Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
310 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23782432 | C2 | semidirect |
| 3. #23781683 | C2 | semidirect |
| 4. #23781631 | C2 | semidirect |
| 5. #23781435 | C2 | semidirect |
| 6. #23781430 | C2 | semidirect |
| 7. #416×C163 | C2 | semidirect |
| 10. #19104765 | C4 | semidirect |
| 12. #19104760 | C4 | semidirect |
| 118. C163 | #1881 | semidirect |
| 123. #416 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782463 | 2 |
| #23782432 | 2 |
| #23781683 | 2 |
| #23781631 | 2 |
| #23781435 | 2 |
| #23781430 | 2 |
| #416×C163 | 2 |
| #1881 | 163 |