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. C2×#19104760 | C2 | semidirect |
| 2. C2×#19104760 | C2 | semidirect |
| 3. #23782432 | C2 | semidirect |
| 4. #23781933 | C2 | semidirect |
| 5. #23781930 | C2 | semidirect |
| 6. #23781713 | C2 | semidirect |
| 7. #23781649 | C2 | semidirect |
| 8. C2×#19104651 | C2 | semidirect |
| 9. #575×C163 | C2 | semidirect |
| 16. C2×#14579686 | C22 | semidirect |
| 18. C2×#14579684 | C22 | semidirect |
| 20. #19104742 | C22 | semidirect |
| 25. #19104670 | C22 | semidirect |
| 26. #19104654 | C22 | semidirect |
| 27. #19104652 | C22 | semidirect |
| 28. #19104651 | C22 | semidirect |
| 32. #137×C163 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C163 | C22 | semidirect |
| 147. C163 | #3068 | semidirect |
| 149. #575 | D163 | semidirect |
| 162. #137 | C2×D163 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| #23782432 | 2 |
| #23781933 | 2 |
| #23781930 | 2 |
| #23781713 | 2 |
| #23781649 | 2 |
| C2×#19104651 | 2 |
| #575×C163 | 2 |
| #3068 | 163 |