Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23782220 | C2 | semidirect |
| 3. #23781971 | C2 | semidirect |
| 4. #23781963 | C2 | semidirect |
| 5. #23781961 | C2 | semidirect |
| 6. #23781955 | C2 | semidirect |
| 7. #23781947 | C2 | semidirect |
| 8. #23781702 | C2 | semidirect |
| 9. C4⋊C8×D163 | C2 | semidirect |
| 11. #474×C163 | C2 | semidirect |
| 44. #14579698 | Q8 | semidirect |
| 134. C163 | #3076 | semidirect |
| 143. #474 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| C4×#14579698 | 2 |
| #23781971 | 2 |
| #23781963 | 2 |
| #23781961 | 2 |
| #23781955 | 2 |
| #23781947 | 2 |
| #23781702 | 2 |
| C4⋊C8×D163 | 2 |
| #23781658 | 2 |
| #474×C163 | 2 |
| #3076 | 163 |