Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23782463 | C2 | semidirect |
| 2. C2×#19104761 | C2 | semidirect |
| 3. #23782432 | C2 | semidirect |
| 4. #23781933 | C2 | semidirect |
| 5. #23781926 | C2 | semidirect |
| 6. #23781713 | C2 | semidirect |
| 7. #23781647 | C2 | semidirect |
| 8. C2×#19104652 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C163 | C2 | semidirect |
| 12. #19104765 | C22 | semidirect |
| 16. #19104760 | C22 | semidirect |
| 18. C2×#14579687 | C22 | semidirect |
| 19. C2×#14579684 | C22 | semidirect |
| 21. #19104742 | C22 | semidirect |
| 26. #19104670 | C22 | semidirect |
| 27. #19104653 | C22 | semidirect |
| 28. #19104652 | C22 | semidirect |
| 29. #19104651 | C22 | semidirect |
| 147. C163 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782463 | 2 |
| C2×#19104761 | 2 |
| #23782432 | 2 |
| #23781933 | 2 |
| #23781926 | 2 |
| #23781713 | 2 |
| #23781647 | 2 |
| C2×#19104652 | 2 |
| C2×AGL(1,ℤ/8)×C163 | 2 |
| #3068 | 163 |