Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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. C2×Q8×Dic163 | C2 | semidirect |
| 3. #23781998 | C2 | semidirect |
| 5. #23781970 | C2 | semidirect |
| 6. #23781889 | C2 | semidirect |
| 8. #23781772 | C2 | semidirect |
| 9. #23781768 | C2 | semidirect |
| 10. #23781719 | C2 | semidirect |
| 11. #451×C163 | C2 | semidirect |
| 131. C163 | #3117 | semidirect |
| 139. #451 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782201 | 2 |
| C2×Q8×Dic163 | 2 |
| #23781998 | 2 |
| #23781984 | 2 |
| #23781970 | 2 |
| #23781889 | 2 |
| #23781804 | 2 |
| #23781772 | 2 |
| #23781768 | 2 |
| #23781719 | 2 |
| #451×C163 | 2 |
| #3117 | 163 |