Finite Group Databasebeta

← #29732229

Subgroups — #29732229

Order 15616.

1132 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840316C211yesmaximal, characteristic
2C2×#16840002C211yesmaximal, characteristic
3C2×#16840000C211yesmaximal, characteristic
4#21454160C211yesmaximal, characteristic
5#21447146C211yesmaximal, characteristic, complemented
6#21447064C211yesmaximal, characteristic, complemented
7#21446958C211yesmaximal, characteristic, complemented
8#21446917C211yesmaximal, characteristic, complemented
9#21446241C211yesmaximal, characteristic
10#21446239C211yesmaximal, characteristic
11#21446163C211yesmaximal, characteristic, complemented
12#21446076C211yesmaximal, characteristic, complemented
13#21446073C211yesmaximal, characteristic, complemented
14#336×D61C211yesmaximal, characteristic
15C61×#1878C211yesmaximal, characteristic, complemented
16C22×#11758202C2211yescharacteristic
17C22×C8×D61C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19#16840316—24no—
20#16840316—24no—
21C2×#14519776C2211yescharacteristic
22C2×#14519775C2211yescharacteristic
23C2×#14519767—21no—
24C2×#14519757C2211yescharacteristic
25C2×#14519755—21no—
26C2×#14519753C2211yescharacteristic
27C2×#14519753C2211yescharacteristic
28C2×C4×Dic122—21no—
29C2×C4×Dic122C2211yescharacteristic
30C2×#14519734—21no—
31C2×C42×D61C2211yescharacteristic
32#16840002—24no—
33#16840000—24no—
34C2×#14519711C2211yescharacteristic
35C2×#14519710C2211yescharacteristic
36C2×#14519702C2211yescharacteristic
37C2×#14519702C2211yescharacteristic
38C2×#14519701C2211yescharacteristic
39C2×#14519701C2211yescharacteristic
40C2×#14519701C2211yescharacteristic
41C2×#14519700C2211yescharacteristic
42#16839669C2211yescharacteristic
43#16839661C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839645—21no—
46#16839644—21no—
47#16839636—21no—
48#16839624—21no—
49#16839619C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839524C2211yescharacteristic
52#16839524C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C22×Q16×C61C2211yescharacteristic
57C2×C4×Q8×C61C2211yescharacteristic
58C2×#103×C61C2211yescharacteristic
59C2×#103×C61C2211yescharacteristic
60C61×#391C2211yescharacteristic
61C61×#340C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×Dic122—21no—
64C22×Dic122C2311yescharacteristic
65C22×C4×D61D411yescharacteristic
66C22×C4×D61D411yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C2×#11758202—22no—
69C2×#11758202—22no—
70C2×#11758202—41no—
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C2×C8×D61—22no—
74C2×C8×D61—22no—
75C2×C8×D61—22no—
76C2×C8×D61—22no—
77C2×C8×D61—41no—
78C2×C8×D61—41no—
79#14519776—22no—
80#14519776—22no—
81#14519775—22no—
82#14519775—22no—
83#14519767—28no—
84#14519757—22no—
85#14519757D414yes—
86#14519755—28no—
87#14519753—22no—
88#14519753—22no—
89#14519753—22no—
90#14519753D414yes—
91C4×Dic122—28no—
92C4×Dic122—22no—
93C4×Dic122—22no—
94#14519734—28no—
95C2×C4⋊Dic61—21no—
96C2×C4⋊Dic61—21no—
97C2×C4⋊Dic61C2311yescharacteristic
98C2×C4⋊Dic61C2311yescharacteristic
