Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 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. #27161799 | C2 | semidirect |
| 2. #27161786 | C2 | semidirect |
| 3. #27161432 | C2 | semidirect |
| 4. #27161430 | C2 | semidirect |
| 5. #27161385 | C2 | semidirect |
| 6. #27161369 | C2 | semidirect |
| 8. #27161284 | C2 | semidirect |
| 9. C8×Dic394 | C2 | semidirect |
| 10. #27161170 | C2 | semidirect |
| 120. C197 | #3360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161799 | 2 |
| #27161786 | 2 |
| #27161432 | 2 |
| #27161430 | 2 |
| #27161385 | 2 |
| #27161369 | 2 |
| #27161292 | 2 |
| #27161284 | 2 |
| C8×Dic394 | 2 |
| #27161170 | 2 |
| C4×D8×C197 | 2 |
| #3360 | 197 |