Finite Group DatabasebetaFinite Group DatabasebetaOrder 28352.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×D443 |
| commutator, socle, cosocle | C22×C443 | C24 |
| Fitting | #126×C443 | C2 |
| prime radical | C2×C22⋊D443 | C22 |
| hypercenter | #126 | D443 |
| hypocenter | C443 | #563 |
| LCS | G ▷ C22×C443 ▷ C443 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28381886 | C2 | semidirect |
| 2. #28381885 | C2 | semidirect |
| 3. #28381881 | C2 | semidirect |
| 4. #28381880 | C2 | semidirect |
| 5. #28381879 | C2 | semidirect |
| 6. #28381877 | C2 | semidirect |
| 7. #28381876 | C2 | semidirect |
| 11. #28381866 | C2 | semidirect |
| 12. #28381864 | C2 | semidirect |
| 13. #28381863 | C2 | semidirect |
| 14. #28381863 | C2 | semidirect |
| 15. #126×C443 | C2 | semidirect |
| 97. C443 | #563 | semidirect |
| 104. #126 | D443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28381886 | 2 |
| #28381885 | 2 |
| #28381881 | 2 |
| #28381880 | 2 |
| #28381879 | 2 |
| #28381877 | 2 |
| #28381876 | 2 |
| #28381872 | 2 |
| #28381870 | 2 |
| #28381868 | 2 |
| #28381866 | 2 |
| #28381864 | 2 |
| #28381863 | 2 |
| #126×C443 | 2 |
| #563 | 443 |