Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782380 | C2 | semidirect |
| 2. #23782319 | C2 | semidirect |
| 3. #23782016 | C2 | semidirect |
| 4. #23782008 | C2 | semidirect |
| 5. #23781955 | C2 | semidirect |
| 6. #23781893 | C2 | semidirect |
| 7. #23781870 | C2 | semidirect |
| 8. #23781807 | C2 | semidirect |
| 9. C8×D652 | C2 | semidirect |
| 10. #23781658 | C2 | semidirect |
| 11. C4×D8×C163 | C2 | semidirect |
| 130. C163 | #3303 | semidirect |
| 140. C4×D8 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782380 | 2 |
| #23782319 | 2 |
| #23782016 | 2 |
| #23782008 | 2 |
| #23781955 | 2 |
| #23781893 | 2 |
| #23781870 | 2 |
| #23781807 | 2 |
| C8×D652 | 2 |
| #23781658 | 2 |
| C4×D8×C163 | 2 |
| #3303 | 163 |