Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×Dic166 | C2 | semidirect |
| 4. #19128052 | C2 | semidirect |
| 6. #19127987 | C2 | semidirect |
| 8. #19127912 | C2 | semidirect |
| 9. #19127809 | C2 | semidirect |
| 11. #446×C83 | C2 | semidirect |
| 117. C83 | #3369 | semidirect |
| 126. #446 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic166 | 2 |
| #19128424 | 2 |
| #19128061 | 2 |
| #19128052 | 2 |
| #19127992 | 2 |
| #19127987 | 2 |
| #19127924 | 2 |
| #19127912 | 2 |
| #19127809 | 2 |
| C4×#13050579 | 2 |
| #446×C83 | 2 |
| #3369 | 83 |