99C2×C4⋊Dic61C2311yescharacteristic
100C2×#11758196—21no—
101C2×#11758196—21no—
102C2×#11758196—21no—
103C2×#11758196—21no—
104C2×#11758196—21no—
105C2×#11758196—21no—
106C2×#11758196—21no—
107C2×#11758198—21no—
108C2×#11758198—21no—
109C2×#11758198—21no—
110C2×#11758198—21no—
111C2×C4×Dic61—21no—
112C2×C4×Dic61D411yescharacteristic
113C2×C4×Dic61D411yescharacteristic
114C2×C4×Dic61C2311yescharacteristic
115C42×D61—22no—
116C42×D61—22no—
117#14519711—22no—
118#14519710—22no—
119#14519702—22no—
120#14519702—22no—
121#14519701—22no—
122#14519701—22no—
123#14519701—22no—
124#14519700—41no—
125#14519684—21no—
126#14519684—21no—
127#14519684—21no—
128#14519684—21no—
129#14519684—21no—
130C22×Q8×C61C2311yescharacteristic
131C22×Q8×C61C2311yescharacteristic
132C2×Q16×C61—22no—
133C2×Q16×C61—22no—
134C2×Q16×C61—41no—
135C22×C8×C61C2311yescharacteristic
136C22×C8×C61C2311yescharacteristic
137C4×Q8×C61—22no—
138C4×Q8×C61—22no—
139C2×C4⋊C4×C61—21no—
140C2×C4⋊C4×C61C2311yescharacteristic
141C2×C4⋊C4×C61C2311yescharacteristic
142C2×C42×C61—21no—
143C2×C42×C61C2311yescharacteristic
144#103×C61—22no—
145#103×C61—41no—
146#95×C61—21no—
147#95×C61—21no—
148C23×D61C2×D411yescharacteristic
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×Q8×C61—21no—
153C2×Q8×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×C61—21no—
156C2×Q8×C61—21no—
157C2×Q8×C61—21no—
158C2×Q8×C61—21no—
159C2×Q8×C61—21no—
160C2×Q8×C61C2×D412yes—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2×D411yescharacteristic
166C22×C4×C61C2×D411yescharacteristic
167C22×C4×C61C2411yescharacteristic
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61—21no—
171C22×Dic61—21no—
172C22×Dic61C2×D411yescharacteristic
173C22×Dic61C2×D411yescharacteristic
174C22×Dic61C2×D411yescharacteristic
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×C4×D61—21no—
181C2×C4×D61—22no—
182C2×C4×D61—22no—
183C2×C4×D61—41no—
184C2×C4×D61Q1614yescomplemented
185C2×C4×D61C2×D412yes—
186C2×C4×D61C2×D412yes—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C2×Dic122—21no—
190C2×Dic122—21no—
191C2×Dic122—24no—
192C2×Dic122—21no—
193C2×Dic122—42no—
194C2×Dic122—42no—
195C2×Dic122C2×D412yes—
196Q16×C61—44no—
197C2×C8×C61—21no—
198C2×C8×C61—21no—
199C2×C8×C61—21no—
200C2×C8×C61—21no—
201C2×C8×C61—21no—
202C2×C8×C61#4112yes—
203C4⋊C4×C61—24no—
204C4⋊C4×C61—21no—
205C4⋊C4×C61—21no—
206C4⋊C4×C61—21no—
207C4⋊C4×C61C2×D412yes—
208C42×C61—24no—
209C42×C61—21no—
210C42×C61—21no—
211#11758202—44no—
212#11758198—24no—
213#11758198—24no—
214#11758198—42no—
215#11758198—42no—
216C4⋊Dic61—21no—
217C4⋊Dic61—24no—
218C4⋊Dic61—21no—
219C4⋊Dic61—21no—
220C4⋊Dic61—21no—
221C4⋊Dic61—21no—
222C4⋊Dic61—42no—
223C4⋊Dic61C2×D412yes—
224#11758196—24no—
225#11758196—24no—
226#11758196—24no—
227#11758196—24no—
228#11758196—24no—
229#11758196—42no—
230#11758196—42no—
231C4×Dic61—24no—
232C4×Dic61—21no—
233C4×Dic61—21no—
234C4×Dic61—22no—
235C4×Dic61—22no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418#4112yes—
242C8×D61—44no—
