Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782289 | C2 | semidirect |
| 2. #23782049 | C2 | semidirect |
| 3. #23782027 | C2 | semidirect |
| 4. #23781924 | C2 | semidirect |
| 6. #23781895 | C2 | semidirect |
| 7. #23781776 | C2 | semidirect |
| 8. #23781771 | C2 | semidirect |
| 9. #23781752 | C2 | semidirect |
| 10. #23781619 | C2 | semidirect |
| 11. #498×C163 | C2 | semidirect |
| 109. C163 | #3173 | semidirect |
| 112. #498 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782289 | 2 |
| #23782049 | 2 |
| #23782027 | 2 |
| #23781924 | 2 |
| #23781919 | 2 |
| #23781895 | 2 |
| #23781776 | 2 |
| #23781771 | 2 |
| #23781752 | 2 |
| #23781619 | 2 |
| #498×C163 | 2 |
| #3173 | 163 |