Finite Group DatabasebetaFinite Group DatabasebetaOrder 11584.
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×D181 |
| commutator, socle, cosocle | C22×C181 | C24 |
| Fitting | #126×C181 | C2 |
| prime radical | #19153789 | C2 |
| hypercenter | #126 | D181 |
| hypocenter | C181 | #539 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19153811 | C2 | semidirect |
| 2. #19153808 | C2 | semidirect |
| 3. #19153807 | C2 | semidirect |
| 4. #19153801 | C2 | semidirect |
| 5. #19153800 | C2 | semidirect |
| 6. #19153798 | C2 | semidirect |
| 7. #19153798 | C2 | semidirect |
| 8. #19153796 | C2 | semidirect |
| 9. #19153794 | C2 | semidirect |
| 10. #19153793 | C2 | semidirect |
| 12. C4×D724 | C2 | semidirect |
| 13. #19153776 | C2 | semidirect |
| 14. C4⋊C4×D181 | C2 | semidirect |
| 15. #126×C181 | C2 | semidirect |
| 103. C181 | #539 | semidirect |
| 106. #126 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153811 | 2 |
| #19153808 | 2 |
| #19153807 | 2 |
| #19153801 | 2 |
| #19153800 | 2 |
| #19153798 | 2 |
| #19153796 | 2 |
| #19153794 | 2 |
| #19153793 | 2 |
| #19153789 | 2 |
| C4×D724 | 2 |
| #19153776 | 2 |
| C4⋊C4×D181 | 2 |
| #126×C181 | 2 |
| #539 | 181 |