Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
398 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 398 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. #19128047 | C2 | semidirect |
| 4. #19128013 | C2 | semidirect |
| 5. #19127997 | C2 | semidirect |
| 6. #19127944 | C2 | semidirect |
| 7. #19127860 | C2 | semidirect |
| 8. C4×#13050580 | C2 | semidirect |
| 9. #19127778 | C2 | semidirect |
| 10. #19127699 | C2 | semidirect |
| 11. #460×C83 | C2 | semidirect |
| 129. C83 | #3333 | semidirect |
| 136. #460 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128411 | 2 |
| #19128371 | 2 |
| #19128047 | 2 |
| #19128013 | 2 |
| #19127997 | 2 |
| #19127944 | 2 |
| #19127860 | 2 |
| C4×#13050580 | 2 |
| #19127778 | 2 |
| #19127699 | 2 |
| #460×C83 | 2 |
| #3333 | 83 |