Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
104 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 104 conjugacy classes of subgroups — too many to draw. Only its 45 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. #27165745 | C2 | semidirect |
| 3. #27165744 | C2 | semidirect |
| 4. #27165672 | C2 | semidirect |
| 5. #27165665 | C2 | semidirect |
| 6. #27165648 | C2 | semidirect |
| 7. #104×C401 | C2 | semidirect |
| 9. #20264356 | C4 | semidirect |
| 10. #20264354 | C4 | semidirect |
| 11. #20264353 | C4 | semidirect |
| 12. #20264351 | C4 | semidirect |
| 51. C401 | #444 | semidirect |
| 58. #104 | D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27165757 | 2 |
| #27165745 | 2 |
| #27165744 | 2 |
| #27165672 | 2 |
| #27165665 | 2 |
| #27165648 | 2 |
| #104×C401 | 2 |
| #444 | 401 |