Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
172 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 16. #19104645 | C4 | semidirect |
| 17. C8×Dic163 | C4 | semidirect |
| 78. C163 | #1833 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104670 | 2 |
| #23781701 | 2 |
| #23781623 | 2 |
| #23781436 | 2 |
| #23781422 | 2 |
| #23781421 | 2 |
| #344×C163 | 2 |
| #1833 | 163 |