Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
112 conjugacy classes of subgroups; only the 23 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 23 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. #23781405 | C2 | semidirect |
| 3. #354×C163 | C2 | semidirect |
| 4. #19104783 | C4 | semidirect |
| 7. #19104654 | C4 | semidirect |
| 53. C163 | #1404 | semidirect |
| 56. #354 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781837 | 2 |
| #23781405 | 2 |
| #354×C163 | 2 |
| #1404 | 163 |