Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
272 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23781511 | C2 | semidirect |
| 3. #23781400 | C2 | semidirect |
| 4. #432×C163 | C2 | semidirect |
| 6. #19104735 | C4 | semidirect |
| 7. #19104732 | C4 | semidirect |
| 12. C4×D652 | C4 | semidirect |
| 83. C163 | #1505 | semidirect |
| 86. #432 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782215 | 2 |
| #23781511 | 2 |
| #23781400 | 2 |
| #432×C163 | 2 |
| #1505 | 163 |