Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 2. Q8×Dic326 | C2 | semidirect |
| 3. #23782026 | C2 | semidirect |
| 5. #23781960 | C2 | semidirect |
| 6. #23781944 | C2 | semidirect |
| 7. #23781889 | C2 | semidirect |
| 9. #23781795 | C2 | semidirect |
| 10. #23781768 | C2 | semidirect |
| 11. C4×Q16×C163 | C2 | semidirect |
| 118. C163 | #3375 | semidirect |
| 130. C4×Q16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782400 | 2 |
| Q8×Dic326 | 2 |
| #23782026 | 2 |
| #23782012 | 2 |
| #23781960 | 2 |
| #23781944 | 2 |
| #23781889 | 2 |
| #23781865 | 2 |
| #23781795 | 2 |
| #23781768 | 2 |
| C4×Q16×C163 | 2 |
| #3375 | 163 |