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. #27161608 | C2 | semidirect |
| 2. #27161481 | C2 | semidirect |
| 3. #27161433 | C2 | semidirect |
| 4. #27161317 | C2 | semidirect |
| 6. #27161305 | C2 | semidirect |
| 7. Q16×Dic197 | C2 | semidirect |
| 8. SD16×Dic197 | C2 | semidirect |
| 9. D8×Dic197 | C2 | semidirect |
| 10. C4×C8×D197 | C2 | semidirect |
| 11. #495×C197 | C2 | semidirect |
| 118. C197 | #3168 | semidirect |
| 122. #495 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161608 | 2 |
| #27161481 | 2 |
| #27161433 | 2 |
| #27161317 | 2 |
| #27161312 | 2 |
| #27161305 | 2 |
| Q16×Dic197 | 2 |
| SD16×Dic197 | 2 |
| D8×Dic197 | 2 |
| C4×C8×D197 | 2 |
| #495×C197 | 2 |
| #3168 | 197 |