Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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. #19128249 | C2 | semidirect |
| 2. #19128236 | C2 | semidirect |
| 3. #19128095 | C2 | semidirect |
| 4. #19128088 | C2 | semidirect |
| 5. #19128071 | C2 | semidirect |
| 6. #19127922 | C2 | semidirect |
| 7. #19127915 | C2 | semidirect |
| 8. #19127864 | C2 | semidirect |
| 9. #19127847 | C2 | semidirect |
| 10. #19127756 | C2 | semidirect |
| 11. #490×C83 | C2 | semidirect |
| 141. C83 | #3219 | semidirect |
| 147. #490 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128249 | 2 |
| #19128236 | 2 |
| #19128095 | 2 |
| #19128088 | 2 |
| #19128071 | 2 |
| #19127922 | 2 |
| #19127915 | 2 |
| #19127864 | 2 |
| #19127847 | 2 |
| #19127756 | 2 |
| #490×C83 | 2 |
| #3219 | 83 |