Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1116 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1116 conjugacy classes of subgroups — too many to draw. Only its 197 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, prime radical | C23×D4×C163 | C2 |
| hypercenter | C23×D4 | D163 |
| hypocenter | C163 | #2405 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#19104716 | C2 | semidirect |
| 2. C22×C22⋊Dic163 | C2 | semidirect |
| 3. #23781579 | C2 | semidirect |
| 4. #23781545 | C2 | semidirect |
| 5. #23781538 | C2 | semidirect |
| 6. #23781521 | C2 | semidirect |
| 7. #23781521 | C2 | semidirect |
| 9. C23×Dic163 | C22 | semidirect |
| 10. C23×Dic163 | C22 | semidirect |
| 12. C2×Dic163⋊C4 | C22 | semidirect |
| 16. C2×C22⋊Dic163 | C22 | semidirect |
| 17. C2×C22⋊Dic163 | C22 | semidirect |
| 18. C2×C22⋊Dic163 | C22 | semidirect |
| 19. C2×C22⋊Dic163 | C22 | semidirect |
| 20. C2×C22⋊Dic163 | C22 | semidirect |
| 21. C163⋊#95 | C22 | semidirect |
| 125. C22×C163 | #123 | semidirect |
| 142. C163 | #2405 | semidirect |
| 268. C22 | #19104716 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104716 | 2 |
| C22×C22⋊Dic163 | 2 |
| #23781579 | 2 |
| #23781545 | 2 |
| #23781538 | 2 |
| #23781521 | 2 |
| C23×D4×C163 | 2 |
| #2405 | 163 |