Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
362 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782277 | C2 | semidirect |
| 2. #23782064 | C2 | semidirect |
| 3. #23782037 | C2 | semidirect |
| 4. #23782035 | C2 | semidirect |
| 5. #23782029 | C2 | semidirect |
| 6. #23781909 | C2 | semidirect |
| 7. #23781892 | C2 | semidirect |
| 8. #23781765 | C2 | semidirect |
| 9. C4×#14579687 | C2 | semidirect |
| 10. #23781621 | C2 | semidirect |
| 108. C163 | #3174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782277 | 2 |
| #23782064 | 2 |
| #23782037 | 2 |
| #23782035 | 2 |
| #23782029 | 2 |
| #23781909 | 2 |
| #23781892 | 2 |
| #23781765 | 2 |
| C4×#14579687 | 2 |
| #23781621 | 2 |
| #540×C163 | 2 |
| #3174 | 163 |