Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782293 | C2 | semidirect |
| 3. #23781968 | C2 | semidirect |
| 4. #23781964 | C2 | semidirect |
| 5. #23781954 | C2 | semidirect |
| 6. #23781944 | C2 | semidirect |
| 7. #23781708 | C2 | semidirect |
| 8. #23781691 | C2 | semidirect |
| 11. #427×C163 | C2 | semidirect |
| 15. #19104734 | C22 | semidirect |
| 17. #19104726 | C22 | semidirect |
| 26. #19104668 | C22 | semidirect |
| 27. #19104666 | C22 | semidirect |
| 28. Dic163⋊C8 | C22 | semidirect |
| 29. Dic163⋊C8 | C22 | semidirect |
| 37. #107×C163 | C22 | semidirect |
| 38. #107×C163 | C22 | semidirect |
| 39. #106×C163 | C22 | semidirect |
| 40. #106×C163 | C22 | semidirect |
| 45. C2×D652 | Q8 | semidirect |
| 124. C163 | #3081 | semidirect |
| 133. #427 | D163 | semidirect |
| 155. #107 | C2×D163 | semidirect |
| 156. #107 | C2×D163 | semidirect |
| 158. #106 | C2×D163 | semidirect |
| 159. #106 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782139 | 2 |
| #23781968 | 2 |
| #23781964 | 2 |
| #23781954 | 2 |
| #23781944 | 2 |
| #23781708 | 2 |
| #23781691 | 2 |
| #23781669 | 2 |
| C2×#19104657 | 2 |
| #427×C163 | 2 |
| #3081 | 163 |