Finite Group DatabasebetaFinite Group DatabasebetaOrder 28096.
218 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 93 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×D439 |
| commutator, socle, cosocle | C22×C439 | C24 |
| Fitting | #126×C439 | C2 |
| prime radical | #28380716 | C2 |
| hypercenter | #126 | D439 |
| hypocenter | C439 | #539 |
| LCS | G ▷ C22×C439 ▷ C439 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28380738 | C2 | semidirect |
| 2. #28380735 | C2 | semidirect |
| 3. #28380734 | C2 | semidirect |
| 4. #28380728 | C2 | semidirect |
| 5. #28380727 | C2 | semidirect |
| 6. #28380725 | C2 | semidirect |
| 7. #28380725 | C2 | semidirect |
| 8. #28380723 | C2 | semidirect |
| 9. #28380721 | C2 | semidirect |
| 10. #28380720 | C2 | semidirect |
| 12. C4×D1756 | C2 | semidirect |
| 13. (C22⋊D439)⋊C4 | C2 | semidirect |
| 14. C4⋊C4×D439 | C2 | semidirect |
| 15. #126×C439 | C2 | semidirect |
| 103. C439 | #539 | semidirect |
| 106. #126 | D439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28380738 | 2 |
| #28380735 | 2 |
| #28380734 | 2 |
| #28380728 | 2 |
| #28380727 | 2 |
| #28380725 | 2 |
| #28380723 | 2 |
| #28380721 | 2 |
| #28380720 | 2 |
| #28380716 | 2 |
| C4×D1756 | 2 |
| (C22⋊D439)⋊C4 | 2 |
| C4⋊C4×D439 | 2 |
| #126×C439 | 2 |
| #539 | 439 |