Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
452 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23782465 | C2 | semidirect |
| 2. C2×#19104757 | C2 | semidirect |
| 3. C2×#19104741 | C2 | semidirect |
| 4. #23781941 | C2 | semidirect |
| 5. #23781936 | C2 | semidirect |
| 6. #23781929 | C2 | semidirect |
| 7. #23781647 | C2 | semidirect |
| 8. C2×#108×C163 | C2 | semidirect |
| 20. C2×Dic652 | C22 | semidirect |
| 21. C2×#14579688 | C22 | semidirect |
| 22. C2×D1304 | C22 | semidirect |
| 30. #19104653 | C22 | semidirect |
| 31. #19104651 | C22 | semidirect |
| 34. #108×C163 | C22 | semidirect |
| 35. #108×C163 | C22 | semidirect |
| 132. C163 | #3067 | semidirect |
| 140. C2×#108 | D163 | semidirect |
| 165. #108 | C2×D163 | semidirect |
| 166. #108 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782465 | 2 |
| C2×#19104757 | 2 |
| C2×#19104741 | 2 |
| #23781941 | 2 |
| #23781936 | 2 |
| #23781929 | 2 |
| #23781647 | 2 |
| C2×#108×C163 | 2 |
| #3067 | 163 |