Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782464 | C2 | semidirect |
| 2. C2×#19104758 | C2 | semidirect |
| 3. #131×D163 | C2 | semidirect |
| 4. #23781937 | C2 | semidirect |
| 5. #23781936 | C2 | semidirect |
| 6. #23781935 | C2 | semidirect |
| 7. #23781931 | C2 | semidirect |
| 8. #23781930 | C2 | semidirect |
| 9. #108×D163 | C2 | semidirect |
| 10. #23781648 | C2 | semidirect |
| 11. #473×C163 | C2 | semidirect |
| 25. C2×#14579686 | C22 | semidirect |
| 26. C2×D1304 | C22 | semidirect |
| 37. #19104671 | C22 | semidirect |
| 38. #19104670 | C22 | semidirect |
| 39. #19104654 | C22 | semidirect |
| 40. #19104651 | C22 | semidirect |
| 41. #19104651 | C22 | semidirect |
| 43. C2×Q16×C163 | C22 | semidirect |
| 45. #108×C163 | C22 | semidirect |
| 46. #101×C163 | C22 | semidirect |
| 166. C163 | #3067 | semidirect |
| 172. #473 | D163 | semidirect |
| 193. C2×Q16 | C2×D163 | semidirect |
| 209. #108 | C2×D163 | semidirect |
| 211. #101 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782464 | 2 |
| C2×#19104758 | 2 |
| #131×D163 | 2 |
| #23781937 | 2 |
| #23781936 | 2 |
| #23781935 | 2 |
| #23781931 | 2 |
| #23781930 | 2 |
| #108×D163 | 2 |
| #23781648 | 2 |
| #473×C163 | 2 |
| #3067 | 163 |