Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
322 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23781975 | C2 | semidirect |
| 3. #23781970 | C2 | semidirect |
| 6. #23781874 | C2 | semidirect |
| 7. #23781873 | C2 | semidirect |
| 97. C163 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782275 | 2 |
| #23781975 | 2 |
| #23781970 | 2 |
| #23781923 | 2 |
| #23781904 | 2 |
| #23781874 | 2 |
| #23781873 | 2 |
| #23781693 | 2 |
| #470×C163 | 2 |
| #3261 | 163 |