Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128433 | C2 | semidirect |
| 2. #19128086 | C2 | semidirect |
| 4. #19127918 | C2 | semidirect |
| 5. #19127913 | C2 | semidirect |
| 6. #19127899 | C2 | semidirect |
| 7. C8×Dic166 | C2 | semidirect |
| 8. Q16×Dic83 | C2 | semidirect |
| 9. C4×D664 | C2 | semidirect |
| 10. D8×Dic83 | C2 | semidirect |
| 11. #495×C83 | C2 | semidirect |
| 121. C83 | #3396 | semidirect |
| 124. #495 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128433 | 2 |
| #19128086 | 2 |
| #19128076 | 2 |
| #19127918 | 2 |
| #19127913 | 2 |
| #19127899 | 2 |
| C8×Dic166 | 2 |
| Q16×Dic83 | 2 |
| C4×D664 | 2 |
| D8×Dic83 | 2 |
| #495×C83 | 2 |
| #3396 | 83 |