Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#13050575 | C2 | semidirect |
| 2. C2×#14581799 | C2 | semidirect |
| 3. #19128265 | C2 | semidirect |
| 4. #19127952 | C2 | semidirect |
| 5. #19127935 | C2 | semidirect |
| 6. #19127737 | C2 | semidirect |
| 7. #19127706 | C2 | semidirect |
| 8. #19127705 | C2 | semidirect |
| 9. #535×C83 | C2 | semidirect |
| 16. C2×#13050574 | C22 | semidirect |
| 18. C22×C83⋊C8 | C22 | semidirect |
| 21. #14581766 | C22 | semidirect |
| 24. #14581725 | C22 | semidirect |
| 25. #14581723 | C22 | semidirect |
| 26. #14581713 | C22 | semidirect |
| 27. #14581712 | C22 | semidirect |
| 32. #121×C83 | C22 | semidirect |
| 46. C2×C83⋊C8 | D4 | semidirect |
| 126. C83 | #3058 | semidirect |
| 130. #535 | D83 | semidirect |
| 152. #121 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050575 | 2 |
| C2×#14581799 | 2 |
| #19128265 | 2 |
| #19127952 | 2 |
| #19127935 | 2 |
| #19127737 | 2 |
| #19127706 | 2 |
| #19127705 | 2 |
| #535×C83 | 2 |
| #3058 | 83 |