Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
322 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23781972 | C2 | semidirect |
| 3. #23781969 | C2 | semidirect |
| 6. #23781875 | C2 | semidirect |
| 7. #23781872 | C2 | semidirect |
| 94. C163 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782277 | 2 |
| #23781972 | 2 |
| #23781969 | 2 |
| #23781921 | 2 |
| #23781904 | 2 |
| #23781875 | 2 |
| #23781872 | 2 |
| #23781692 | 2 |
| #541×C163 | 2 |
| #3261 | 163 |