Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#14579688 | C2 | semidirect |
| 2. #23782236 | C2 | semidirect |
| 4. #23781911 | C2 | semidirect |
| 5. #23781894 | C2 | semidirect |
| 6. #23781703 | C2 | semidirect |
| 7. #23781675 | C2 | semidirect |
| 8. #23781671 | C2 | semidirect |
| 9. C2×#131×C163 | C2 | semidirect |
| 20. #19104714 | C22 | semidirect |
| 25. #19104669 | C22 | semidirect |
| 26. #19104667 | C22 | semidirect |
| 27. #19104660 | C22 | semidirect |
| 32. C2×M16×C163 | C22 | semidirect |
| 34. C22×C8×C163 | C22 | semidirect |
| 67. C2×C8×C163 | D4 | semidirect |
| 120. C163 | #3057 | semidirect |
| 123. C2×#131 | D163 | semidirect |
| 139. C2×M16 | C2×D163 | semidirect |
| 141. C22×C8 | C2×D163 | semidirect |
| 179. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| #23782236 | 2 |
| #23782229 | 2 |
| #23781911 | 2 |
| #23781894 | 2 |
| #23781703 | 2 |
| #23781675 | 2 |
| #23781671 | 2 |
| C2×#131×C163 | 2 |
| #3057 | 163 |