Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 41 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. #23782408 | C2 | semidirect |
| 2. #23781853 | C2 | semidirect |
| 3. #23781851 | C2 | semidirect |
| 4. #23781845 | C2 | semidirect |
| 5. #23781459 | C2 | semidirect |
| 6. #23781453 | C2 | semidirect |
| 7. AΣL(1,𝔽16)×C163 | C2 | semidirect |
| 27. C23×D163 | D4 | semidirect |
| 31. C2×Dic326 | D4 | semidirect |
| 48. C22⋊Dic163 | D4 | semidirect |
| 54. C4×Dic163 | D4 | semidirect |
| 55. C24×C163 | D4 | semidirect |
| 61. C22⋊C4×C163 | D4 | semidirect |
| 130. C163 | #2199 | semidirect |
| 138. AΣL(1,𝔽16) | D163 | semidirect |
| 159. C24 | D652 | semidirect |
| 190. C22⋊C4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782408 | 2 |
| #23781853 | 2 |
| #23781851 | 2 |
| #23781845 | 2 |
| #23781459 | 2 |
| #23781453 | 2 |
| AΣL(1,𝔽16)×C163 | 2 |
| #2199 | 163 |