Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782026 | C2 | semidirect |
| 4. #23782021 | C2 | semidirect |
| 5. #23781674 | C2 | semidirect |
| 8. M16×Dic163 | C2 | semidirect |
| 9. #419×C163 | C2 | semidirect |
| 12. #19104734 | C22 | semidirect |
| 13. #19104726 | C22 | semidirect |
| 22. #19104659 | C22 | semidirect |
| 25. #19104645 | C22 | semidirect |
| 26. C8×Dic163 | C22 | semidirect |
| 30. #103×C163 | C22 | semidirect |
| 104. C163 | #3140 | semidirect |
| 111. #419 | D163 | semidirect |
| 131. #103 | 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×#19104724 | 2 |
| #23782026 | 2 |
| #23782021 | 2 |
| #23781674 | 2 |
| #23781671 | 2 |
| #23781669 | 2 |
| M16×Dic163 | 2 |
| #419×C163 | 2 |
| #3140 | 163 |