Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23778827 | C2 | semidirect |
| 2. #23778826 | C2 | semidirect |
| 3. #23778813 | C2 | semidirect |
| 4. #23778808 | C2 | semidirect |
| 5. #23778802 | C2 | semidirect |
| 6. C2×#19099563 | C2 | semidirect |
| 7. #131×C317 | C2 | semidirect |
| 10. #19099574 | C22 | semidirect |
| 12. C2×Dic634 | C22 | semidirect |
| 16. Dic1268 | C22 | semidirect |
| 17. #19099563 | C22 | semidirect |
| 18. #19099563 | C22 | semidirect |
| 19. #19099563 | C22 | semidirect |
| 20. D2536 | C22 | semidirect |
| 22. M16×C317 | C22 | semidirect |
| 23. C2×C8×C317 | C22 | semidirect |
| 53. C317 | #577 | semidirect |
| 61. #131 | D317 | semidirect |
| 76. M16 | C2×D317 | semidirect |
| 77. C2×C8 | C2×D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778827 | 2 |
| #23778826 | 2 |
| #23778813 | 2 |
| #23778808 | 2 |
| #23778802 | 2 |
| C2×#19099563 | 2 |
| #131×C317 | 2 |
| #577 | 317 |