Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1088 conjugacy classes of subgroups; only the 261 normal subgroups are shown.
This group has 1088 conjugacy classes of subgroups — too many to draw. Only its 261 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×#379 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #379 | D43 |
| hypocenter | C43 | #2280 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #379 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063281 | C2 | semidirect |
| 3. #14582760 | C2 | semidirect |
| 4. #14582757 | C2 | semidirect |
| 6. C22⋊C4×Dic43 | C2 | semidirect |
| 9. C23×Dic43 | C4 | semidirect |
| 15. C2×Dic43⋊C4 | C22 | semidirect |
| 18. C2×C4×Dic43 | C22 | semidirect |
| 19. C43⋊#95 | C22 | semidirect |
| 67. C2×Dic43 | C22⋊C4 | semidirect |
| 80. C22×C43 | #117 | semidirect |
| 102. C43 | #2280 | semidirect |
| 175. C22 | #13063281 | semidirect |