Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
766 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 161 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063294 |
| commutator | C23×C43 | C24 |
| Frattini | C23 | C23×D43 |
| Fitting | C43×#585 | C2 |
| socle | C2×C43 | C2×#120 |
| hypercenter | #585 | D43 |
| hypocenter | C43 | #3025 |
| LCS | G ▷ C23×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #585 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583406 | C2 | semidirect |
| 2. #14583089 | C2 | semidirect |
| 3. #14583086 | C2 | semidirect |
| 4. #14582873 | C2 | semidirect |
| 5. C43×#585 | C2 | semidirect |
| 6. C22×C4×D43 | C22 | semidirect |
| 7. #13063306 | C22 | semidirect |
| 10. #13063293 | C22 | semidirect |
| 12. #13063284 | C22 | semidirect |
| 13. #13063240 | C22 | semidirect |
| 26. C2×Q8×C43 | D4 | semidirect |
| 29. C2×D4×C43 | D4 | semidirect |
| 32. C22×C4×C43 | D4 | semidirect |
| 83. #585 | D43 | semidirect |
| 88. C43 | #3025 | semidirect |
| 109. C2×Q8 | C22⋊D43 | semidirect |
| 113. C2×D4 | C22⋊D43 | semidirect |
| 119. C22×C4 | C22⋊D43 | semidirect |