Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
740 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 205 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D47 |
| commutator | C22×C47 | C23×C4 |
| Fitting | C2×C4×D4×C47 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | C2×C4×D4 | D47 |
| hypocenter | C47 | #2328 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ C2×C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C4×D188 | C2 | semidirect |
| 3. #15689026 | C2 | semidirect |
| 4. #15689024 | C2 | semidirect |
| 5. #15689002 | C2 | semidirect |
| 6. #15688999 | C2 | semidirect |
| 7. #15688988 | C2 | semidirect |
| 8. #15688969 | C2 | semidirect |
| 9. C2×C4×D4×C47 | C2 | semidirect |
| 13. #13094020 | C4 | semidirect |
| 34. C2×D4×C47 | C2×C4 | semidirect |
| 43. C2×C22⋊D47 | C2×C4 | semidirect |
| 49. C2×D188 | C2×C4 | semidirect |
| 54. C42×C47 | D4 | semidirect |
| 60. C4×Dic47 | C2×C4 | semidirect |
| 126. C2×C4×D4 | D47 | semidirect |
| 133. C47 | #2328 | semidirect |
| 164. C2×D4 | C4×D47 | semidirect |
| 184. C42 | C22⋊D47 | semidirect |