Finite Group DatabasebetaFinite Group DatabasebetaOrder 6016.
1144 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 269 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 | C47×#381 | C2 |
| socle | C23×C47 | C24 |
| hypercenter | #381 | D47 |
| hypocenter | C47 | C2×#381 |
| LCS | G ▷ C22×C47 ▷ C47 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #15688986 | C2 | semidirect |
| 4. #15688985 | C2 | semidirect |
| 5. #15688984 | C2 | semidirect |
| 6. #95×D47 | C2 | semidirect |
| 7. C47×#381 | C2 | semidirect |
| 11. C22×C4×D47 | C4 | semidirect |
| 18. C47⋊#95 | C22 | semidirect |
| 19. C47⋊#95 | C22 | semidirect |
| 22. #95×C47 | C22 | semidirect |
| 30. C22×C4×C47 | C2×C4 | semidirect |
| 34. C22×Dic47 | C2×C4 | semidirect |
| 43. C2×C4×D47 | C2×C4 | semidirect |
| 96. D47 | #381 | direct (N × H) |
| 102. #381 | D47 | direct (N × H) |
| 104. C47 | C2×#381 | semidirect |
| 119. #95 | C2×D47 | semidirect |
| 138. C22×C4 | C4×D47 | semidirect |