Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
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 | #15689757 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#472 | C2 |
| socle | C2×C47 | D42 |
| hypercenter | #472 | D47 |
| hypocenter | C47 | #3290 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #472 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689940 | C2 | semidirect |
| 2. #15689933 | C2 | semidirect |
| 3. #15689924 | C2 | semidirect |
| 4. #15689506 | C2 | semidirect |
| 5. #15689399 | C2 | semidirect |
| 6. #15689385 | C2 | semidirect |
| 7. #15689303 | C2 | semidirect |
| 8. #15689294 | C2 | semidirect |
| 9. #15689239 | C2 | semidirect |
| 10. #15689238 | C2 | semidirect |
| 11. C47×#472 | C2 | semidirect |
| 12. #13094071 | C22 | semidirect |
| 16. #13094057 | C22 | semidirect |
| 27. C2×Dic188 | C22 | semidirect |
| 28. C2×#10625335 | C22 | semidirect |
| 31. #13094032 | C22 | semidirect |
| 33. #13094011 | C22 | semidirect |
| 34. #13093959 | C22 | semidirect |
| 35. #13093951 | C22 | semidirect |
| 37. #13093950 | C22 | semidirect |
| 38. #13093942 | C22 | semidirect |
| 39. C8×Dic47 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C47 | C22 | semidirect |
| 42. #131×C47 | C22 | semidirect |
| 43. #108×C47 | C22 | semidirect |
| 44. #100×C47 | C22 | semidirect |
| 155. #472 | D47 | semidirect |
| 161. C47 | #3290 | semidirect |
| 171. AGL(1,ℤ/8) | C2×D47 | semidirect |
| 185. #131 | C2×D47 | semidirect |
| 188. #108 | C2×D47 | semidirect |
| 193. #100 | C2×D47 | semidirect |