Finite Group Databasebeta

← #10799117

Subgroups — #10799117

Order 768.

1566 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#918C211yesmaximal, characteristic
2C2×#4861C211yesmaximal, characteristic, complemented
3C2×#4803C211yesmaximal, characteristic
4C2×#4802C211yesmaximal, characteristic, complemented
5C2×#4707C211yesmaximal, characteristic, complemented
6D3×#391C211yesmaximal, characteristic, complemented
7#76478C211yesmaximal, characteristic
8C3×#1971C211yesmaximal, characteristic, complemented
9#72066C211yesmaximal, characteristic, complemented
10#70574C211yesmaximal, characteristic, complemented
11#70258C211yesmaximal, characteristic, complemented
12#70257C211yesmaximal, characteristic, complemented
13#69826C211yesmaximal, characteristic, complemented
14#69679C211yesmaximal, characteristic, complemented
15#69678C211yesmaximal, characteristic, complemented
16#21237—31nomaximal, Sylow
17C22×#239C2211yescharacteristic
18C22×D3×Q8C2211yescharacteristic
19C22×C3×Q16C2211yescharacteristic
20C22×#216C2211yescharacteristic
21C22×#215C2211yescharacteristic
22C2×#918—24no—
23C2×#918—24no—
24C2×#918C418yescomplemented
25C22×#204C2211yescharacteristic
26C22×ΓL(1,𝔽25)C2211yescharacteristic
27C22×ΓL(1,𝔽25)C2211yescharacteristic
28C2×#892C2211yescharacteristic
29C2×D3×C4⋊C4C2211yescharacteristic
30C2×C42×D3C2211yescharacteristic
31C2×C3×#106C2211yescharacteristic
32C2×C3×#103C2211yescharacteristic
33C2×C3×#103C2211yescharacteristic
34C2×C3×#97C2211yescharacteristic
35C3×#391C2211yescharacteristic
36C3×#391C2211yescharacteristic
37#5229C2211yescharacteristic
38#5229C2211yescharacteristic
39C2×#835C2211yescharacteristic
40C2×#835C2211yescharacteristic
41C2×#821C2211yescharacteristic
42C2×#818C2211yescharacteristic
43C2×#816C2211yescharacteristic
44C2×C8×Dic3C2211yescharacteristic
45C2×C8×Dic3C2211yescharacteristic
46#4988C2211yescharacteristic
47#4973C2211yescharacteristic
48C2×#810C2211yescharacteristic
49C2×#809C2211yescharacteristic
50C2×#808C2211yescharacteristic
51C2×#807C2211yescharacteristic
52#4939C2211yescharacteristic
53#4929C2211yescharacteristic
54C2×#803C2211yescharacteristic
55#4861—24no—
56#4803—24no—
57#4802—24no—
58#4707—24no—
59#4666—22no—
60#4665—22no—
61D3×#95—22no—
62#4646—22no—
63C22×#137—31no—
64C2×#428—31no—
65C2×#417—31no—
66C2×#419—31no—
67C2×C4×M16—31no—
68#2297—31no—
69C2×#391—31no—
70#1973—31no—
71#1973—31no—
72#1971—31no—
73#1971D311yescharacteristic, complemented
74#1969—31no—
75#1969—31no—
76#1968—31no—
77#1968—31no—
78C22×C3×Q8C2311yescharacteristic
