Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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 | C22×C89 | C23×C4 |
| Fitting | #384×C89 | C2 |
| socle, cosocle | C23×C89 | C24 |
| prime radical | C23×D89 | C23 |
| hypercenter | #384 | D89 |
| hypocenter | C89 | #2317 |
| LCS | G ▷ C22×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #19151493 | C2 | semidirect |
| 6. #19151467 | C2 | semidirect |
| 7. #19151464 | C2 | semidirect |
| 8. #19151463 | C2 | semidirect |
| 9. #384×C89 | C2 | semidirect |
| 13. #15667969 | C4 | semidirect |
| 44. #13083553 | C2×C4 | semidirect |
| 48. C4×Dic89 | C2×C4 | semidirect |
| 56. C42×C89 | C2×C4 | semidirect |
| 84. C4×D89 | C4⋊C4 | semidirect |
| 110. C89 | #2317 | semidirect |
| 117. #384 | D89 | semidirect |
| 166. C42 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667970 | 2 |
| C2×#15667969 | 2 |
| C2×C4⋊C4×D89 | 2 |
| #19151493 | 2 |
| #19151469 | 2 |
| #19151467 | 2 |
| #19151464 | 2 |
| #19151463 | 2 |
| #384×C89 | 2 |
| #2317 | 89 |