Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
104 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 47 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. #27165743 | C2 | semidirect |
| 3. #27165672 | C2 | semidirect |
| 4. #27165664 | C2 | semidirect |
| 5. #27165663 | C2 | semidirect |
| 6. #27165647 | C2 | semidirect |
| 7. #131×C401 | C2 | semidirect |
| 9. #20264356 | C4 | semidirect |
| 10. #20264354 | C4 | semidirect |
| 11. #20264353 | C4 | semidirect |
| 12. #20264351 | C4 | semidirect |
| 51. C401 | #444 | semidirect |
| 55. #131 | D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27165757 | 2 |
| #27165743 | 2 |
| #27165672 | 2 |
| #27165664 | 2 |
| #27165663 | 2 |
| #27165647 | 2 |
| #131×C401 | 2 |
| #444 | 401 |