Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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. #23782431 | C2 | semidirect |
| 3. #23781682 | C2 | semidirect |
| 4. #23781638 | C2 | semidirect |
| 5. #23781426 | C2 | semidirect |
| 6. #23781424 | C2 | semidirect |
| 7. #421×C163 | C2 | semidirect |
| 13. #19104733 | C4 | semidirect |
| 14. #19104731 | C4 | semidirect |
| 15. #19104724 | C4 | semidirect |
| 16. #19104722 | C4 | semidirect |
| 38. #14579683 | D4 | semidirect |
| 61. M16×C163 | D4 | semidirect |
| 125. C163 | #1884 | semidirect |
| 130. #421 | D163 | semidirect |
| 176. M16 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782431 | 2 |
| #23782211 | 2 |
| #23781682 | 2 |
| #23781638 | 2 |
| #23781426 | 2 |
| #23781424 | 2 |
| #421×C163 | 2 |
| #1884 | 163 |