Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 217 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. C2×#19104742 | C2 | semidirect |
| 2. #23781787 | C2 | semidirect |
| 3. #23781782 | C2 | semidirect |
| 4. #23781714 | C2 | semidirect |
| 5. #23781682 | C2 | semidirect |
| 6. #23781623 | C2 | semidirect |
| 10. #19104742 | C22 | semidirect |
| 11. #19104742 | C22 | semidirect |
| 17. #19104671 | C22 | semidirect |
| 18. #19104662 | C22 | semidirect |
| 19. #19104645 | C22 | semidirect |
| 20. C8×Dic163 | C22 | semidirect |
| 22. #137×C163 | C4 | semidirect |
| 23. AGL(1,ℤ/8)×C163 | C4 | semidirect |
| 89. C163 | #2955 | semidirect |
| 99. #137 | Dic163 | semidirect |
| 100. AGL(1,ℤ/8) | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104742 | 2 |
| #23781787 | 2 |
| #23781782 | 2 |
| #23781714 | 2 |
| #23781682 | 2 |
| #23781623 | 2 |
| #575×C163 | 2 |
| #2955 | 163 |