Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 370 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. #23782270 | C2 | semidirect |
| 2. #23781966 | C2 | semidirect |
| 3. #23781918 | C2 | semidirect |
| 4. #23781901 | C2 | semidirect |
| 5. #23781861 | C2 | semidirect |
| 6. #424×C163 | C2 | semidirect |
| 71. C163 | #3259 | semidirect |
| 78. #424 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782270 | 2 |
| #23781966 | 2 |
| #23781918 | 2 |
| #23781901 | 2 |
| #23781861 | 2 |
| #424×C163 | 2 |
| #3259 | 163 |