Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23782293 | C2 | semidirect |
| 3. #23781973 | C2 | semidirect |
| 4. #23781966 | C2 | semidirect |
| 5. #23781956 | C2 | semidirect |
| 6. #23781951 | C2 | semidirect |
| 7. #23781707 | C2 | semidirect |
| 8. C2×#19104667 | C2 | semidirect |
| 11. #424×C163 | C2 | semidirect |
| 42. #14579699 | Q8 | semidirect |
| 123. C163 | #3084 | semidirect |
| 133. #424 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782293 | 2 |
| #23782145 | 2 |
| #23781973 | 2 |
| #23781966 | 2 |
| #23781956 | 2 |
| #23781951 | 2 |
| #23781707 | 2 |
| C2×#19104667 | 2 |
| #23781667 | 2 |
| #23781662 | 2 |
| #424×C163 | 2 |
| #3084 | 163 |