Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 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. #27161809 | C2 | semidirect |
| 4. #27161431 | C2 | semidirect |
| 5. #27161363 | C2 | semidirect |
| 7. #27161290 | C2 | semidirect |
| 8. #27161206 | C2 | semidirect |
| 9. #27161185 | C2 | semidirect |
| 116. C197 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161809 | 2 |
| #27161799 | 2 |
| #27161437 | 2 |
| #27161431 | 2 |
| #27161363 | 2 |
| #27161300 | 2 |
| #27161290 | 2 |
| #27161206 | 2 |
| #27161185 | 2 |
| C4×#15691346 | 2 |
| #476×C197 | 2 |
| #3369 | 197 |