Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
360 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 121 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. #27161775 | C2 | semidirect |
| 2. #27161481 | C2 | semidirect |
| 3. #27161404 | C2 | semidirect |
| 4. #27161393 | C2 | semidirect |
| 5. #27161380 | C2 | semidirect |
| 6. #27161332 | C2 | semidirect |
| 7. C4×D1576 | C2 | semidirect |
| 8. #27161121 | C2 | semidirect |
| 9. #436×C197 | C2 | semidirect |
| 102. C197 | #3355 | semidirect |
| 111. #436 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161775 | 2 |
| #27161481 | 2 |
| #27161404 | 2 |
| #27161393 | 2 |
| #27161380 | 2 |
| #27161332 | 2 |
| C4×D1576 | 2 |
| #27161121 | 2 |
| #436×C197 | 2 |
| #3355 | 197 |