Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D188 |
| commutator | C2×C4×C47 | C24 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#405 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #405 | D47 |
| hypocenter | C47 | #3136 |
| LCS | G ▷ C2×C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ #117 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #15689751 | C2 | semidirect |
| 3. #15689488 | C2 | semidirect |
| 4. #15689483 | C2 | semidirect |
| 5. #15689478 | C2 | semidirect |
| 6. #15689470 | C2 | semidirect |
| 7. #15689129 | C2 | semidirect |
| 8. #15689125 | C2 | semidirect |
| 9. #15689120 | C2 | semidirect |
| 10. C2×#13093946 | C2 | semidirect |
| 11. C47×#405 | C2 | semidirect |
| 14. #13094024 | C22 | semidirect |
| 17. #13094016 | C22 | semidirect |
| 26. #13093949 | C22 | semidirect |
| 27. #13093949 | C22 | semidirect |
| 28. #13093949 | C22 | semidirect |
| 33. #13093946 | C22 | semidirect |
| 34. #13093946 | C22 | semidirect |
| 35. #13093946 | C22 | semidirect |
| 39. #97×C47 | C22 | semidirect |
| 40. C4×C8×C47 | C22 | semidirect |
| 146. #405 | D47 | semidirect |
| 147. C47 | #3136 | semidirect |
| 175. #97 | C2×D47 | semidirect |
| 176. C4×C8 | C2×D47 | semidirect |