Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23781719 | C2 | semidirect |
| 3. #23781516 | C2 | semidirect |
| 4. #23781402 | C2 | semidirect |
| 7. #328×C163 | C2 | semidirect |
| 9. #19104726 | C4 | semidirect |
| 10. #19104724 | C4 | semidirect |
| 13. Q8×Dic163 | C4 | semidirect |
| 14. #19104697 | C4 | semidirect |
| 109. C163 | #1509 | semidirect |
| 115. #328 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782201 | 2 |
| #23781719 | 2 |
| #23781516 | 2 |
| #23781402 | 2 |
| #23781400 | 2 |
| #23781398 | 2 |
| #328×C163 | 2 |
| #1509 | 163 |