Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
392 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 392 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. #19127998 | C2 | semidirect |
| 3. #19127986 | C2 | semidirect |
| 4. #19127981 | C2 | semidirect |
| 5. #19127952 | C2 | semidirect |
| 6. #19127949 | C2 | semidirect |
| 7. #19127913 | C2 | semidirect |
| 8. #19127901 | C2 | semidirect |
| 9. #19127896 | C2 | semidirect |
| 10. #19127725 | C2 | semidirect |
| 11. #529×C83 | C2 | semidirect |
| 142. C83 | #3251 | semidirect |
| 144. #529 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128251 | 2 |
| #19127998 | 2 |
| #19127986 | 2 |
| #19127981 | 2 |
| #19127952 | 2 |
| #19127949 | 2 |
| #19127913 | 2 |
| #19127901 | 2 |
| #19127896 | 2 |
| #19127725 | 2 |
| #529×C83 | 2 |
| #3251 | 83 |