243C8×D61—44no—
244C23×C61C22×D411yescharacteristic
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61#12012yes—
250C22×D61C2×Q1612yes—
251C22×D61#13712yes—
252Q8×C61—22no—
253Q8×C61—22no—
254Q8×C61—41no—
255Q8×C61—41no—
256Q8×C61—41no—
257Q8×C61—41no—
258Q8×C61—41no—
259Q8×C61—41no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—41no—
268C2×C4×C61—41no—
269C2×C4×C61—41no—
270C2×C4×C61—41no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61C2×Q1612yes—
278C2×C4×C61C22×D411yescharacteristic
279C2×C4×C61C22×D411yescharacteristic
280C2×C4×C61C2×#4111yescharacteristic
281C2×C4×C61C2×#4111yescharacteristic
282C2×C4×C61H(5,𝔽2)11yescharacteristic
283C2×C4×C612−1+411yescharacteristic
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—22no—
291C2×Dic61—22no—
292C2×Dic61—41no—
293C2×Dic61—41no—
294C2×Dic61—41no—
295C2×Dic61—41no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61#12012yes—
303C2×Dic61C2×Q1612yes—
304C2×Dic61#13512yes—
305C4×D61—28no—
306C4×D61—22no—
307C4×D61—22no—
308C4×D61—22no—
309C4×D61—22no—
310C4×D61—44no—
311Dic122—22no—
312Dic122—22no—
313Dic122—48no—
314Dic122—41no—
315Dic122—41no—
316C8×C61—22no—
317C8×C61—41no—
318#92418—22no—
319#92418—41no—
320#25498—611nomaximal, Sylow
321C22×C61C2×#12011yescharacteristic
322C22×C61#53211yescharacteristic
323C22×C61#53711yescharacteristic
324C22×C61C22×Q1611yescharacteristic
325C22×C61C2×#13511yescharacteristic
326C22×C61C2×#13711yescharacteristic
327C22×C61#57511yescharacteristic
328C2×D61—22no—
329C2×D61—22no—
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61#45114yes—
335C4×C61—22no—
336C4×C61—42no—
337C4×C61—42no—
338C4×C61—41no—
339C4×C61—81no—
340C4×C61—81no—
341C4×C61#54611yescharacteristic
342C4×C61#54611yescharacteristic
343C4×C61#54711yescharacteristic
344C4×C61#54711yescharacteristic
345Dic61—22no—
346Dic61—22no—
347Dic61—22no—
348Dic61—42no—
349Dic61—42no—
350Dic61—81no—
351Dic61—81no—
352C2×#533—611no—
353C2×#467—611no—
354C2×#467—611no—
355#2855—611no—
356#2057—611no—
357#2043—611no—
358#2024—611no—
359#2016—611no—
360#1892—611no—
361#1892—611no—
362#1878—611no—
363#1878D6111yescharacteristic, complemented
364#1863—611no—
365#1863—611no—
366C2×#336—611no—
367C2×C61#243011yescharacteristic
368C2×C61C2×#45111yescharacteristic
369C2×C61#300211yescharacteristic
370C2×C61#317011yescharacteristic
371C2×C61#318111yescharacteristic
372C2×C61#324811yescharacteristic
373C2×C61#324911yescharacteristic
374D61—24no—
375C22×Q16—611no—
376C22×Q16C2×D6111yescharacteristic
377C23×C8—611no—
378C23×C8—611no—
379#533—1224no—
380#533—1224no—
381C2×C4⋊Q8—611no—
382C2×C4⋊Q8—611no—
383C2×#125—1221no—
384C2×C22⋊Q8—611no—
385C2×C22⋊Q8—611no—
386C2×C22⋊Q8—611no—
387C2×C22⋊Q8—1221no—
388C2×C4×Q8—611no—
389C2×C4×Q8—1221no—
390C2×C4×Q8C2×D6111yescharacteristic
391C2×#117—1221no—
392C22×C42—611no—
393#467—1224no—
394#467—1224no—
395C2×#107—611no—
396C2×#107—611no—
397C2×#103—611no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×#103C2×D6111yescharacteristic
404C2×#103C2×D6111yescharacteristic
