Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
272 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23781815 | C2 | semidirect |
| 3. #23781582 | C2 | semidirect |
| 4. #23781402 | C2 | semidirect |
| 5. #23781399 | C2 | semidirect |
| 6. #23781391 | C2 | semidirect |
| 7. #539×C163 | C2 | semidirect |
| 123. C163 | #1597 | semidirect |
| 125. #539 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781815 | 2 |
| #23781798 | 2 |
| #23781582 | 2 |
| #23781402 | 2 |
| #23781399 | 2 |
| #23781391 | 2 |
| #539×C163 | 2 |
| #1597 | 163 |