Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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. #23782409 | C2 | semidirect |
| 2. #23782052 | C2 | semidirect |
| 3. #23782029 | C2 | semidirect |
| 4. #23781406 | C2 | semidirect |
| 5. #23781405 | C2 | semidirect |
| 6. #23781404 | C2 | semidirect |
| 7. #496×C163 | C2 | semidirect |
| 107. C163 | #1656 | semidirect |
| 111. #496 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782409 | 2 |
| #23782052 | 2 |
| #23782029 | 2 |
| #23781406 | 2 |
| #23781405 | 2 |
| #23781404 | 2 |
| #496×C163 | 2 |
| #1656 | 163 |