Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1102 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 181 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 | #381×C163 | C2 |
| prime radical | C2×#19104705 | C2 |
| hypercenter | #381 | D163 |
| hypocenter | C163 | #2849 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C4×D163 | C2 | semidirect |
| 2. C2×#19104719 | C2 | semidirect |
| 3. C2×#19104718 | C2 | semidirect |
| 5. #23781543 | C2 | semidirect |
| 6. #23781539 | C2 | semidirect |
| 7. #23781526 | C2 | semidirect |
| 8. #23781520 | C2 | semidirect |
| 9. #381×C163 | C2 | semidirect |
| 21. C2×C4⋊Dic163 | C22 | semidirect |
| 22. C2×Dic163⋊C4 | C22 | semidirect |
| 26. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 27. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 28. C163⋊#95 | C22 | semidirect |
| 32. #95×C163 | C22 | semidirect |
| 46. C22×Dic163 | D4 | semidirect |
| 64. C22×C4×C163 | D4 | semidirect |
| 125. C2×D163 | #123 | semidirect |
| 139. C163 | #2849 | semidirect |
| 148. #381 | D163 | semidirect |
| 172. #95 | C2×D163 | semidirect |
| 197. C22×C4 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C4×D163 | 2 |
| C2×#19104719 | 2 |
| C2×#19104718 | 2 |
| C2×#19104705 | 2 |
| #23781543 | 2 |
| #23781539 | 2 |
| #23781526 | 2 |
| #23781520 | 2 |
| #381×C163 | 2 |
| #2849 | 163 |