Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
688 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 688 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 | #386×C89 | C2 |
| prime radical | C2×#15667980 | C2 |
| hypercenter | #386 | D89 |
| hypocenter | C89 | #2684 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #386 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667999 | C2 | semidirect |
| 3. #19151523 | C2 | semidirect |
| 4. #19151514 | C2 | semidirect |
| 5. #19151511 | C2 | semidirect |
| 6. #19151490 | C2 | semidirect |
| 7. #19151477 | C2 | semidirect |
| 8. #19151453 | C2 | semidirect |
| 9. #386×C89 | C2 | semidirect |
| 11. C22×Dic178 | C22 | semidirect |
| 15. C2×C4⋊Dic89 | C22 | semidirect |
| 18. C2×C22⋊Dic89 | C22 | semidirect |
| 24. C2×C4×Dic89 | C22 | semidirect |
| 25. #15667919 | C22 | semidirect |
| 26. #15667919 | C22 | semidirect |
| 27. #15667919 | C22 | semidirect |
| 29. C23×C4×C89 | C22 | semidirect |
| 31. C2×C22⋊C4×C89 | C22 | semidirect |
| 32. #95×C89 | C22 | semidirect |
| 153. C89 | #2684 | semidirect |
| 161. #386 | D89 | semidirect |
| 167. C23×C4 | C2×D89 | semidirect |
| 180. C2×C22⋊C4 | C2×D89 | semidirect |
| 185. #95 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667999 | 2 |
| C2×#15667980 | 2 |
| #19151523 | 2 |
| #19151514 | 2 |
| #19151511 | 2 |
| #19151490 | 2 |
| #19151477 | 2 |
| #19151453 | 2 |
| #386×C89 | 2 |
| #2684 | 89 |