Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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 | #380×C89 | C2 |
| prime radical | C24×D89 | C22 |
| hypercenter | #380 | D89 |
| hypocenter | C89 | #2626 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #380 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15667991 | C2 | semidirect |
| 3. #19151535 | C2 | semidirect |
| 4. #19151520 | C2 | semidirect |
| 5. #19151511 | C2 | semidirect |
| 6. #19151473 | C2 | semidirect |
| 8. #380×C89 | C2 | semidirect |
| 10. C22×Dic178 | C22 | semidirect |
| 13. C2×C4⋊Dic89 | C22 | semidirect |
| 14. C2×C4⋊Dic89 | C22 | semidirect |
| 15. C2×#13083553 | C22 | semidirect |
| 22. #15667919 | C22 | semidirect |
| 24. C2×C4⋊C4×C89 | C22 | semidirect |
| 26. #95×C89 | C22 | semidirect |
| 31. C23×D89 | Q8 | semidirect |
| 118. C89 | #2626 | semidirect |
| 125. #380 | D89 | semidirect |
| 135. C2×C4⋊C4 | C2×D89 | semidirect |
| 144. #95 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15667991 | 2 |
| C22×#13083551 | 2 |
| #19151535 | 2 |
| #19151520 | 2 |
| #19151511 | 2 |
| #19151473 | 2 |
| #19151453 | 2 |
| #380×C89 | 2 |
| #2626 | 89 |