Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
440 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23781968 | C2 | semidirect |
| 4. #23781964 | C2 | semidirect |
| 5. #23781954 | C2 | semidirect |
| 6. #23781944 | C2 | semidirect |
| 7. #23781705 | C2 | semidirect |
| 8. #23781688 | C2 | semidirect |
| 11. #428×C163 | C2 | semidirect |
| 15. #19104734 | C22 | semidirect |
| 16. #19104734 | C22 | semidirect |
| 17. #19104726 | C22 | semidirect |
| 18. #19104726 | C22 | semidirect |
| 30. #19104668 | C22 | semidirect |
| 31. #19104666 | C22 | semidirect |
| 32. Dic163⋊C8 | C22 | semidirect |
| 33. Dic163⋊C8 | C22 | semidirect |
| 41. #107×C163 | C22 | semidirect |
| 42. #106×C163 | C22 | semidirect |
| 48. C2×D652 | Q8 | semidirect |
| 138. C163 | #3077 | semidirect |
| 147. #428 | D163 | semidirect |
| 173. #107 | C2×D163 | semidirect |
| 175. #106 | 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×#19104697 | 2 |
| #23781968 | 2 |
| #23781964 | 2 |
| #23781954 | 2 |
| #23781944 | 2 |
| #23781705 | 2 |
| #23781688 | 2 |
| #23781671 | 2 |
| #23781669 | 2 |
| #428×C163 | 2 |
| #3077 | 163 |