Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23782215 | C2 | semidirect |
| 2. C2×C4×D652 | C2 | semidirect |
| 3. #23781979 | C2 | semidirect |
| 4. #23781946 | C2 | semidirect |
| 5. #23781861 | C2 | semidirect |
| 6. #23781801 | C2 | semidirect |
| 7. C4×D1304 | C2 | semidirect |
| 8. #431×C163 | C2 | semidirect |
| 13. #19104735 | C22 | semidirect |
| 14. #19104732 | C22 | semidirect |
| 23. C4×D652 | C22 | semidirect |
| 26. #19104669 | C22 | semidirect |
| 28. #19104657 | C22 | semidirect |
| 30. C4⋊C8×C163 | C22 | semidirect |
| 32. C4×C8×C163 | C22 | semidirect |
| 76. D652 | #41 | semidirect |
| 87. C2×C4×C163 | D8 | semidirect |
| 120. C163 | #3100 | semidirect |
| 129. #431 | D163 | semidirect |
| 149. C4⋊C8 | C2×D163 | semidirect |
| 153. C4×C8 | C2×D163 | semidirect |
| 208. C2×C4 | D1304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782215 | 2 |
| C2×C4×D652 | 2 |
| #23781979 | 2 |
| #23781946 | 2 |
| #23781861 | 2 |
| #23781801 | 2 |
| C4×D1304 | 2 |
| #431×C163 | 2 |
| #3100 | 163 |