Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
772 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 145 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. #23782501 | C2 | semidirect |
| 2. #23782234 | C2 | semidirect |
| 3. #23782229 | C2 | semidirect |
| 4. #23781853 | C2 | semidirect |
| 5. #23781638 | C2 | semidirect |
| 6. #410×C163 | C2 | semidirect |
| 15. C22×D652 | C22 | semidirect |
| 22. #19104705 | C22 | semidirect |
| 23. #19104703 | C22 | semidirect |
| 24. #19104694 | C22 | semidirect |
| 25. #19104649 | C22 | semidirect |
| 27. #117×C163 | C22 | semidirect |
| 28. #99×C163 | C22 | semidirect |
| 41. C2×Dic326 | D4 | semidirect |
| 49. C2×D652 | D4 | semidirect |
| 56. C2×C4×D163 | D4 | semidirect |
| 64. C2×Q8×C163 | D4 | semidirect |
| 65. C2×D4×C163 | D4 | semidirect |
| 67. C22×C4×C163 | D4 | semidirect |
| 134. C163 | #3027 | semidirect |
| 141. #410 | D163 | semidirect |
| 161. #117 | C2×D163 | semidirect |
| 163. #99 | C2×D163 | semidirect |
| 180. C2×Q8 | D652 | semidirect |
| 193. C2×D4 | D652 | semidirect |
| 197. C22×C4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782501 | 2 |
| #23782234 | 2 |
| #23782229 | 2 |
| #23781853 | 2 |
| #23781638 | 2 |
| #410×C163 | 2 |
| #3027 | 163 |