Finite Group Databasebeta

← #10828503

Subgroups — #10828503

Order 768.

1176 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5680C211yesmaximal, characteristic
2C2×#4805C211yesmaximal, characteristic, complemented
3C2×#4774C211yesmaximal, characteristic
4D3×#389C211yesmaximal, characteristic, complemented
5C3×#2042C211yesmaximal, characteristic, complemented
6#71722C211yesmaximal, characteristic, complemented
7#70268C211yesmaximal, characteristic, complemented
8#70236C211yesmaximal, characteristic, complemented
9#70235C211yesmaximal, characteristic, complemented
10#70200C211yesmaximal, characteristic
11#70170C211yesmaximal, characteristic, complemented
12#70169C211yesmaximal, characteristic, complemented
13#69606C211yesmaximal, characteristic, complemented
14#68664C211yesmaximal, characteristic, complemented
15#68634C211yesmaximal, characteristic, complemented
16#24066—31nomaximal, Sylow
17C2×C3×#124C2211yescharacteristic
18C2×#946C2211yescharacteristic
19C2×Q8×Dic3C2211yescharacteristic
20C2×#938C2211yescharacteristic
21C2×D4×Dic3C2211yescharacteristic
22#5680—24no—
23#5680—24no—
24C2×D3×C4⋊C4—21no—
25C2×D3×C4⋊C4C2211yescharacteristic
26C2×D3×C4⋊C4C2211yescharacteristic
27C2×#883—21no—
28C2×#67⋊C4—21no—
29C2×#879—21no—
30C2×#877—21no—
31C2×C42×D3C2211yescharacteristic
32C2×#870C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#103C2211yescharacteristic
35C2×C3×#102C2211yescharacteristic
36C2×C3×#102C2211yescharacteristic
37C3×#389C2211yescharacteristic
38C2×#835C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#832C2211yescharacteristic
41C2×#832C2211yescharacteristic
42C2×(C2×D3)⋊C8C2211yescharacteristic
43C2×(C2×D3)⋊C8C2211yescharacteristic
44C2×#818C2211yescharacteristic
45C2×#817C2211yescharacteristic
46#4984C2211yescharacteristic
47#4976—21no—
48#4972C2211yescharacteristic
49C2×#808C2211yescharacteristic
50C2×#807C2211yescharacteristic
51#4928C2211yescharacteristic
52#4805—24no—
53#4774—24no—
54D3×#95—21no—
55#4647—21no—
56C3×#336C2211yescharacteristic
57#4551C2211yescharacteristic
58#4551C2211yescharacteristic
59#4550C2211yescharacteristic
60#4550C2211yescharacteristic
61#4529C2211yescharacteristic
62#4529C2211yescharacteristic
63#4524C2211yescharacteristic
64C2×#529—31no—
65C2×#483—31no—
66C2×#480—31no—
67C2×#389—31no—
68#2059—31no—
69#2059—31no—
70#2042—31no—
71#2042D311yescharacteristic, complemented
72#1874—31no—
73#1872—31no—
74#1864—31no—
75#1864—31no—
76#1863—31no—
77#1863—31no—
78#1817—31no—
79C22×C3×Q8C2311yescharacteristic
80C22×C3×D4C2311yescharacteristic
81C22×#67—21no—
82C23×Dic3—21no—
83C22×C4×D3—21no—
84C22×C4×D3—21no—
85C22×C4×D3D411yescharacteristic
86C22×C4×D3D411yescharacteristic
87C22×C4×D3C2311yescharacteristic
88C22×C3×C8C2311yescharacteristic
89C22×C3×C8C2311yescharacteristic
90C3×#124—22no—
91C3×#124—22no—
92C2×C3×C4⋊C4—21no—
93C2×C3×C4⋊C4C2311yescharacteristic
94C2×C3×C4⋊C4C2311yescharacteristic
95C2×C3×C22⋊C4—21no—
96C2×C3×C22⋊C4—21no—
97C2×C3×C42C2311yescharacteristic
98C2×#217—21no—
99C2×#217—21no—
100#946—22no—
