Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23781989 | C2 | semidirect |
| 3. #23781972 | C2 | semidirect |
| 4. #23781865 | C2 | semidirect |
| 5. #23781804 | C2 | semidirect |
| 6. #23781763 | C2 | semidirect |
| 7. C4×#14579686 | C2 | semidirect |
| 8. #23781726 | C2 | semidirect |
| 9. #519×C163 | C2 | semidirect |
| 101. C163 | #3126 | semidirect |
| 104. #519 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782270 | 2 |
| #23781989 | 2 |
| #23781972 | 2 |
| #23781865 | 2 |
| #23781804 | 2 |
| #23781763 | 2 |
| C4×#14579686 | 2 |
| #23781726 | 2 |
| #519×C163 | 2 |
| #3126 | 163 |