Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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. #23782480 | C2 | semidirect |
| 2. #23782479 | C2 | semidirect |
| 3. #23782043 | C2 | semidirect |
| 4. #23781940 | C2 | semidirect |
| 5. #23781938 | C2 | semidirect |
| 6. #23781937 | C2 | semidirect |
| 7. #23781848 | C2 | semidirect |
| 8. #23781846 | C2 | semidirect |
| 9. #23781782 | C2 | semidirect |
| 10. #23781780 | C2 | semidirect |
| 11. #578×C163 | C2 | semidirect |
| 146. C163 | #3293 | semidirect |
| 150. #578 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782480 | 2 |
| #23782479 | 2 |
| #23782043 | 2 |
| #23781940 | 2 |
| #23781938 | 2 |
| #23781937 | 2 |
| #23781848 | 2 |
| #23781846 | 2 |
| #23781782 | 2 |
| #23781780 | 2 |
| #578×C163 | 2 |
| #3293 | 163 |