Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23782335 | C2 | semidirect |
| 2. #23781862 | C2 | semidirect |
| 3. #23781857 | C2 | semidirect |
| 4. #23781409 | C2 | semidirect |
| 5. #23781397 | C2 | semidirect |
| 6. #23781394 | C2 | semidirect |
| 7. #493×C163 | C2 | semidirect |
| 54. Dic326 | D8 | semidirect |
| 107. C163 | #1621 | semidirect |
| 110. #493 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782335 | 2 |
| #23781862 | 2 |
| #23781857 | 2 |
| #23781409 | 2 |
| #23781397 | 2 |
| #23781394 | 2 |
| #493×C163 | 2 |
| #1621 | 163 |