Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
266 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23781649 | C2 | semidirect |
| 2. #23781639 | C2 | semidirect |
| 3. #23781452 | C2 | semidirect |
| 12. C22×D4×C163 | C4 | semidirect |
| 17. #120×C163 | C4 | semidirect |
| 19. #117×C163 | C4 | semidirect |
| 99. C163 | #2122 | semidirect |
| 106. C22×D4 | Dic163 | semidirect |
| 112. #120 | Dic163 | semidirect |
| 115. #117 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781649 | 2 |
| #23781639 | 2 |
| #23781452 | 2 |
| #535×C163 | 2 |
| #2122 | 163 |