101#946D414yes—
102Q8×Dic3—22no—
103Q8×Dic3—22no—
104#938—22no—
105#938D414yes—
106D4×Dic3—22no—
107D4×Dic3—22no—
108C2×(C2×D3)⋊C4—21no—
109C2×C4⋊Dic3—21no—
110C2×C4⋊Dic3—21no—
111C2×C4⋊Dic3C2311yescharacteristic
112C2×C4⋊Dic3C2311yescharacteristic
113C2×C4⋊Dic3C2311yescharacteristic
114C2×C4⋊Dic3C2311yescharacteristic
115C2×Dic3⋊C4—21no—
116C2×Dic3⋊C4—21no—
117C2×Dic3⋊C4—21no—
118C2×Dic3⋊C4—21no—
119C2×Dic3⋊C4—21no—
120C2×Dic3⋊C4—21no—
121C2×Dic3⋊C4—21no—
122C2×C4×Dic3—21no—
123C2×C4×Dic3D411yescharacteristic
124C2×C4×Dic3D411yescharacteristic
125C2×C4×Dic3C2311yescharacteristic
126C22×C3⋊C8C2311yescharacteristic
127C22×C3⋊C8C2311yescharacteristic
128D3×C4⋊C4—22no—
129D3×C4⋊C4—22no—
130D3×C4⋊C4—22no—
131D3×C4⋊C4—22no—
132D3×C4⋊C4—44no—
133#883—28no—
134#67⋊C4—28no—
135#879—28no—
136#877—28no—
137C42×D3—22no—
138C42×D3—22no—
139#870—22no—
140#870—22no—
141C3×#103—22no—
142C3×#103—22no—
143C3×#102—22no—
144C3×#102—22no—
145C3×#95—21no—
146#835—22no—
147#835—22no—
148#832—22no—
149#832—22no—
150C3⋊#95—21no—
151C3⋊#95—21no—
152C3⋊#95—21no—
153(C2×D3)⋊C8—22no—
154(C2×D3)⋊C8—22no—
155#818—22no—
156#817—22no—
157#808—22no—
158#807—22no—
159#529—64no—
160#529—64no—
161C2×#126—61no—
162C2×#125—31no—
163C2×#124C2×D311yescharacteristic
164C2×#123—61no—
165C2×C22⋊Q8—31no—
166C2×#121—31no—
167C2×C4×Q8—31no—
168C2×C4×D4—31no—
169C2×C4×D4—61no—
170C2×#117—61no—
171C22×C4⋊C4—31no—
172C22×C4⋊C4—31no—
173C22×C4⋊C4—61no—
174C22×C42—31no—
175#483—64no—
176#480—64no—
177C2×#107—31no—
178C2×#107—31no—
179C2×#106—31no—
180C2×#106—31no—
181C2×#103—31no—
182C2×#103—31no—
183C2×#103C2×D311yescharacteristic
184C2×#103C2×D311yescharacteristic
185C2×#102—31no—
186C2×#102—31no—
187C2×#102C2×D311yescharacteristic
188C2×#102C2×D311yescharacteristic
189C2×C22⋊C8—31no—
190C2×C22⋊C8—31no—
191#389—31no—
192#389—31no—
193#389—31no—
194#389—61no—
195#389—61no—
196#389C2×D311yescharacteristic
197C2×#95—61no—
198#340—31no—
199#340—31no—
200#340—31no—
201#340—31no—
202#336—31no—
203#336—31no—
204#336—31no—
205#336C2×D311yescharacteristic
206C24×C3—21no—
207C23×D3C2×D411yescharacteristic
208C2×C3×Q8—21no—
209C2×C3×Q8—21no—
210C2×C3×Q8—21no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8C2×D412yes—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4C2×D412yes—
220C22×C3×C4—21no—
221C22×C3×C4—21no—
222C22×C3×C4—21no—
223C22×C3×C4C2×D411yescharacteristic
224C22×C3×C4C2×D411yescharacteristic
225C22×C3×C4C2411yescharacteristic
226C2×#67—24no—
227C2×#67—42no—
228C2×#67—42no—
229C22×Dic3—24no—
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3—21no—
234C22×Dic3—42no—
235C22×Dic3—42no—
236C22×Dic3C2×D411yescharacteristic
237C22×Dic3C2×D411yescharacteristic
238C22×Dic3C2×D411yescharacteristic
239C2×C4×D3—21no—
240C2×C4×D3—21no—
241C2×C4×D3—21no—
242C2×C4×D3—21no—
243C2×C4×D3—24no—
244C2×C4×D3—22no—
245C2×C4×D3—22no—
246C2×C4×D3—22no—
247C2×C4×D3—22no—
248C2×C4×D3—22no—
249C2×C4×D3—41no—
250C2×C4×D3—42no—
251C2×C4×D3—42no—
252C2×C4×D3—42no—
253C2×C4×D3—42no—
254C2×C4×D3—42no—
255C2×C4×D3C2×D412yes—
