Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
312 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 3. #23781674 | C2 | semidirect |
| 5. #23781422 | C2 | semidirect |
| 6. #23781421 | C2 | semidirect |
| 7. #419×C163 | C2 | semidirect |
| 13. #19104733 | C4 | semidirect |
| 14. #19104724 | C4 | semidirect |
| 109. C163 | #1909 | semidirect |
| 114. #419 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782431 | 2 |
| #23782239 | 2 |
| #23781674 | 2 |
| #23781638 | 2 |
| #23781422 | 2 |
| #23781421 | 2 |
| #419×C163 | 2 |
| #1909 | 163 |