Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
272 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 13. #19104668 | C4 | semidirect |
| 14. #19104666 | C4 | semidirect |
| 15. #19104646 | C4 | semidirect |
| 54. C163⋊C8 | C42 | semidirect |
| 98. C163 | #1776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104668 | 2 |
| C2×#19104666 | 2 |
| C2×#19104646 | 2 |
| C4×C4⋊Dic163 | 2 |
| #23781427 | 2 |
| C4×C4⋊C4×C163 | 2 |
| #1776 | 163 |