Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
338 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 97 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×#19104653 | C2 | semidirect |
| 4. #23781433 | C2 | semidirect |
| 88. C22×C163 | #101 | semidirect |
| 104. C163 | #1901 | semidirect |
| 193. C22 | #19104653 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104714 | 2 |
| C2×#19104653 | 2 |
| #23781629 | 2 |
| #23781433 | 2 |
| C22×M16×C163 | 2 |
| #1901 | 163 |