Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
262 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 262 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. #23781649 | C2 | semidirect |
| 3. #23781461 | C2 | semidirect |
| 4. #413×C163 | C2 | semidirect |
| 14. #19104654 | C22 | semidirect |
| 18. #101×C163 | C22 | semidirect |
| 98. C163 | #2134 | semidirect |
| 102. #413 | D163 | semidirect |
| 116. #101 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782229 | 2 |
| #23781649 | 2 |
| #23781461 | 2 |
| #413×C163 | 2 |
| #2134 | 163 |