Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
596 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 596 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 | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#493 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #493 | D59 |
| hypocenter | C59 | #3155 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #493 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273751 | C2 | semidirect |
| 2. C2×#14273746 | C2 | semidirect |
| 3. C2×D8×D59 | C2 | semidirect |
| 4. #16837965 | C2 | semidirect |
| 5. #16837790 | C2 | semidirect |
| 6. #16837789 | C2 | semidirect |
| 7. #16837786 | C2 | semidirect |
| 8. #16837785 | C2 | semidirect |
| 9. #16837777 | C2 | semidirect |
| 10. #16837356 | C2 | semidirect |
| 11. C59×#493 | C2 | semidirect |
| 16. C2×Dic236 | C22 | semidirect |
| 17. C2×#11745660 | C22 | semidirect |
| 18. C2×#11745670 | C22 | semidirect |
| 19. C2×#11745670 | C22 | semidirect |
| 22. C2×#11745669 | C22 | semidirect |
| 26. #14273723 | C22 | semidirect |
| 27. #14273715 | C22 | semidirect |
| 28. #14273714 | C22 | semidirect |
| 32. #14273638 | C22 | semidirect |
| 33. #14273637 | C22 | semidirect |
| 34. C8×Dic59 | C22 | semidirect |
| 36. C2×D8×C59 | C22 | semidirect |
| 37. C2×D8×C59 | C22 | semidirect |
| 38. #127×C59 | C22 | semidirect |
| 39. C4×C8×C59 | C22 | semidirect |
| 75. #11745659 | D4 | semidirect |
| 76. C8×D59 | D4 | semidirect |
| 139. #493 | D59 | semidirect |
| 141. C59 | #3155 | semidirect |
| 155. C2×D8 | C2×D59 | semidirect |
| 156. C2×D8 | C2×D59 | semidirect |
| 160. #127 | C2×D59 | semidirect |
| 169. C4×C8 | C2×D59 | semidirect |