Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161435 | C2 | semidirect |
| 4. #27161429 | C2 | semidirect |
| 5. #27161427 | C2 | semidirect |
| 6. #27161426 | C2 | semidirect |
| 7. #27161074 | C2 | semidirect |
| 8. C4×C8×D197 | C2 | semidirect |
| 9. #487×C197 | C2 | semidirect |
| 111. C197 | #3131 | semidirect |
| 117. #487 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #27161630 | 2 |
| #27161435 | 2 |
| #27161429 | 2 |
| #27161427 | 2 |
| #27161426 | 2 |
| #27161074 | 2 |
| C4×C8×D197 | 2 |
| #487×C197 | 2 |
| #3131 | 197 |