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. #23782336 | C2 | semidirect |
| 2. D4×Dic326 | C2 | semidirect |
| 3. #23782012 | C2 | semidirect |
| 4. #23782010 | C2 | semidirect |
| 5. #23781945 | C2 | semidirect |
| 6. #23781944 | C2 | semidirect |
| 7. #23781860 | C2 | semidirect |
| 8. #23781858 | C2 | semidirect |
| 9. C8×Dic326 | C2 | semidirect |
| 10. #23781745 | C2 | semidirect |
| 11. C4×D8×C163 | C2 | semidirect |
| 78. Dic326 | D8 | semidirect |
| 96. D4×C163 | #41 | semidirect |
| 131. C163 | #3358 | semidirect |
| 143. C4×D8 | D163 | semidirect |
| 222. D4 | #14579699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782336 | 2 |
| D4×Dic326 | 2 |
| #23782012 | 2 |
| #23782010 | 2 |
| #23781945 | 2 |
| #23781944 | 2 |
| #23781860 | 2 |
| #23781858 | 2 |
| C8×Dic326 | 2 |
| #23781745 | 2 |
| C4×D8×C163 | 2 |
| #3358 | 163 |