Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
338 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 338 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. #23782395 | C2 | semidirect |
| 5. #23781948 | C2 | semidirect |
| 7. #23781872 | C2 | semidirect |
| 8. #23781795 | C2 | semidirect |
| 9. #23781769 | C2 | semidirect |
| 11. #487×C163 | C2 | semidirect |
| 116. C163 | #3369 | semidirect |
| 121. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782395 | 2 |
| #23782389 | 2 |
| #23782026 | 2 |
| #23781952 | 2 |
| #23781948 | 2 |
| #23781890 | 2 |
| #23781872 | 2 |
| #23781795 | 2 |
| #23781769 | 2 |
| C4×#14579688 | 2 |
| #487×C163 | 2 |
| #3369 | 163 |