Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 4. #23781526 | C2 | semidirect |
| 5. #23781526 | C2 | semidirect |
| 6. #23781431 | C2 | semidirect |
| 7. #342×C163 | C2 | semidirect |
| 11. #19104719 | C4 | semidirect |
| 40. C22×Dic163 | C2×C4 | semidirect |
| 62. C22⋊C4×C163 | C2×C4 | semidirect |
| 134. C163 | #1890 | semidirect |
| 142. #342 | D163 | semidirect |
| 196. C22⋊C4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104719 | 2 |
| #23782138 | 2 |
| C2×#19104649 | 2 |
| #23781526 | 2 |
| #23781431 | 2 |
| #342×C163 | 2 |
| #1890 | 163 |