Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
222 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 35 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. #23781432 | C2 | semidirect |
| 3. #323×C163 | C2 | semidirect |
| 4. C22×D652 | C4 | semidirect |
| 8. C163⋊#95 | C4 | semidirect |
| 88. C163 | #1343 | semidirect |
| 92. #323 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781574 | 2 |
| #23781432 | 2 |
| #323×C163 | 2 |
| #1343 | 163 |