Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782337 | C2 | semidirect |
| 2. #23782031 | C2 | semidirect |
| 3. #23782013 | C2 | semidirect |
| 4. #23781962 | C2 | semidirect |
| 5. #23781952 | C2 | semidirect |
| 6. #23781860 | C2 | semidirect |
| 7. #23781860 | C2 | semidirect |
| 8. #23781796 | C2 | semidirect |
| 9. #23781775 | C2 | semidirect |
| 10. C4×#14579684 | C2 | semidirect |
| 11. #554×C163 | C2 | semidirect |
| 94. D4×C163 | #41 | semidirect |
| 129. C163 | #3366 | semidirect |
| 131. #554 | D163 | semidirect |
| 218. D4 | #14579700 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782337 | 2 |
| #23782031 | 2 |
| #23782013 | 2 |
| #23781962 | 2 |
| #23781952 | 2 |
| #23781860 | 2 |
| #23781796 | 2 |
| #23781775 | 2 |
| C4×#14579684 | 2 |
| #554×C163 | 2 |
| #3366 | 163 |