256C2×C4×D3C2×D412yes—
257C2×C3×C8—21no—
258C2×C3×C8—21no—
259C2×C3×C8—21no—
260C2×C3×C8—21no—
261C2×C3×C8—21no—
262C2×C3×C8—21no—
263C3×C4⋊C4—21no—
264C3×C4⋊C4—21no—
265C3×C4⋊C4—21no—
266C3×C4⋊C4—42no—
267C3×C4⋊C4#4112yes—
268C3×C22⋊C4—24no—
269C3×C22⋊C4—24no—
270C3×C42—21no—
271C3×C42—21no—
272#217—24no—
273#217—24no—
274(C2×D3)⋊C4—24no—
275C4⋊Dic3—24no—
276C4⋊Dic3—21no—
277C4⋊Dic3—21no—
278C4⋊Dic3—21no—
279C4⋊Dic3—21no—
280C4⋊Dic3—21no—
281C4⋊Dic3—42no—
282C4⋊Dic3C2×D412yes—
283C4⋊Dic3C2×D412yes—
284C4⋊Dic3#4112yes—
285Dic3⋊C4—24no—
286Dic3⋊C4—24no—
287Dic3⋊C4—24no—
288Dic3⋊C4—24no—
289Dic3⋊C4—42no—
290Dic3⋊C4—42no—
291Dic3⋊C4—42no—
292C4×Dic3—24no—
293C4×Dic3—21no—
294C4×Dic3—21no—
295C4×Dic3—22no—
296C4×Dic3—22no—
297C2×C3⋊C8—21no—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—21no—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C22×Q8C22×D311yescharacteristic
304C22×D4—61no—
305C22×D4C22×D311yescharacteristic
306C23×C4—31no—
307C23×C4—31no—
308C23×C4—31no—
309C23×C4—61no—
310C23×C4—61no—
311C23×C4—61no—
312C22×C8—31no—
313C22×C8—31no—
314C22×C8C22×D311yescharacteristic
315C22×C8C22×D311yescharacteristic
316#126—68no—
317#125—62no—
318#125—62no—
319#124—22no—
320#124—22no—
321#123—68no—
322C22⋊Q8—34no—
323C22⋊Q8—62no—
324#121—34no—
325#121—62no—
326C4×Q8—62no—
327C4×Q8—62no—
328C4×D4—68no—
329C4×D4—62no—
330C4×D4—62no—
331#117—68no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—31no—
334C2×C4⋊C4—31no—
335C2×C4⋊C4—31no—
336C2×C4⋊C4—31no—
337C2×C4⋊C4—62no—
338C2×C4⋊C4—62no—
339C2×C4⋊C4—62no—
340C2×C4⋊C4—61no—
341C2×C4⋊C4—61no—
342C2×C4⋊C4—61no—
343C2×C4⋊C4—61no—
344C2×C4⋊C4—61no—
345C2×C4⋊C4—62no—
346C2×C4⋊C4—61no—
347C2×C4⋊C4—61no—
348C2×C4⋊C4—61no—
349C2×C4⋊C4—61no—
350C2×C4⋊C4—124no—
351C2×C4⋊C4C22×D311yescharacteristic
352C2×C4⋊C4C22×D311yescharacteristic
353C2×C22⋊C4—21no—
354C2×C22⋊C4—21no—
355C2×C22⋊C4—61no—
356C2×C22⋊C4—61no—
357C2×C22⋊C4—61no—
358C2×C42—31no—
359C2×C42—31no—
360C2×C42—31no—
361C2×C42—62no—
362C2×C42—62no—
363C2×C42—61no—
364C2×C42C22×D311yescharacteristic
365#107—62no—
366#107—62no—
367#106—62no—
368#106—62no—
369#103—22no—
370#103—22no—
371#103—62no—
372#103—62no—
373#102—22no—
374#102—22no—
375#102—62no—
376#102—62no—
377C22⋊C8—62no—
378C22⋊C8—62no—
379#95—21no—
380#95—61no—
381#95—61no—
382#95—61no—
383C23×C3—22no—
384C23×C3—41no—
385C23×C3—41no—
386C23×C3—41no—
387C23×C3—41no—
388C23×C3—41no—
389C23×C3—41no—
390C23×C3C22×D411yescharacteristic
391C22×D3—21no—
392C22×D3—21no—
393C22×D3—21no—
394C22×D3—21no—
395C22×D3#12012yes—
396C22×D3#13512yes—
397C22×D3AGL(1,ℤ/8)12yes—
398C3×Q8—22no—
399C3×Q8—22no—
400C3×Q8—41no—
401C3×Q8—41no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—41no—
405C3×D4—41no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—21no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—41no—
417C2×C3×C4—41no—
418C2×C3×C4—41no—
419C2×C3×C4—41no—
420C2×C3×C4—41no—
421C2×C3×C4C22×D411yescharacteristic
422C2×C3×C4C22×D411yescharacteristic
423C2×C3×C4C2×#4111yescharacteristic
