Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16838036 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#472 | C2 |
| socle | C2×C59 | D42 |
| hypercenter | #472 | D59 |
| hypocenter | C59 | #3290 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #16838219 | C2 | semidirect |
| 2. #16838212 | C2 | semidirect |
| 3. #16838203 | C2 | semidirect |
| 4. #16837785 | C2 | semidirect |
| 5. #16837678 | C2 | semidirect |
| 6. #16837664 | C2 | semidirect |
| 7. #16837582 | C2 | semidirect |
| 8. #16837573 | C2 | semidirect |
| 9. #16837518 | C2 | semidirect |
| 10. #16837517 | C2 | semidirect |
| 11. C59×#472 | C2 | semidirect |
| 12. #14273774 | C22 | semidirect |
| 16. #14273760 | C22 | semidirect |
| 27. C2×Dic236 | C22 | semidirect |
| 28. C2×#11745670 | C22 | semidirect |
| 31. #14273735 | C22 | semidirect |
| 33. #14273714 | C22 | semidirect |
| 34. #14273662 | C22 | semidirect |
| 35. #14273654 | C22 | semidirect |
| 37. #14273653 | C22 | semidirect |
| 38. #14273645 | C22 | semidirect |
| 39. C8×Dic59 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C59 | C22 | semidirect |
| 42. #131×C59 | C22 | semidirect |
| 43. #108×C59 | C22 | semidirect |
| 44. #100×C59 | C22 | semidirect |
| 155. #472 | D59 | semidirect |
| 161. C59 | #3290 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D59 | semidirect |
| 185. #131 | C2×D59 | semidirect |
| 188. #108 | C2×D59 | semidirect |
| 193. #100 | C2×D59 | semidirect |