Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19128329 | C2 | semidirect |
| 2. #19128065 | C2 | semidirect |
| 3. #19128060 | C2 | semidirect |
| 4. #19128055 | C2 | semidirect |
| 5. #19128047 | C2 | semidirect |
| 6. #19127706 | C2 | semidirect |
| 7. #19127702 | C2 | semidirect |
| 8. #19127697 | C2 | semidirect |
| 9. C2×#14581713 | C2 | semidirect |
| 10. #19127657 | C2 | semidirect |
| 14. #14581792 | C22 | semidirect |
| 16. #14581784 | C22 | semidirect |
| 21. #14581716 | C22 | semidirect |
| 22. #14581716 | C22 | semidirect |
| 23. #14581716 | C22 | semidirect |
| 28. #14581713 | C22 | semidirect |
| 29. #14581713 | C22 | semidirect |
| 30. #14581713 | C22 | semidirect |
| 31. #14581703 | C22 | semidirect |
| 32. C4×C83⋊C8 | C22 | semidirect |
| 136. C83 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19128065 | 2 |
| #19128060 | 2 |
| #19128055 | 2 |
| #19128047 | 2 |
| #19127706 | 2 |
| #19127702 | 2 |
| #19127697 | 2 |
| C2×#14581713 | 2 |
| #19127657 | 2 |
| #535×C83 | 2 |
| #3136 | 83 |