Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
232 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23781993 | C2 | semidirect |
| 2. #23781976 | C2 | semidirect |
| 3. #23781590 | C2 | semidirect |
| 4. #23781402 | C2 | semidirect |
| 5. #23781399 | C2 | semidirect |
| 6. #23781389 | C2 | semidirect |
| 113. C163 | #1612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781993 | 2 |
| #23781976 | 2 |
| #23781590 | 2 |
| #23781402 | 2 |
| #23781399 | 2 |
| #23781389 | 2 |
| #538×C163 | 2 |
| #1612 | 163 |