Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782320 | C2 | semidirect |
| 2. #23782017 | C2 | semidirect |
| 3. #23782006 | C2 | semidirect |
| 4. #23781952 | C2 | semidirect |
| 5. #23781892 | C2 | semidirect |
| 6. #23781870 | C2 | semidirect |
| 7. #23781808 | C2 | semidirect |
| 8. C4×#14579684 | C2 | semidirect |
| 9. D4×C163⋊C8 | C2 | semidirect |
| 10. #23781659 | C2 | semidirect |
| 11. #555×C163 | C2 | semidirect |
| 130. C163 | #3303 | semidirect |
| 132. #555 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782320 | 2 |
| #23782017 | 2 |
| #23782006 | 2 |
| #23781952 | 2 |
| #23781892 | 2 |
| #23781870 | 2 |
| #23781808 | 2 |
| C4×#14579684 | 2 |
| D4×C163⋊C8 | 2 |
| #23781659 | 2 |
| #555×C163 | 2 |
| #3303 | 163 |