Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 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. #27161614 | C2 | semidirect |
| 2. #27161463 | C2 | semidirect |
| 3. #27161436 | C2 | semidirect |
| 4. #27161321 | C2 | semidirect |
| 6. #27161309 | C2 | semidirect |
| 7. #27161173 | C2 | semidirect |
| 8. #27161166 | C2 | semidirect |
| 9. #27161161 | C2 | semidirect |
| 10. C4×C8×D197 | C2 | semidirect |
| 11. #499×C197 | C2 | semidirect |
| 118. C197 | #3168 | semidirect |
| 121. #499 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161614 | 2 |
| #27161463 | 2 |
| #27161436 | 2 |
| #27161321 | 2 |
| #27161316 | 2 |
| #27161309 | 2 |
| #27161173 | 2 |
| #27161166 | 2 |
| #27161161 | 2 |
| C4×C8×D197 | 2 |
| #499×C197 | 2 |
| #3168 | 197 |