Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×D8×D163 | C2 | semidirect |
| 2. C2×#19104741 | C2 | semidirect |
| 3. #23782231 | C2 | semidirect |
| 4. #23781917 | C2 | semidirect |
| 5. #23781916 | C2 | semidirect |
| 6. #23781902 | C2 | semidirect |
| 7. #23781901 | C2 | semidirect |
| 8. #23781898 | C2 | semidirect |
| 9. #23781702 | C2 | semidirect |
| 10. #23781668 | C2 | semidirect |
| 11. #466×C163 | C2 | semidirect |
| 18. C2×#14579683 | C22 | semidirect |
| 20. C2×#14579682 | C22 | semidirect |
| 22. C2×C8×D163 | C22 | semidirect |
| 25. #19104710 | C22 | semidirect |
| 26. #19104709 | C22 | semidirect |
| 27. #19104706 | C22 | semidirect |
| 31. #19104669 | C22 | semidirect |
| 32. #19104666 | C22 | semidirect |
| 33. #19104657 | C22 | semidirect |
| 34. #19104656 | C22 | semidirect |
| 35. #19104655 | C22 | semidirect |
| 37. C22×C8×C163 | C22 | semidirect |
| 38. #121×C163 | C22 | semidirect |
| 39. #107×C163 | C22 | semidirect |
| 40. #102×C163 | C22 | semidirect |
| 65. C8×D163 | D4 | semidirect |
| 150. C163 | #3058 | semidirect |
| 160. #466 | D163 | semidirect |
| 175. C22×C8 | C2×D163 | semidirect |
| 181. #121 | C2×D163 | semidirect |
| 186. #107 | C2×D163 | semidirect |
| 191. #102 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×D163 | 2 |
| C2×#19104741 | 2 |
| #23782231 | 2 |
| #23781917 | 2 |
| #23781916 | 2 |
| #23781902 | 2 |
| #23781901 | 2 |
| #23781898 | 2 |
| #23781702 | 2 |
| #23781668 | 2 |
| #466×C163 | 2 |
| #3058 | 163 |