Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
144 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23782083 | C2 | semidirect |
| 2. #23782082 | C2 | semidirect |
| 4. #23781485 | C2 | semidirect |
| 5. #23781448 | C2 | semidirect |
| 6. #23781440 | C2 | semidirect |
| 7. #350×C163 | C2 | semidirect |
| 71. C163 | #2171 | semidirect |
| 78. #350 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782083 | 2 |
| #23782082 | 2 |
| #23781780 | 2 |
| #23781485 | 2 |
| #23781448 | 2 |
| #23781440 | 2 |
| #350×C163 | 2 |
| #2171 | 163 |