Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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. #19128425 | C2 | semidirect |
| 2. #19128366 | C2 | semidirect |
| 3. #19128062 | C2 | semidirect |
| 4. #19127994 | C2 | semidirect |
| 5. #19127978 | C2 | semidirect |
| 7. #19127903 | C2 | semidirect |
| 8. #19127831 | C2 | semidirect |
| 9. #19127804 | C2 | semidirect |
| 11. #487×C83 | C2 | semidirect |
| 123. C83 | #3367 | semidirect |
| 127. #487 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128425 | 2 |
| #19128366 | 2 |
| #19128062 | 2 |
| #19127994 | 2 |
| #19127978 | 2 |
| #19127919 | 2 |
| #19127903 | 2 |
| #19127831 | 2 |
| #19127804 | 2 |
| C4×D664 | 2 |
| #487×C83 | 2 |
| #3367 | 83 |