Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782319 | C2 | semidirect |
| 2. #23782061 | C2 | semidirect |
| 3. #23781989 | C2 | semidirect |
| 4. #23781981 | C2 | semidirect |
| 5. #23781952 | C2 | semidirect |
| 6. #23781945 | C2 | semidirect |
| 7. #23781916 | C2 | semidirect |
| 8. C4×#14579684 | C2 | semidirect |
| 9. #23781743 | C2 | semidirect |
| 10. #23781708 | C2 | semidirect |
| 11. #555×C163 | C2 | semidirect |
| 85. C163⋊C8 | #41 | semidirect |
| 127. C163 | #3354 | semidirect |
| 129. #555 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782319 | 2 |
| #23782061 | 2 |
| #23781989 | 2 |
| #23781981 | 2 |
| #23781952 | 2 |
| #23781945 | 2 |
| #23781916 | 2 |
| C4×#14579684 | 2 |
| #23781743 | 2 |
| #23781708 | 2 |
| #555×C163 | 2 |
| #3354 | 163 |