Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C22×#14579689 | C2 | semidirect |
| 4. #23781938 | C2 | direct (N × H) |
| 5. C2×#19104670 | C2 | semidirect |
| 6. C2×#19104654 | C2 | semidirect |
| 7. C2×#19104653 | C2 | semidirect |
| 16. C2×#14579689 | C22 | semidirect |
| 25. #19104670 | C22 | semidirect |
| 26. #19104654 | C22 | semidirect |
| 27. #19104653 | C22 | semidirect |
| 131. C2×C163 | #473 | semidirect |
| 133. C163 | C2×#473 | semidirect |
| 265. C2 | #23781938 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104765 | 2 |
| C22×#14579689 | 2 |
| C2×#19104742 | 2 |
| #23781938 | 2 |
| C2×#19104670 | 2 |
| C2×#19104654 | 2 |
| C2×#19104653 | 2 |
| C2×#137×C163 | 2 |
| C2×#473 | 163 |