Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 388 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. #19128411 | C2 | semidirect |
| 3. #19128051 | C2 | semidirect |
| 4. #19128030 | C2 | semidirect |
| 5. #19127992 | C2 | semidirect |
| 6. #19127956 | C2 | semidirect |
| 7. #19127862 | C2 | semidirect |
| 8. C4×#13050577 | C2 | semidirect |
| 9. #19127778 | C2 | semidirect |
| 10. #19127701 | C2 | semidirect |
| 11. #462×C83 | C2 | semidirect |
| 127. C83 | #3331 | semidirect |
| 134. #462 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128411 | 2 |
| #19128354 | 2 |
| #19128051 | 2 |
| #19128030 | 2 |
| #19127992 | 2 |
| #19127956 | 2 |
| #19127862 | 2 |
| C4×#13050577 | 2 |
| #19127778 | 2 |
| #19127701 | 2 |
| #462×C83 | 2 |
| #3331 | 83 |