Finite Group DatabasebetaFinite Group DatabasebetaOrder 25664.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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. #27165732 | C2 | semidirect |
| 2. #27165730 | C2 | semidirect |
| 3. #27165727 | C2 | semidirect |
| 4. #27165723 | C2 | semidirect |
| 5. #27165722 | C2 | semidirect |
| 6. #27165719 | C2 | semidirect |
| 7. #27165715 | C2 | semidirect |
| 9. C4×Dic802 | C2 | semidirect |
| 10. C4×D1604 | C2 | semidirect |
| 11. C4×C22⋊D401 | C2 | semidirect |
| 12. C4×C22⋊D401 | C2 | semidirect |
| 13. #27165694 | C2 | semidirect |
| 14. C42×D401 | C2 | semidirect |
| 15. #117×C401 | C2 | semidirect |
| 103. C401 | #529 | semidirect |
| 118. #117 | D401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27165732 | 2 |
| #27165730 | 2 |
| #27165727 | 2 |
| #27165723 | 2 |
| #27165722 | 2 |
| #27165719 | 2 |
| #27165715 | 2 |
| #27165710 | 2 |
| C4×Dic802 | 2 |
| C4×D1604 | 2 |
| C4×C22⋊D401 | 2 |
| #27165694 | 2 |
| C42×D401 | 2 |
| #117×C401 | 2 |
| #529 | 401 |