Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
424 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 137 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 | #381×C89 | C2 |
| prime radical | C24×C89 | C23 |
| hypercenter | #381 | D89 |
| hypocenter | C89 | #2665 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19151540 | C2 | semidirect |
| 3. #19151519 | C2 | semidirect |
| 5. #19151502 | C2 | semidirect |
| 6. #19151481 | C2 | semidirect |
| 48. C22×C4×C89 | Q8 | semidirect |
| 109. C89 | #2665 | semidirect |
| 149. C22×C4 | Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19151540 | 2 |
| #19151521 | 2 |
| #19151519 | 2 |
| #19151510 | 2 |
| #19151502 | 2 |
| #19151481 | 2 |
| #19151458 | 2 |
| C4×C22⋊Dic89 | 2 |
| #381×C89 | 2 |
| #2665 | 89 |