Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
716 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 2. #23782239 | C2 | semidirect |
| 3. #23781854 | C2 | semidirect |
| 4. #23781639 | C2 | semidirect |
| 5. #23781638 | C2 | semidirect |
| 6. #536×C163 | C2 | semidirect |
| 17. #19104718 | C22 | semidirect |
| 19. #19104694 | C22 | semidirect |
| 20. #19104650 | C22 | semidirect |
| 21. #19104649 | C22 | semidirect |
| 23. C22×Q8×C163 | C22 | semidirect |
| 26. #123×C163 | C22 | semidirect |
| 28. #117×C163 | C22 | semidirect |
| 128. C163 | #3028 | semidirect |
| 132. #536 | D163 | semidirect |
| 145. C22×Q8 | C2×D163 | semidirect |
| 151. #123 | C2×D163 | semidirect |
| 155. #117 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| #23782239 | 2 |
| #23781854 | 2 |
| #23781639 | 2 |
| #23781638 | 2 |
| #536×C163 | 2 |
| #3028 | 163 |