Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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×#19104760 | C2 | semidirect |
| 2. C22×D1304 | C2 | semidirect |
| 3. #23781935 | C2 | direct (N × H) |
| 4. C2×#19104671 | C2 | semidirect |
| 5. C2×#19104651 | C2 | semidirect |
| 6. C2×#131×C163 | C2 | semidirect |
| 9. #19104760 | C22 | semidirect |
| 14. C2×D1304 | C22 | semidirect |
| 17. #19104671 | C22 | semidirect |
| 18. #19104651 | C22 | semidirect |
| 21. #131×C163 | C22 | semidirect |
| 105. C2×C163 | #472 | semidirect |
| 108. C163 | C2×#472 | semidirect |
| 112. C2×#131 | D163 | semidirect |
| 127. #131 | C2×D163 | semidirect |
| 215. C2 | #23781935 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| C22×D1304 | 2 |
| #23781935 | 2 |
| C2×#19104671 | 2 |
| C2×#19104651 | 2 |
| C2×#131×C163 | 2 |
| C2×#472 | 163 |