79C22×C3×Q8C2311yescharacteristic
80C2×#239—22no—
81C2×#239—22no—
82C2×#239—22no—
83C2×#239—22no—
84C2×#239—22no—
85C2×#239C2×C414yes—
86C2×D3×Q8—22no—
87C2×D3×Q8—22no—
88C2×D3×Q8—22no—
89C2×D3×Q8—22no—
90C2×D3×Q8—22no—
91C2×D3×Q8C2×C414yes—
92C22×D12—21no—
93C22×D12C2311yescharacteristic
94C22×C4×D3—21no—
95C22×C4×D3—21no—
96C22×C4×D3—21no—
97C22×C4×D3D412yes—
98C22×C4×D3C2311yescharacteristic
99C22×Dic6—21no—
100C22×Dic6C2311yescharacteristic
101C2×C3×Q16—22no—
102C2×C3×Q16—22no—
103C2×C3×Q16C2×C414yescomplemented
104C22×C3×C8C2311yescharacteristic
105C22×C3×C8C2311yescharacteristic
106C2×C3×C4⋊C4C2311yescharacteristic
107C2×C3×C4⋊C4C2311yescharacteristic
108C2×C3×C42C2311yescharacteristic
109C2×#216—22no—
110C2×#216—22no—
111C2×#216C2×C414yescomplemented
112C2×#215—22no—
113C2×#215—22no—
114C2×#215C2×C414yescomplemented
115C2×(C2×D3)⋊C4—21no—
116C2×(C2×D3)⋊C4—22no—
117C2×(C2×D3)⋊C4—22no—
118C2×C4⋊Dic3C2311yescharacteristic
119C2×C4⋊Dic3C2311yescharacteristic
120C2×Dic3⋊C4—21no—
121C2×C4×Dic3—21no—
122C2×C4×Dic3D412yes—
123C2×C4×Dic3C2311yescharacteristic
124C22×C3⋊C8C2311yescharacteristic
125C22×C3⋊C8C2311yescharacteristic
126#918—232no—
127C2×#204—22no—
128C2×#204—22no—
129C2×#204C2×C414yescomplemented
130C2×ΓL(1,𝔽25)—22no—
131C2×ΓL(1,𝔽25)—22no—
132C2×ΓL(1,𝔽25)C2×C414yes—
133C2×ΓL(1,𝔽25)D414yes—
134C2×ΓL(1,𝔽25)D414yes—
135C2×ΓL(1,𝔽25)D414yes—
136#892—22no—
137#892—22no—
138D3×C4⋊C4—22no—
139D3×C4⋊C4—22no—
140C42×D3—22no—
141C42×D3—22no—
142C3×#106—22no—
143C3×#103—22no—
144C3×#103—22no—
145C3×#97—22no—
146C3×#95—22no—
147C3×#95—22no—
148#835—22no—
149#835—22no—
150C3⋊#95—22no—
151C3⋊#95—22no—
152C3⋊#95—22no—
153C3⋊#95—22no—
154#821—22no—
155#818—22no—
156#816—22no—
157C8×Dic3—22no—
158C8×Dic3—22no—
159#810—22no—
160#809—22no—
161#808—22no—
162#807—22no—
163#803—22no—
164C22×#41—31no—
165C23×Q8—31no—
166C2×#137—38no—
167C2×#137—64no—
168C2×#137—64no—
169C22×Q16—31no—
170C22×Q16C2×D311yescharacteristic
171C22×SD16—31no—
172C22×SD16—31no—
173C22×M16—31no—
174C22×M16—31no—
175C2×#117—31no—
176C22×C4⋊C4—31no—
177C22×C42—31no—
178#428—64no—
179C2×#107—31no—
180C2×#107—31no—
181C2×#106—31no—
182C2×#106C2×D311yescharacteristic
183#419—64no—
184#417—64no—
185C2×#103—31no—
186C2×#103—31no—
187C2×#103—31no—
188C2×#103—31no—
189C2×#103C2×D311yescharacteristic
190C2×#103C2×D311yescharacteristic
191C2×#102—31no—
192C2×#102—31no—
193C4×M16—64no—
194C2×#97—31no—
195C2×#97C2×D311yescharacteristic
196C2×C4×C8—31no—
197C2×C4×C8—31no—
198#391—31no—
199#391—31no—
200#391—31no—
201#391—31no—
202#391—62no—
