Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
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×D236 |
| commutator | C4×C59 | C25 |
| Frattini | C4 | C24×D59 |
| Fitting | C59×#568 | C2 |
| socle | C2×C59 | C23×D4 |
| hypercenter | #568 | D59 |
| hypocenter | C59 | #3586 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C2×#41 ◁ #568 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838238 | C2 | semidirect |
| 2. C2×#14273774 | C2 | semidirect |
| 3. #16838219 | C2 | semidirect |
| 4. #16838214 | C2 | semidirect |
| 5. #16838202 | C2 | semidirect |
| 6. C2×#14273760 | C2 | semidirect |
| 7. C59×#568 | C2 | semidirect |
| 10. #14273774 | C22 | semidirect |
| 11. #14273774 | C22 | semidirect |
| 12. #14273773 | C22 | semidirect |
| 15. C2×#11745685 | C22 | semidirect |
| 18. C22×Dic118 | C22 | semidirect |
| 20. #14273760 | C22 | semidirect |
| 21. #14273760 | C22 | semidirect |
| 22. #14273760 | C22 | semidirect |
| 23. #14273755 | C22 | semidirect |
| 24. #14273755 | C22 | semidirect |
| 25. #14273749 | C22 | semidirect |
| 26. C2×Dic236 | C22 | semidirect |
| 27. C2×#11745660 | C22 | semidirect |
| 29. #131×C59 | C22 | semidirect |
| 30. C2×M16×C59 | C22 | semidirect |
| 119. #568 | D59 | semidirect |
| 120. C59 | #3586 | semidirect |
| 142. #131 | C2×D59 | semidirect |
| 143. C2×M16 | C2×D59 | semidirect |