Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
266 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23781646 | C2 | semidirect |
| 3. #23781637 | C2 | semidirect |
| 4. #23781453 | C2 | semidirect |
| 5. #23781452 | C2 | semidirect |
| 6. #23781451 | C2 | semidirect |
| 7. AΣL(1,𝔽16)×C163 | C2 | semidirect |
| 9. C22×C22⋊D163 | C4 | semidirect |
| 15. #19104705 | C4 | semidirect |
| 16. #19104704 | C4 | semidirect |
| 19. #19104691 | C4 | semidirect |
| 129. C163 | #2122 | semidirect |
| 137. AΣL(1,𝔽16) | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782230 | 2 |
| #23781646 | 2 |
| #23781637 | 2 |
| #23781453 | 2 |
| #23781452 | 2 |
| #23781451 | 2 |
| AΣL(1,𝔽16)×C163 | 2 |
| #2122 | 163 |