Finite Group DatabasebetaFinite Group DatabasebetaOrder 23872.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D373 |
| commutator, socle, cosocle | C22×C373 | C24 |
| Fitting | #123×C373 | C2 |
| prime radical | #26045764 | C2 |
| hypercenter | #123 | D373 |
| hypocenter | C373 | #529 |
| LCS | G ▷ C22×C373 ▷ C373 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26045787 | C2 | semidirect |
| 2. #26045785 | C2 | semidirect |
| 3. #26045782 | C2 | semidirect |
| 4. #26045778 | C2 | semidirect |
| 5. #26045775 | C2 | semidirect |
| 6. #26045769 | C2 | semidirect |
| 8. #26045757 | C2 | semidirect |
| 9. D4×Dic373 | C2 | semidirect |
| 10. #26045752 | C2 | semidirect |
| 11. #26045752 | C2 | semidirect |
| 12. #26045750 | C2 | semidirect |
| 13. #26045748 | C2 | semidirect |
| 14. C2×C4×Dic373 | C2 | semidirect |
| 15. #123×C373 | C2 | semidirect |
| 103. C373 | #529 | semidirect |
| 110. #123 | D373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26045787 | 2 |
| #26045785 | 2 |
| #26045782 | 2 |
| #26045778 | 2 |
| #26045775 | 2 |
| #26045769 | 2 |
| #26045764 | 2 |
| #26045757 | 2 |
| D4×Dic373 | 2 |
| #26045752 | 2 |
| #26045750 | 2 |
| #26045748 | 2 |
| C2×C4×Dic373 | 2 |
| #123×C373 | 2 |
| #529 | 373 |