Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
388 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #27161431 | C2 | semidirect |
| 4. #27161416 | C2 | semidirect |
| 5. #27161321 | C2 | semidirect |
| 6. #27161290 | C2 | semidirect |
| 7. #27161236 | C2 | semidirect |
| 8. C4×#15691348 | C2 | semidirect |
| 10. #103×D197 | C2 | semidirect |
| 11. #477×C197 | C2 | semidirect |
| 82. D788 | Q16 | semidirect |
| 122. C197 | #3299 | semidirect |
| 128. #477 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161790 | 2 |
| Q8×D788 | 2 |
| #27161431 | 2 |
| #27161416 | 2 |
| #27161321 | 2 |
| #27161290 | 2 |
| #27161236 | 2 |
| C4×#15691348 | 2 |
| #27161144 | 2 |
| #103×D197 | 2 |
| #477×C197 | 2 |
| #3299 | 197 |