Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 244 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. #23782222 | C2 | semidirect |
| 5. #23781436 | C2 | semidirect |
| 6. #23781421 | C2 | semidirect |
| 7. #339×C163 | C2 | semidirect |
| 28. C2×Dic326 | Q8 | semidirect |
| 29. C2×D652 | Q8 | semidirect |
| 101. C163 | #2031 | semidirect |
| 108. #339 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| #23781681 | 2 |
| C2×#19104663 | 2 |
| #23781638 | 2 |
| #23781436 | 2 |
| #23781421 | 2 |
| #339×C163 | 2 |
| #2031 | 163 |