Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
426 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782335 | C2 | semidirect |
| 2. D4×Dic326 | C2 | semidirect |
| 3. #23782011 | C2 | semidirect |
| 4. #23782010 | C2 | semidirect |
| 5. #23781946 | C2 | semidirect |
| 6. #23781943 | C2 | semidirect |
| 7. #23781858 | C2 | semidirect |
| 8. #23781789 | C2 | semidirect |
| 9. D8×Dic163 | C2 | semidirect |
| 10. C4×#14579684 | C2 | semidirect |
| 11. #459×C163 | C2 | semidirect |
| 78. Dic326 | D8 | semidirect |
| 99. D4×C163 | #41 | semidirect |
| 131. C163 | #3358 | semidirect |
| 140. #459 | D163 | semidirect |
| 222. D4 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782335 | 2 |
| D4×Dic326 | 2 |
| #23782011 | 2 |
| #23782010 | 2 |
| #23781946 | 2 |
| #23781943 | 2 |
| #23781858 | 2 |
| #23781789 | 2 |
| D8×Dic163 | 2 |
| C4×#14579684 | 2 |
| #459×C163 | 2 |
| #3358 | 163 |