Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23782400 | C2 | semidirect |
| 2. #23782054 | C2 | semidirect |
| 3. #23782049 | C2 | semidirect |
| 4. #23781888 | C2 | semidirect |
| 5. #23781881 | C2 | semidirect |
| 6. #23781861 | C2 | semidirect |
| 7. #23781767 | C2 | semidirect |
| 8. C4×D1304 | C2 | semidirect |
| 9. #446×C163 | C2 | semidirect |
| 108. C163 | #3403 | semidirect |
| 116. #446 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782400 | 2 |
| #23782054 | 2 |
| #23782049 | 2 |
| #23781888 | 2 |
| #23781881 | 2 |
| #23781861 | 2 |
| #23781767 | 2 |
| C4×D1304 | 2 |
| #446×C163 | 2 |
| #3403 | 163 |