Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 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×Q16×D163 | C2 | semidirect |
| 4. #23781922 | C2 | semidirect |
| 5. #23781921 | C2 | semidirect |
| 6. #23781907 | C2 | semidirect |
| 7. #23781906 | C2 | semidirect |
| 8. #23781903 | C2 | semidirect |
| 9. #23781702 | C2 | semidirect |
| 10. #23781672 | C2 | semidirect |
| 11. #467×C163 | C2 | semidirect |
| 137. C163 | #3059 | semidirect |
| 147. #467 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D163 | 2 |
| C2×#19104741 | 2 |
| #23782238 | 2 |
| #23781922 | 2 |
| #23781921 | 2 |
| #23781907 | 2 |
| #23781906 | 2 |
| #23781903 | 2 |
| #23781702 | 2 |
| #23781672 | 2 |
| #467×C163 | 2 |
| #3059 | 163 |