Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 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. #27161636 | C2 | semidirect |
| 2. #27161383 | C2 | semidirect |
| 3. #27161374 | C2 | semidirect |
| 4. #27161369 | C2 | semidirect |
| 5. #27161335 | C2 | semidirect |
| 7. #27161298 | C2 | semidirect |
| 8. #27161289 | C2 | semidirect |
| 9. #27161284 | C2 | semidirect |
| 10. #27161103 | C2 | semidirect |
| 133. C197 | #3252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161636 | 2 |
| #27161383 | 2 |
| #27161374 | 2 |
| #27161369 | 2 |
| #27161335 | 2 |
| #27161323 | 2 |
| #27161298 | 2 |
| #27161289 | 2 |
| #27161284 | 2 |
| #27161103 | 2 |
| #529×C197 | 2 |
| #3252 | 197 |