Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
244 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063314 |
| commutator | C22×C4×C43 | C23 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#533 | C2 |
| socle | C2×C43 | #393 |
| hypercenter | #533 | D43 |
| hypocenter | C43 | #2031 |
| LCS | G ▷ C22×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #533 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #14582669 | C2 | semidirect |
| 5. #14582659 | C2 | semidirect |
| 6. #14582655 | C2 | semidirect |
| 7. C43×#533 | C2 | semidirect |
| 31. C2×D172 | Q8 | semidirect |
| 33. C2×Dic86 | Q8 | semidirect |
| 102. #533 | D43 | semidirect |
| 109. C43 | #2031 | semidirect |