Finite Group DatabasebetaFinite Group DatabasebetaOrder 11584.
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×D181 |
| commutator, socle, cosocle | C22×C181 | C24 |
| Fitting | #126×C181 | C2 |
| prime radical | C2×C22⋊D181 | C22 |
| hypercenter | #126 | D181 |
| hypocenter | C181 | #563 |
| 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. #19153816 | C2 | semidirect |
| 2. #19153815 | C2 | semidirect |
| 3. #19153811 | C2 | semidirect |
| 4. #19153810 | C2 | semidirect |
| 5. #19153809 | C2 | semidirect |
| 6. #19153807 | C2 | semidirect |
| 7. #19153806 | C2 | semidirect |
| 11. #19153796 | C2 | semidirect |
| 12. #19153794 | C2 | semidirect |
| 13. #19153793 | C2 | semidirect |
| 14. #19153793 | C2 | semidirect |
| 15. #126×C181 | C2 | semidirect |
| 97. C181 | #563 | semidirect |
| 104. #126 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153816 | 2 |
| #19153815 | 2 |
| #19153811 | 2 |
| #19153810 | 2 |
| #19153809 | 2 |
| #19153807 | 2 |
| #19153806 | 2 |
| #19153802 | 2 |
| #19153800 | 2 |
| #19153798 | 2 |
| #19153796 | 2 |
| #19153794 | 2 |
| #19153793 | 2 |
| #126×C181 | 2 |
| #563 | 181 |