Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
390 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19128255 | C2 | semidirect |
| 3. #19128092 | C2 | semidirect |
| 4. #19128059 | C2 | semidirect |
| 5. #19127912 | C2 | semidirect |
| 6. #19127911 | C2 | semidirect |
| 7. #19127898 | C2 | semidirect |
| 8. #19127864 | C2 | semidirect |
| 9. #19127860 | C2 | semidirect |
| 10. #19127757 | C2 | semidirect |
| 11. #460×C83 | C2 | semidirect |
| 141. C83 | #3216 | semidirect |
| 149. #460 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128255 | 2 |
| #19128249 | 2 |
| #19128092 | 2 |
| #19128059 | 2 |
| #19127912 | 2 |
| #19127911 | 2 |
| #19127898 | 2 |
| #19127864 | 2 |
| #19127860 | 2 |
| #19127757 | 2 |
| #460×C83 | 2 |
| #3216 | 83 |