424C2×C3×C4C2×#4111yescharacteristic
425C2×C3×C42−1+411yescharacteristic
426C2×C3×C42−1+411yescharacteristic
427#67—48no—
428C2×Dic3—21no—
429C2×Dic3—21no—
430C2×Dic3—21no—
431C2×Dic3—21no—
432C2×Dic3—21no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—21no—
437C2×Dic3—21no—
438C2×Dic3—48no—
439C2×Dic3—41no—
440C2×Dic3—41no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—41no—
446C2×Dic3—41no—
447C2×Dic3—41no—
448C2×Dic3#12012yes—
449C2×Dic3#13712yes—
450C4×D3—22no—
451C4×D3—22no—
452C4×D3—22no—
453C4×D3—22no—
454C4×D3—44no—
455C4×D3—48no—
456C4×D3—44no—
457C4×D3—84no—
458C3×C8—41no—
459C3×C8—41no—
460C3⋊C8—41no—
461C3⋊C8—41no—
462C24—21no—
463C24—31no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—21no—
469C2×Q8D3×D412yes—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—64no—
476C2×D4—122no—
477C2×D4—122no—
478C2×D4D3×D412yes—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—31no—
483C22×C4—31no—
484C22×C4—32no—
485C22×C4—32no—
486C22×C4—31no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—62no—
490C22×C4—62no—
491C22×C4—62no—
492C22×C4—64no—
493C22×C4—61no—
494C22×C4—61no—
495C22×C4—61no—
496C22×C4—61no—
497C22×C4—64no—
498C22×C4—61no—
499C22×C4—61no—
500C22×C4—61no—
501C22×C4—61no—
502C22×C4—121no—
503C22×C4—122no—
504C22×C4—122no—
505C22×C4—122no—
506C22×C4—122no—
507C22×C4—122no—
508C22×C4—122no—
509C22×C4—122no—
510C22×C4D3×D411yescharacteristic
511C22×C4D3×D411yescharacteristic
512C22×C4C23×D311yescharacteristic
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—61no—
520C2×C8—61no—
521C2×C8—61no—
522C2×C8—61no—
523C2×C8—61no—
524C2×C8—61no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—32no—
529C4⋊C4—32no—
530C4⋊C4—32no—
531C4⋊C4—42no—
532C4⋊C4—64no—
533C4⋊C4—64no—
534C4⋊C4—64no—
535C4⋊C4—64no—
536C4⋊C4—64no—
537C4⋊C4—61no—
538C4⋊C4—61no—
539C4⋊C4—61no—
540C4⋊C4—61no—
541C4⋊C4—61no—
542C4⋊C4—122no—
543C4⋊C4—122no—
544C4⋊C4—122no—
545C4⋊C4—122no—
546C4⋊C4#23712yes—
547C22⋊C4—24no—
548C22⋊C4—24no—
549C22⋊C4—64no—
550C22⋊C4—64no—
551C22⋊C4—64no—
552C42—21no—
553C42—21no—
554C42—62no—
555C42—62no—
556C42—64no—
557C42—61no—
558C42—61no—
559C22×C3—42no—
560C22×C3—42no—
561C22×C3—42no—
562C22×C3—81no—
563C22×C3—81no—
564C22×C3—81no—
565C22×C3—81no—
566C22×C3C2×#12011yescharacteristic
567C22×C3#52511yescharacteristic
568C22×C3#53611yescharacteristic
569C22×C3C2×#13511yescharacteristic
570C22×C3C2×AGL(1,ℤ/8)11yescharacteristic
571C22×C3C2×#13711yescharacteristic
572C22×C3#57511yescharacteristic
573C2×D3—22no—
574C2×D3—22no—
575C2×D3—22no—
576C2×D3—22no—
577C2×D3—22no—
578C2×D3—22no—
579C2×D3#44914yes—
580C3×C4—42no—
581C3×C4—42no—
582C3×C4—41no—
583C3×C4—41no—
584C3×C4—81no—
585C3×C4#54711yescharacteristic
586C3×C4#54711yescharacteristic
587C3×C4#54711yescharacteristic
588C3×C4#54711yescharacteristic
589Dic3—22no—
590Dic3—22no—
591Dic3—42no—
592Dic3—41no—
593Dic3—42no—
594Dic3—42no—
595Dic3—81no—
596C23—22no—
597C23—32no—
598C23—32no—
599C23—32no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—61no—
607C23—61no—
608C23—61no—
