Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D188 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#443 | C2 |
| socle | C2×C47 | D42 |
| hypercenter | #443 | D47 |
| hypocenter | C47 | #3290 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689937 | C2 | semidirect |
| 2. #15689935 | C2 | semidirect |
| 3. #15689925 | C2 | semidirect |
| 4. #15689507 | C2 | semidirect |
| 5. #15689399 | C2 | semidirect |
| 6. #15689394 | C2 | semidirect |
| 7. #15689386 | C2 | semidirect |
| 8. #15689302 | C2 | semidirect |
| 9. #15689297 | C2 | semidirect |
| 10. #15689241 | C2 | semidirect |
| 11. C47×#443 | C2 | semidirect |
| 12. #13094071 | C22 | semidirect |
| 16. #13094054 | C22 | semidirect |
| 19. #13094052 | C22 | semidirect |
| 26. C2×Dic188 | C22 | semidirect |
| 29. C2×#10625325 | C22 | semidirect |
| 33. #13094030 | C22 | semidirect |
| 34. #13094012 | C22 | semidirect |
| 35. #13093960 | C22 | semidirect |
| 37. #13093952 | C22 | semidirect |
| 38. #13093942 | C22 | semidirect |
| 39. #13093940 | C22 | semidirect |
| 41. #131×C47 | C22 | semidirect |
| 42. #108×C47 | C22 | semidirect |
| 43. #104×C47 | C22 | semidirect |
| 44. C4×C8×C47 | C22 | semidirect |
| 160. #443 | D47 | semidirect |
| 161. C47 | #3290 | semidirect |
| 185. #131 | C2×D47 | semidirect |
| 188. #108 | C2×D47 | semidirect |
| 191. #104 | C2×D47 | semidirect |
| 194. C4×C8 | C2×D47 | semidirect |