Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
752 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 752 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, Frattini | C23 | C23×D43 |
| commutator, socle | C23×C43 | C24 |
| Fitting | C43×#390 | C2 |
| hypercenter | #390 | D43 |
| hypocenter | C43 | #2858 |
| LCS | G ▷ C23×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063324 | C2 | semidirect |
| 3. C2×#13063311 | C2 | semidirect |
| 4. #14582802 | C2 | semidirect |
| 5. #14582801 | C2 | semidirect |
| 6. #14582800 | C2 | semidirect |
| 7. #14582799 | C2 | semidirect |
| 8. C42×Dic43 | C2 | semidirect |
| 9. C43×#390 | C2 | semidirect |
| 62. C4×Dic43 | D4 | semidirect |
| 113. C4×C43 | #124 | semidirect |
| 116. Dic43 | #124 | semidirect |
| 133. #390 | D43 | semidirect |
| 135. C43 | #2858 | semidirect |
| 243. C4 | #13063311 | semidirect |