609C23—61no—
610C23C2×D3×D411yescharacteristic
611Q8—22no—
612Q8—22no—
613Q8—41no—
614Q8—41no—
615D4—22no—
616D4—22no—
617D4—41no—
618D4—41no—
619D4—128no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—32no—
629C2×C4—32no—
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—62no—
642C2×C4—62no—
643C2×C4—62no—
644C2×C4—62no—
645C2×C4—61no—
646C2×C4—61no—
647C2×C4—61no—
648C2×C4—62no—
649C2×C4—62no—
650C2×C4—62no—
651C2×C4—124no—
652C2×C4—124no—
653C2×C4—128no—
654C2×C4—128no—
655C2×C4—121no—
656C2×C4—121no—
657C2×C4—121no—
658C2×C4—121no—
659C2×C4—121no—
660C2×C4—121no—
661C2×C4—121no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—244no—
665C2×C4C2×D3×D411yescharacteristic
666C2×C4C2×D3×D411yescharacteristic
667C2×C4C2×#23711yescharacteristic
668C2×C4D3×#4111yescharacteristic
669C2×C4#101011yescharacteristic
670C2×C4#101011yescharacteristic
671C8—41no—
672C8—41no—
673C8—121no—
674C8—121no—
675C2×C3—82no—
676C2×C3#240611yescharacteristic
677C2×C3C2×#44911yescharacteristic
678C2×C3#300711yescharacteristic
679C2×C3#310811yescharacteristic
680C2×C3#311411yescharacteristic
681C2×C3#323211yescharacteristic
682C2×C3#323811yescharacteristic
683D3—24no—
684C22—34no—
685C22—42no—
686C22—42no—
687C22—42no—
688C22—62no—
689C22—62no—
690C22—62no—
691C22—62no—
692C22—62no—
693C22—62no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22D3×#12011yescharacteristic
699C22#560611yescharacteristic
700C22#567511yescharacteristic
701C22D3×#13511yescharacteristic
702C22#576811yescharacteristic
703C22D3×AGL(1,ℤ/8)11yescharacteristic
704C22D3×#13711yescharacteristic
705C4—42no—
706C4—41no—
707C4—42no—
708C4—41no—
709C4—62no—
710C4—62no—
711C4—81no—
712C4—122no—
713C4—122no—
714C4—121no—
715C4—122no—
716C4—241no—
717C4#561111yescharacteristic
718C4#561111yescharacteristic
719C4#565511yescharacteristic
720C4#565511yescharacteristic
721C3#2406611yescharacteristic, complemented, Sylow
722C2—64no—
723C2—82no—
724C2#7710711yescharacteristic
725C2D3×#44911yescharacteristic
726C2#8022811yescharacteristic
727C2#8050711yescharacteristic
728C2#8056911yescharacteristic
729C2#8164811yescharacteristic
730C2#8169011yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutator, cosocleC22×C3×C4C24
FrattiniC22×C4C23×D3
FittingC3×#2042C2
socleC23×C3C22×D4
prime radicalC2×#938C22
hypercenter#2042D3
hypocenterC3#24066
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2042

Complements

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

NH ≅ G/Ntype
2. C2×#4805C2semidirect
4. D3×#389C2semidirect
5. C3×#2042C2semidirect
6. #71722C2semidirect
7. #70268C2semidirect
8. #70236C2semidirect
9. #70235C2semidirect
11. #70170C2semidirect
12. #70169C2semidirect
13. #69606C2semidirect
14. #68664C2semidirect
15. #68634C2semidirect
71. #2042D3semidirect
721. C3#24066semidirect

Maximal subgroups

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

subgroupindex
C2×#56802
C2×#48052
C2×#47742
D3×#3892
C3×#20422
#717222
#702682
#702362
#702352
#702002
#701702
#701692
#696062
#686642
#686342
#240663