Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 238 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 |
|---|---|---|
| 2. #23781460 | C2 | semidirect |
| 8. C22×Q8×C163 | C4 | semidirect |
| 9. C4⋊Q8×C163 | C4 | semidirect |
| 13. #117×C163 | C4 | semidirect |
| 64. C163 | #2129 | semidirect |
| 70. C22×Q8 | Dic163 | semidirect |
| 71. C4⋊Q8 | Dic163 | semidirect |
| 76. #117 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781639 | 2 |
| #23781460 | 2 |
| #536×C163 | 2 |
| #2129 | 163 |