Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 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. #23782389 | C2 | semidirect |
| 2. #23782330 | C2 | semidirect |
| 3. #23782026 | C2 | semidirect |
| 4. #23781958 | C2 | semidirect |
| 5. #23781942 | C2 | semidirect |
| 7. #23781867 | C2 | semidirect |
| 8. #23781795 | C2 | semidirect |
| 9. #23781768 | C2 | semidirect |
| 11. #487×C163 | C2 | semidirect |
| 122. C163 | #3367 | semidirect |
| 127. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782389 | 2 |
| #23782330 | 2 |
| #23782026 | 2 |
| #23781958 | 2 |
| #23781942 | 2 |
| #23781883 | 2 |
| #23781867 | 2 |
| #23781795 | 2 |
| #23781768 | 2 |
| C4×D1304 | 2 |
| #487×C163 | 2 |
| #3367 | 163 |