Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D89 |
| commutator, socle, cosocle | C23×C89 | C24 |
| Fitting | #396×C89 | C2 |
| prime radical | C22×C22⋊D89 | C22 |
| hypercenter | #396 | D89 |
| hypocenter | C89 | #2643 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #396 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89⋊#401 | C2 | semidirect |
| 2. #19151536 | C2 | semidirect |
| 3. #19151526 | C2 | semidirect |
| 5. #19151469 | C2 | semidirect |
| 6. #95×D89 | C2 | semidirect |
| 7. #396×C89 | C2 | semidirect |
| 79. C89 | #2643 | semidirect |
| 83. #396 | D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89⋊#401 | 2 |
| #19151536 | 2 |
| #19151526 | 2 |
| #19151474 | 2 |
| #19151469 | 2 |
| #95×D89 | 2 |
| #396×C89 | 2 |
| #2643 | 89 |