Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161803 | C2 | semidirect |
| 3. #27161416 | C2 | semidirect |
| 4. #27161406 | C2 | semidirect |
| 5. #27161361 | C2 | semidirect |
| 6. #27161356 | C2 | semidirect |
| 7. #27161326 | C2 | semidirect |
| 8. C4×#15691347 | C2 | semidirect |
| 9. #27161158 | C2 | semidirect |
| 10. #27161120 | C2 | semidirect |
| 11. #500×C197 | C2 | semidirect |
| 99. C8×C197 | #41 | semidirect |
| 122. C197 | #3353 | semidirect |
| 126. #500 | D197 | semidirect |
| 222. C8 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161803 | 2 |
| #27161732 | 2 |
| #27161416 | 2 |
| #27161406 | 2 |
| #27161361 | 2 |
| #27161356 | 2 |
| #27161326 | 2 |
| C4×#15691347 | 2 |
| #27161158 | 2 |
| #27161120 | 2 |
| #500×C197 | 2 |
| #3353 | 197 |