Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782393 | C2 | semidirect |
| 4. #23782016 | C2 | semidirect |
| 5. #23781973 | C2 | semidirect |
| 8. #23781876 | C2 | semidirect |
| 9. C4×Dic652 | C2 | semidirect |
| 11. C8×Q8×C163 | C2 | semidirect |
| 115. C163 | #3364 | semidirect |
| 125. C8×Q8 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782393 | 2 |
| #23782388 | 2 |
| #23782020 | 2 |
| #23782016 | 2 |
| #23781973 | 2 |
| #23781946 | 2 |
| #23781888 | 2 |
| #23781876 | 2 |
| C4×Dic652 | 2 |
| C4×#14579688 | 2 |
| C8×Q8×C163 | 2 |
| #3364 | 163 |