Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
814 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 814 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 | #386×C163 | C2 |
| prime radical | C2×#19104703 | C2 |
| hypercenter | #386 | D163 |
| hypocenter | C163 | #2412 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19104716 | C2 | semidirect |
| 3. C22×(C2×D163)⋊C4 | C2 | semidirect |
| 4. C2×C22⋊C4×D163 | C2 | semidirect |
| 5. #23781594 | C2 | semidirect |
| 6. #23781580 | C2 | semidirect |
| 7. #23781541 | C2 | semidirect |
| 8. #23781538 | C2 | semidirect |
| 9. #23781526 | C2 | semidirect |
| 10. #23781524 | C2 | semidirect |
| 11. #386×C163 | C2 | semidirect |
| 19. C2×Dic163⋊C4 | C22 | semidirect |
| 20. C2×Dic163⋊C4 | C22 | semidirect |
| 23. C2×C22⋊Dic163 | C22 | semidirect |
| 31. C163⋊#95 | C22 | semidirect |
| 32. C163⋊#95 | C22 | semidirect |
| 33. C163⋊#95 | C22 | semidirect |
| 37. C2×C22⋊C4×C163 | C22 | semidirect |
| 38. #95×C163 | C22 | semidirect |
| 64. C22⋊Dic163 | D4 | semidirect |
| 158. C2×D163 | #123 | semidirect |
| 175. C163 | #2412 | semidirect |
| 184. #386 | D163 | semidirect |
| 210. C2×C22⋊C4 | C2×D163 | semidirect |
| 214. #95 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104716 | 2 |
| C2×#19104703 | 2 |
| C22×(C2×D163)⋊C4 | 2 |
| C2×C22⋊C4×D163 | 2 |
| #23781594 | 2 |
| #23781580 | 2 |
| #23781541 | 2 |
| #23781538 | 2 |
| #23781526 | 2 |
| #23781524 | 2 |
| #386×C163 | 2 |
| #2412 | 163 |