Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23782291 | C2 | semidirect |
| 5. #23781432 | C2 | semidirect |
| 6. #23781431 | C2 | semidirect |
| 7. #342×C163 | C2 | semidirect |
| 21. C23×D163 | Q8 | semidirect |
| 32. C22×Dic163 | Q8 | semidirect |
| 117. C163 | #2032 | semidirect |
| 125. #342 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782291 | 2 |
| C2×#19104649 | 2 |
| #23781432 | 2 |
| #23781431 | 2 |
| #342×C163 | 2 |
| #2032 | 163 |