Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
612 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19104649 | C2 | semidirect |
| 3. #23781528 | C2 | semidirect |
| 4. #381×C163 | C2 | semidirect |
| 8. C22×Dic326 | C4 | semidirect |
| 9. C22×D652 | C4 | semidirect |
| 11. C22×C4×D163 | C4 | semidirect |
| 93. C163 | #1782 | semidirect |
| 98. #381 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C2×#19104649 | 2 |
| #23781528 | 2 |
| #381×C163 | 2 |
| #1782 | 163 |