Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
356 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23782384 | C2 | semidirect |
| 2. #23782056 | C2 | semidirect |
| 3. #23781884 | C2 | semidirect |
| 5. #23781873 | C2 | semidirect |
| 6. #23781795 | C2 | semidirect |
| 7. #23781766 | C2 | semidirect |
| 8. C4×Dic652 | C2 | semidirect |
| 102. C163 | #3402 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782384 | 2 |
| #23782056 | 2 |
| #23781884 | 2 |
| #23781878 | 2 |
| #23781873 | 2 |
| #23781795 | 2 |
| #23781766 | 2 |
| C4×Dic652 | 2 |
| #495×C163 | 2 |
| #3402 | 163 |