Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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×#19104650 | C2 | semidirect |
| 3. #23781459 | C2 | semidirect |
| 4. #23781457 | C2 | semidirect |
| 5. C2×#99×C163 | C2 | semidirect |
| 6. C2×#14579699 | C4 | semidirect |
| 7. #19104731 | C4 | semidirect |
| 9. #19104722 | C4 | semidirect |
| 15. #19104694 | C4 | semidirect |
| 25. C2×Dic326 | C2×C4 | semidirect |
| 26. C2×D652 | C2×C4 | semidirect |
| 42. C4×Dic163 | C2×C4 | semidirect |
| 43. C4×Dic163 | C2×C4 | semidirect |
| 127. C163 | #2127 | semidirect |
| 131. C2×#99 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782232 | 2 |
| C2×#19104650 | 2 |
| #23781459 | 2 |
| #23781457 | 2 |
| C2×#99×C163 | 2 |
| #2127 | 163 |