Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
6560 conjugacy classes of subgroups; only the 3221 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D59 |
| commutator | C2×C59 | C26 |
| Frattini | C2 | C25×D59 |
| Fitting | C22×#41×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C22×#41 | D59 |
| hypocenter | C59 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14273773 | C2 | direct (N × H) |
| 2. C22×#11745689 | C2 | semidirect |
| 3. C22×#11745685 | C2 | semidirect |
| 4. C23×D236 | C2 | semidirect |
| 5. C22×D4×D59 | C2 | semidirect |
| 6. C22×#41×C59 | C2 | semidirect |
| 7. C24×D59 | C22 | semidirect |
| 8. #14273773 | C22 | direct (N × H) |
| 9. C2×#11745689 | C22 | semidirect |
| 10. C2×#11745685 | C22 | semidirect |
| 11. C22×Dic118 | C22 | semidirect |
| 12. C22×D236 | C22 | semidirect |
| 13. C22×D236 | C22 | semidirect |
| 14. C22×D236 | C22 | semidirect |
| 15. C22×C22⋊D59 | C22 | semidirect |
| 16. C2×D4×D59 | C22 | semidirect |
| 17. C22×C4×D59 | C22 | semidirect |
| 18. C2×#41×C59 | C22 | semidirect |
| 19. C22×Q8×C59 | C22 | semidirect |
| 20. C22×D4×C59 | C22 | semidirect |
| 21. C23×C4×C59 | C22 | semidirect |
| 25. C23×D59 | C23 | semidirect |
| 26. #41×C59 | C23 | semidirect |
| 27. C2×Q8×C59 | C23 | semidirect |
| 28. C2×D4×C59 | C23 | semidirect |
| 31. C22×C4×C59 | C23 | semidirect |
| 32. C2×C22⋊D59 | C23 | semidirect |
| 34. #11745689 | C23 | semidirect |
| 35. D4×D59 | C23 | semidirect |
| 36. #11745685 | C23 | semidirect |
| 37. C2×D236 | C23 | semidirect |
| 38. C2×D236 | C23 | semidirect |
| 39. C2×D236 | C23 | semidirect |
| 40. C2×C4×D59 | C23 | semidirect |
| 41. C2×Dic118 | C23 | semidirect |
| 48. C22×D59 | C24 | semidirect |
| 49. Q8×C59 | C24 | semidirect |
| 50. D4×C59 | C24 | semidirect |
| 53. C2×C4×C59 | C24 | semidirect |
| 54. C22⋊D59 | C24 | semidirect |
| 56. D236 | C24 | semidirect |
| 57. D236 | C24 | semidirect |
| 58. C4×D59 | C24 | semidirect |
| 59. Dic118 | C24 | semidirect |
| 61. C22×C59 | H(5,𝔽2) | semidirect |
| 72. C2×C59 | C2×H(5,𝔽2) | semidirect |
| 78. C22×#41 | D59 | semidirect |
| 81. C59 | C22×H(5,𝔽2) | semidirect |
| 86. C2×#41 | C2×D59 | semidirect |
| 88. C22×Q8 | C2×D59 | semidirect |
| 94. C22×D4 | C2×D59 | semidirect |
| 96. C23×C4 | C2×D59 | semidirect |
| 103. #41 | C22×D59 | semidirect |
| 105. C2×Q8 | C22×D59 | semidirect |
| 111. C2×D4 | C22×D59 | semidirect |
| 116. C22×C4 | C22×D59 | semidirect |
| 125. Q8 | C23×D59 | semidirect |
| 129. D4 | C23×D59 | semidirect |
| 134. C2×C4 | C23×D59 | semidirect |
| 139. C22 | #14273773 | direct (N × H) |
| 147. C2 | C2×#14273773 | direct (N × H) |