Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
484 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D47 |
| commutator | C4×C47 | C23×C4 |
| Frattini | C2×C4 | C23×D47 |
| Fitting | C47×#442 | C2 |
| socle | C22×C47 | C22×D4 |
| hypercenter | #442 | D47 |
| hypocenter | C47 | #2952 |
| LCS | G ▷ C4×C47 ▷ C2×C47 ▷ C47 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #442 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #15689602 | C2 | semidirect |
| 3. #15689235 | C2 | semidirect |
| 4. #15689231 | C2 | semidirect |
| 5. #15689229 | C2 | semidirect |
| 6. #15689214 | C2 | semidirect |
| 7. C4×#10625335 | C2 | semidirect |
| 8. #106×D47 | C2 | semidirect |
| 9. #15689121 | C2 | semidirect |
| 10. #15689080 | C2 | semidirect |
| 11. C47×#442 | C2 | semidirect |
| 13. #13094043 | C4 | semidirect |
| 46. #10625352 | C2×C4 | semidirect |
| 50. D8×C47 | C2×C4 | semidirect |
| 57. #10625335 | C2×C4 | semidirect |
| 69. Dic188 | C2×C4 | semidirect |
| 71. C8×D47 | C2×C4 | semidirect |
| 118. #442 | D47 | semidirect |
| 126. C47 | #2952 | semidirect |
| 167. D8 | C4×D47 | semidirect |