Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23782398 | C2 | semidirect |
| 2. #23782053 | C2 | semidirect |
| 3. #23782049 | C2 | semidirect |
| 4. #23781886 | C2 | semidirect |
| 5. #23781880 | C2 | semidirect |
| 6. #23781859 | C2 | semidirect |
| 7. #23781795 | C2 | semidirect |
| 8. #23781764 | C2 | semidirect |
| 9. C4×D8×C163 | C2 | semidirect |
| 108. C163 | #3403 | semidirect |
| 118. C4×D8 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782398 | 2 |
| #23782053 | 2 |
| #23782049 | 2 |
| #23781886 | 2 |
| #23781880 | 2 |
| #23781859 | 2 |
| #23781795 | 2 |
| #23781764 | 2 |
| C4×D8×C163 | 2 |
| #3403 | 163 |