Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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 |
| 2. C22×#13050578 | C2 | semidirect |
| 3. C2×#14581779 | C2 | semidirect |
| 4. #19128084 | C2 | direct (N × H) |
| 5. C2×C8×Dic83 | C2 | semidirect |
| 9. C2×Dic332 | C22 | semidirect |
| 11. C2×#13050578 | C22 | semidirect |
| 14. #14581779 | C22 | semidirect |
| 17. C8×Dic83 | C22 | semidirect |
| 76. C2×C83 | #495 | semidirect |
| 80. C83 | C2×#495 | semidirect |
| 156. C2 | #19128084 | 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 |
| #19128084 | 2 |
| C2×C8×Dic83 | 2 |
| C22×D8×C83 | 2 |
| C2×#495 | 83 |