Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
418 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782401 | C2 | semidirect |
| 2. #23782336 | C2 | semidirect |
| 3. #23782053 | C2 | semidirect |
| 4. #23782041 | C2 | semidirect |
| 5. #23781879 | C2 | semidirect |
| 6. #23781866 | C2 | semidirect |
| 7. #23781858 | C2 | semidirect |
| 8. #23781792 | C2 | semidirect |
| 9. #23781774 | C2 | semidirect |
| 10. C4×#14579687 | C2 | semidirect |
| 11. #459×C163 | C2 | semidirect |
| 94. C163⋊C8 | #41 | semidirect |
| 134. C163 | #3399 | semidirect |
| 143. #459 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782401 | 2 |
| #23782336 | 2 |
| #23782053 | 2 |
| #23782041 | 2 |
| #23781879 | 2 |
| #23781866 | 2 |
| #23781858 | 2 |
| #23781792 | 2 |
| #23781774 | 2 |
| C4×#14579687 | 2 |
| #459×C163 | 2 |
| #3399 | 163 |