Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 2. #23782003 | C2 | semidirect |
| 3. #23781957 | C2 | semidirect |
| 4. #23781952 | C2 | semidirect |
| 5. #23781872 | C2 | semidirect |
| 6. #23781867 | C2 | semidirect |
| 8. #23781770 | C2 | semidirect |
| 9. #23781763 | C2 | semidirect |
| 10. #23781722 | C2 | semidirect |
| 11. #533×C163 | C2 | semidirect |
| 136. C163 | #3116 | semidirect |
| 138. #533 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579699 | 2 |
| #23782003 | 2 |
| #23781957 | 2 |
| #23781952 | 2 |
| #23781872 | 2 |
| #23781867 | 2 |
| #23781825 | 2 |
| #23781770 | 2 |
| #23781763 | 2 |
| #23781722 | 2 |
| #533×C163 | 2 |
| #3116 | 163 |