Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782218 | C2 | semidirect |
| 3. #23782028 | C2 | semidirect |
| 4. #23782010 | C2 | semidirect |
| 5. #23781671 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. #23781669 | C2 | semidirect |
| 8. M16×Dic163 | C2 | semidirect |
| 9. #418×C163 | C2 | semidirect |
| 13. #19104734 | C22 | semidirect |
| 17. #19104726 | C22 | semidirect |
| 22. #19104657 | C22 | semidirect |
| 23. #19104656 | C22 | semidirect |
| 24. #19104655 | C22 | semidirect |
| 25. #19104645 | C22 | semidirect |
| 26. C8×Dic163 | C22 | semidirect |
| 30. #102×C163 | C22 | semidirect |
| 111. C163 | #3138 | semidirect |
| 120. #418 | D163 | semidirect |
| 140. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782218 | 2 |
| C2×#19104731 | 2 |
| #23782028 | 2 |
| #23782010 | 2 |
| #23781671 | 2 |
| #23781670 | 2 |
| #23781669 | 2 |
| M16×Dic163 | 2 |
| #418×C163 | 2 |
| #3138 | 163 |