Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
4544 conjugacy classes of subgroups; only the 661 normal subgroups are shown.
This group has 4544 conjugacy classes of subgroups — too many to draw. Only its 661 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 | C22×C59 | C25 |
| Frattini | C22 | C24×D59 |
| Fitting | C2×#120×C59 | C2 |
| socle | C23×C59 | C24 |
| hypercenter | C2×#120 | D59 |
| hypocenter | C59 | C22×#120 |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C25×D59 | C2 | semidirect |
| 2. C22×D4×D59 | C2 | semidirect |
| 3. C2×#14273697 | C2 | semidirect |
| 4. C2×#14273696 | C2 | semidirect |
| 5. C2×#14273695 | C2 | semidirect |
| 6. #120×D59 | C2 | direct (N × H) |
| 7. C2×C22⋊C4×D59 | C2 | semidirect |
| 8. C2×#120×C59 | C2 | semidirect |
| 11. C24×D59 | C22 | semidirect |
| 12. C24×D59 | C22 | semidirect |
| 13. C24×D59 | C22 | semidirect |
| 14. C22×D236 | C22 | semidirect |
| 15. C22×C22⋊D59 | C22 | semidirect |
| 16. C22×C22⋊D59 | C22 | semidirect |
| 18. C2×D4×D59 | C22 | semidirect |
| 19. C22×C4×D59 | C22 | semidirect |
| 20. #14273697 | C22 | semidirect |
| 21. #14273696 | C22 | semidirect |
| 22. #14273695 | C22 | semidirect |
| 23. C2×C22⋊Dic59 | C22 | semidirect |
| 24. C2×(C2×D59)⋊C4 | C22 | semidirect |
| 25. C22⋊C4×D59 | C22 | semidirect |
| 26. C25×C59 | C22 | semidirect |
| 27. C22×D4×C59 | C22 | semidirect |
| 28. #120×C59 | C22 | semidirect |
| 29. C2×C22⋊C4×C59 | C22 | semidirect |
| 32. C24×C59 | C23 | semidirect |
| 33. C24×C59 | C23 | semidirect |
| 40. C23×D59 | D4 | semidirect |
| 44. C23×D59 | C23 | semidirect |
| 45. C23×D59 | C23 | semidirect |
| 46. C23×D59 | C23 | semidirect |
| 48. C2×D4×C59 | C23 | semidirect |
| 49. C22×C4×C59 | C23 | semidirect |
| 52. C2×C22⋊D59 | C23 | semidirect |
| 53. C2×C22⋊D59 | C23 | semidirect |
| 54. C22×Dic59 | C23 | semidirect |
| 57. C2×D236 | C23 | semidirect |
| 59. C2×C4×D59 | C23 | semidirect |
| 60. C22⋊C4×C59 | C23 | semidirect |
| 61. C22⋊Dic59 | C23 | semidirect |
| 62. (C2×D59)⋊C4 | C23 | semidirect |
| 67. C23×C59 | C2×D4 | semidirect |
| 70. C23×C59 | C24 | semidirect |
| 82. C22×D59 | C2×D4 | semidirect |
| 83. C22×D59 | C2×D4 | semidirect |
| 86. C22×D59 | C24 | semidirect |
| 89. C2×C4×C59 | C24 | semidirect |
| 93. C2×Dic59 | C24 | semidirect |
| 102. C22×C59 | C22×D4 | semidirect |
| 111. C2×D59 | #120 | direct (N × H) |
| 113. C2×D59 | C22×D4 | semidirect |
| 119. C2×C59 | C2×#120 | semidirect |
| 123. D59 | C2×#120 | direct (N × H) |
| 130. C2×#120 | D59 | direct (N × H) |
| 132. C59 | C22×#120 | semidirect |
| 138. C25 | C2×D59 | semidirect |
| 144. C22×D4 | C2×D59 | semidirect |
| 149. #120 | C2×D59 | direct (N × H) |
| 153. C2×C22⋊C4 | C2×D59 | semidirect |
| 169. C24 | C22×D59 | semidirect |
| 170. C24 | C22×D59 | semidirect |
| 179. C2×D4 | C22×D59 | semidirect |
| 183. C22×C4 | C22×D59 | semidirect |
| 186. C22⋊C4 | C22×D59 | semidirect |
| 207. C23 | D4×D59 | semidirect |
| 210. C23 | C23×D59 | semidirect |
| 219. C2×C4 | C23×D59 | semidirect |
| 236. C22 | C2×D4×D59 | semidirect |
| 245. C2 | #120×D59 | direct (N × H) |