Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
106 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 40 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. #23778868 | C2 | semidirect |
| 2. #23778867 | C2 | semidirect |
| 3. #23778850 | C2 | semidirect |
| 4. #23778845 | C2 | semidirect |
| 5. #23778844 | C2 | semidirect |
| 6. C8×#11929639 | C2 | semidirect |
| 18. #19099564 | C4 | semidirect |
| 19. #19099563 | C4 | semidirect |
| 20. #19099559 | C4 | semidirect |
| 22. SD16×C317 | C4 | semidirect |
| 51. C317 | #443 | semidirect |
| 64. SD16 | #11929639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778868 | 2 |
| #23778867 | 2 |
| #23778850 | 2 |
| #23778845 | 2 |
| #23778844 | 2 |
| C8×#11929639 | 2 |
| #23778801 | 2 |
| #443 | 317 |