Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
426 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 135 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. C22×D1268 | C2 | semidirect |
| 2. C22×D1268 | C2 | semidirect |
| 3. C22×C4×D317 | C2 | semidirect |
| 4. #23778755 | C2 | direct (N × H) |
| 5. C2×#19099551 | C2 | semidirect |
| 6. C2×C4⋊C4×C317 | C2 | semidirect |
| 11. C2×D1268 | C22 | semidirect |
| 12. C2×D1268 | C22 | semidirect |
| 15. C2×C4×D317 | C22 | semidirect |
| 16. #19099551 | C22 | semidirect |
| 19. C4⋊C4×C317 | C22 | semidirect |
| 25. C22×D317 | D4 | semidirect |
| 35. C2×C4×C317 | D4 | semidirect |
| 49. C2×D317 | C2×D4 | semidirect |
| 51. C4×C317 | C2×D4 | semidirect |
| 53. C2×C317 | #121 | semidirect |
| 59. C317 | C2×#121 | semidirect |
| 65. C2×C4⋊C4 | D317 | semidirect |
| 78. C4⋊C4 | C2×D317 | semidirect |
| 95. C2×C4 | D1268 | semidirect |
| 112. C4 | C2×D1268 | semidirect |
| 115. C2 | #23778755 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1268 | 2 |
| C22×C4×D317 | 2 |
| #23778755 | 2 |
| C2×#19099551 | 2 |
| C2×C4⋊C4×C317 | 2 |
| C2×#121 | 317 |