Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
288 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 4. #23781403 | C2 | semidirect |
| 5. #23781402 | C2 | semidirect |
| 6. #23781401 | C2 | semidirect |
| 7. #328×C163 | C2 | semidirect |
| 8. C2×Q8×D163 | C4 | semidirect |
| 11. #19104715 | C4 | semidirect |
| 15. #19104711 | C4 | semidirect |
| 18. C4⋊C4×D163 | C4 | semidirect |
| 123. C163 | #1520 | semidirect |
| 131. #328 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22⋊Q8×D163 | 2 |
| C22⋊C8×D163 | 2 |
| #23781524 | 2 |
| #23781403 | 2 |
| #23781402 | 2 |
| #23781401 | 2 |
| #328×C163 | 2 |
| #1520 | 163 |