Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
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×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#381 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #381 | D43 |
| hypocenter | C43 | C2×#381 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #381 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582762 | C2 | semidirect |
| 4. #14582761 | C2 | semidirect |
| 5. #14582760 | C2 | semidirect |
| 6. #95×D43 | C2 | semidirect |
| 7. C43×#381 | C2 | semidirect |
| 11. C22×C4×D43 | C4 | semidirect |
| 18. C43⋊#95 | C22 | semidirect |
| 19. C43⋊#95 | C22 | semidirect |
| 22. #95×C43 | C22 | semidirect |
| 30. C22×C4×C43 | C2×C4 | semidirect |
| 34. C22×Dic43 | C2×C4 | semidirect |
| 43. C2×C4×D43 | C2×C4 | semidirect |
| 96. D43 | #381 | direct (N × H) |
| 102. #381 | D43 | direct (N × H) |
| 104. C43 | C2×#381 | semidirect |
| 119. #95 | C2×D43 | semidirect |
| 138. C22×C4 | C4×D43 | semidirect |