Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
390 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 111 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. #19128256 | C2 | semidirect |
| 3. #19128093 | C2 | semidirect |
| 4. #19128061 | C2 | semidirect |
| 5. #19128060 | C2 | semidirect |
| 6. #19127909 | C2 | semidirect |
| 7. #19127899 | C2 | semidirect |
| 8. #19127862 | C2 | semidirect |
| 9. #19127860 | C2 | semidirect |
| 10. #19127756 | C2 | semidirect |
| 11. #497×C83 | C2 | semidirect |
| 142. C83 | #3216 | semidirect |
| 146. #497 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128256 | 2 |
| #19128250 | 2 |
| #19128093 | 2 |
| #19128061 | 2 |
| #19128060 | 2 |
| #19127909 | 2 |
| #19127899 | 2 |
| #19127862 | 2 |
| #19127860 | 2 |
| #19127756 | 2 |
| #497×C83 | 2 |
| #3216 | 83 |