Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
396 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 396 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 |
|---|---|---|
| 1. #27161799 | C2 | semidirect |
| 3. #27161426 | C2 | semidirect |
| 4. #27161404 | C2 | semidirect |
| 5. #27161365 | C2 | semidirect |
| 6. #27161308 | C2 | semidirect |
| 7. #27161280 | C2 | semidirect |
| 8. #27161243 | C2 | semidirect |
| 9. C4×Dic788 | C2 | semidirect |
| 10. #27161076 | C2 | semidirect |
| 11. C8×D4×C197 | C2 | semidirect |
| 127. C197 | #3304 | semidirect |
| 138. C8×D4 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161799 | 2 |
| #27161750 | 2 |
| #27161426 | 2 |
| #27161404 | 2 |
| #27161365 | 2 |
| #27161308 | 2 |
| #27161280 | 2 |
| #27161243 | 2 |
| C4×Dic788 | 2 |
| #27161076 | 2 |
| C8×D4×C197 | 2 |
| #3304 | 197 |