405#391—611no—
406#391C2×D6111yescharacteristic
407#389—611no—
408#389—611no—
409#387—1221no—
410#387—1221no—
411#385—1221no—
412#381—1221no—
413#380—611no—
414#340—611no—
415#340—611no—
416#340—611no—
417#340C2×D6111yescharacteristic
418#336—611no—
419#336—611no—
420#336—611no—
421#336C2×D6111yescharacteristic
422C61#2549811yescharacteristic, complemented, Sylow
423C22×Q8—611no—
424C22×Q8—1221no—
425C22×Q8C22×D6111yescharacteristic
426C22×Q8C22×D6111yescharacteristic
427C23×C4—611no—
428C23×C4—611no—
429C23×C4—611no—
430C2×Q16—22no—
431C2×Q16—22no—
432C2×Q16—41no—
433C2×Q16—1222no—
434C2×Q16—1222no—
435C2×Q16—2441no—
436C22×C8—611no—
437C22×C8—611no—
438C22×C8—1222no—
439C22×C8—1222no—
440C22×C8—1222no—
441C22×C8—1222no—
442C22×C8—2441no—
443C22×C8—2441no—
444C22×C8C22×D6111yescharacteristic
445C22×C8C22×D6111yescharacteristic
446C4⋊Q8—1222no—
447C4⋊Q8—1222no—
448C4⋊Q8—1222no—
449C4⋊Q8—1222no—
450#125—1228no—
451C22⋊Q8—614no—
452C22⋊Q8—614no—
453C22⋊Q8—1222no—
454C22⋊Q8—1228no—
455C22⋊Q8—1222no—
456C22⋊Q8—1222no—
457C22⋊Q8—1222no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—1222no—
461C4×Q8—1222no—
462C4×Q8—1228no—
463#117—1228no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—611no—
466C2×C4⋊C4—611no—
467C2×C4⋊C4—611no—
468C2×C4⋊C4—1221no—
469C2×C4⋊C4—1221no—
470C2×C4⋊C4—1221no—
471C2×C4⋊C4—1221no—
472C2×C4⋊C4—1221no—
473C2×C4⋊C4—1221no—
474C2×C4⋊C4—1221no—
475C2×C4⋊C4—1221no—
476C2×C4⋊C4—1221no—
477C2×C4⋊C4C22×D6111yescharacteristic
478C2×C4⋊C4C22×D6111yescharacteristic
479C2×C22⋊C4—1221no—
480C2×C22⋊C4—1221no—
481C2×C22⋊C4—1221no—
482C2×C22⋊C4—1221no—
483C2×C42—21no—
484C2×C42—611no—
485C2×C42—611no—
486C2×C42—611no—
487C2×C42—1222no—
488C2×C42—1222no—
489C2×C42—1221no—
490C2×C42C22×D6111yescharacteristic
491#107—1222no—
492#107—1222no—
493#103—22no—
494#103—41no—
495#103—1222no—
496#103—1222no—
497#103—1222no—
498#103—1222no—
499#103—1222no—
500#103—2441no—
501#95—21no—
502#95—21no—
503#95—1221no—
504#95—1221no—
505#95—1221no—
506#95—1221no—
507#95—1221no—
508C24—611no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—612no—
521C2×Q8—1224no—
522C2×Q8—1221no—
523C2×Q8—1221no—
524C2×Q8—1221no—
525C2×Q8—1221no—
526C2×Q8—1221no—
527C2×Q8—2442no—
528C2×Q8—2442no—
529C2×Q8D4×D6112yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—611no—
535C22×C4—611no—
536C22×C4—611no—
537C22×C4—612no—
538C22×C4—612no—
539C22×C4—614no—
540C22×C4—1222no—
541C22×C4—1222no—
542C22×C4—1222no—
543C22×C4—1222no—
544C22×C4—1221no—
545C22×C4—1221no—
546C22×C4—1221no—
547C22×C4—1221no—
548C22×C4—1221no—
549C22×C4—1221no—
550C22×C4—1221no—
551C22×C4—1221no—
552C22×C4—2441no—
553C22×C4D4×D6111yescharacteristic
554C22×C4D4×D6111yescharacteristic
555C22×C4C23×D6111yescharacteristic
556Q16—44no—
557Q16—2444no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—612no—
564C2×C8—1221no—
565C2×C8—1221no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—2444no—
570C2×C8—2444no—
571C2×C8#1175822212yes—
572C4⋊C4—24no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—612no—
