Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | #121×D47 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#472 | C2 |
| socle | C2×C47 | C2×#121 |
| hypercenter | #472 | D47 |
| hypocenter | C47 | #3067 |
| 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. #15689919 | C2 | semidirect |
| 2. C2×#13094043 | C2 | semidirect |
| 3. #131×D47 | C2 | semidirect |
| 4. #15689399 | C2 | semidirect |
| 5. #15689398 | C2 | semidirect |
| 6. #15689390 | C2 | semidirect |
| 7. #15689385 | C2 | semidirect |
| 8. #15689384 | C2 | semidirect |
| 9. #108×D47 | C2 | semidirect |
| 10. #15689104 | C2 | semidirect |
| 11. C47×#472 | C2 | semidirect |
| 25. C2×Dic188 | C22 | semidirect |
| 26. C2×#10625335 | C22 | semidirect |
| 37. #13093960 | C22 | semidirect |
| 38. #13093959 | C22 | semidirect |
| 39. #13093942 | C22 | semidirect |
| 40. #13093942 | C22 | semidirect |
| 41. #13093941 | C22 | semidirect |
| 43. C2×D8×C47 | C22 | semidirect |
| 45. #108×C47 | C22 | semidirect |
| 46. #100×C47 | C22 | semidirect |
| 173. #472 | D47 | semidirect |
| 178. C47 | #3067 | semidirect |
| 195. C2×D8 | C2×D47 | semidirect |
| 209. #108 | C2×D47 | semidirect |
| 213. #100 | C2×D47 | semidirect |