Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
350 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782388 | C2 | semidirect |
| 2. #23782375 | C2 | semidirect |
| 3. #23782020 | C2 | semidirect |
| 4. #23782016 | C2 | semidirect |
| 5. #23781973 | C2 | semidirect |
| 6. #23781956 | C2 | semidirect |
| 8. #23781871 | C2 | semidirect |
| 9. C4×#14579688 | C2 | semidirect |
| 11. C8×Q8×C163 | C2 | semidirect |
| 120. C163 | #3360 | semidirect |
| 130. C8×Q8 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782388 | 2 |
| #23782375 | 2 |
| #23782020 | 2 |
| #23782016 | 2 |
| #23781973 | 2 |
| #23781956 | 2 |
| #23781881 | 2 |
| #23781871 | 2 |
| C4×#14579688 | 2 |
| C4×D1304 | 2 |
| C8×Q8×C163 | 2 |
| #3360 | 163 |