Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
410 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 137 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. #23782006 | C2 | semidirect |
| 3. #23782000 | C2 | semidirect |
| 4. #23781995 | C2 | semidirect |
| 5. #23781708 | C2 | semidirect |
| 6. #23781673 | C2 | semidirect |
| 18. #19104668 | C22 | semidirect |
| 19. #19104666 | C22 | semidirect |
| 20. #19104658 | C22 | semidirect |
| 21. #19104658 | C22 | semidirect |
| 116. C163 | #3095 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104714 | 2 |
| #23782006 | 2 |
| #23782000 | 2 |
| #23781995 | 2 |
| #23781708 | 2 |
| #23781673 | 2 |
| #23781629 | 2 |
| C2×#117×C163 | 2 |
| #3095 | 163 |