Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
184 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 49 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. #23782075 | C2 | semidirect |
| 2. #23782035 | C2 | semidirect |
| 4. #23781407 | C2 | semidirect |
| 5. #23781407 | C2 | semidirect |
| 89. C163 | #1664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782075 | 2 |
| #23782035 | 2 |
| #23782024 | 2 |
| #23781407 | 2 |
| #23781405 | 2 |
| #563×C163 | 2 |
| #1664 | 163 |