Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 416 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 |
|---|---|---|
| 1. C4⋊Q8×D163 | C2 | semidirect |
| 3. #23781959 | C2 | semidirect |
| 4. #23781953 | C2 | semidirect |
| 5. #23781951 | C2 | semidirect |
| 6. #23781947 | C2 | semidirect |
| 7. #23781945 | C2 | semidirect |
| 8. #23781706 | C2 | semidirect |
| 9. #23781687 | C2 | semidirect |
| 11. #474×C163 | C2 | semidirect |
| 44. #14579698 | Q8 | semidirect |
| 86. Dic326 | C2×Q8 | semidirect |
| 105. D4×C163 | C2×Q8 | semidirect |
| 137. C163 | #3079 | semidirect |
| 146. #474 | D163 | semidirect |
| 229. D4 | Q8×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D163 | 2 |
| C4×#14579698 | 2 |
| #23781959 | 2 |
| #23781953 | 2 |
| #23781951 | 2 |
| #23781947 | 2 |
| #23781945 | 2 |
| #23781706 | 2 |
| #23781687 | 2 |
| #23781663 | 2 |
| #474×C163 | 2 |
| #3079 | 163 |