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. #23782461 | C2 | semidirect |
| 2. C2×#19104754 | C2 | semidirect |
| 3. #131×D163 | C2 | semidirect |
| 4. #23781941 | C2 | semidirect |
| 5. #23781940 | C2 | semidirect |
| 6. #23781932 | C2 | semidirect |
| 7. #23781927 | C2 | semidirect |
| 8. #23781926 | C2 | semidirect |
| 9. #108×D163 | C2 | semidirect |
| 10. #23781646 | C2 | semidirect |
| 11. #472×C163 | C2 | semidirect |
| 25. C2×Dic652 | C22 | semidirect |
| 26. C2×#14579687 | C22 | semidirect |
| 37. #19104671 | C22 | semidirect |
| 38. #19104670 | C22 | semidirect |
| 39. #19104653 | C22 | semidirect |
| 40. #19104653 | C22 | semidirect |
| 41. #19104652 | C22 | semidirect |
| 43. C2×D8×C163 | C22 | semidirect |
| 45. #108×C163 | C22 | semidirect |
| 46. #100×C163 | C22 | semidirect |
| 166. C163 | #3067 | semidirect |
| 174. #472 | D163 | semidirect |
| 195. C2×D8 | C2×D163 | semidirect |
| 209. #108 | C2×D163 | semidirect |
| 213. #100 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782461 | 2 |
| C2×#19104754 | 2 |
| #131×D163 | 2 |
| #23781941 | 2 |
| #23781940 | 2 |
| #23781932 | 2 |
| #23781927 | 2 |
| #23781926 | 2 |
| #108×D163 | 2 |
| #23781646 | 2 |
| #472×C163 | 2 |
| #3067 | 163 |