Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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. #27161634 | C2 | semidirect |
| 3. #27161372 | C2 | semidirect |
| 4. #27161360 | C2 | semidirect |
| 5. #27161359 | C2 | semidirect |
| 6. #27161328 | C2 | semidirect |
| 7. #27161322 | C2 | semidirect |
| 8. #27161281 | C2 | semidirect |
| 9. #27161277 | C2 | semidirect |
| 10. #27161101 | C2 | semidirect |
| 11. #461×C197 | C2 | semidirect |
| 142. C197 | #3254 | semidirect |
| 152. #461 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #27161626 | 2 |
| #27161372 | 2 |
| #27161360 | 2 |
| #27161359 | 2 |
| #27161328 | 2 |
| #27161322 | 2 |
| #27161281 | 2 |
| #27161277 | 2 |
| #27161101 | 2 |
| #461×C197 | 2 |
| #3254 | 197 |