Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D236 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#424 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #424 | D59 |
| hypocenter | C59 | #3045 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #424 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273755 | C2 | semidirect |
| 2. C2×#14273749 | C2 | semidirect |
| 3. #16837971 | C2 | semidirect |
| 4. #16837882 | C2 | semidirect |
| 5. #16837625 | C2 | semidirect |
| 6. #16837618 | C2 | semidirect |
| 7. #16837603 | C2 | semidirect |
| 8. #16837598 | C2 | semidirect |
| 9. #16837404 | C2 | semidirect |
| 10. C2×#14273649 | C2 | semidirect |
| 11. C59×#424 | C2 | semidirect |
| 17. C2×Dic236 | C22 | semidirect |
| 19. C2×#11745660 | C22 | semidirect |
| 20. C2×#11745660 | C22 | semidirect |
| 22. C2×D472 | C22 | semidirect |
| 28. C4×Dic118 | C22 | semidirect |
| 29. C4×D236 | C22 | semidirect |
| 34. #14273652 | C22 | semidirect |
| 37. #14273649 | C22 | semidirect |
| 41. C4⋊C8×C59 | C22 | semidirect |
| 42. C4⋊C8×C59 | C22 | semidirect |
| 51. #11745685 | D4 | semidirect |
| 163. #424 | D59 | semidirect |
| 166. C59 | #3045 | semidirect |
| 192. C4⋊C8 | C2×D59 | semidirect |
| 193. C4⋊C8 | C2×D59 | semidirect |