Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 3. #19128035 | C2 | semidirect |
| 4. #19127993 | C2 | semidirect |
| 5. #19127941 | C2 | semidirect |
| 6. #19127908 | C2 | semidirect |
| 7. #19127858 | C2 | semidirect |
| 8. C4×Dic332 | C2 | semidirect |
| 10. #103×D83 | C2 | semidirect |
| 11. #487×C83 | C2 | semidirect |
| 90. D332 | Q16 | semidirect |
| 123. C83 | #3299 | semidirect |
| 126. #487 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128412 | 2 |
| #19128366 | 2 |
| #19128035 | 2 |
| #19127993 | 2 |
| #19127941 | 2 |
| #19127908 | 2 |
| #19127858 | 2 |
| C4×Dic332 | 2 |
| C8×D332 | 2 |
| #103×D83 | 2 |
| #487×C83 | 2 |
| #3299 | 83 |