Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C2×#19104741 | C2 | semidirect |
| 2. #23782232 | C2 | semidirect |
| 3. #23781915 | C2 | semidirect |
| 4. #23781898 | C2 | semidirect |
| 5. #23781703 | C2 | semidirect |
| 6. #23781670 | C2 | semidirect |
| 7. C22×D8×C163 | C2 | semidirect |
| 11. C2×#14579682 | C22 | semidirect |
| 12. C2×C8×D163 | C22 | semidirect |
| 15. #19104706 | C22 | semidirect |
| 18. #19104669 | C22 | semidirect |
| 19. #19104667 | C22 | semidirect |
| 20. #19104656 | C22 | semidirect |
| 49. C2×C8×C163 | D4 | semidirect |
| 93. C163 | #3058 | semidirect |
| 95. C22×D8 | D163 | semidirect |
| 139. C2×C8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104741 | 2 |
| #23782232 | 2 |
| #23781915 | 2 |
| #23781898 | 2 |
| #23781703 | 2 |
| #23781670 | 2 |
| C22×D8×C163 | 2 |
| #3058 | 163 |