Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23781435 | C2 | semidirect |
| 6. #23781421 | C2 | semidirect |
| 7. #519×C163 | C2 | semidirect |
| 11. C2×#14579689 | C4 | semidirect |
| 12. C2×#14579686 | C4 | semidirect |
| 109. C163 | #1905 | semidirect |
| 112. #519 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104766 | 2 |
| #23781683 | 2 |
| #23781674 | 2 |
| #23781638 | 2 |
| #23781435 | 2 |
| #23781421 | 2 |
| #519×C163 | 2 |
| #1905 | 163 |