Finite Group DatabasebetaFinite Group DatabasebetaOrder 11584.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #121×C181 | C2 |
| hypercenter | #121 | D181 |
| hypocenter | C181 | #540 |
| LCS | G ▷ C22×C181 ▷ C181 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19153812 | C2 | semidirect |
| 2. #19153807 | C2 | semidirect |
| 3. #19153800 | C2 | semidirect |
| 4. #19153798 | C2 | semidirect |
| 5. #19153790 | C2 | semidirect |
| 6. #19153788 | C2 | semidirect |
| 7. #19153787 | C2 | semidirect |
| 8. D4×Dic181 | C2 | semidirect |
| 9. #19153778 | C2 | semidirect |
| 10. #19153775 | C2 | semidirect |
| 11. #121×C181 | C2 | semidirect |
| 79. C181 | #540 | semidirect |
| 88. #121 | D181 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153812 | 2 |
| #19153807 | 2 |
| #19153800 | 2 |
| #19153798 | 2 |
| #19153790 | 2 |
| #19153788 | 2 |
| #19153787 | 2 |
| D4×Dic181 | 2 |
| #19153778 | 2 |
| #19153775 | 2 |
| #121×C181 | 2 |
| #540 | 181 |