Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #27161808 | C2 | semidirect |
| 3. #27161435 | C2 | semidirect |
| 5. #27161382 | C2 | semidirect |
| 6. #27161364 | C2 | semidirect |
| 7. #27161303 | C2 | semidirect |
| 9. C8×Dic394 | C2 | semidirect |
| 10. #27161164 | C2 | semidirect |
| 11. C4×Q16×C197 | C2 | semidirect |
| 117. C197 | #3365 | semidirect |
| 128. C4×Q16 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161814 | 2 |
| #27161808 | 2 |
| #27161435 | 2 |
| #27161426 | 2 |
| #27161382 | 2 |
| #27161364 | 2 |
| #27161303 | 2 |
| #27161279 | 2 |
| C8×Dic394 | 2 |
| #27161164 | 2 |
| C4×Q16×C197 | 2 |
| #3365 | 197 |