Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D59 |
| commutator | C2×C59 | C26 |
| Frattini | C2 | C25×D59 |
| Fitting | C2×2−1+4×C59 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | C2×2−1+4 | D59 |
| hypocenter | C59 | C2×#585 |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838239 | C2 | direct (N × H) |
| 2. C2×#14273775 | C2 | semidirect |
| 3. C2×#14273773 | C2 | semidirect |
| 4. C22×#11745689 | C2 | semidirect |
| 5. C2×#41×D59 | C2 | semidirect |
| 6. C2×2−1+4×C59 | C2 | semidirect |
| 7. #14273775 | C22 | semidirect |
| 8. #14273773 | C22 | semidirect |
| 9. C2×#11745689 | C22 | semidirect |
| 10. C2×#11745689 | C22 | semidirect |
| 11. C2×#11745689 | C22 | semidirect |
| 12. C2×#11745685 | C22 | semidirect |
| 13. C2×#11745687 | C22 | semidirect |
| 14. #41×D59 | C22 | semidirect |
| 15. C2×Q8×D59 | C22 | semidirect |
| 16. C22×D236 | C22 | semidirect |
| 17. C2×D4×D59 | C22 | semidirect |
| 18. C22×C4×D59 | C22 | semidirect |
| 19. 2−1+4×C59 | C22 | semidirect |
| 20. C2×#41×C59 | C22 | semidirect |
| 21. C22×Q8×C59 | C22 | semidirect |
| 23. #41×C59 | C23 | semidirect |
| 25. C2×Q8×C59 | C23 | semidirect |
| 30. #11745689 | C23 | semidirect |
| 31. #11745689 | C23 | semidirect |
| 32. Q8×D59 | C23 | semidirect |
| 33. #11745687 | C23 | semidirect |
| 34. D4×D59 | C23 | semidirect |
| 35. #11745685 | C23 | semidirect |
| 37. C2×D236 | C23 | semidirect |
| 40. C2×C4×D59 | C23 | semidirect |
| 69. C2×C59 | #585 | semidirect |
| 74. C2×2−1+4 | D59 | semidirect |
| 78. C59 | C2×#585 | semidirect |
| 80. 2−1+4 | C2×D59 | semidirect |
| 88. C2×#41 | C2×D59 | semidirect |
| 90. C22×Q8 | C2×D59 | semidirect |
| 99. #41 | C22×D59 | semidirect |
| 103. C2×Q8 | C22×D59 | semidirect |
| 141. C2 | #16838239 | direct (N × H) |