Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
376 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 376 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 |
|---|---|---|
| 3. #23781971 | C2 | semidirect |
| 4. #23781970 | C2 | semidirect |
| 5. #23781957 | C2 | semidirect |
| 6. #23781951 | C2 | semidirect |
| 7. #23781950 | C2 | semidirect |
| 11. #477×C163 | C2 | semidirect |
| 47. Q8×D163 | Q8 | semidirect |
| 130. C163 | #3078 | semidirect |
| 137. #477 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| C4×Q8×D163 | 2 |
| #23781971 | 2 |
| #23781970 | 2 |
| #23781957 | 2 |
| #23781951 | 2 |
| #23781950 | 2 |
| #23781706 | 2 |
| #23781687 | 2 |
| #23781672 | 2 |
| #477×C163 | 2 |
| #3078 | 163 |