Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782380 | C2 | semidirect |
| 2. #23782320 | C2 | semidirect |
| 3. #23782016 | C2 | semidirect |
| 4. #23782007 | C2 | semidirect |
| 5. #23781956 | C2 | semidirect |
| 6. #23781894 | C2 | semidirect |
| 7. #23781871 | C2 | semidirect |
| 8. #23781812 | C2 | semidirect |
| 9. C4×D1304 | C2 | semidirect |
| 10. #23781662 | C2 | semidirect |
| 11. C8×D4×C163 | C2 | semidirect |
| 130. C163 | #3303 | semidirect |
| 141. C8×D4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782380 | 2 |
| #23782320 | 2 |
| #23782016 | 2 |
| #23782007 | 2 |
| #23781956 | 2 |
| #23781894 | 2 |
| #23781871 | 2 |
| #23781812 | 2 |
| C4×D1304 | 2 |
| #23781662 | 2 |
| C8×D4×C163 | 2 |
| #3303 | 163 |