Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23782216 | C2 | semidirect |
| 2. C4×#14579698 | C2 | semidirect |
| 3. #23781992 | C2 | semidirect |
| 4. #23781947 | C2 | semidirect |
| 5. #23781866 | C2 | semidirect |
| 6. #23781860 | C2 | semidirect |
| 7. #23781811 | C2 | semidirect |
| 8. #23781774 | C2 | semidirect |
| 9. #23781764 | C2 | semidirect |
| 10. #23781721 | C2 | semidirect |
| 11. #474×C163 | C2 | semidirect |
| 86. Dic326 | #41 | semidirect |
| 109. D4×C163 | #41 | semidirect |
| 144. C163 | #3115 | semidirect |
| 150. #474 | D163 | semidirect |
| 241. D4 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782216 | 2 |
| C4×#14579698 | 2 |
| #23781992 | 2 |
| #23781947 | 2 |
| #23781866 | 2 |
| #23781860 | 2 |
| #23781811 | 2 |
| #23781774 | 2 |
| #23781764 | 2 |
| #23781721 | 2 |
| #474×C163 | 2 |
| #3115 | 163 |