Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
314 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23781952 | C2 | semidirect |
| 3. #23781409 | C2 | semidirect |
| 4. #23781394 | C2 | semidirect |
| 5. #492×C163 | C2 | semidirect |
| 11. C4⋊(C163⋊C8) | C22 | semidirect |
| 14. C4⋊Q8×C163 | C22 | semidirect |
| 16. C4×C8×C163 | C22 | semidirect |
| 38. D652 | SD16 | semidirect |
| 69. C163 | #1629 | semidirect |
| 72. #492 | D163 | semidirect |
| 78. C4⋊Q8 | C2×D163 | semidirect |
| 86. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782300 | 2 |
| #23781952 | 2 |
| #23781409 | 2 |
| #23781394 | 2 |
| #492×C163 | 2 |
| #1629 | 163 |