Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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×#19104741 | C2 | semidirect |
| 2. #23782239 | C2 | semidirect |
| 4. #23781908 | C2 | semidirect |
| 5. #23781891 | C2 | semidirect |
| 6. #23781703 | C2 | semidirect |
| 7. #23781674 | C2 | semidirect |
| 8. #23781670 | C2 | semidirect |
| 9. C22×SD16×C163 | C2 | semidirect |
| 13. C2×#14579682 | C22 | semidirect |
| 14. C2×C8×D163 | C22 | semidirect |
| 20. #19104711 | C22 | semidirect |
| 25. #19104669 | C22 | semidirect |
| 26. #19104667 | C22 | semidirect |
| 27. #19104659 | C22 | semidirect |
| 68. C2×C8×C163 | D4 | semidirect |
| 120. C163 | #3057 | semidirect |
| 122. C22×SD16 | D163 | semidirect |
| 180. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104741 | 2 |
| #23782239 | 2 |
| #23782232 | 2 |
| #23781908 | 2 |
| #23781891 | 2 |
| #23781703 | 2 |
| #23781674 | 2 |
| #23781670 | 2 |
| C22×SD16×C163 | 2 |
| #3057 | 163 |