Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
786 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 786 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D163 |
| commutator, socle, cosocle | C23×C163 | C24 |
| Fitting | #379×C163 | C2 |
| prime radical | C2×#19104704 | C2 |
| hypercenter | #379 | D163 |
| hypocenter | C163 | #2411 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19104719 | C2 | semidirect |
| 3. C2×#19104691 | C2 | semidirect |
| 4. C22×C22⋊Dic163 | C2 | semidirect |
| 5. #23781588 | C2 | semidirect |
| 6. #23781580 | C2 | semidirect |
| 7. #23781565 | C2 | semidirect |
| 8. #23781558 | C2 | semidirect |
| 9. #23781542 | C2 | semidirect |
| 10. #23781537 | C2 | semidirect |
| 11. #379×C163 | C2 | semidirect |
| 19. C2×C4⋊Dic163 | C22 | semidirect |
| 20. C2×C4⋊Dic163 | C22 | semidirect |
| 21. C2×Dic163⋊C4 | C22 | semidirect |
| 22. C2×Dic163⋊C4 | C22 | semidirect |
| 28. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 29. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 30. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 31. C2×C4×Dic163 | C22 | semidirect |
| 32. C163⋊#95 | C22 | semidirect |
| 33. C163⋊#95 | C22 | semidirect |
| 50. C22×Dic163 | D4 | semidirect |
| 170. C163 | #2411 | semidirect |
| 182. #379 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104719 | 2 |
| C2×#19104704 | 2 |
| C2×#19104691 | 2 |
| C22×C22⋊Dic163 | 2 |
| #23781588 | 2 |
| #23781580 | 2 |
| #23781565 | 2 |
| #23781558 | 2 |
| #23781542 | 2 |
| #23781537 | 2 |
| #379×C163 | 2 |
| #2411 | 163 |