Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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×#19104766 | C2 | semidirect |
| 2. C2×M16×D163 | C2 | semidirect |
| 4. C2×#19104711 | C2 | semidirect |
| 5. #23781922 | C2 | semidirect |
| 6. #23781914 | C2 | semidirect |
| 7. #23781905 | C2 | semidirect |
| 8. #23781897 | C2 | semidirect |
| 9. #23781708 | C2 | semidirect |
| 10. #23781667 | C2 | semidirect |
| 11. #419×C163 | C2 | semidirect |
| 15. C2×#14579689 | C22 | semidirect |
| 16. C2×#14579686 | C22 | semidirect |
| 36. #19104668 | C22 | semidirect |
| 37. #19104666 | C22 | semidirect |
| 38. #19104660 | C22 | semidirect |
| 39. #19104657 | C22 | semidirect |
| 43. #103×C163 | C22 | semidirect |
| 44. #103×C163 | C22 | semidirect |
| 64. #14579683 | D4 | semidirect |
| 145. C2×D163 | #137 | semidirect |
| 163. C163 | #3056 | semidirect |
| 174. #419 | D163 | semidirect |
| 206. #103 | C2×D163 | semidirect |
| 207. #103 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| C2×M16×D163 | 2 |
| #23782177 | 2 |
| C2×#19104711 | 2 |
| #23781922 | 2 |
| #23781914 | 2 |
| #23781905 | 2 |
| #23781897 | 2 |
| #23781708 | 2 |
| #23781667 | 2 |
| #419×C163 | 2 |
| #3056 | 163 |