Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
482 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#14581821 | C2 | semidirect |
| 3. #19128366 | C2 | semidirect |
| 4. #19127944 | C2 | semidirect |
| 5. #19127908 | C2 | semidirect |
| 6. #19127898 | C2 | semidirect |
| 7. #19127860 | C2 | semidirect |
| 8. #19127838 | C2 | semidirect |
| 9. C4×Dic332 | C2 | semidirect |
| 10. #19127780 | C2 | semidirect |
| 11. #492×C83 | C2 | semidirect |
| 55. Dic332 | D4 | semidirect |
| 123. C4×C83 | #137 | semidirect |
| 137. C83 | #3278 | semidirect |
| 141. #492 | D83 | semidirect |
| 265. C4 | #14581821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581821 | 2 |
| #19128371 | 2 |
| #19128366 | 2 |
| #19127944 | 2 |
| #19127908 | 2 |
| #19127898 | 2 |
| #19127860 | 2 |
| #19127838 | 2 |
| C4×Dic332 | 2 |
| #19127780 | 2 |
| #492×C83 | 2 |
| #3278 | 83 |