Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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 | #3041 |
| 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. C22×D472 | C2 | semidirect |
| 3. #16837971 | C2 | semidirect |
| 4. #16837876 | C2 | semidirect |
| 5. #16837618 | C2 | semidirect |
| 6. #16837598 | C2 | semidirect |
| 7. #16837408 | C2 | semidirect |
| 8. #16837399 | C2 | semidirect |
| 9. C59×#424 | C2 | semidirect |
| 14. C2×#11745660 | C22 | semidirect |
| 17. C2×D472 | C22 | semidirect |
| 18. #14273724 | C22 | semidirect |
| 19. #14273715 | C22 | semidirect |
| 22. C4×D236 | C22 | semidirect |
| 26. #14273652 | C22 | semidirect |
| 27. #14273649 | C22 | semidirect |
| 28. #14273649 | C22 | semidirect |
| 32. C4⋊C8×C59 | C22 | semidirect |
| 45. C2×D236 | D4 | semidirect |
| 128. #424 | D59 | semidirect |
| 131. C59 | #3041 | semidirect |
| 151. C4⋊C8 | C2×D59 | semidirect |