Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. C2×#19104768 | C2 | semidirect |
| 3. C2×#19104765 | C2 | semidirect |
| 4. #23782241 | C2 | semidirect |
| 5. #23781849 | C2 | semidirect |
| 6. #23781844 | C2 | semidirect |
| 7. #23781683 | C2 | semidirect |
| 8. #23781647 | C2 | semidirect |
| 9. #421×C163 | C2 | semidirect |
| 22. C22×Dic326 | C22 | semidirect |
| 24. #19104768 | C22 | semidirect |
| 26. #19104765 | C22 | semidirect |
| 31. C2×#14579683 | C22 | semidirect |
| 32. #19104735 | C22 | semidirect |
| 33. #19104723 | C22 | semidirect |
| 36. #19104663 | C22 | semidirect |
| 37. #19104653 | C22 | semidirect |
| 38. #19104651 | C22 | semidirect |
| 40. C2×M16×C163 | C22 | semidirect |
| 41. #117×C163 | C22 | semidirect |
| 42. #104×C163 | C22 | semidirect |
| 192. C163 | #3022 | semidirect |
| 201. #421 | D163 | semidirect |
| 226. C2×M16 | C2×D163 | semidirect |
| 231. #117 | C2×D163 | semidirect |
| 233. #104 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| C2×#19104768 | 2 |
| C2×#19104765 | 2 |
| #23782241 | 2 |
| #23781849 | 2 |
| #23781844 | 2 |
| #23781683 | 2 |
| #23781647 | 2 |
| #421×C163 | 2 |
| #3022 | 163 |