203#391C2×D311yescharacteristic
204#391C2×D311yescharacteristic
205#390—31no—
206#390—31no—
207#386—62no—
208C4×C22⋊C4—62no—
209C2×#95—62no—
210C23×D3—21no—
211C23×D3C2×D411yescharacteristic
212C2×C3×Q8—21no—
213C2×C3×Q8—21no—
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×Q8C22×C412yes—
223C2×C3×Q8C22×C412yes—
224C22×C3×C4—21no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4C2×D412yes—
229C22×C3×C4C2411yescharacteristic
230C22×Dic3—21no—
231C22×Dic3—21no—
232C22×Dic3—21no—
233C22×Dic3C2×D412yes—
234C22×Dic3C2×D411yescharacteristic
235#239—28no—
236#239—28no—
237#239—44no—
238#239—44no—
239D3×Q8—28no—
240D3×Q8—28no—
241D3×Q8—44no—
242D3×Q8—44no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—24no—
248C2×D12—21no—
249C2×D12—42no—
250C2×D12—42no—
251C2×D12C22×C412yes—
252C2×C4×D3—24no—
253C2×C4×D3—24no—
254C2×C4×D3—24no—
255C2×C4×D3—24no—
256C2×C4×D3—42no—
257C2×C4×D3—42no—
258C2×C4×D3—42no—
259C2×C4×D3—42no—
260C2×C4×D3—42no—
261C2×C4×D3—44no—
262C2×C4×D3—42no—
263C2×C4×D3C22×C412yes—
264C2×C4×D3C2×D412yes—
265C2×C4×D3C2×D412yes—
266C2×C4×D3C2×D412yes—
267C2×C4×D3#4112yes—
268C2×C4×D3#4112yes—
269C2×Dic6—21no—
270C2×Dic6—21no—
271C2×Dic6—21no—
272C2×Dic6—21no—
273C2×Dic6—21no—
274C2×Dic6—24no—
275C2×Dic6—42no—
276C2×Dic6—42no—
277C2×Dic6C22×C412yes—
278C3×Q16—28no—
279C2×C3×C8—21no—
280C2×C3×C8—21no—
281C2×C3×C8C22×C412yes—
282C2×C3×C8C2×D412yes—
283C2×C3×C8C2×D412yes—
284C2×C3×C8C2×D412yes—
285C3×C4⋊C4—21no—
286C3×C4⋊C4—21no—
287C3×C4⋊C4—21no—
288C3×C4⋊C4—21no—
289C3×C42—21no—
290C3×C42—21no—
291#216—28no—
292#215—28no—
293(C2×D3)⋊C4—44no—
294(C2×D3)⋊C4—42no—
295(C2×D3)⋊C4—44no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298C4⋊Dic3—21no—
299C4⋊Dic3—21no—
300Dic3⋊C4—42no—
301C4×Dic3—21no—
302C4×Dic3—21no—
303C4×Dic3—24no—
304C4×Dic3—42no—
305C2×C3⋊C8—21no—
306C2×C3⋊C8—21no—
307C2×C3⋊C8C22×C412yes—
308C2×C3⋊C8C2×D412yes—
309C2×C3⋊C8C2×D412yes—
310C2×C3⋊C8C2×D412yes—
311#204—28no—
312ΓL(1,𝔽25)—28no—
313ΓL(1,𝔽25)C22⋊C4116yescomplemented
314C2×#41—34no—
315C2×#41—62no—
316C2×#41—62no—
317C2×#41—62no—
318C2×#41—62no—
319C2×#41—62no—
320C22×Q8—34no—
321C22×Q8—31no—
322C22×Q8—61no—
323C22×Q8—62no—
324C22×Q8—62no—
325C22×Q8—62no—
326C22×Q8—62no—
327C22×Q8—62no—
328C22×Q8C22×D311yescharacteristic
329C22×Q8C22×D311yescharacteristic
330C22×D4—31no—
331C22×D4—61no—
332C23×C4—31no—
333C23×C4—32no—
334C23×C4—61no—
335C23×C4—61no—
336C23×C4—61no—
337#137—632no—
338C2×Q16—22no—
339C2×Q16—22no—
340C2×Q16—34no—
341C2×Q16—62no—
342C2×Q16—62no—
343C2×Q16C4×D314yescomplemented
344C2×SD16—34no—
