Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
484 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×#19104758 | C2 | semidirect |
| 2. C2×#19104743 | C2 | semidirect |
| 3. #23782245 | C2 | semidirect |
| 4. #23781920 | C2 | semidirect |
| 5. #23781919 | C2 | semidirect |
| 6. #23781918 | C2 | semidirect |
| 7. #23781897 | C2 | semidirect |
| 8. #23781896 | C2 | semidirect |
| 9. #106×D163 | C2 | semidirect |
| 10. #23781665 | C2 | semidirect |
| 11. #470×C163 | C2 | semidirect |
| 65. C8×D163 | D4 | semidirect |
| 139. C163 | #3060 | semidirect |
| 145. #470 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104758 | 2 |
| C2×#19104743 | 2 |
| #23782245 | 2 |
| #23781920 | 2 |
| #23781919 | 2 |
| #23781918 | 2 |
| #23781897 | 2 |
| #23781896 | 2 |
| #106×D163 | 2 |
| #23781665 | 2 |
| #470×C163 | 2 |
| #3060 | 163 |