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. #27161430 | C2 | semidirect |
| 4. #27161416 | C2 | semidirect |
| 5. #27161374 | C2 | semidirect |
| 6. #27161319 | C2 | semidirect |
| 7. #27161289 | C2 | semidirect |
| 8. #27161233 | C2 | semidirect |
| 10. #103×D197 | C2 | semidirect |
| 11. C4×Q16×C197 | C2 | semidirect |
| 81. D788 | Q16 | semidirect |
| 122. C197 | #3299 | semidirect |
| 132. C4×Q16 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161789 | 2 |
| Q8×D788 | 2 |
| #27161430 | 2 |
| #27161416 | 2 |
| #27161374 | 2 |
| #27161319 | 2 |
| #27161289 | 2 |
| #27161233 | 2 |
| C8×D788 | 2 |
| #103×D197 | 2 |
| C4×Q16×C197 | 2 |
| #3299 | 197 |