577C4⋊C4—1224no—
578C4⋊C4—1224no—
579C4⋊C4—1224no—
580C4⋊C4—1224no—
581C4⋊C4—1224no—
582C4⋊C4—1224no—
583C4⋊C4—1221no—
584C4⋊C4—1221no—
585C4⋊C4—1221no—
586C4⋊C4—1221no—
587C4⋊C4—1221no—
588C4⋊C4—2442no—
589C4⋊C4—2442no—
590C4⋊C4—2442no—
591C4⋊C4D4×D6112yes—
592C22⋊C4—1224no—
593C22⋊C4—1224no—
594C22⋊C4—2442no—
595C22⋊C4—2442no—
596C42—24no—
597C42—21no—
598C42—21no—
599C42—1222no—
600C42—1222no—
601C42—1224no—
602C42—1221no—
603C42—1221no—
604C23—612no—
605C23—612no—
606C23—612no—
607C23—1221no—
608C23—1221no—
609C23—1221no—
610C23—1221no—
611C23C2×D4×D6111yescharacteristic
612Q8—22no—
613Q8—22no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—1222no—
621Q8—1222no—
622Q8—2448no—
623Q8—2441no—
624Q8—2441no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—612no—
643C2×C4—612no—
644C2×C4—612no—
645C2×C4—1228no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1222no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—2444no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4—2441no—
666C2×C4—2441no—
667C2×C4—2441no—
668C2×C4—2441no—
669C2×C4Q16×D6112yes—
670C2×C4C2×D4×D6111yescharacteristic
671C2×C4C2×D4×D6111yescharacteristic
672C2×C4#41×D6111yescharacteristic
673C2×C4C2×#1175822211yescharacteristic
674C2×C4#1451982211yescharacteristic
675C2×C4#1451982411yescharacteristic
676C8—22no—
677C8—41no—
678C8—1222no—
679C8—2441no—
680C22—614no—
681C22—1222no—
682C22—1222no—
683C22—1222no—
684C22—1222no—
685C22—1222no—
686C22—1222no—
687C22#120×D6111yescharacteristic
688C22#1684030911yescharacteristic
689C22#1684034111yescharacteristic
690C22C2×Q16×D6111yescharacteristic
691C22#135×D6111yescharacteristic
692C22#137×D6111yescharacteristic
693C22#1684056111yescharacteristic
694C4—22no—
695C4—41no—
696C4—42no—
697C4—42no—
698C4—81no—
699C4—81no—
700C4—1222no—
701C4—1222no—
702C4—1222no—
703C4—4881no—
704C4—4881no—
705C4—2442no—
706C4—2442no—
707C4#1684040211yescharacteristic
708C4#1684040911yescharacteristic
709C4#1684041011yescharacteristic
710C4#1684041711yescharacteristic
711C2—1224no—
712C2#2144942611yescharacteristic
713C2#451×D6111yescharacteristic
714C2#2145504011yescharacteristic
715C2#2145640211yescharacteristic
716C2#2145652611yescharacteristic
717C2#2145715311yescharacteristic
718C2#2145716211yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1878C2
socleC23×C61C22×D4
prime radicalC23×D61C2×D4
hypercenter#1878D61
hypocenterC61#25498
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
5. #21447146C2semidirect
6. #21447064C2semidirect
7. #21446958C2semidirect
8. #21446917C2semidirect
11. #21446163C2semidirect
12. #21446076C2semidirect
13. #21446073C2semidirect
15. C61×#1878C2semidirect
184. C2×C4×D61Q16semidirect
363. #1878D61semidirect
422. C61#25498semidirect

Maximal subgroups

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

subgroupindex
C2×#168403162
C2×#168400022
C2×#168400002
#214541602
#214471462
#214470642
#214469582
#214469172
#214462412
#214462392
#214461632
#214460762
#214460732
#336×D612
C61×#18782
#2549861