Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D4×D43 |
| commutator | C4×C43 | C23×C4 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C43×#430 | C2 |
| socle | C2×C43 | C2×C4×D4 |
| hypercenter | #430 | D43 |
| hypocenter | C43 | #2955 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #430 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063333 | C2 | semidirect |
| 3. #14583020 | C2 | semidirect |
| 4. #14583015 | C2 | semidirect |
| 5. #14582915 | C2 | semidirect |
| 6. #14582857 | C2 | semidirect |
| 7. C43×#430 | C2 | semidirect |
| 9. #13063358 | C4 | semidirect |
| 10. #13063353 | C4 | semidirect |
| 14. #13063333 | C22 | semidirect |
| 15. #13063333 | C22 | semidirect |
| 20. #13063251 | C22 | semidirect |
| 21. #13063235 | C22 | semidirect |
| 22. C8×Dic43 | C22 | semidirect |
| 25. #108×C43 | C22 | semidirect |
| 94. #430 | D43 | semidirect |
| 97. C43 | #2955 | semidirect |
| 112. #108 | C2×D43 | semidirect |