Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
780 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 780 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 | #379×C163 | C2 |
| prime radical | C25×C163 | C22 |
| hypercenter | #379 | D163 |
| hypocenter | C163 | #2437 |
| 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×#19104712 | C2 | semidirect |
| 3. #23781601 | C2 | semidirect |
| 4. #23781588 | C2 | semidirect |
| 5. #23781577 | C2 | semidirect |
| 6. #23781540 | C2 | semidirect |
| 7. #23781537 | C2 | semidirect |
| 8. #23781523 | C2 | semidirect |
| 10. C22×Dic326 | C22 | semidirect |
| 14. C2×C4⋊Dic163 | C22 | semidirect |
| 15. C2×C4⋊Dic163 | C22 | semidirect |
| 16. C2×Dic163⋊C4 | C22 | semidirect |
| 17. C2×Dic163⋊C4 | C22 | semidirect |
| 18. C2×Dic163⋊C4 | C22 | semidirect |
| 24. C163⋊#95 | C22 | semidirect |
| 25. C163⋊#95 | C22 | semidirect |
| 26. C163⋊#95 | C22 | semidirect |
| 27. C163⋊#95 | C22 | semidirect |
| 58. C24×C163 | Q8 | semidirect |
| 120. C22×C163 | C22⋊Q8 | semidirect |
| 140. C163 | #2437 | semidirect |
| 178. C24 | Dic326 | semidirect |
| 261. C22 | #19104712 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104712 | 2 |
| C22×C22⋊Dic163 | 2 |
| #23781601 | 2 |
| #23781588 | 2 |
| #23781577 | 2 |
| #23781540 | 2 |
| #23781537 | 2 |
| #23781523 | 2 |
| #379×C163 | 2 |
| #2437 | 163 |