Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
852 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×Dic326 | C2 | semidirect |
| 2. C2×#19104723 | C2 | semidirect |
| 4. #23781578 | C2 | semidirect |
| 5. #23781571 | C2 | semidirect |
| 6. #23781542 | C2 | semidirect |
| 7. C4×C22⋊C4×C163 | C2 | semidirect |
| 31. C2×Dic326 | D4 | semidirect |
| 81. C22×C163 | #124 | semidirect |
| 101. C163 | #2436 | semidirect |
| 109. C4×C22⋊C4 | D163 | semidirect |
| 187. C22 | #19104723 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic326 | 2 |
| C2×#19104723 | 2 |
| C2×#19104709 | 2 |
| #23781578 | 2 |
| #23781571 | 2 |
| #23781542 | 2 |
| C4×C22⋊C4×C163 | 2 |
| #2436 | 163 |