Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#19104700 | C2 | semidirect |
| 4. #23781571 | C2 | semidirect |
| 5. #23781559 | C2 | semidirect |
| 6. #23781537 | C2 | semidirect |
| 7. #23781534 | C2 | semidirect |
| 8. #23781511 | C2 | semidirect |
| 12. #19104722 | C4 | semidirect |
| 32. C2×Dic326 | C2×C4 | semidirect |
| 44. C22⋊Dic163 | C2×C4 | semidirect |
| 46. C4×Dic163 | C2×C4 | semidirect |
| 111. C163 | #2326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104722 | 2 |
| C2×#19104700 | 2 |
| C2×D4×Dic163 | 2 |
| #23781571 | 2 |
| #23781559 | 2 |
| #23781537 | 2 |
| #23781534 | 2 |
| #23781511 | 2 |
| #390×C163 | 2 |
| #2326 | 163 |