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×#19104754 | C2 | semidirect |
| 2. C2×#19104743 | C2 | semidirect |
| 3. #23782244 | C2 | semidirect |
| 4. #23781924 | C2 | semidirect |
| 5. #23781923 | C2 | semidirect |
| 6. #23781915 | C2 | semidirect |
| 7. #23781893 | C2 | semidirect |
| 8. #23781892 | C2 | semidirect |
| 9. #106×D163 | C2 | semidirect |
| 10. #23781663 | C2 | semidirect |
| 11. #469×C163 | C2 | semidirect |
| 64. C8×D163 | D4 | semidirect |
| 139. C163 | #3060 | semidirect |
| 147. #469 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104754 | 2 |
| C2×#19104743 | 2 |
| #23782244 | 2 |
| #23781924 | 2 |
| #23781923 | 2 |
| #23781915 | 2 |
| #23781893 | 2 |
| #23781892 | 2 |
| #106×D163 | 2 |
| #23781663 | 2 |
| #469×C163 | 2 |
| #3060 | 163 |