Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
408 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161794 | C2 | semidirect |
| 2. #27161750 | C2 | semidirect |
| 3. #27161426 | C2 | semidirect |
| 4. #27161404 | C2 | semidirect |
| 5. #27161375 | C2 | semidirect |
| 6. #27161315 | C2 | semidirect |
| 7. #27161275 | C2 | semidirect |
| 8. #27161226 | C2 | semidirect |
| 9. C4×#15691347 | C2 | semidirect |
| 10. #27161076 | C2 | semidirect |
| 11. C8×D4×C197 | C2 | semidirect |
| 132. C197 | #3305 | semidirect |
| 143. C8×D4 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161794 | 2 |
| #27161750 | 2 |
| #27161426 | 2 |
| #27161404 | 2 |
| #27161375 | 2 |
| #27161315 | 2 |
| #27161275 | 2 |
| #27161226 | 2 |
| C4×#15691347 | 2 |
| #27161076 | 2 |
| C8×D4×C197 | 2 |
| #3305 | 197 |