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. #23781958 | C2 | semidirect |
| 4. #23781954 | C2 | semidirect |
| 5. #23781950 | C2 | semidirect |
| 6. #23781946 | C2 | semidirect |
| 7. #23781942 | C2 | semidirect |
| 8. #23781704 | C2 | semidirect |
| 9. #23781687 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 44. #14579700 | Q8 | semidirect |
| 88. D652 | C2×Q8 | semidirect |
| 105. Q8×C163 | C2×Q8 | semidirect |
| 137. C163 | #3079 | semidirect |
| 144. #475 | D163 | semidirect |
| 226. Q8 | 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×#14579700 | 2 |
| #23781958 | 2 |
| #23781954 | 2 |
| #23781950 | 2 |
| #23781946 | 2 |
| #23781942 | 2 |
| #23781704 | 2 |
| #23781687 | 2 |
| #23781665 | 2 |
| #475×C163 | 2 |
| #3079 | 163 |