Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782390 | C2 | semidirect |
| 4. #23781970 | C2 | semidirect |
| 7. #23781872 | C2 | semidirect |
| 8. C8×Dic326 | C2 | semidirect |
| 9. #23781757 | C2 | semidirect |
| 11. #487×C163 | C2 | semidirect |
| 115. C163 | #3364 | semidirect |
| 120. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782390 | 2 |
| #23782389 | 2 |
| #23782021 | 2 |
| #23781970 | 2 |
| #23781942 | 2 |
| #23781890 | 2 |
| #23781872 | 2 |
| C8×Dic326 | 2 |
| #23781757 | 2 |
| C4×#14579688 | 2 |
| #487×C163 | 2 |
| #3364 | 163 |