Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23781803 | C2 | semidirect |
| 2. #23781577 | C2 | semidirect |
| 3. #23781399 | C2 | semidirect |
| 4. #23781389 | C2 | semidirect |
| 6. C22×Dic326 | C22 | semidirect |
| 10. C22⋊(C163⋊C8) | C22 | semidirect |
| 12. C163⋊#95 | C22 | semidirect |
| 59. C23×C163 | SD16 | semidirect |
| 98. C163 | #1601 | semidirect |
| 149. C23 | #14579687 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781803 | 2 |
| #23781577 | 2 |
| #23781399 | 2 |
| #23781389 | 2 |
| #534×C163 | 2 |
| #1601 | 163 |