Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23781708 | C2 | semidirect |
| 4. #23781621 | C2 | semidirect |
| 5. #23781433 | C2 | semidirect |
| 6. #23781429 | C2 | semidirect |
| 16. #19104652 | C4 | semidirect |
| 100. C163 | #1931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781708 | 2 |
| C2×#19104656 | 2 |
| C2×#19104652 | 2 |
| #23781621 | 2 |
| #23781433 | 2 |
| #23781429 | 2 |
| #418×C163 | 2 |
| #1931 | 163 |