Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×Dic332 | C2 | semidirect |
| 4. C2×#14581757 | C2 | semidirect |
| 5. #19127922 | C2 | direct (N × H) |
| 6. C2×Dic83⋊C8 | C2 | semidirect |
| 7. C2×#14581715 | C2 | semidirect |
| 12. C2×Dic332 | C22 | semidirect |
| 19. #14581757 | C22 | semidirect |
| 25. Dic83⋊C8 | C22 | semidirect |
| 26. #14581715 | C22 | semidirect |
| 111. C2×C83 | #464 | semidirect |
| 116. C83 | C2×#464 | semidirect |
| 227. C2 | #19127922 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic332 | 2 |
| C22×#13050578 | 2 |
| C2×#14581779 | 2 |
| C2×#14581757 | 2 |
| #19127922 | 2 |
| C2×Dic83⋊C8 | 2 |
| C2×#14581715 | 2 |
| C2×#102×C83 | 2 |
| C2×#464 | 83 |