Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 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. #23782270 | C2 | semidirect |
| 2. #23782064 | C2 | semidirect |
| 3. #23782041 | C2 | semidirect |
| 4. #23782031 | C2 | semidirect |
| 5. #23782029 | C2 | semidirect |
| 6. #23781916 | C2 | semidirect |
| 7. #23781899 | C2 | semidirect |
| 8. #23781775 | C2 | semidirect |
| 9. C4×#14579684 | C2 | semidirect |
| 10. #23781621 | C2 | semidirect |
| 11. #540×C163 | C2 | semidirect |
| 114. C163 | #3176 | semidirect |
| 117. #540 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782270 | 2 |
| #23782064 | 2 |
| #23782041 | 2 |
| #23782031 | 2 |
| #23782029 | 2 |
| #23781916 | 2 |
| #23781899 | 2 |
| #23781775 | 2 |
| C4×#14579684 | 2 |
| #23781621 | 2 |
| #540×C163 | 2 |
| #3176 | 163 |