Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 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. #27161744 | C2 | semidirect |
| 3. #27161408 | C2 | semidirect |
| 4. #27161361 | C2 | semidirect |
| 5. #27161311 | C2 | semidirect |
| 6. #27161281 | C2 | semidirect |
| 7. #27161219 | C2 | semidirect |
| 8. C4×#15691347 | C2 | semidirect |
| 9. C8×D788 | C2 | semidirect |
| 10. #103×D197 | C2 | semidirect |
| 11. #487×C197 | C2 | semidirect |
| 81. Dic394 | #41 | semidirect |
| 85. D788 | SD16 | semidirect |
| 128. C197 | #3298 | semidirect |
| 132. #487 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161744 | 2 |
| #27161732 | 2 |
| #27161408 | 2 |
| #27161361 | 2 |
| #27161311 | 2 |
| #27161281 | 2 |
| #27161219 | 2 |
| C4×#15691347 | 2 |
| C8×D788 | 2 |
| #103×D197 | 2 |
| #487×C197 | 2 |
| #3298 | 197 |