Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
440 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23782220 | C2 | semidirect |
| 3. #23781968 | C2 | semidirect |
| 4. #23781967 | C2 | semidirect |
| 5. #23781956 | C2 | semidirect |
| 6. #23781955 | C2 | semidirect |
| 7. #23781942 | C2 | semidirect |
| 8. #23781706 | C2 | semidirect |
| 9. #23781687 | C2 | semidirect |
| 11. #474×C163 | C2 | semidirect |
| 15. #19104735 | C22 | semidirect |
| 16. #19104726 | C22 | semidirect |
| 30. #19104668 | C22 | semidirect |
| 31. #19104667 | C22 | semidirect |
| 32. #19104666 | C22 | semidirect |
| 33. C4⋊(C163⋊C8) | C22 | semidirect |
| 34. Dic163⋊C8 | C22 | semidirect |
| 38. C4⋊Q8×C163 | C22 | semidirect |
| 40. #107×C163 | C22 | semidirect |
| 41. C4⋊C8×C163 | C22 | semidirect |
| 48. D4×D163 | Q8 | semidirect |
| 144. C163 | #3077 | semidirect |
| 153. #474 | D163 | semidirect |
| 161. C4⋊Q8 | C2×D163 | semidirect |
| 178. #107 | C2×D163 | semidirect |
| 183. C4⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| C4×D4×D163 | 2 |
| #23781968 | 2 |
| #23781967 | 2 |
| #23781956 | 2 |
| #23781955 | 2 |
| #23781942 | 2 |
| #23781706 | 2 |
| #23781687 | 2 |
| #23781668 | 2 |
| #474×C163 | 2 |
| #3077 | 163 |