Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23781683 | C2 | semidirect |
| 3. C2×#19104652 | C2 | semidirect |
| 4. #23781421 | C2 | semidirect |
| 5. #518×C163 | C2 | semidirect |
| 8. #19104731 | C4 | semidirect |
| 9. #19104722 | C4 | semidirect |
| 21. C2×Dic326 | C2×C4 | semidirect |
| 22. C2×D652 | C2×C4 | semidirect |
| 32. C4×Dic163 | C2×C4 | semidirect |
| 43. C42×C163 | D4 | semidirect |
| 88. C163 | #1911 | semidirect |
| 91. #518 | D163 | semidirect |
| 132. C42 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782232 | 2 |
| #23781683 | 2 |
| C2×#19104652 | 2 |
| #23781421 | 2 |
| #518×C163 | 2 |
| #1911 | 163 |