345C2×SD16—34no—
346C2×SD16—62no—
347C2×SD16—62no—
348C2×SD16—62no—
349C2×SD16—62no—
350C2×M16—34no—
351C2×M16—34no—
352C2×M16—34no—
353C2×M16—34no—
354C2×M16—62no—
355C2×M16—62no—
356C22×C8—31no—
357C22×C8—31no—
358C22×C8C22×D311yescharacteristic
359C22×C8C22×D311yescharacteristic
360#117—62no—
361#117—62no—
362C2×C4⋊C4—31no—
363C2×C4⋊C4—31no—
364C2×C4⋊C4—62no—
365C2×C4⋊C4—62no—
366C2×C4⋊C4—61no—
367C2×C4⋊C4C22×D311yescharacteristic
368C2×C4⋊C4C22×D311yescharacteristic
369C2×C22⋊C4—62no—
370C2×C22⋊C4—61no—
371C2×C22⋊C4—62no—
372C2×C42—32no—
373C2×C42—31no—
374C2×C42—62no—
375C2×C42—62no—
376C2×C42—61no—
377C2×C42C22×D311yescharacteristic
378#107—62no—
379#107—62no—
380#106—22no—
381#106—62no—
382#103—22no—
383#103—22no—
384#103—62no—
385#103—62no—
386#103—62no—
387#103—62no—
388#102—62no—
389#102—62no—
390#97—22no—
391#97—62no—
392C4×C8—62no—
393C4×C8—62no—
394#95—22no—
395#95—22no—
396#95—62no—
397#95—62no—
398#95—62no—
399#95—62no—
400C23×C3C22×D411yescharacteristic
401C22×D3—22no—
402C22×D3—22no—
403C22×D3—22no—
404C22×D3—41no—
405C22×D3—41no—
406C22×D3—42no—
407C22×D3—42no—
408C22×D3C4×D412yes—
409C22×D3#12112yes—
410C22×D3#12712yes—
411C3×Q8—22no—
412C3×Q8—22no—
413C3×Q8—22no—
414C3×Q8—22no—
415C3×Q8—41no—
416C3×Q8—41no—
417C3×Q8—41no—
418C3×Q8—41no—
419C2×C3×C4—22no—
420C2×C3×C4—22no—
421C2×C3×C4—22no—
422C2×C3×C4—22no—
423C2×C3×C4—22no—
424C2×C3×C4—41no—
425C2×C3×C4—41no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4—42no—
431C2×C3×C4—42no—
432C2×C3×C4C23×C411yescharacteristic
433C2×C3×C4C22×D411yescharacteristic
434C2×C3×C4C22×D411yescharacteristic
435C2×C3×C4C22×D411yescharacteristic
436C2×C3×C4C2×#4111yescharacteristic
437C2×C3×C4C2×#4111yescharacteristic
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—41no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—41no—
445C2×Dic3—42no—
446C2×Dic3—42no—
447C2×Dic3C4×D412yes—
448C2×Dic3#12112yes—
449C2×Dic3#12712yes—
450C2×Dic3#13714yescomplemented
451D12—22no—
452D12—22no—
453D12—48no—
454D12—41no—
455D12—41no—
456C4×D3—48no—
457C4×D3—48no—
458C4×D3—48no—
459C4×D3—84no—
460C4×D3C2×C22⋊C414yes—
461C4×D3C4×D414yes—
462C4×D3#12114yes—
463C4×D3#12414yes—
464Dic6—22no—
465Dic6—22no—
466Dic6—41no—
467Dic6—41no—
468Dic6—48no—
469C3×C8—22no—
470C3×C8C2×C22⋊C414yes—
471C3⋊C8—22no—
472C3⋊C8C2×C22⋊C414yes—
473C24—31no—
474C24—61no—
475#41—68no—
476#41—68no—
477#41—124no—
478#41—124no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—21no—
483C2×Q8—21no—
484C2×Q8—21no—
485C2×Q8—21no—
486C2×Q8—21no—
487C2×Q8—21no—
488C2×Q8—21no—
489C2×Q8—32no—
