Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
326 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 87 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×#19104734 | C2 | semidirect |
| 5. #23781427 | C2 | semidirect |
| 6. #23781419 | C2 | semidirect |
| 7. #340×C163 | C2 | semidirect |
| 32. C2×D652 | Q8 | semidirect |
| 123. C163 | #2023 | semidirect |
| 130. #340 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104734 | 2 |
| C2×#19104657 | 2 |
| C2×#19104655 | 2 |
| #23781566 | 2 |
| #23781427 | 2 |
| #23781419 | 2 |
| #340×C163 | 2 |
| #2023 | 163 |