Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#14579689 | C2 | semidirect |
| 4. #23781921 | C2 | direct (N × H) |
| 5. C2×#19104666 | C2 | semidirect |
| 6. C2×#19104659 | C2 | semidirect |
| 7. C2×#19104658 | C2 | semidirect |
| 11. C2×#14579689 | C22 | semidirect |
| 21. #19104666 | C22 | semidirect |
| 22. #19104659 | C22 | semidirect |
| 23. #19104658 | C22 | semidirect |
| 111. C2×C163 | #470 | semidirect |
| 115. C163 | C2×#470 | semidirect |
| 227. C2 | #23781921 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579689 | 2 |
| C22×#14579683 | 2 |
| C2×#19104714 | 2 |
| #23781921 | 2 |
| C2×#19104666 | 2 |
| C2×#19104659 | 2 |
| C2×#19104658 | 2 |
| C2×C22⋊Q8×C163 | 2 |
| C2×#470 | 163 |