Finite Group DatabasebetaFinite Group DatabasebetaOrder 11584.
236 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #117×C181 | C2 |
| hypercenter | #117 | D181 |
| hypocenter | C181 | #555 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19153815 | C2 | semidirect |
| 2. #19153804 | C2 | semidirect |
| 3. #19153802 | C2 | semidirect |
| 4. #19153791 | C2 | semidirect |
| 5. #19153790 | C2 | semidirect |
| 6. #19153789 | C2 | semidirect |
| 7. #19153778 | C2 | semidirect |
| 8. C4×C22⋊D181 | C2 | semidirect |
| 9. #19153774 | C2 | semidirect |
| 10. #19153773 | C2 | semidirect |
| 11. #117×C181 | C2 | semidirect |
| 78. C181 | #555 | semidirect |
| 90. #117 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153815 | 2 |
| #19153804 | 2 |
| #19153802 | 2 |
| #19153791 | 2 |
| #19153790 | 2 |
| #19153789 | 2 |
| #19153778 | 2 |
| C4×C22⋊D181 | 2 |
| #19153774 | 2 |
| #19153773 | 2 |
| #117×C181 | 2 |
| #555 | 181 |