Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128426 | C2 | semidirect |
| 3. #19128064 | C2 | semidirect |
| 4. #19128049 | C2 | semidirect |
| 5. #19128004 | C2 | semidirect |
| 6. #19127902 | C2 | semidirect |
| 7. #19127900 | C2 | semidirect |
| 8. #19127828 | C2 | semidirect |
| 9. #19127800 | C2 | semidirect |
| 10. C4×#13050578 | C2 | semidirect |
| 11. #474×C83 | C2 | semidirect |
| 98. Dic166 | #41 | semidirect |
| 125. C83 | #3368 | semidirect |
| 131. #474 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128426 | 2 |
| #19128372 | 2 |
| #19128064 | 2 |
| #19128049 | 2 |
| #19128004 | 2 |
| #19127902 | 2 |
| #19127900 | 2 |
| #19127828 | 2 |
| #19127800 | 2 |
| C4×#13050578 | 2 |
| #474×C83 | 2 |
| #3368 | 83 |