Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
496 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 496 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. C2×#19104754 | C2 | semidirect |
| 2. #23782213 | C2 | semidirect |
| 3. C4×#14579698 | C2 | semidirect |
| 4. #23781886 | C2 | semidirect |
| 5. #23781878 | C2 | semidirect |
| 6. #23781876 | C2 | semidirect |
| 7. #23781870 | C2 | semidirect |
| 8. #23781862 | C2 | semidirect |
| 9. C4⋊C8×D163 | C2 | semidirect |
| 10. #23781658 | C2 | semidirect |
| 11. #459×C163 | C2 | semidirect |
| 47. #14579698 | D4 | semidirect |
| 135. C4×C163 | #135 | semidirect |
| 150. C163 | #3035 | semidirect |
| 160. #459 | D163 | semidirect |
| 292. C4 | #19104754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104754 | 2 |
| #23782213 | 2 |
| C4×#14579698 | 2 |
| #23781886 | 2 |
| #23781878 | 2 |
| #23781876 | 2 |
| #23781870 | 2 |
| #23781862 | 2 |
| C4⋊C8×D163 | 2 |
| #23781658 | 2 |
| #459×C163 | 2 |
| #3035 | 163 |