Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
568 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×C4×Dic326 | C2 | semidirect |
| 3. #23781605 | C2 | semidirect |
| 4. #23781592 | C2 | semidirect |
| 6. #23781578 | C2 | semidirect |
| 7. C4×(C2×D163)⋊C4 | C2 | semidirect |
| 8. #376×C163 | C2 | semidirect |
| 96. C163 | #2398 | semidirect |
| 105. #376 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Dic326 | 2 |
| C2×C4×D652 | 2 |
| #23781605 | 2 |
| #23781592 | 2 |
| #23781583 | 2 |
| #23781578 | 2 |
| C4×(C2×D163)⋊C4 | 2 |
| #376×C163 | 2 |
| #2398 | 163 |