Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
384 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782400 | C2 | semidirect |
| 2. Q8×D652 | C2 | semidirect |
| 3. #23782025 | C2 | semidirect |
| 4. #23782012 | C2 | semidirect |
| 5. #23781956 | C2 | semidirect |
| 6. #23781951 | C2 | semidirect |
| 7. #23781881 | C2 | semidirect |
| 9. #23781778 | C2 | semidirect |
| 10. C4×#14579688 | C2 | semidirect |
| 11. #446×C163 | C2 | semidirect |
| 124. C163 | #3373 | semidirect |
| 134. #446 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782400 | 2 |
| Q8×D652 | 2 |
| #23782025 | 2 |
| #23782012 | 2 |
| #23781956 | 2 |
| #23781951 | 2 |
| #23781881 | 2 |
| #23781861 | 2 |
| #23781778 | 2 |
| C4×#14579688 | 2 |
| #446×C163 | 2 |
| #3373 | 163 |