Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
350 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 350 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. #27161803 | C2 | semidirect |
| 2. #27161790 | C2 | semidirect |
| 3. #27161435 | C2 | semidirect |
| 4. #27161388 | C2 | semidirect |
| 5. #27161366 | C2 | semidirect |
| 7. #27161281 | C2 | semidirect |
| 8. C8×Dic394 | C2 | semidirect |
| 9. #27161164 | C2 | semidirect |
| 11. #487×C197 | C2 | semidirect |
| 120. C197 | #3360 | semidirect |
| 125. #487 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161803 | 2 |
| #27161790 | 2 |
| #27161435 | 2 |
| #27161388 | 2 |
| #27161366 | 2 |
| #27161297 | 2 |
| #27161281 | 2 |
| C8×Dic394 | 2 |
| #27161164 | 2 |
| C4×D1576 | 2 |
| #487×C197 | 2 |
| #3360 | 197 |