Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
738 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×Dic326 | C2 | semidirect |
| 2. C2×#19104765 | C2 | semidirect |
| 3. #23781820 | C2 | semidirect |
| 4. #23781803 | C2 | semidirect |
| 5. #23781673 | C2 | semidirect |
| 6. #23781629 | C2 | semidirect |
| 15. C2×#14579689 | C22 | semidirect |
| 16. C2×#14579687 | C22 | semidirect |
| 18. #19104658 | C22 | semidirect |
| 34. C2×Dic326 | D4 | semidirect |
| 95. C22×C163 | #137 | semidirect |
| 108. C163 | #3004 | semidirect |
| 204. C22 | #19104765 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic326 | 2 |
| C2×#19104765 | 2 |
| #23781820 | 2 |
| #23781803 | 2 |
| #23781673 | 2 |
| #23781629 | 2 |
| #525×C163 | 2 |
| #3004 | 163 |