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×#19104741 | C2 | semidirect |
| 3. #23782245 | C2 | semidirect |
| 4. #23781914 | C2 | semidirect |
| 5. #23781913 | C2 | semidirect |
| 6. #23781903 | C2 | semidirect |
| 7. #23781902 | C2 | semidirect |
| 8. #23781901 | C2 | semidirect |
| 9. #107×D163 | C2 | semidirect |
| 10. #23781665 | C2 | semidirect |
| 11. #467×C163 | C2 | semidirect |
| 65. C8×D163 | D4 | semidirect |
| 143. C163 | #3061 | semidirect |
| 151. #467 | 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×#19104741 | 2 |
| #23782245 | 2 |
| #23781914 | 2 |
| #23781913 | 2 |
| #23781903 | 2 |
| #23781902 | 2 |
| #23781901 | 2 |
| #107×D163 | 2 |
| #23781665 | 2 |
| #467×C163 | 2 |
| #3061 | 163 |