Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 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. #23778788 | C2 | semidirect |
| 3. #23778787 | C2 | semidirect |
| 4. #23778715 | C2 | semidirect |
| 5. #23778708 | C2 | semidirect |
| 6. C4×#14579261 | C2 | semidirect |
| 7. #104×C317 | C2 | semidirect |
| 9. #19099564 | C4 | semidirect |
| 10. #19099562 | C4 | semidirect |
| 11. #19099561 | C4 | semidirect |
| 12. #19099559 | C4 | semidirect |
| 51. C317 | #443 | semidirect |
| 58. #104 | D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778800 | 2 |
| #23778788 | 2 |
| #23778787 | 2 |
| #23778715 | 2 |
| #23778708 | 2 |
| C4×#14579261 | 2 |
| #104×C317 | 2 |
| #443 | 317 |