Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
426 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 139 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. Q8×D652 | C2 | semidirect |
| 3. #23782012 | C2 | semidirect |
| 4. #23781946 | C2 | semidirect |
| 5. #23781861 | C2 | semidirect |
| 6. C4×D1304 | C2 | semidirect |
| 7. C8×Q8×C163 | C2 | semidirect |
| 52. D652 | #41 | semidirect |
| 57. Q8×C163 | D8 | semidirect |
| 81. C163 | #3358 | semidirect |
| 88. C8×Q8 | D163 | semidirect |
| 129. Q8 | D1304 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782337 | 2 |
| Q8×D652 | 2 |
| #23782012 | 2 |
| #23781946 | 2 |
| #23781861 | 2 |
| C4×D1304 | 2 |
| C8×Q8×C163 | 2 |
| #3358 | 163 |