Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
1412 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1412 conjugacy classes of subgroups — too many to draw. Only its 545 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C23×D356 |
| commutator, cosocle | C4×C89 | C25 |
| Frattini | C4 | C24×D89 |
| Fitting | #568×C89 | C2 |
| socle | C2×C89 | C23×D4 |
| hypercenter | #568 | D89 |
| hypocenter | C89 | #3586 |
| LCS | G ▷ C4×C89 ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #19152434 | C2 | semidirect |
| 2. C2×#15668059 | C2 | semidirect |
| 3. #19152415 | C2 | semidirect |
| 4. #19152410 | C2 | semidirect |
| 5. #19152398 | C2 | semidirect |
| 6. C2×#15668045 | C2 | semidirect |
| 7. #568×C89 | C2 | semidirect |
| 10. #15668059 | C22 | semidirect |
| 11. #15668059 | C22 | semidirect |
| 12. #15668058 | C22 | semidirect |
| 15. C2×#13083574 | C22 | semidirect |
| 18. C22×Dic178 | C22 | semidirect |
| 20. #15668045 | C22 | semidirect |
| 21. #15668045 | C22 | semidirect |
| 22. #15668045 | C22 | semidirect |
| 23. #15668040 | C22 | semidirect |
| 24. #15668040 | C22 | semidirect |
| 25. #15668034 | C22 | semidirect |
| 26. C2×Dic356 | C22 | semidirect |
| 27. C2×#13083563 | C22 | semidirect |
| 29. #131×C89 | C22 | semidirect |
| 30. C2×M16×C89 | C22 | semidirect |
| 113. C89 | #3586 | semidirect |
| 120. #568 | D89 | semidirect |
| 142. #131 | C2×D89 | semidirect |
| 143. C2×M16 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152434 | 2 |
| C2×#15668059 | 2 |
| #19152415 | 2 |
| #19152410 | 2 |
| #19152398 | 2 |
| C2×#15668045 | 2 |
| #568×C89 | 2 |
| #3586 | 89 |