Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 258 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. #23782346 | C2 | semidirect |
| 2. #23781855 | C2 | semidirect |
| 3. #23781843 | C2 | semidirect |
| 4. #23781459 | C2 | semidirect |
| 5. #23781454 | C2 | semidirect |
| 6. #23781452 | C2 | semidirect |
| 27. C2×Dic326 | D4 | semidirect |
| 30. C22×Dic163 | D4 | semidirect |
| 46. C22⋊Dic163 | D4 | semidirect |
| 48. C4×Dic163 | D4 | semidirect |
| 121. C163 | #2197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782346 | 2 |
| #23781855 | 2 |
| #23781843 | 2 |
| #23781459 | 2 |
| #23781454 | 2 |
| #23781452 | 2 |
| B(4,𝔽2)×C163 | 2 |
| #2197 | 163 |