Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
160 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 160 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 |
|---|---|---|
| 4. #23781418 | C2 | semidirect |
| 5. #23781414 | C2 | semidirect |
| 6. #23781411 | C2 | semidirect |
| 7. #498×C163 | C2 | semidirect |
| 59. C8×C163 | SD16 | semidirect |
| 76. C163 | #1691 | semidirect |
| 78. #498 | D163 | semidirect |
| 136. C8 | #14579686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781952 | 2 |
| #23781867 | 2 |
| #23781744 | 2 |
| #23781418 | 2 |
| #23781414 | 2 |
| #23781411 | 2 |
| #498×C163 | 2 |
| #1691 | 163 |