Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19128251 | C2 | semidirect |
| 2. #19128235 | C2 | semidirect |
| 3. #19128085 | C2 | semidirect |
| 4. #19128056 | C2 | semidirect |
| 5. #19127912 | C2 | semidirect |
| 6. #19127907 | C2 | semidirect |
| 7. #19127902 | C2 | semidirect |
| 8. #19127897 | C2 | semidirect |
| 9. #19127865 | C2 | semidirect |
| 10. #19127848 | C2 | semidirect |
| 11. #431×C83 | C2 | semidirect |
| 145. C83 | #3212 | semidirect |
| 156. #431 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19128235 | 2 |
| #19128085 | 2 |
| #19128056 | 2 |
| #19127912 | 2 |
| #19127907 | 2 |
| #19127902 | 2 |
| #19127897 | 2 |
| #19127865 | 2 |
| #19127848 | 2 |
| #431×C83 | 2 |
| #3212 | 83 |