Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
524 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 524 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×D1304 | C2 | semidirect |
| 2. #23782229 | C2 | semidirect |
| 3. #23781918 | C2 | semidirect |
| 4. #23781901 | C2 | semidirect |
| 5. #23781703 | C2 | semidirect |
| 6. #23781671 | C2 | semidirect |
| 7. C2×#131×C163 | C2 | semidirect |
| 14. #19104709 | C22 | semidirect |
| 17. #19104669 | C22 | semidirect |
| 18. #19104667 | C22 | semidirect |
| 19. #19104657 | C22 | semidirect |
| 23. C2×M16×C163 | C22 | semidirect |
| 25. C22×C8×C163 | C22 | semidirect |
| 48. C2×C8×C163 | D4 | semidirect |
| 93. C163 | #3058 | semidirect |
| 96. C2×#131 | D163 | semidirect |
| 109. C2×M16 | C2×D163 | semidirect |
| 111. C22×C8 | C2×D163 | semidirect |
| 138. 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×D1304 | 2 |
| #23782229 | 2 |
| #23781918 | 2 |
| #23781901 | 2 |
| #23781703 | 2 |
| #23781671 | 2 |
| C2×#131×C163 | 2 |
| #3058 | 163 |