Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
440 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23781629 | C2 | semidirect |
| 3. #23781388 | C2 | semidirect |
| 4. #407×C163 | C2 | semidirect |
| 15. C22⋊(C163⋊C8) | C22 | semidirect |
| 19. C22⋊C8×C163 | C22 | semidirect |
| 57. C22×D163 | M16 | semidirect |
| 110. C163 | #1462 | semidirect |
| 114. #407 | D163 | semidirect |
| 130. C22⋊C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D163)⋊C4 | 2 |
| #23781629 | 2 |
| #23781388 | 2 |
| #407×C163 | 2 |
| #1462 | 163 |