
C2×#50922
C2×#48132
C2×#47902
#762212
C3×#20432
#702812
#702732
#702582
#702392
#696192
#686472
#686312
#254153