490C2×Q8—64no—
491C2×Q8—68no—
492C2×Q8—68no—
493C2×Q8—61no—
494C2×Q8—61no—
495C2×Q8—61no—
496C2×Q8—61no—
497C2×Q8—61no—
498C2×Q8—122no—
499C2×Q8—122no—
500C2×Q8—124no—
501C2×Q8—124no—
502C2×Q8C2×C4×D312yes—
503C2×Q8C2×C4×D312yes—
504C2×D4—32no—
505C2×D4—64no—
506C2×D4—61no—
507C2×D4—61no—
508C2×D4—61no—
509C2×D4—61no—
510C2×D4—61no—
511C2×D4—122no—
512C2×D4—122no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—31no—
518C22×C4—32no—
519C22×C4—32no—
520C22×C4—32no—
521C22×C4—32no—
522C22×C4—32no—
523C22×C4—32no—
524C22×C4—32no—
525C22×C4—64no—
526C22×C4—64no—
527C22×C4—64no—
528C22×C4—64no—
529C22×C4—61no—
530C22×C4—61no—
531C22×C4—61no—
532C22×C4—122no—
533C22×C4—122no—
534C22×C4—122no—
535C22×C4—122no—
536C22×C4—122no—
537C22×C4—122no—
538C22×C4—124no—
539C22×C4D3×D412yes—
540C22×C4C23×D311yescharacteristic
541Q16—28no—
542Q16—68no—
543SD16—68no—
544SD16—68no—
545M16—316no—
546M16—68no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—32no—
550C2×C8—32no—
551C2×C8—32no—
552C2×C8—32no—
553C2×C8—61no—
554C2×C8—61no—
555C2×C8C2×C4×D312yes—
556C2×C8D3×D412yes—
557C2×C8D3×D412yes—
558C2×C8D3×D412yes—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—61no—
564C4⋊C4—61no—
565C4⋊C4—61no—
566C4⋊C4—61no—
567C4⋊C4—122no—
568C22⋊C4—124no—
569C22⋊C4—124no—
570C22⋊C4—122no—
571C42—21no—
572C42—21no—
573C42—64no—
574C42—61no—
575C42—61no—
576C42—122no—
577C22×C3C2×C4×D411yescharacteristic
578C22×C3C2×#12111yescharacteristic
579C22×C3C2×#12711yescharacteristic
580C22×C3C2×#13712yes—
581C22×C3#57512yes—
582C2×D3—22no—
583C2×D3—22no—
584C2×D3—24no—
585C2×D3—24no—
586C2×D3—44no—
587C2×D3—42no—
588C2×D3—81no—
589C2×D3—81no—
590C2×D3—82no—
591C2×D3#39014yes—
592C3×C4—42no—
593C3×C4—42no—
594C3×C4—42no—
595C3×C4—81no—
596C3×C4—81no—
597C3×C4C22×C22⋊C411yescharacteristic
598C3×C4C2×C4×D411yescharacteristic
599C3×C4C2×#12111yescharacteristic
600C3×C4C2×#12411yescharacteristic
601Dic3—24no—
602Dic3—42no—
603Dic3—81no—
604Dic3—81no—
605Dic3#39014yes—
606C23—32no—
607C23—32no—
608C23—32no—
609C23—62no—
610C23—62no—
611C23—62no—
612C23—121no—
613C23—122no—
614C23—122no—
615C23—121no—
616C23C2×D3×D411yescharacteristic
617Q8—22no—
618Q8—22no—
619Q8—22no—
620Q8—22no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—62no—
626Q8—62no—
627Q8—128no—
628Q8—121no—
629Q8—121no—
630D4—62no—
631D4—62no—
632D4—128no—
633D4—121no—
634D4—121no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—32no—
641C2×C4—32no—
642C2×C4—32no—
643C2×C4—34no—
644C2×C4—34no—
645C2×C4—34no—
646C2×C4—34no—
