Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23782216 | C2 | semidirect |
| 2. C4×#14579700 | C2 | semidirect |
| 3. #23781991 | C2 | semidirect |
| 4. #23781942 | C2 | semidirect |
| 5. #23781865 | C2 | semidirect |
| 6. #23781861 | C2 | semidirect |
| 7. #23781813 | C2 | semidirect |
| 8. #23781776 | C2 | semidirect |
| 9. #23781768 | C2 | semidirect |
| 10. #23781721 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 93. D652 | #41 | semidirect |
| 109. Q8×C163 | #41 | semidirect |
| 144. C163 | #3115 | semidirect |
| 149. #475 | D163 | semidirect |
| 233. Q8 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782216 | 2 |
| C4×#14579700 | 2 |
| #23781991 | 2 |
| #23781942 | 2 |
| #23781865 | 2 |
| #23781861 | 2 |
| #23781813 | 2 |
| #23781776 | 2 |
| #23781768 | 2 |
| #23781721 | 2 |
| #475×C163 | 2 |
| #3115 | 163 |