Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
950 conjugacy classes of subgroups; only the 449 normal subgroups are shown.
This group has 950 conjugacy classes of subgroups — too many to draw. Only its 449 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 | C24×D89 |
| commutator, socle, cosocle | C22×C89 | C25 |
| Fitting | #564×C89 | C2 |
| hypercenter | #564 | D89 |
| hypocenter | C89 | #3567 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C22 ◁ #564 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19152346 | C2 | semidirect |
| 2. #19152301 | C2 | semidirect |
| 3. #19152280 | C2 | semidirect |
| 4. #19152204 | C2 | semidirect |
| 5. #19152196 | C2 | semidirect |
| 6. #19152133 | C2 | semidirect |
| 7. #564×C89 | C2 | semidirect |
| 100. C89 | #3567 | semidirect |
| 101. #564 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152346 | 2 |
| #19152301 | 2 |
| #19152280 | 2 |
| #19152204 | 2 |
| #19152196 | 2 |
| #19152133 | 2 |
| #564×C89 | 2 |
| #3567 | 89 |