Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
342 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #27161363 | C2 | semidirect |
| 4. #27161361 | C2 | semidirect |
| 7. #27161290 | C2 | semidirect |
| 8. #27161289 | C2 | semidirect |
| 9. #27161288 | C2 | semidirect |
| 11. #475×C197 | C2 | semidirect |
| 129. C197 | #3255 | semidirect |
| 135. #475 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #27161633 | 2 |
| #27161363 | 2 |
| #27161361 | 2 |
| #27161338 | 2 |
| #27161336 | 2 |
| #27161290 | 2 |
| #27161289 | 2 |
| #27161288 | 2 |
| #27161101 | 2 |
| #475×C197 | 2 |
| #3255 | 197 |