Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 2. #23782035 | C2 | semidirect |
| 3. #23782027 | C2 | semidirect |
| 4. #23782022 | C2 | semidirect |
| 5. #23782017 | C2 | semidirect |
| 6. #23781673 | C2 | semidirect |
| 9. C2×#19104658 | C2 | semidirect |
| 10. #23781621 | C2 | semidirect |
| 11. #544×C163 | C2 | semidirect |
| 127. C163 | #3137 | semidirect |
| 129. #544 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782241 | 2 |
| #23782035 | 2 |
| #23782027 | 2 |
| #23782022 | 2 |
| #23782017 | 2 |
| #23781673 | 2 |
| #23781664 | 2 |
| #23781659 | 2 |
| C2×#19104658 | 2 |
| #23781621 | 2 |
| #544×C163 | 2 |
| #3137 | 163 |