Finite Group DatabasebetaFinite Group DatabasebetaOrder 26176.
106 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 106 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. #27189723 | C2 | semidirect |
| 3. #27189652 | C2 | semidirect |
| 4. #27189644 | C2 | semidirect |
| 5. #27189643 | C2 | semidirect |
| 6. C8×Dic409 | C2 | semidirect |
| 7. #131×C409 | C2 | semidirect |
| 9. #20266978 | C4 | semidirect |
| 10. #20266976 | C4 | semidirect |
| 11. #20266975 | C4 | semidirect |
| 12. #20266973 | C4 | semidirect |
| 51. C409 | #443 | semidirect |
| 55. #131 | D409 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27189737 | 2 |
| #27189723 | 2 |
| #27189652 | 2 |
| #27189644 | 2 |
| #27189643 | 2 |
| C8×Dic409 | 2 |
| #131×C409 | 2 |
| #443 | 409 |