Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
346 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 346 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 |
|---|---|---|
| 1. #23782286 | C2 | semidirect |
| 2. #23781961 | C2 | semidirect |
| 3. #23781946 | C2 | semidirect |
| 4. #23781911 | C2 | semidirect |
| 5. #23781906 | C2 | semidirect |
| 7. #23781888 | C2 | semidirect |
| 8. #23781881 | C2 | semidirect |
| 9. #424×C163 | C2 | semidirect |
| 105. C163 | #3262 | semidirect |
| 115. #424 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782286 | 2 |
| #23781961 | 2 |
| #23781946 | 2 |
| #23781911 | 2 |
| #23781906 | 2 |
| #23781901 | 2 |
| #23781888 | 2 |
| #23781881 | 2 |
| #424×C163 | 2 |
| #3262 | 163 |