647C2×C4—34no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—62no—
657C2×C4—62no—
658C2×C4—62no—
659C2×C4—128no—
660C2×C4—128no—
661C2×C4—128no—
662C2×C4—121no—
663C2×C4—121no—
664C2×C4—121no—
665C2×C4—121no—
666C2×C4—122no—
667C2×C4—122no—
668C2×C4—244no—
669C2×C4C22×C4×D311yescharacteristic
670C2×C4C2×D3×D411yescharacteristic
671C2×C4C2×D3×D411yescharacteristic
672C2×C4C2×D3×D411yescharacteristic
673C2×C4D3×#4111yescharacteristic
674C2×C4D3×#4111yescharacteristic
675C8—22no—
676C8—34no—
677C8—62no—
678C8D3×C22⋊C414yes—
679C2×C3C2×#39011yescharacteristic
680C2×C3C4×#13712yes—
681C2×C3#305612yes—
682C2×C3#315211yescharacteristic
683C2×C3#315311yescharacteristic
684D3—24no—
685D3—82no—
686C22—34no—
687C22—64no—
688C22—62no—
689C22—62no—
690C22—64no—
691C22—122no—
692C22—124no—
693C22—242no—
694C22—241no—
695C22—241no—
696C22C4×D3×D411yescharacteristic
697C22D3×#12111yescharacteristic
698C22D3×#12711yescharacteristic
699C22D3×#13712yes—
700C22#577712yes—
701C4—34no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—64no—
706C4—81no—
707C4—81no—
708C4—122no—
709C4—241no—
710C4—241no—
711C4C2×D3×C22⋊C411yescharacteristic
712C4C4×D3×D411yescharacteristic
713C4D3×#12111yescharacteristic
714C4D3×#12411yescharacteristic
715C3#2123711yescharacteristic, complemented, Sylow
716C2—64no—
717C2—242no—
718C2D3×#39011yescharacteristic
719C2#7982912yes—
720C2#8090412yes—
721C2#8187011yescharacteristic
722C2#8187111yescharacteristic
subgroupG/H
centerC23C2×D3×D4
commutatorC2×C3×C4C23×C4
FrattiniC22×C4C23×D3
FittingC3×#1971C2
socleC23×C3C22×D4
prime radicalC22×#239C22
cosocleC22×C3×C4C24
hypercenter#1971D3
hypocenterC3#21237
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1971

Complements

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

NH ≅ G/Ntype
2. C2×#4861C2semidirect
4. C2×#4802C2semidirect
5. C2×#4707C2semidirect
6. D3×#391C2semidirect
8. C3×#1971C2semidirect
9. #72066C2semidirect
10. #70574C2semidirect
11. #70258C2semidirect
12. #70257C2semidirect
13. #69826C2semidirect
14. #69679C2semidirect
15. #69678C2semidirect
24. C2×#918C4semidirect
73. #1971D3semidirect
103. C2×C3×Q16C2×C4semidirect
111. C2×#216C2×C4semidirect
114. C2×#215C2×C4semidirect
129. C2×#204C2×C4semidirect
313. ΓL(1,𝔽25)C22⋊C4semidirect
343. C2×Q16C4×D3semidirect
450. C2×Dic3#137semidirect
715. C3#21237semidirect

Maximal subgroups

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

subgroupindex
C22×#9182
C2×#48612
C2×#48032
C2×#48022
C2×#47072
D3×#3912
#764782
C3×#19712
#720662
#705742
#702582
#702572
#698262
#696792
#696782
#212373