Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
220 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 1. #23782100 | C2 | semidirect |
| 2. C2×#19104676 | C2 | semidirect |
| 3. #23781935 | C2 | semidirect |
| 4. #23781478 | C2 | semidirect |
| 5. #23781472 | C2 | semidirect |
| 6. #23781449 | C2 | semidirect |
| 7. #576×C163 | C2 | semidirect |
| 9. C2×D1304 | C22 | semidirect |
| 13. #19104675 | C22 | semidirect |
| 14. C2×C163⋊C16 | C22 | semidirect |
| 15. #19104671 | C22 | semidirect |
| 93. C163 | #2192 | semidirect |
| 95. #576 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782100 | 2 |
| C2×#19104676 | 2 |
| #23781935 | 2 |
| #23781478 | 2 |
| #23781472 | 2 |
| #23781449 | 2 |
| #576×C163 | 2 |
| #2192 | 163 |